复合材料层合板壳非线性力学的研究进展

刘人怀; 薛江红

doi:10.6052/0459-1879-16-253

复合材料层合板壳非线性力学的研究进展

doi: 10.6052/0459-1879-16-253

刘人怀^,,
薛江红^,

暨南大学力学与建筑工程学院应用力学研究所, 广州 510632
暨南大学重大工程灾害与控制教育部重点实验室, 广州 510632

基金项目:

国家自然科学基金资助项目 11032005

详细信息

通讯作者:
2) 刘人怀, 院士, 教授, 主要从事板壳力学和复合材料非线性结构力学研究.E-mail:lrh@jnu.edu.cn

3) 薛江红, 教授, 主要从事不完善复合材料板壳结构的失效机理研究.E-mail:txuej@jnu.edu.cn

中图分类号: O34
计量
- 文章访问数: 1881
- HTML全文浏览量: 377
- PDF下载量: 1164
- 被引次数: 0
出版历程
- 收稿日期: 2016-09-08
- 网络出版日期: 2016-12-02
- 刊出日期: 2017-05-18

DEVELOPMENT OF NONLINEAR MECHANICS FOR LAMINATED COMPOSITE PLATES AND SHELLS

Liu Renhuai^,,
Xue Jianghong^,

Institute of Applied Mechanics, College of Mechanics and Constructional Engineering, Jinan University, Guangzhou 510632, China
Key Lab of Disaster Forecast and Control in Engineering of Ministry of Education, Jinan University, Guangzhou 510632, China

摘要

摘要: 复合材料层合板壳是由多种组分材料组合而成。与单一材料的板壳结构相比，它无明确的材料主方向，各层间材料间断和不连续，具有明显的几何非线性和材料非线性等新的特点。其失效模式也远比单一材料的情况复杂，具有如基体开裂、脱胶、分层、分层裂纹偏转、多分层以及分层传播等多种模式。各国学者基于不同的考虑，提出了多种方法研究复合材料层合板壳的失效。首先，在简要介绍了层合板壳线性力学基本理论的基础上，重点回顾了层合板壳结构非线性力学几种基本理论发展的过程，主要阐述了经典大挠度非线性理论、一阶剪切变形理论、高阶剪切变形理论、锯齿理论、广义分层理论的理论体系及基本公式，并对几种理论之间的联系和差异进行了总结；其次，介绍了当前层合结构非线性领域的研究进展，综述了典型复合材料板壳结构的失效机理及优化设计、复合材料板壳结构在复杂环境下的破坏机理、复合材料板壳结构的物理非线性、含脱层纤维增强复合材料板壳结构的破坏机理等各研究热点的最新研究成果；最后，对该领域未来的研究方向进行了展望。
- 复合材料 /
- 层合板壳 /
- 非线性力学
Abstract: Laminated composite plates and shells are made from a variety of materials. They have quite different mechanical features compared with those made of single material, such as uncertain principal direction of the material, discontinuity of material between layers, highly geometrical and material nonlinearity, etc. Their failure modes include matrix cracking, debonding, delamination, crack deflection, multi delamination and delamination propagation, which are much more complex than those of single material. Based on different considerations, various methods have been proposed by scholars from different countries to study the failure of laminated composite plates and shells. This paper summarizes the fundamental theory of linear mechanics and reviews the development of nonlinear theories for laminated plates and shells. In particularly, theoretical systems and basic formulas are expatiated for the classical nonlinear theory of large deformation, the first order shear deformation theory, the high order shear deformation theory, the zig-zag theory, and the layer-wise theory. The relevance and differences among these theories are stated. Current research progress in the field of nonlinear mechanics for laminated composite plates and shells are overviewed and the latest achievements are introduced in research hotspots regarding the failure mechanism and optimization design of typical laminated composite plates and shells, the failure mechanism of laminated composite plates and shells in complex environments, material nonlinearity of composite plates and shells, failure mechanism of fiber reinforced delaminated composite plates and shells, and so on. Based on the review, prospects for future research in the area of nonlinear mechanics of laminated composite plates and shells are proposed.
- composite materials /
- laminated plates and shells /
- nonlinear mechanics

HTML全文

参考文献(293)

[1]	刘人怀.板壳力学.北京:机械工业出版社, 1990 Liu Renhuai. Mechanics of Plates and Shells. Beijing:Machinery Industry Press, 1990 (in Chinese)
[2]	徐芝纶.弹性力学(下).北京:高等教育出版社, 2006 Xu Zhilun. Elasticity. Beijing:Higher Education Press, 2006 (in Chinese)
[3]	沈观林, 胡更开.复合材料力学.北京:清华大学出版社, 2006 Shen Guanlin, Hu Gengkai. Mechanics of Composite Materials. Beijing:Tsinghua University Press, 2006 (in Chinese)
[4]	von Kármán Th.V. Festigkeits Problem in Maschinenban, Enzyklopädie der Mathematjschen Wissenschaften, Bd. IV., art. 27, 1910
[5]	Liu RH. Study on Nonlinear Mechanics of Plates and Shells. New York, Beijing, Guangzhou:Science Press and Jinan University Press, 1998
[6]	刘人怀.复合材料层合板壳理论探索.广州:暨南大学出版社, 2006 Liu Renhuai. Probe into the Theory of Laminated Composite Plates and Shells. Guangzhou:Jinan University Press, 2006 (in Chinese)
[7]	Stavsky Y. On the general theory of heterogeneous aeolotropic plates. Aeronautic Quart, 1964, 15:29 doi: 10.1017/S0001925900002997
[8]	Whitney JM, Leissa AW. Analysis of heterogenous anisotropic plates. ASME Journal of Applied Mechanics, 1968, 36(3):261-266 http://appliedmechanics.asmedigitalcollection.asme.org/data/Journals/JAMCAV/25889/261_1.pdf
[9]	Chia CY. Nonlinear Analysis of Plates. New York:McGraw-Hill, 1980
[10]	Chia CY. Large deflection of heterogeneous anisotropic rectangular plates. International Journal of Solids and Structures, 1974, 10(9): 965-976 doi: 10.1016/0020-7683(74)90004-3
[11]	Chia CY, Prabhakara MK. Large deflection of unsymmetric crossply and angle-ply plates. ARCHIVE Journal of Mechanical Engineering Science, 1976, 18(3):179-183 http://www.sciencedirect.com/science/article/pii/0022460X76908786
[12]	Prabhakara MK, Chia CY. Finite deflections of unsymmetrically layered anisotropic rectangular plates subjected to the combined action of transverse and inplane loads. ASME Journal of Applied Mechanics, 1975, 42(2):517-518 doi: 10.1115/1.3423623
[13]	Prabhakara MK, Chia CY. Nonlinear analysis of laminated crossply plates. Journal of the Engineering Mechanics Division, 1977, 103(3):749-753 doi: 10.1177/073168449201100303
[14]	Prabhakara MK, Chia CY. Non-linear flexural vibrations of orthotropic rectangular plates. Journal of Sound and Vibration, 1977, 52(3):511-518 http://www.sciencedirect.com/science/article/pii/0022460X77903674?via=sd
[15]	Prabhakara MK. Finite deflection of unsymmetric angle-ply anisotropic rectangular plates under edge moments. ASME Journal of Applied Mechanics, 1977, 44(1):171-172 doi: 10.1115/1.3423988
[16]	Chia CY. Nonlinear bending of unsymmetric angleply plates with edges elastically restrained against rotation. Acta Mechanica, 1984, 53(3-4):201-212 doi: 10.1007/BF01177951
[17]	Chia CY. Large deflection of unsymmetric laminates with mixed boundary conditions. International Journal of Non-Linear Mechanics, 1985, 20(3):273-282 https://www.researchgate.net/publication/222728942_Large_deflection_of_unsymmetric_laminates_with_mixed_boundary_conditions
[18]	叶开沅, 刘人怀, 平庆元等.圆底扁薄球壳的非线性稳定问题-在对称线布载荷作用下的圆底扁薄球壳的非线性稳定简题.科学通报, 1965, 16(2):142-145 http://www.cnki.com.cn/Article/CJFDTOTAL-LDZK196502001.htm Ye Kaiyuan, Liu Renhuai, Ping Qingyuan, et al. Nonlinear stability of shallow spherical shells with round bottom-nonlinear stability of thin spherical shells with circular bottom under symmetrical linear load. Chinese Science Bulletin. 1965, 16(2):142-145 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-LDZK196502001.htm
[19]	叶开沅, 刘人怀, 张传智等.圆底扁薄球壳的非线性稳定问题-圆底扁薄球壳在边缘力矩作用下的非线性稳定问题.科学通报, 1965, 16(2):145-147 http://www.cnki.com.cn/Article/CJFDTOTAL-KXTB196502007.htm Ye Kaiyuan, Liu Renhuai, Zhang Chuanzhi, et al. Nonlinear stability of shallow spherical shells with round bottom-nonlinear stability of thin spherical shells with circular bottom under the action of edge moment. Chinese Science Bulletin, 1965, 16(2):145-147 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-KXTB196502007.htm
[20]	刘人怀.在内边缘均布力矩作用下中心开孔圆底扁球壳的非线性稳定问题.科学通报, 1965, 16(3):253-255 http://www.cnki.com.cn/Article/CJFDTOTAL-KXTB196503008.htm Liu Renhuai. Nonlinear stability of a shallow spherical shell with a central opening under the action of the uniformly distributed moments at the interior edge. Chinese Science Bulletin, 1965, 16(3):253-255 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-KXTB196503008.htm
[21]	刘人怀.在内边缘均布载荷作用下中心开孔圆底扁球壳的轴对称稳定性.力学学报, 1977, 13(2):206-212 http://www.cnki.com.cn/Article/CJFDTOTAL-LXXB197703009.htm Liu Renhuai. Axisymmetric stability of a shallow spherical shell with a central opening under uniformly distributed load at the interior edge. Acta Mechanica Sinica, 1977, 13(2):206-212 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-LXXB197703009.htm
[22]	刘人怀.波纹圆板的特征关系式.力学学报, 1978, 14(1):47-52 http://lxxb.cstam.org.cn/CN/abstract/abstract138764.shtml Liu Renhuai. Characteristic formula of corrugated circular plates. Acta Mechanica Sinica, 1978, 14(1):47-52 (in Chinese) http://lxxb.cstam.org.cn/CN/abstract/abstract138764.shtml
[23]	叶开沅, 刘人怀, 张传智等.弹性圆底扁球壳在边缘均布力矩作用下的非线性稳定问题.应用数学和力学, 1980, 1(1):71-87 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX198001008.htm Yeh Kaiyuan, Liu Renhuai, Zhang Chuanzhi, et al. Nonlinear stabi1ity of thin elastic circular shallow spherical shell under the action of uniform edge moment. Applied Mathematics and Mechanics, 1980, 1(1):71-87 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX198001008.htm
[24]	刘人怀.夹层圆板的非线性弯曲.应用数学和力学, 1981, 2(2): 173-190 http://cdmd.cnki.com.cn/Article/CDMD-10056-2004074849.htm Liu Renhuai. Nonlinear bending of circular sandwich plates. Applied Mathematics and Mechanics, 1981, 2(2):173-190 (in Chinese) http://cdmd.cnki.com.cn/Article/CDMD-10056-2004074849.htm
[25]	Liu RH. Nonlinear thermal stability of bimetallic shallow shells of revolution. International Journal of Non-Linear Mechanics, 1983, 18(4):409-429 https://www.researchgate.net/publication/245213555_Non-linear_thermal_stability_of_bimetallic_shallow_shells_of_revolution
[26]	Liu RH. Large deflection of corrugated circular plate with a plane central region under the action of concentrated loads at the center. International Journal of Non-Linear Mechanics, 1984, 19(4):409-415 https://www.researchgate.net/publication/239373879_Large_deplection_of_corrugated_circular_plate_with_a_plane_central_region_under_the_action_of_concentrated_loads_at_the_center
[27]	刘人怀.波纹环形板的非线性弯曲.中国科学(A辑), 1984, (2): 247-253 http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX198901004.htm Liu Renhuai. Nonlinear bending of corrugated annular plates. Science in China Series A, 1984, (2):247-253 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX198901004.htm
[28]	Liu RH. Large deflection of corrugated circular plate with plane boundary region. Solid Mechanics Archives, 1984, 9(3):383-406 http://cat.inist.fr/?aModele=afficheN&cpsidt=8448785
[29]	刘人怀.在复杂载荷作用下波纹环形板的非线性弯曲.中国科学(A辑), 1985 (6):537-545 http://www.cnki.com.cn/Article/CJFDTOTAL-JAXK198506006.htm Liu Renhuai. Nonlinear analysis of corrugated annular plates under compound load. Science in China Series A, 1985 (6):537-545 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JAXK198506006.htm
[30]	Liu RH. Nonlinear bending of circular sandwich plates under the action of axisymmetric uniformly distributed line loads. Progress in Applied Mechanics, Dordrecht:Martinns Nijhoff Publishers, 1987, 293-321 https://www.researchgate.net/publication/267475065_Nonlinear_bending_of_circular_sandwich_plates_under_the_action_of_axisymmetric_uniformly_distributed_line_loads
[31]	刘人怀, 成振强.集中载荷作用下开顶扁球壳的非线性稳定问题.应用数学和力学, 1986, 9(2):95-105 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX199103011.htm Liu Renhuai, Cheng Zhen-qiang. On the nonlinear stability of truncated shallow spherical under a concentrated load. Applied Mathematics and Mechanics, 1986, 9(2):95-105 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX199103011.htm
[32]	刘人怀, 李东.均布载荷作用下开顶扁球壳的非线性稳定问题.应用数学和力学, 1988, 9(2):205-217 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX198803002.htm Liu Renhuai, Li Dong. On the nonlinear stability of truncated shallow spherical under a uniformly load. Applied Mathematics and Mechanics, 1988, 9(2):205-217 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX198803002.htm
[33]	刘人怀.复合载荷作用下波纹圆板的非线性分析.应用数学和力学, 1988, 9(6):661-674 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX198808000.htm Liu Renhuai. Nonlinear analysis of a corrugated circular plate under combined lateral loading. Applied Mathematics and Mechanics, 1988, 9(6):661-674 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX198808000.htm
[34]	Liu RH, He LH. On the nonlinear stability of a truncated shallow spherical shell under axisymmetrically distributed load. Solid Mechanics Archives, 1989, 14(2):81-102 https://www.researchgate.net/publication/225622755_On_the_nonlinear_stability_of_a_truncated_shallow_spherical_shell_under_A_uniformly_distributed_load
[35]	Liu RH, Li D. On the nonlinear bending and vibration of corrugated circular plates. International Journal Non-linear Mechanics, 1989, 24(2):165-176 https://www.researchgate.net/publication/222882164_On_the_non-linear_bending_and_vibration_of_corrugated_circular_plates
[36]	刘人怀, 朱金福.夹层壳非线性理论.北京:机械工业出版社, 1993 Liu Renhuai, Zhu Jinfu. Nonlinear Theory of Sandwich Shell. Beijing:Machinery Industry Press, 1993 (in Chinese)
[37]	刘人怀.精密仪器仪表弹性元件的设计原理.广州:暨南大学出版社, 2006 Liu Renhuai. Principle for Designing Elastic Elements in Precision-Lnstruments Manufacture. Guangzhou:Jinan University Press, 2006 (in Chinese)
[38]	刘人怀.夹层板壳非线性理论分析.广州:暨南大学出版社, 2007 Liu Renhuai. Nonlinear Theory and Analysis of Sandwich Plates and Shells. Guangzhou:Jinan University Press, 2007 (in Chinese)
[39]	刘人怀.网壳结构的非线性弯曲、稳定和振动.北京:科学出版社, 2011 Liu Renhuai. Nonlinear bending, stability and vibration of reticulated shells. Beijing:Science Press, 2011 (in Chinese)
[40]	刘人怀, 何陵辉.四边简支对称正交层合矩形板的非线性弯曲问题.应用数学和力学, 1990, 11(7):753-759 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX199009001.htm Liu Renhuai, He Linghui. Nonlinear bending of simply supported symmetric laminated cross-ply rectangular plates. Applied Mathematics and Mechanics, 1990, 11(7):753-759 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX199009001.htm
[41]	刘人怀.对称圆柱正交异性层合扁球壳的非线性稳定问题.应用数学和力学, 1991, 12(2):252-258 http://www.cnki.com.cn/Article/CJFDTOTAL-JAXK199107007.htm Liu Renhuai. On the nonlinear stability of symmetrically laminated cylindrically orthotropic shallow spherical shells. Applied Mathematics and Mechanics, 1991, 12(2):252-258 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JAXK199107007.htm
[42]	刘人怀. 复合材料层合扁锥壳的非线性稳定问题. 第九届全国复合材料学术会议论文集. 北京: 世界图书出版社公司, 1996: 249-255 Liu Renhuai. Nonlinear stability of composite laminated shallow conical shells//Proceedings of the Ninth National Conference on Composite Materials. Beijing:World Books Publishing Company, 1996:249-255 (in Chinese)
[43]	Turvey GJ, Wittrick WH. The large deflection and postbuckling behavior of some laminated plates. Aeronaut Q, 1973, 24:77
[44]	Zaghloul SA, Kennedy JB. Nonlinear behavior of symmetrically laminated plates. Journal of Applied Mechanics, 1975, 42(1):234-236 doi: 10.1115/1.3423532
[45]	Chandra R. Nonlinear bending of antisymmetric angle-ply laminated plates. Fibre Science & Technology, 1977, 10(2):123-137 https://www.researchgate.net/publication/232328578_Non-linear_bending_of_antisymmetric_angle_ply_laminated_plates
[46]	周次青.对称正交铺设矩形叠层板的非线性弯曲.应用数学和力学, 1985, 6(7):819-832 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX198509007.htm Zhou Ciqing. Nonlinear bendings of rectangular symmetrically laminated cross-ply plates under various supports. Applied Mathematics and Mechanics, 1985, 6(7):819-832 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX198509007.htm
[47]	周次青.不对称的各向异性叠层矩形板的非线性弯曲.应用数学和力学, 1986, 7(11):1003-1020 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX198611005.htm Zhou Ciqing. Nonlinear bendings of unsymmetrically layered anisotropic rectangular plates. Applied Mathematics and Mechanics, 1986, 7(11):1003-1020 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX198611005.htm
[48]	周次青.对称铺设各向异性叠层矩形板的非线性弯曲.应用数学和力学, 1988, 9(2):267-280 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX198803007.htm Zhou Ciqing. Nonlinear bendings of symmetrically layered anisotropic rectangular plates. Applied Mathematics and Mechanics, 1988, 9(2):267-280 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX198803007.htm
[49]	Reissner E. The effect of transverse shear deformation on the bending of elastic plates. Journal of Applied Mechanics, 1945, 12:69-77 https://www.researchgate.net/publication/36278556_The_effect_of_transverse_shear_deformation_on_the_bending_of_an_elastic_rectangular_plate_subjected_to_a_concentrated_load
[50]	Mindlin RD. Influence of rotatory inertial and shear on flexural motion of isotropic elastic plates. Journal of Applied Mechanics, 1951, 18(1):31-38 http://www.oalib.com/references/14324140
[51]	Stavsky Y. On the theory of heterogeneous anisotrophic plates.[PhD Thesis]. MIT, Cambridge, MA, 1959
[52]	Yang P, Norris CH, Stavsky Y. Elastic wave propagation in heterogeneous plates. International Journal of Solids and Structures, 1966, 2(4):665-684 doi: 10.1016/0020-7683(66)90045-X
[53]	Ambartsumyan SA. Theory of Anisotropic Plates. Stamford:Technomic Publishing Co., Inc, 1970
[54]	Bert CW. Nonlinear vibration of a rectangular plate arbitrarily laminated of anisotropic materials. Journal of Applied Mechanics, 1973, 40(2):452-458 doi: 10.1115/1.3423005
[55]	Whitney JM. Structural analysis of laminated anisotropic plates. Stamford:Technomic Publishing Co., Inc, 1987
[56]	Dong SB, Tso FKW. On a laminated orthotropic shell theory including transverse shear deformation. Journal of Applied Mechanics, 1972, 39(4):1091-1097 doi: 10.1115/1.3422834
[57]	Reddy JN. A small strain and moderate rotation theory of laminated anisotropic plates. Journal of Applied Mechanics, 1987, 54(3): 623-626 doi: 10.1115/1.3173079
[58]	Schmidt R, Reddy JN. A refined small strain and moderate rotation theory of elastic anisotropic shells. Journal of Applied Mechanics, 1988, 55(3):611-617 doi: 10.1115/1.3125837
[59]	Palmerio AF, Reddy JN, Schmidt R. On a moderate rotation theory of elastic anisotropic shells. Part 1. Theory. International Journal of Non-Linear Mechanics, 1990, 25(6):687-700 doi: 10.1016/0020-7462(90)90007-V
[60]	Palmerio AF, Reddy JN, Schmidt R. On a moderate rotation theory of elastic anisotropic shells. Part 2. FE analysis. International Journal of Non-Linear Mechanics, 1990, 25(6):701-714 doi: 10.1016/0020-7462(90)90008-W
[61]	Kreja I, Schmidt R, Reddy JN. Finite elements based on a first-order shear deformation moderate rotation shell theory with applications to the analysis of composite structures. International Journal of Non-Linear Mechanics, 1991, 32(6):1123-1142
[62]	Iu VP, Chia CY. Effect of transverse shear on nonlinear vibration and postbuckling of anti-symmetric cross-ply imperfect cylindrical shells. International Journal of Mechanical Sciences, 1988, 30(8): 705-718 https://www.researchgate.net/publication/237043576_Effect_of_transverse_shear_on_nonlinear_vibration_and_postbuckling_of_anti-symmetric_cross-ply_imperfect_cylindrical_shells
[63]	Fu YM, Chia CY. Non-linear vibration and postbuckling of generally laminated circular cylindrical thick shells with non-uniform boundary conditions. International Journal of Non-Linear Mechanics, 1993, 28(3):313-327 doi: 10.1016/0020-7462(93)90038-M
[64]	Fu YM, Chia CY. Multi-mode nonlinear vibration and postbuckling of anti-symmetric imperfect angle-ply cylindrical thick panels. International Journal of Non-Linear Mechanics, 1989, 24(5):365-381 doi: 10.1016/0020-7462(89)90025-5
[65]	Sivakumaran KS, Chia CY. Large-amplitude oscillations of unsymmetrically laminated anisotropic rectangular plates including shear, rotatory inertia and transverse normal strains. ASME Journal of Applied Mechanics, 1985, 52(3):536-542 doi: 10.1115/1.3169097
[66]	Xu CS, Xia ZQ, Chia CY. Non-linear theory and vibration analysis of laminated truncated, thick, conical shells. International Journal of Non-Linear Mechanics, 1996, 31(2):139-151 doi: 10.1016/0020-7462(95)00051-8
[67]	Fares ME. Non-linear bending analysis of composite laminated plates using a refined first-order theory. Composite Structures, 1999, 46(3):257-266 doi: 10.1016/S0263-8223(99)00062-8
[68]	Fares ME, Zenkour AM. Mixed variational formula for the thermal bending of laminated plates. Journal of Thermal Stresses, 1999, 22(2):347-365 doi: 10.1080/014957399280913?scroll=top&needAccess=true
[69]	Fares ME. Mixed variational formulation in geometrically nonlinear elasticity and a generalized nth-order beam theory. International Journal of Non-Linear Mechanics, 1999, 34(2):685-691 https://www.researchgate.net/publication/245215300_Mixed_variational_formulation_in_geometrically_non-linear_elasticity_and_a_generalized_nth-order_beam_theory
[70]	Fares ME. Generalized non-linear thermoelasticity for composite laminated structures using a mixed variational approach. International Journal of Non-Linear Mechanics, 2000, 35(2):439-446 http://www.sciencedirect.com/science/article/pii/S0020746299000293
[71]	Whiteny JM, Pagano NJ. Shear deformation in heterogeneous anisotropic plates. Journal of Applied Mechanics, 1970, 37(4): 1031-1036 doi: 10.1115/1.3408654
[72]	Fortier RC, Rossettos JN. On the vibration of shear deformable curved anisotropic composite plates. Journal of Applied Mechanics, 1973, 40(1):299-301 doi: 10.1115/1.3422948
[73]	Sinha PK, Rath AK. Vibration and buckling of cross-ply laminated circular cylindrical panels. Aeronaut Quart, 1975, 26:211-218 doi: 10.1017/S0001925900007356
[74]	Bert CW, Chen TL. Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular plates. International Journal of Solids and Structures, 1978, 14(6):465-473 doi: 10.1016/0020-7683(78)90011-2
[75]	刘人怀.考虑横向剪切的对称层合圆柱正交异性扁球壳的非线性稳定问题.中国科学(A辑), 1991 (7):742-751 http://www.cnki.com.cn/Article/CJFDTOTAL-JAXK199107007.htm Liu Renhuai. Nonlinear stability of symmetric laminated orthotropic cylindrical shallow spherical shells with transverse shear. Science in China, Series. A, 1991 (7):742-751 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JAXK199107007.htm
[76]	刘人怀, 王璠.复合材料层合扁球壳的非线性强迫振动.力学学报, 1997, 29(2):236-241 http://lxxb.cstam.org.cn/CN/abstract/abstract139979.shtml Liu Renhuai, Wang Fan. Nonlinear forced vibration of laminated composite shallow spherical shells. Acta Mechanica Sinica, 1997, 29(2):236-241 (in Chinese) http://lxxb.cstam.org.cn/CN/abstract/abstract139979.shtml
[77]	Liu RH, Wang F. Nonlinear dynamic buckling of symmetrically laminated cylindrically orthotropic shallow spherical shells. Archive of Applied Mechanics, 1998, 68(6):375-384 doi: 10.1007/s004190050172
[78]	刘人怀, 徐加初.直线型正交异性层合圆板的大挠度问题.暨南大学学报, 1998, 19(4):1-10 http://www.cnki.com.cn/Article/CJFDTOTAL-JNDX805.000.htm Liu Renhuai, Xu Jiachu. Large deflection of symmetrically laminated rectilinearly orthotropic circular plates. Journal of Jinan University, 1998, 19(4):1-10 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JNDX805.000.htm
[79]	刘人怀, 徐加初.剪切变形对直线型正交异性层合圆板大幅度受迫振动的影响.应用数学和力学, 1998, 19(2):105-112 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX802.001.htm Liu Renhuai, Xu Jiachu. Shear effects on large amplitude forced vibration of symmetrically laminated rectilinearly orthotropic circular plates. Applied Mathematics and Mechanics, 1998, 19(2):105-112 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX802.001.htm
[80]	Liu RH, Xu JC, Zhai SZ. Large-deflection bending of symmetrically laminated rectilinearly orthotropic elliptical plates including transverse shear. Archive of Applied Mechanics, 1997, 67(7):507-520 doi: 10.1007/s004190050135
[81]	Liu RH. On non-linear buckling of symmetrically laminated, cylindrical orthotropic, truncated, shallow, spherical shells considering uniform pressure including shear effects. International Journal of Non-Linear Mechanics, 1996, 31(1):101-115 doi: 10.1016/0020-7462(95)00045-3
[82]	刘人怀, 钟诚.考虑横向剪切变形的对称层合圆柱正交异性中心开孔扁球壳的非线性屈曲.暨南大学学报, 1994, 15(1):1-11 http://www.cnki.com.cn/Article/CJFDTOTAL-JNDX401.000.htm Liu Renhuai, Zhong Cheng. Nonlinear buckling of symmetrically laminated cylindrically orthotropic shallow spherical shells with a circular hole at the center including transverse shear. Journal of Jinan University, 1994, 15(1):1-11 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JNDX401.000.htm
[83]	刘人怀, 王璠, 肖谭. 阻尼对层合复合材料中心开孔扁球壳非线性振动的影响. 刘人怀等主编. 应用力学研究与实践, 广州: 暨南大学出版社, 2000: 35-43 Liu Ren-Huai, Wang Fan, Xiao Tan. Effect of damping on nonlinear vibration of Laminated Shallow Spherical Shell with center opening//Liu Renhuai et al. eds. Research and Practice in Applied Mechanics, Guangzhou:Jinan University Press, 2000:35-43 (in Chinese)
[84]	王璠, 刘人怀.复合材料层合开顶扁球壳的非线性动态屈曲, 固体力学学报, 2001, 22(2):309-314 http://www.cnki.com.cn/Article/CJFDTOTAL-GTLX200103014.htm Wang Fan, Liu Renhuai. Nonlinear dynamic buckling of symmetrically laminated truncated spherical shell. Acta Mechanica Solida Sinica, 2001, 22(2):309-314 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GTLX200103014.htm
[85]	Liu RH. Non-linear buckling of symmetrically laminated, cylindrically orthotropic, shallow, conical shells considering shear. International Journal of Non-Linear Mechanics, 1996, 31(1):89-99 doi: 10.1016/0020-7462(95)00046-1
[86]	刘人怀, 王志伟.复合材料面层夹层板中转动一致有效理论.上海力学, 1996, 17(2):222-228 http://www.cnki.com.cn/Article/CJFDTOTAL-SHLX199603007.htm Liu Renhuai, Wang Zhiwei. The theory of consistent moderate rotation of sandwich plates faced with laminated composites. Shanghai Journal of Mechanics, 1996, 17(2): 222-228 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-SHLX199603007.htm
[87]	刘人怀, 王志伟. 考虑横向剪切应力连续的复合材料面层夹层壳非线性一致有效理论. 刘人怀等主编. 应用力学研究与实践, 广州: 暨南大学出版社, 2000: 1-12 Liu Renhuai, Wang Zhiwei. Nonlinear consistent theory for sandwich plates of laminated composite faces with transverse shear stress//Liu Renhuai et al. eds. Research and Practice in Applied Mechanics, Guangzhou:Jinan University Press, 2000:1-12 (in Chinese)
[88]	王志伟, 刘人怀.正交复合材料面层夹层板非线性理论及应用.应用力学学报, 1998, 15(2):18-24 http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX802.003.htm Wang Zhiwei, Liu Renhuai. A refined nonlinear theory for sandwich plates faced with orthotropic laminated composites and its application. Chinese Journal of Applied Mechanics, 1998, 15(2):18-24 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX802.003.htm
[89]	Wang ZW, Liu RH. Nonlinear buckling for sandwich shallow shells accounting for continuity conditions of stresses at interfaces//Proceedings of the 3rd Int. Conf. on Nonlinear Mechcanics, Shanghai:Shanghai University Press, 1988:381-386
[90]	王志伟, 刘人怀.复合材料面层夹层扁壳非线性精化理论及应用.应用力学学报, 2000, 17(3):86-91 http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX200004014.htm Wang Zhiwei, Liu Renhuai. A new refined nonlinear theory for sandwich shallow with orthotropic laminated faces and its application. Chinese Journal of Applied Mechanics, 2000, 17(3):86-91 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX200004014.htm
[91]	徐加初, 王乘, 刘人怀.具有夹层的正交异性复合材料圆锥壳体的非线性轴对称屈曲分析.工程力学, 2001, 18(3):28-37 Xu Jiachu, Wang Cheng, Liu Renhuai. Nonlinear axisymmetric buckling of conical sandwich shells with orthotropic skins. Engineering Mechanics, 2001, 18(3):28-37 (in Chinese)
[92]	Chow TS. On the propagation of flexural waves in an orthotropic laminated plate and its response to an impulsive load. Journal of Composite Materials, 1971, 5(3):306-319 doi: 10.1177/002199837100500302
[93]	Whitney JM. Shear correction factors for orthotropic laminates under static load. Journal of Applied Mechanics, 1973, 40(1):302-304 doi: 10.1115/1.3422950
[94]	Noor AK, Burton WS. Assessment of shear deformation theories for multilayered composite plates. Applied Mechanics Review, 1989, 42(1):1-13 doi: 10.1115/1.3152418
[95]	Noor AK, Burton WS. Stress and free vibration analyses of multilayered composite plates. Composite Structures, 1989, 11(3):183-204 doi: 10.1016/0263-8223(89)90058-5
[96]	Vlachoutsis S. Shear correction factors for plates and shells. International Journal for Numerical Methods in Engineering, 1992, 33(7):1537-1552 doi: 10.1002/(ISSN)1097-0207
[97]	Laitinen M, Lahtinen H, Sjolind SG. Transverse shear correction factors for laminates in cylindrical bending. Communications in Numerical Methods in Engineering, 1995, 11(1):41-47 doi: 10.1002/cnm.1640110107
[98]	Reddy JN. A simple higher-order theory for laminated composites. Journal of Applied Mechanics, 1984, 51(3):745-752 http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?articleid=1407769&resultClick=1
[99]	Reddy JN. Energy and Variational Methods in Applied Mechanics with an Introduction to the Finite-Element Method. New York:Wiley, 1984:364-371 http://www.worldcat.org/title/energy-and-variational-methods-in-applied-mechanics-with-an-introduction-to-the-finite-element-method/oclc/10457603
[100]	Reddy JN. A refined nonlinear theory of plates with transverse shear deformation. International Journal of Solids and Structures, 1984, 20(9-10):881-896 doi: 10.1016/0020-7683(84)90056-8
[101]	Reddy JN, Liu CF. A higher-order shear deformation theory of laminated elastic shells. International Journal of Engineering Science, 1985, 23(3):319-330 doi: 10.1016/0020-7225(85)90051-5
[102]	Simitses GJ, Anastasiadis JS. Shear deformable theories for cylindrical laminates-equilibrium and buckling with applications. AIAA Journal, 1992, 30(3):826-834 doi: 10.2514/3.10991
[103]	Huang NN. Influence of shear correction factors in the higher order shear deformation laminated shell theory. International Journal of Solid and Structures, 1994, 31(9):1263-1277 doi: 10.1016/0020-7683(94)90120-1
[104]	Sheikh AH, Chakrabarti A. A new plate bending element based on higher-order shear deformation theory for the analysis of composite plates. Finite Elements in Analysis and Design, 2003, 39(7):883-903 https://www.researchgate.net/publication/222138832_A_new_plate_bending_element_based_on_higher-order_shear_deformation_theory_for_the_analysis_of_composite_plates
[105]	Nayak AK, Moy SSJ, Shenoi RA. Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory. Composites:Part B, 2002, 33(7):505-519 doi: 10.1016/S1359-8368(02)00035-5
[106]	Nayak AK, Moy SSJ, Shenoi RA. A higher order finite element theory for buckling and vibration analysis of initially stressed composite sandwich plates. Journal of Sound and Vibration, 2005, 286(4-5):763-780 doi: 10.1016/j.jsv.2004.10.055
[107]	Shahrokh HH, Fadaee M, Taher HRD. Exact solutions for free flexural vibration of Levy-type rectangular thick plates via third-order shear deformation plate theory. Applied Mathematical Modelling, 2011, 35(2):708-727 doi: 10.1016/j.apm.2010.07.028
[108]	Di S, Rothert H. Solution of laminated cylindrical shells using an unconstrained third-order theory. Composite Structures, 1995, 32(4):667-680 https://www.researchgate.net/publication/222129913_Solution_of_a_laminated_cylindrical_shell_using_an_unconstrained_third-order_theory
[109]	Nayak AK, Moy SJ, Shenoi RA. Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory. Composites:Part B-Engineering, 2002, 33(7):505-519 doi: 10.1016/S1359-8368(02)00035-5
[110]	Kant T, Swaminathan K. Free vibration of isotropic, orthotropic, and multilayer plates based on higher order refined theories. Journal of Sound and Vibration, 2001, 241(2):319-327 doi: 10.1006/jsvi.2000.3232
[111]	Kant T, Swaminathan K. Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory. Composite Structures, 2001, 53(1):73-85 doi: 10.1016/S0263-8223(00)00180-X
[112]	Kant T, Swaminathan K. Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory. Composite Structures, 2002, 56(4):329-344 doi: 10.1016/S0263-8223(02)00017-X
[113]	Barut A, et al. Analysis of thick sandwich comstruction by a f3, 2gorder theory. International Journal of Solids and Structures, 2001, 38(34-35):6063-6077 doi: 10.1016/S0020-7683(00)00367-X
[114]	Liu RH, He LH. A simple theory for non-linear bending of laminated composite rectangular plates including higher-order effects. International Journal of Non-Linear Mechanics, 1991, 26(4):537-545 https://www.researchgate.net/publication/256203278_A_simple_theory_for_non-linear_bending_of_laminated_composite_rectangular_plates_including_higher-order_effects
[115]	Kuppusamy T, Reddy AN. A three-dimensional nonlinear analysis of cross-ply rectangular composite plates. Computers and Structures, 1984, 18(2):263-272 doi: 10.1016/0045-7949(84)90124-X
[116]	沈惠申.高阶剪切变形板理论Karman型方程及在热后屈曲分析中的应用.应用数学和力学, 1997, 18(9):1059-1073 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX199712001.htm Shen Huishen. Karman-type equations for a higher-order shear deformation plate theory and its use in the thermal postbuckling analysis. Applied Mathematics and Mechanics, 1997, 18(9):1059-1073 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX199712001.htm
[117]	沈惠申.复合材料层合剪切圆柱曲板在侧压作用下的后屈曲.应用数学和力学, 2003, 24(3):357-366 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX200304003.htm Shen Huishen. Postbuckling of pressure-loaded shear deformable laminated cylindrical panels. Applied Mathematics and Mechanics, 2003, 24(3):357-366 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX200304003.htm
[118]	冯世宁, 陈浩然.基于高阶剪切理论的层合板非线性动力稳定性.大连理工大学学报, 2006, 6(1):1-6 http://www.cnki.com.cn/Article/CJFDTOTAL-DLLG200601000.htm Feng Shining, Chen Haoran. Analysis of nonlinear dynamic stability of composite laminates based on higher order shear deformation theory. Journal of Dalian University of Technology, 2006, 6(1):1-6 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-DLLG200601000.htm
[119]	张雨, 向锦武.复合材料层合厚圆柱壳高阶理论的改进及其应用.复合材料学报, 2002, 19(3):86-91 http://www.cnki.com.cn/Article/CJFDTOTAL-FUHE200204017.htm Zhang Yu, Xiang Jinwu. Higher-order theory and its finite element method for thick laminated composite cylindrical shells. Acta Materiae Compositae Sinica, 2002, 19(3):86-91 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-FUHE200204017.htm
[120]	Whitney JM, Sun CT. A higher order theory for extensional motion of laminated composites. Journal of Sound and Vibration, 1973, 30(1):85-97 doi: 10.1016/S0022-460X(73)80052-5
[121]	傅晓华, 陈浩然, 王振鸣.复合材料多层厚板的精化高阶理论及其有限元法.复合材料学报, 1992, 9(2):39-47 http://www.cnki.com.cn/Article/CJFDTOTAL-FUHE199202006.htm Fu Xiaohua, Chen Haoran, Wang Zhenming. A refined higher-order theory and its finite element method for thick laminated plates. Acta Materiae Compositae Sinica, 1992, 9(2):39-47 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-FUHE199202006.htm
[122]	范业立, 曾加雄.筒形弯曲和球壳弯曲的一个新的高阶理论解.华南理工大学学报, 1991, 19(4):44-53 http://www.cnki.com.cn/Article/CJFDTOTAL-HNLG199104006.htm Fan Yeli, Zeng Jiaxiong. A new higher-order theory of laminated plates to cylindrical bending and spherical shell bending. Journal of South China University of Technology, 1991, 19(4):44-53 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-HNLG199104006.htm
[123]	陈浩然, 温玄玲, 左庄太.含分层损伤轴对称复合材料层合壳的高阶理论及有限元分析.大连理工大学学报, 1999, 39(5):601-606 http://www.cnki.com.cn/Article/CJFDTOTAL-DLLG199905002.htm Chen Haoran, Wen Xuanling, Zuo Zhuangtai. A high-order theory and finite element analysis for axis-symmetrical composite laminated shell with delamination. Journal of Dalian University of Technology, 1999, 39(5):601-606 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-DLLG199905002.htm
[124]	Matsunaga H. Assessment of a global higher-order deformation theory for laminated composite and sandwich plates. Composite Structures, 2002, 56(3):279-291 doi: 10.1016/S0263-8223(02)00013-2
[125]	Matsunaga H. A comparison between 2-D single-layer and 3-D layerwise theories for computing interlaminar stresses of laminated composite and sandwich plates subjected to thermal loadings. Composite Structures, 2004, 64(2):161-177 doi: 10.1016/j.compstruct.2003.08.001
[126]	Matsunaga H. Interlaminar stress analysis of laminated composite and sandwich circular arches subjected to thermal/mechanical loading. Composite Structures, 2003, 60(2):345-358 https://www.researchgate.net/publication/223259651_Interlaminar_stress_analysis_of_laminated_composite_and_sandwich_circular_arches_subjected_to_thermalmechanical_loading
[127]	Matsunaga H. Stress analysis of functionally graded plates subjected to thermal and mechanical loadings. Composite Structures, 2009, 87(3):344-357 https://www.researchgate.net/publication/248205185_Stress_analysis_of_functionally_graded_plates_subjected_to_thermal_and_mechanical_loadings
[128]	Matsunaga H. Effects of higher order deformations on in-plane vibration and stability of thick circular rings. Acta Mechanica, 1997, 124(1):47-61 doi: 10.1007/bf01213017.pdf
[129]	Matsunaga H. Vibration and buckling of multilayered composite beam according to higher order deformation theories. Journal of Sound and Vibration, 2001, 246(l):47-56 https://www.researchgate.net/publication/243365600_Vibration_and_buckling_of_multilayered_composite_beams_according_to_higher_order_deformation_theories
[130]	Reissner E. A twelfth-order theory of transverse bending of transversely isotropic plates. Zeitschrift für Angewandte Mathematic und Mechanik, 1983, 63(7):285-289 doi: 10.1002/(ISSN)1521-4001
[131]	Ambartsumian SA. On theory of bending plates. Isz Otd Tech Nauk AN SSSR, 1958, 5:69-77 http://www.sciencedirect.com/science/article/pii/0020768376900019
[132]	Kaczkowski Z. Plates-Statical Calculations. Arkady:Warsaw, 1968
[133]	Panc V. Theories of Elastic Plates. Prague:Academia, 1975
[134]	Levinson M. An accurate simple theory of the statics and dynamics of elastic plates. Mechanics Research Communications, 1980, 7(6):343-350 doi: 10.1016/0093-6413(80)90049-X
[135]	Ghugal YM, Sayyad AS. Free vibration of thick orthotropic plates using trigonometric shear deformation theory. Latin American Journal of Solids and Structures, 2011, 8(3):229-243 doi: 10.1590/S1679-78252011000300002
[136]	El Meiche N, Tounsi A, Ziane N, et al. A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate. International Journal of Mechanical Science, 2011, (3):237-247 http://linkinghub.elsevier.com/retrieve/pii/S0020740311000142
[137]	Matsunaga H. Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory. Composite Structures, 2000, 48(3):231-244 http://eportfolio.lib.ksu.edu.tw/~T097000001/repository/fetch/Cross-ply_laminated%20composite%20plate_vibration-Matsunaga2000.pdf
[138]	Karama M, Afaq KS, Mistou S. Mechanical behavior of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity. International Journal of Solid and Structures, 2003, 40(6):1525-1546 doi: 10.1016/S0020-7683(02)00647-9
[139]	Karama M, Afaq KS, Mistou S. A new theory for laminated composite Plates//Proceedings of the IMechE Conference 2009.
[140]	Karama M, Abouharb B, Mistou S, et al. Bending, buckling and free vibration of laminated composite with transverse shear stress continuity model. Composites:Part B-Engineering, 1998, 29B:223-234
[141]	Aydogdu M. Comparison of various shear deformation theories for bending, buckling and vibration of rectangular symmetric cross-ply plate with simply supported edges. Journal of Composite Materials, 2006, 40(23):2143-2155 doi: 10.1177/0021998306062313
[142]	Aydogdu M. A new shear deformation theory for laminated composite plates. Composite Structures, 2009, 89(1):94-101 doi: 10.1016/j.compstruct.2008.07.008
[143]	Neves AMA, Ferreira AJM, Carrera E, et al. A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates. Composites Part B-Engineering, 2012, 43(2):711-725 doi: 10.1016/j.compositesb.2011.08.009
[144]	Murakami H. Laminated composite plate theory with improved inplane response. Journal of Applied Mechanics, 1986, 53(3):661-666 doi: 10.1115/1.3171828
[145]	Murakami H, Toledano A. A higher-order laminated plate theory with improved in-plane response. International Journal of Solid and Structures, 1987, 23(1):111-131 doi: 10.1016/0020-7683(87)90034-5
[146]	Carrera E. On the use of the Murakami's zig-zag function in the modeling of layered plates and shells. Computers and Structures, 2004, 82(7-8):541-554 doi: 10.1016/j.compstruc.2004.02.006
[147]	Bhaskar B, Varadan TK. A higher-order theory for bending analysis of laminated shells of revolution. Computers and Structures, 1991, 40(3):815-819 https://www.researchgate.net/publication/223682435_A_higher-order_theory_for_bending_analysis_of_laminated_shells_of_revolution
[148]	Vidal P, Polit O. A sine finite element using a zig-zag function for the analysis of laminated composite beams. Composites:Part BEngineering, 2011, 42(6):1671-1682 doi: 10.1016/j.compositesb.2011.03.012
[149]	Ferreira AJM, Roque CMC, Carrera E, et al. Radial basis functions collocation and a unified formulation for bending, vibration and buckling analysis of laminated plates, according to a variation of Murakami's zig-zag theory. European Journal of Mechanics -A/Solids, 2011, 30(3):559-570 http://en.journals.sid.ir/ViewPaper.aspx?ID=355167
[150]	Rodrigues JD, Roque CMC, Ferreira AJM, et al. Radial basis functions-finite differences collocation and a unified formulation for bending, vibration and buckling analysis of laminated plates, according to Murakami's zig-zag theory. Composite Structures, 2011, 93(5):1613-1620 https://www.researchgate.net/publication/229363595_Radial_basis_functions-finite_differences_collocation_and_a_Unified_Formulation_for_bending_vibration_and_buckling_analysis_of_laminated_plates_according_to_Murakami%27s_zig-zag_theory
[151]	Rao KM, Meyer-Piening HR. Analysis of thick laminated anisotropic composites plates by the finite element method. Composite Structures, 1990, 15(3):185-213 doi: 10.1016/0263-8223(90)90031-9
[152]	Brank B, Carrera E. Multilayered shell finite element with interlaminar continuous shear stresses:a refinement of the Reissner-Mindlin formulation. International Journal of Numerical Methods in Engineering, 2000, 48(6):843-874 doi: 10.1002/(ISSN)1097-0207
[153]	Carrera E, Parisch H. An evaluation of geometrical nonlinear effects of thin and moderately thick multilayered composite shells. Com-posite Structures, 1998, 40(1):11-24 https://www.researchgate.net/publication/223311587_An_evaluation_of_geometrical_nonlinear_effects_of_thin_and_moderately_thick_multilayered_composite_shells
[154]	Auricchio F, Sacco E. Refined first-order shear deformation theory models for composite laminates. Journal of Applied Mechanics, 2003, 70(3):381-390 doi: 10.1115/1.1572901
[155]	Carrera E, Demasi L. Multilayered finite plate element based on Reissner mixed variational theorem, part I:theory and part Ⅱ:numerical analysis. International Journal for Numerical Methods in Engineering, 2002, 55(2):191-231 doi: 10.1002/(ISSN)1097-0207
[156]	Di Sciuva M. An improved shear-deformation theory for moderately thick multilayered anisotropic shells and plates. Journal of Applied Mechanics, 1987, 54(3):589-596 doi: 10.1115/1.3173074
[157]	Di Sciuva M. Bending, vibration and buckling of simply supported thick multilayered orthotropic plates:an evaluation of a new displacement model. Journal of Sound and Vibration, 1986, 105(3):425-442 doi: 10.1016/0022-460X(86)90169-0
[158]	Tessler A, Di Sciuva M, Gherlone M. A refined zigzag beam theory for composite and sandwich beams. Journal of Composite Materials, 2009, 43(7):1051-1081 https://www.researchgate.net/publication/249354821_A_Refined_Zigzag_Beam_Theory_for_Composite_and_Sandwich_Beams
[159]	Cho M, Parmerter PR. An efficient higher-order plate theory for laminated composites. Composite Structures, 1992, 20(2):113-123 doi: 10.1016/0263-8223(92)90067-M
[160]	Cho M, Parmerter PR. Efficient higher order plate theory for general lamination configurations. AIAA Journal, 1993, 31(7):1299-1308 doi: 10.2514/3.11767
[161]	Cho M, Kim KO, Kim MH. Efficient higher-order shell theory for laminated composites. Composite Structures, 1996, 34(34):197-212 https://www.researchgate.net/publication/245425529_Efficient_Higher-Order_Shell_Theory_for_Laminated_Composites_with_Multiple_Delaminations
[162]	Ali JSM, Bhaskar K, Varadan TK. A new theory for accurate thermal/mechanical flexural analysis of symmetric laminated plates. Composite Structures, 1999, 45(3):227-232 doi: 10.1016/S0263-8223(99)00028-8
[163]	Cho M, Oh J. Higher order zig-zag plate theory under thermoelectric-mechanical loads combined. Composites:Part BEngineering, 2003, 34(1):67-82 https://www.researchgate.net/publication/238378077_Higher_order_zig-zag_plate_theory_under_thermo-electric-mechanical_loads_combined
[164]	Oh J, Cho M, Kim JS. Buckling analysis of a composite shell with multiple delaminations based on a higher order zig-zag theory. Finite Elements in Analysis and Design, 2008, 44(11):675-685 doi: 10.1016/j.finel.2008.03.007
[165]	Nguyen SN, Lee J, Cho M. Efficient higher-order zig-zag theory for viscoelastic laminated composite plates. International Journal of Solids and Structures, 2015, 62:174-185 doi: 10.1016/j.ijsolstr.2015.02.027
[166]	Azharia F, Boroomanda B, Shahbazib M. Exponential basis functions in the solution of laminated plates using a higher-order Zig-Zag theory. Composite Structures, 2013, 105(8):398-407 http://boroomand.iut.ac.ir/azhari-f-boroomand-b-shahbazi-m-2013-%E2%80%9Cexponential-basis-functions-solution-laminated-plates-using
[167]	Icardi U. A three-dimensional zig-zag theory for analysis of thick laminated beam. Composite Structures, 2001, 52(1):123-135 doi: 10.1016/S0263-8223(00)00189-6
[168]	Icardi U. Higher-order zig-zag model for analysis of thick composite beams with inclusion of transverse normal stress and sublaminates approximations. Composites:Part B-Engineering, 2001, 32(3):343-354 http://linkinghub.elsevier.com/retrieve/pii/S1359836801000166
[169]	何陵辉, 刘人怀.一种考虑层间位移和横向剪应力连续条件的层合板理论.固体力学学报, 1994, 15(3):319-326 http://www.cnki.com.cn/Article/CJFDTOTAL-GTLX404.005.htm He Linghui, Liu Renhuai. A theory for laminated plates considering continuity conditions of interlayer displacements and transverse shear stress. Acta Mechanica Solida Sinica, 1994, 15(3):319-326 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GTLX404.005.htm
[170]	舒小平.满足板面载荷和横向剪应力连续的层板理论.复合材料学报, 1994, 11(3):61-68 http://www.cnki.com.cn/Article/CJFDTOTAL-FUHE404.010.htm Shu Xiaoping. A laminates and theory accounting for loads on the surfaces and continue of interface shear stresses. Acta Materiae Compositae Sinica, 1994, 11(3):61-68 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-FUHE404.010.htm
[171]	舒小平.复合材料层合板壳热弹性动力响应.复合材料学报, 1997, 14(2):103-107 http://www.cnki.com.cn/Article/CJFDTOTAL-FUHE702.019.htm Shu Xiaoping. Thermomechanical dynamic response of laminated composite plates and shells. Acta Materiae Compositae Sinica, 1997, 14(2):103-107 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-FUHE702.019.htm
[172]	白瑞祥, 陈浩然.含界面脱粘及表板基体开裂损伤的复合材料夹层板非线性稳定性的研究.复合材料学报, 2002, 19(2):80-84 http://www.cnki.com.cn/Article/CJFDTOTAL-FUHE200202015.htm Bai Ruixiang, Chen Haoran. Investigation of nonlinear buckling behavior of composite sandwich plates with interfacial delamination and matrix micro-cracks. Acta Materiae Compositae Sinica, 2002, 19(2):80-84 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-FUHE200202015.htm
[173]	任晓辉, 陈万吉. C⁰型高阶锯齿理论及复合材料厚梁热应力分析.计算力学学报, 2015, 32(1):77-82 doi: 10.7511/jslx201501013 Ren Xiaohui, Chen Wanji. Thermal stress analysis of thick composite beams based on C⁰-type higher-order zig-zag theory. Chinese Journal of Computational Mechanics, 2015, 32(1):77-82 (in Chinese) doi: 10.7511/jslx201501013
[174]	Oh J, Cho M, Kim JS. Dynamic analysis of composite plate with multiple delaminations based on higher-order zigzag theory. International Journal of Solids and Structures, 2005, 42(23):6122-6140 doi: 10.1016/j.ijsolstr.2005.06.006
[175]	Cho M, Choi YJ. A new postprocessing method for laminated composites of general lamination fonfigurations. Composite Structures, 2001, 54(4):397-406 doi: 10.1016/S0263-8223(01)00076-9
[176]	Chalak HD, Chakrabarti A, Iqbal MA, et al. Free vibration analysis of laminated soft core sandwich plates. Journal of Vibration and Acoustics-Transactions of the ASME, 2013, 135(135):011013 https://www.researchgate.net/publication/262581820_Free_vibration_analysis_of_laminated_soft_core_sandwich_plates
[177]	Zhen W, Lo SH, Sze KY, et al. A higher order finite element including transverse normal strain for linear elastic composite plates with general lamination configurations. Finite Elements in Analysis and Design, 2012, 48(1):1346-1357 doi: 10.1016/j.finel.2011.08.003
[178]	Xiaohui R, Wanji C, Zhen W. A C⁰-type zig-zag theory and finite element for laminated composite and sandwich plates with general configurations. Archive of Applied Mechanics, 2012, 82(2):391-406 doi: 10.1007/s00419-011-0563-7
[179]	Reddy JN. A generalization of two-dimensional theories of laminated composite plates. Communications in Applied Numerical Methods, 1987, 3(3):173-180 doi: 10.1002/(ISSN)1555-2047
[180]	Reddy JN, Barbero EJ, Teply JL. A plate bending element based on a generalized laminated plate theory. International Journal for Numerical Methods in Engineering, 1989, 28(10):2275-2292 doi: 10.1002/(ISSN)1097-0207
[181]	Barbero EJ, Reddy JN, Teply JL. General two-dimensional theory of laminated cylindrical shells. AIAA Journal, 1990, 28(2):544-553 https://www.researchgate.net/publication/245423251_General_two-dimensional_theory_of_laminated_cylindrical_shells
[182]	Barbero EJ, Reddy JN. Modeling of delamination in composite laminates using a layer-wise plate theory. International Journal of Solids and Structures, 1991, 28(2):373-388 https://www.researchgate.net/publication/222477517_Modeling_of_delamination_in_composite_laminates_using_a_layer-wise_plate_theory
[183]	Di Sciuva M, Gherlone M. A global/local third-order Hermitian displacement field with damaged interfaces and transverse extensibility:FEM formulation. Composite Structures, 2003, 59(3):433-444 http://linkinghub.elsevier.com/retrieve/pii/S0263822302001691
[184]	Gherlone M, Di Sciuva M. Thermo-mechanics of undamaged and damaged multilayered composite plates:a sub-laminates finite element approach. Composite Structures, 2007, 81(1):125-136 doi: 10.1016/j.compstruct.2006.08.004
[185]	Gherlone M, Di Sciuva M. Thermo-mechanics of undamaged and damaged multilayered composite plates:assessment of the FEM sublaminates approach. Composite Structures, 2007, 81(1):137-155 doi: 10.1016/j.compstruct.2006.08.005
[186]	Pai PF, Palazotto AN. A high-order sandwich plate theory accounting for 3-D stresses. International Journal of Solids and Structures, 2001, 38(30-31):5045-5062 doi: 10.1016/S0020-7683(00)00356-5
[187]	Carrera E. Mixed layer-wise models for multilayered plates analysis. Composite Structures, 1998, 43(1):57-70 doi: 10.1016/S0263-8223(98)00097-X
[188]	Carrera E. Evaluation of layerwise mixed theories for laminated plates analysis. AIAA Journal, 1998, 36(4):830-839 https://www.researchgate.net/publication/245424926_Evaluation_of_Layerwise_Mixed_Theories_for_Laminated_Plates_Analysis
[189]	Carrera E. Theories and finite elements for multilayered plates and shells. Archives of Computational Methods in Engineering, 2003, 10(2):215-296 doi: 10.1007%2FBF02736649
[190]	Carrera E, Demasi L. Two benchmarks to assess two-dimensional theories of sandwich composite plates. AIAA Journal, 2003, 41(5):1356-1362 http://core.ac.uk/display/11370216
[191]	Icardi U. Layerwise mixed element with sublaminates approximation and 3D zig-zag field, for analysis of local effects in laminated and sandwich composites. International Journal for Numerical Methods in Engineering, 2007, 70(1):94-125 doi: 10.1002/(ISSN)1097-0207
[192]	Marjanovic' M, Vuksanovic' DJ. Layerwise solution of free vibrations and buckling of laminated composite and sandwich plates with embedded delaminations. Composite Structures, 2014, 108(1):9-20 https://www.researchgate.net/profile/Miroslav_Marjanovic2/publication/256524227_Layerwise_solution_of_free_vibrations_and_buckling_of_laminated_composite_and_sandwich_plates_with_embedded_delaminations/links/56e3ef6e08ae98445c1eed13.pdf?inViewer=0&pdfJsDownload=0&origin=publication_detail
[193]	Alnefaie K. Finite element modeling of composite plates with internal delamination. Composite Structures, 2009, 90(1):21-27 doi: 10.1016/j.compstruct.2009.01.004
[194]	Basar Y, Itskov M, Eckstein A. Composite laminates:nonlinear interlaminar stress analysis by multi-layer shell elements. Computer Methods in Applied Mechanics and Engineering, 2000, 185(2-4):367-397 doi: 10.1016/S0045-7825(99)00267-4
[195]	Basar Y, Omurtag MH. Free-vibration analysis of thin/thick laminated structures by layer-wise shell models. Computers and Structures, 2000, 74(3):409-427 https://www.deepdyve.com/lp/elsevier/free-vibration-analysis-of-thin-thick-laminated-structures-by-layer-arAFlRXxNR
[196]	Botello S, Onate E, Canet JM. A layer-wise triangle for analysis of laminated composite plates and shells. Computers and Structures, 1999, 70(6):635-646 doi: 10.1016/S0045-7949(98)00165-5
[197]	Ghoshal A, Kim HS, Chattopadhyay A, et al. Effect of delamination on transient history of smart composite plates. Finite Elements in Analysis and Design, 2005, 41(9-10):850-874 doi: 10.1016/j.finel.2004.10.006
[198]	Chattopadhyay A, Kim HS, Ghoshal A. Non-linear vibration analysis of smart composite structures with discrete delamination using a refined layerwise theory. Journal of Sound and Vibration, 2004, 273(1-2):387-407 doi: 10.1016/S0022-460X(03)00561-3
[199]	胡明勇, 王安稳, 姜伟等.复合材料层合板的动力响应和横向应力分析.船舶力学, 2008, 12(4):778-784 http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200805015.htm Hu Mingyong, Wang Anwen, Jiang Wei, et al. Dynamic response and transverse stresses analysis of composite laminated plates. Journal of Ship Mechanics, 2008, 12(4):778-784 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200805015.htm
[200]	胡明勇, 王安稳.纤维增强粘弹性复合材料层合板的自由振动和应力分析.工程力学, 2010, 27(6):10-20 http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201008004.htm Hu Mingyong, Wang Anwen. Free vibration and stresses analysis of fiber-reinforced viscoelastic composite laminated plates. Engineering Mechanics, 2010, 27(6):10-20 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201008004.htm
[201]	赵龙胜, 吴锦武, 赵飞等.复合材料简支板固有频率与振型分析.南昌航空大学学报:自然科学版, 2013, 27(2):10-17 http://www.cnki.com.cn/Article/CJFDTOTAL-NCHK201302002.htm Zhao Longsheng, Wu Jinwu, Zhao Fei, et al. Natural frequency and modal shape analysis of the simply supported composite plates. Journal of Nanchang Hangkong University:Natural Sciences, 2013, 27(2):10-17 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-NCHK201302002.htm
[202]	杨少红, 王安稳.粘弹层合板的稳态振动和层间应力.应用力学学报, 2003, 20(3):112-117 http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX200304025.htm Yang Shaohong, Wang Anwen. The steady state vibration and interlaminar stresses of viscoelastic laminated plates. Chinese Journal of Applied Mechanics, 2003, 20(3):112-117 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX200304025.htm
[203]	Pandey S, Pradyumna S. A new C0 higher-order layerwise finite element formulation for the analysis of laminated and sandwich plates. Composite Structures, 2015, 131(1):1-16 https://www.researchgate.net/publication/276297105_A_new_C0_Higher-order_Layerwise_Finite_Element_Formulation_for_the_Analysis_of_Laminated_and_Sandwich_Plates
[204]	Plagianakos TS, Saravanos DA. Higher-order layerwise laminate theory for the prediction of interlaminar shear stresses in thick composite and sandwich composite plates. Composite Structures, 2009, 87(1):23-35 doi: 10.1016/j.compstruct.2007.12.002
[205]	Reddy JN, Robbins DH. Theories and computational models of composite laminates. Applied Mechanics Reviews, 1994, 47 (6):21-35 http://en.journals.sid.ir/ViewPaper.aspx?ID=291171
[206]	Noor AK, Burton WS, Bert CW. Computational models for sandwich panels and shells. Applied Mechanics Reviews, 1996, 49 (2):155-199 https://www.researchgate.net/publication/252898378_Computational_Models_for_Sandwich_Panels_and_Shells
[207]	Kant MT. A critical review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches. Composite Structures, 1993, 23 (3):293-312 https://www.civil.iitb.ac.in/~tkant/papers/TKant-IITB-JP057.pdf
[208]	Altenbach H. Theories for laminated and sandwich plates. Mechanics of Composite Materials, 1998, 34 (2):243-252 doi: 10.1007/bf02256043.pdf
[209]	Zhang YX, Yang CH. Recent developments in finite element analysis for laminated composite plates. Composite Structures, 2009, 88 (1):147-157 doi: 10.1016/j.compstruct.2008.02.014
[210]	Kreja I. A literature review on computational models for laminated composite and sandwich panels. Central European Journal of Engineering, 2011, 1 (1):59-80 https://www.researchgate.net/publication/225481280_A_literature_review_on_computational_models_for_laminated_composite_and_sandwich_panels
[211]	Khandan R, Noroozi S, Sewell P, et al. The development of laminated composite plate theories:a review. Journal of Materials Science, 2012, 47 (16):5901-5910 doi: 10.1007/s10853-012-6329-y
[212]	Liu RH, Su W. Nonlinear stability of symmetrically laminated cylindrically orthotropic truncated shallow conical shells including transverse shear. International Journal of Applied Mechanics and Engineering, 2009, 14(2):769-790 http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.baztech-article-BPZ2-0041-0029
[213]	安娜, 王璠, 刘人怀.复合材料层合圆柱正交异性扁球壳在线布载荷作用下的非线性稳定性.暨南大学学报(自然科学版), 2006, 27(2):398-405 http://www.cnki.com.cn/Article/CJFDTOTAL-JNDX200603012.htm An Na, Wang Fan, Liu Renhuai. Nonlinear bending of symmetrically laminated cylindrically orthotropic shallow spherical shells under linear load. Journal of Jinan University (Natural Science), 2006, 27(2):398-405 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JNDX200603012.htm
[214]	丁磊, 刘人怀, 王璠.复合材料浅球壳模态分析与结构优化设计.材料科学与工程学报, 2007, 25(2):439-442 http://www.cnki.com.cn/Article/CJFDTOTAL-CLKX200703028.htm Ding Lei, Liu Renhuai, Wang Fan. Finite element analysis on vibration modes and structure optimal design of the symmetrically laminated orthotropic shallow shells. Journal of Materials Science & Engineering, 2007, 25(2):439-442 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-CLKX200703028.htm
[215]	杨增涛, 徐加初, 王璠.复合材料层合扁锥壳的冲击屈曲.振动工程学报, 2007, 20(1):19-23 http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC200701003.htm Yang Zengtao, Xu Jiachu, Wang Fan. Impact buckling of laminated composite shallow conical shells. Journal of Vibration Engineering, 2007, 20(1):19-23 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC200701003.htm
[216]	徐加初, 杨增涛.复合材料层合开顶扁球壳在集中冲击下的非线性动力屈曲.振动与冲击, 2007, 26(1):1-4 http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ200701000.htm Xu Jiachu, Yang Zengtao. Dynamic buckling of laminated composite truncated, shallow spherical shells under a concentrated impact. Journal of Vibration and Shock, 2007, 26(1):1-4 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ200701000.htm
[217]	徐加初, 杨增涛.爆炸冲击下复合材料层合扁球壳的动力屈曲.爆炸与冲击, 2007, 2(2):116-120 doi: 10.11883/1001-1455(2007)02-0116-05 Xu Jiachu, Yang Zengtao. Dynamic buckling of laminated composite shallow spherical shells subjected to explosive impact. Explosion and Shock Waves, 2007, 2(2):116-120 (in Chinese) doi: 10.11883/1001-1455(2007)02-0116-05
[218]	王璠.开孔复合材料扁球壳非线性动力响应.哈尔滨工业大学学报, 2000, 32(1):37-44 http://www.cnki.com.cn/Article/CJFDTOTAL-HEBX200001009.htm Wang Fan. Nonlinear dynamic response of symmetrically laminated cylindrically orthotropic truncated shallow shells. Journal of Harbin Institute of Technology, 2000, 32(1):37-44 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-HEBX200001009.htm
[219]	王志伟, 姚著.蜂窝纸板冲击压缩的试验研究和有限元分析.机械工程学报, 2012, 48(14):49-55 http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201212010.htm Wang Zhiwei, Yao Zhu. Experimental investigation and finite element analysis for impact compression of honeycomb paperboards. Journal of Mechanical Engineering, 2012, 48(14):49-55 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201212010.htm
[220]	Wang DM, Wang ZW. Experimental investigation into the cushioning properties of honeycomb paperboard. Packaging Technology and Science, 2008, 21(6):309-316 doi: 10.1002/pts.v21:6
[221]	王志伟, 王立军, 徐晨翼.多次低强度冲击对蜂窝纸板缓冲性能的影响.应用力学学报, 2015, 32(2):441-445 http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX201503016.htm Wang Zhiwei, Wang Lijun, Xu Chenyi. Effects of low-strength repeated impacts on cushioning performance of honeycomb paperboard. Chinese Journal of Applied Mechanics, 2015, 32(2):441-445 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX201503016.htm
[222]	Song ZH, Wang ZH, Ma HW, et al. Mechanical behavior and failure mode of woven carbon/epoxy laminate composites under dynamic compressive loading. Composites:Part B-Engineering, 2014, 60(3):531-536 https://www.researchgate.net/publication/271013762_Mechanical_behavior_and_failure_mode_of_woven_carbonepoxy_laminate_composites_under_dynamic_compressive_loading
[223]	Fan H, Zhao L, Chen H, et al. Ductile deformation mechanisms and designing instructions for integrated woven textile sandwich composites. Composite Science and Technology, 2012, 72(9):1338-1343 https://www.researchgate.net/publication/257100349_Ductile_deformation_mechanisms_and_designing_instructions_for_integrated_woven_textile_sandwich_composites
[224]	Fan H, Zhao L, Chen H, et al. Dynamic compression failure mechanisms and dynamic effects of integrated woven sandwich composites. Journal of Composite Materials, 2014, 48(3):427-443 doi: 10.1177/0021998312473859
[225]	何陵辉, 成振强, 刘人怀.含非均匀界面相碳/碳纤维复合材料等效热传导性质的研究.应用数学和力学, 1997, 18(2):193-201 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX199703000.htm He Linghui, Cheng Zhenqiang, Liu Renhuai. Investigation on the effective conductivities of carbon/carbon fiber composites with inhomogeneous interphase. Applied Mathematics and Mechanics, 1997, 18(2):193-201 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX199703000.htm
[226]	何陵辉, 刘人怀.球面各向同性颗粒复合材料膨胀系数的界限.应用数学和力学, 1997, 18(3):317-323 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX199704003.htm He Linghui, Liu Renhuai. Bounds of the expansion coefficients of composites reinforced by spherically isotropic particles. Applied Mathematics and Mechanics, 1997, 18(3):317-323 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX199704003.htm
[227]	何陵辉, 成振强, 刘人怀.空心球复合材料热弹性性质的一些精确结果.应用数学和力学, 1998, 19(4):399-406 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX805.002.htm He Linghui, Cheng Zhenqiang, Liu Renhuai. Some exact results concerning thermoelastic properties of hollow sphere composites. Applied Mathematics and Mechanics, 1998, 19(4):399-406 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX805.002.htm
[228]	王璠, 何一帆, 宋毅等.引发方式、铺层对纤维增强复合材料圆柱壳吸能特性影响的冲击试验研究.振动工程学报, 2013, 26(1):33-40 http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201301010.htm Wang fan, He Yifan, Song Yi, et al. The impact experimental study of evoking type and Layup type on absorption energy of fiber reinforced composite cylindrical shell. Journal of Vibration Engineering, 2013, 26(1):33-40 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201301010.htm
[229]	郑伟玲, 肖潭, 朱朦琪等.聚苯乙炔包覆多壁碳纳米管的制备及其分散性.物理化学学报, 2009, 25(11):2373-2379 doi: 10.3866/PKU.WHXB20091130 Zheng Weiling, Xiao Tan, Zhu Mengqi, et al. Preparation and dispersivity of multiwalled carbon nanotubes coated by poly (phenylacetylene). Acta Physico-Chimica Sinica, 2009, 25(11):2373-2379 (in Chinese) doi: 10.3866/PKU.WHXB20091130
[230]	卫保娟, 肖潭, 李雄俊等.石墨烯与多壁碳纳米管增强环氧树脂复合材料的制备及性能.复合材料学报, 2012, 29(4):53-59 http://www.cnki.com.cn/Article/CJFDTOTAL-FUHE201205011.htm Wei Baojuan, Xiao Tan, Li Xiongjun, et al. Preparation and properties of graphene and MWCNTs reinforced epoxy resin composites. Acta Materiae Compositae Sinica, 2012, 29(4):53-59 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-FUHE201205011.htm
[231]	朱朦琪, 肖潭, 郑伟玲等.混杂功能化碳纳米管/聚氨酯复合材料的制备及性能.材料研究学报, 2012, 26(2):191-198 http://www.cnki.com.cn/Article/CJFDTOTAL-CYJB201202016.htm Zhu Mengqi, Xiao Tan, Zheng Weiling, et al. Preparation and properties of hybrid functionalized carbon nanotube polyurethane composites. Chinese Journal of Materials Research, 2012, 26(2):191-198 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-CYJB201202016.htm
[232]	姜久红, 王志伟.蜂窝型缓冲包装系统的振动特性分析.湖北工业大学学报, 2006, 21(2):18-20 http://cpfd.cnki.com.cn/Article/CPFDTOTAL-JXGC200603001007.htm Jiang Jiuhong, Wang Zhiwei. The research on the vibration Characteristics for honeycomb paperboard cushioning package system. Journal of Hubei University of Technology, 2006, 21(2):18-20 (in Chinese) http://cpfd.cnki.com.cn/Article/CPFDTOTAL-JXGC200603001007.htm
[233]	Wang ZW, E YP. Energy-absorbing properties of paper honeycombs under low and intermediate strain rates. Packaging Technology and Science, 2012, 25(2):173-185 https://www.researchgate.net/publication/264371519_Energy-Absorbing_Properties_of_Paper_Honeycombs_under_Low_and_Intermediate_Strain_Rates
[234]	宁志华, 刘人怀, 刘稀南. 径向约束下含非均匀界面层纤维增强复合材料的热弹性分析//第十三届现代数学和力学学术会议暨钱伟长诞辰100周年纪念大会论文集, 上海, 2012-10-6-2012-10-8 Ning Zhihua, Liu Renhuai, Liu Xinan. Thermal analysis for fiber-reinforced composites containing inhomogeneous interphase subjected to a radial constrain//Preceeding of the Conference of 13th Modern Mathematics and Mechanics (MMM-XⅢ) & the 100th Anniversary of Weichang Chien's Birth. Shanghai, 6th-8th Oct., 2012-10-6-2012-10-8 (in Chinese)
[235]	Ning ZH, Liu XN. Thermal analysis for fiber-reinforced composites containing inhomogeneous interphase subject to a radial constraint. Advanced Materials Research, 2013, 652-654:77-83 doi: 10.4028/www.scientific.net/AMR.652-654
[236]	刘述伦, 薛江红, 王璠.纤维增强正交各向异性复合材料层合板的湿热屈曲.暨南大学学报(自然科学版), 2013, 34(4):489-494 http://www.cnki.com.cn/Article/CJFDTOTAL-JNDX201305012.htm Liu Shulun, Xue Jianghong, Wang Fan. Hygrothermal buckling of fiber-reinforced, symmetrical cross-ply composite plates. Journal of Jinan University (Natural Science), 2013, 34(4):489-494 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JNDX201305012.htm
[237]	刘述伦, 薛江红, 王璠等.含脱层纤维增强复合材料层合板在湿热环境下的屈曲分析.工程力学, 2015, 32(2):1-8 http://cdmd.cnki.com.cn/Article/CDMD-10559-1012030841.htm Liu Shulun, Xue Jianghong, Wang Fan, et al. Buckling analysis of fiberreinforced laminated composite plate with delamination under hygrothermal environments. Engineering Mechanics, 2015, 32(2):1-8 (in Chinese) http://cdmd.cnki.com.cn/Article/CDMD-10559-1012030841.htm
[238]	朱永安, 王璠.均布载荷和温度场联合作用下的扁球壳的热屈曲.南昌大学学报, 2007, 31(增刊):205-207 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX201503004.htm Zhu Yongan, Wang Fan. Thermal buckling of shallow spherical shell under uniformly distributed load and temperature field. Journal of Nanchang University, 2007, 31(sup):205-207 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX201503004.htm
[239]	朱永安, 王璠, 刘人怀.考虑横向剪切的对称圆柱正交异性层合扁球壳的热屈曲.应用数学和力学, 2008, 29(2):263-271 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX200803003.htm Zhu Yongan, Wang Fan, Liu Renhuai. Thermal buckling of axisymmetrically laminated cylindrically orthotropic shallow spherical shells including transverse shear. Applied Mathematics and Mechanics, 2008, 29(2):263-271 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX200803003.htm
[240]	E YP, Wang ZW. Effect of relative humidity on energy absorption properties of honeycomb paperboards. Packaging Technology and Science, 2010, 23(6):471-483 https://www.cabdirect.org/cabdirect/abstract/20113052709
[241]	E YP, Wang ZW. Plateau stress of paper honeycomb as response to various relative humidities. Packaging Technology and Science, 2010, 23(3):203-216 https://www.researchgate.net/publication/230343138_Plateau_Stress_of_Paper_Honeycomb_as_Response_to_Various_Relative_Humidities
[242]	陈炎, 韩景龙, 刘人怀.横观各向同性压电矩形薄板的非线性振动.南京航空航天大学学报, 2003, 35(1):18-24 http://www.cnki.com.cn/Article/CJFDTOTAL-NJHK200301003.htm Chen Yan, Han Jinglong, Liu Renhuai. Nonlinear vibration of transversely isotropic piezoelectric rectangular plate. Journal of Nanjing University of Aeronautics & Astronautics, 2003, 35(1):18-24 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-NJHK200301003.htm
[243]	陈炎, 刘人怀.压电矩形薄板的非线性强迫振动.华南理工大学学报(自然科学版), 2003, 31 http://www.cnki.com.cn/Article/CJFDTOTAL-HNLG2003S1016.htm S1):63-66 (Chen Yan, Liu Renhuai. Nonlinear force vibration of piezoelectric rectangular thin plate. Journal of South China University of Technology (Natural Science Edition), 2003, 31(S1):63-66 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-HNLG2003S1016.htm
[244]	陈炎, 刘人怀.单向轴压下压电矩形薄板的动态后屈曲问题.振动工程学报, 2008, 21(3):335-342 http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC200804004.htm Chen Yan, Liu Renhuai. Dynamic post-buckling of piezoelectric rectangular thin plate under unilateral axially-pressure. Journal of Vibration Engineering, 2008, 21(3):335-342 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC200804004.htm
[245]	陈炎, 刘人怀. 考虑位移场和电场高阶分布的压电板耦合非线性理论. 刘人怀等主编. 工程力学科学与实践, 广州: 暨南大学出版社, 2010: 183-214 Chen Yan, Liu Renhuai. A Nonlinear Theory for Piezoelectric Plates With Coupling Effects of High Order Displacement and Electric Field. Liu Renhuai et al. Eds. Science and practice in engineering mechanics. Guangzhou:Jinan University Press, 2010:183-214 (in Chinese)
[246]	Wang H, Hu Y, Wang J. On the nonlinear behavior of a multilayer circular piezoelectric plate-like transformer operating near resonance. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2013, 60(3):752-757 https://www.researchgate.net/publication/283469370_Experimental_study_on_influence_factors_on_equivalent_circuit_parameters_of_piezoelectric_transformers
[247]	Wang H, Hu Y, Wang J. Nonlinear analysis of a 5-layer beam-like piezoelectric transformer near resonance. Acta Mechanica Solida Sinica, 2014, 27(2):195-201 doi: 10.1016/S0894-9166(14)60029-X
[248]	傅衣铭, 李升, 姜叶洁.具界面损伤压电智能层合板的非线性自由振动分析.应用数学和力学, 2009, 30(2):127-141 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX200902004.htm Fu Yiming, Li Sheng, Jiang Yejie. Non-linear free vibration analysis of piezoelastic laminated plates with interfacial damage. Applied Mathematics and Mechanics, 2009, 30(2):127-141 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX200902004.htm
[249]	郑玉芳, 傅衣铭, 王锋.具损伤压电层合板的非线性动力稳定性分析.力学学报, 2006, 38(3):570-576 http://www.cnki.com.cn/Article/CJFDTOTAL-LXXB200604020.htm Zheng Yufang, Fu Yiming, Wang Feng. Nonlinear dynamic stability for piezoelectric laminated plates with damage. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(3):570-576 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-LXXB200604020.htm
[250]	Rao MN, Schmidt R, Schröder KU. Geometrically nonlinear static FE-simulation of multilayered magneto-electro-elastic composite structures. Composite Structures, 2015, 127:120-131 doi: 10.1016/j.compstruct.2015.03.002
[251]	Xiao Y, Zhou HM, Cui XL. Nonlinear resonant magnetoelectric coupling effect with thermal, stress and magnetic loadings in laminated composites. Composite Structures, 2015, 128:35-41 doi: 10.1016/j.compstruct.2015.03.039
[252]	Yu GL, Zhang HW, Li YX, et al. Theoretical study of nonlinear magnetoelectric response in laminated magnetoelectric composites. Composite Structures, 2014, 108:287-294 doi: 10.1016/j.compstruct.2013.09.039
[253]	Shi Y, Gao YW. Theoretical study on nonlinear magnetoelectric effect and harmonic distortion behavior in laminated composite. Journal of Alloys and Compounds, 2015, 646:351-359 doi: 10.1016/j.jallcom.2015.05.229
[254]	舒小平.压电复合材料层板柱面弯曲的精化理论.应用力学学报, 2005, 22(1):44-48 http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX200501009.htm Shu Xiaoping. Accurate theory of laminated piezoelectric composite plates under cylindrical bending. Chinese Journal of Applied Mechanics, 2005, 22(1):44-48(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX200501009.htm
[255]	Xue JH, Wang YO, Yuan D. A shear deformation theory for bending and buckling of undersea sandwich pipes. Composite Structures, 2015, 132:633-643 doi: 10.1016/j.compstruct.2015.06.004
[256]	Xue JH. Asymptotic analysis for buckling of undersea corroded pipelines. ASME Transaction-Journal of Pressure Vessel Technology, 2008, 130 (2):021705 doi: 10.1115/1.2894293
[257]	Xue JH. A nonlinear finite element analysis of buckle propagation in subsea corroded pipelines. Finite Elements in Analysis and Design, 2006, 42(14-15):1211-1219 doi: 10.1016/j.finel.2006.05.003
[258]	Xue J, Hoo Fatt MS. Symmetric and anti-symmetric buckle propagation modes in subsea corroded pipelines. Marine Structures, 2005, 18(1):43-61 doi: 10.1016/j.marstruc.2005.08.001
[259]	Williams JG, Hadavinia H. Analytical solutions for cohesive zone models. Journal of the Mechanics and Physics of Solids, 2002, 50(4):809-825 doi: 10.1016/S0022-5096(01)00095-3
[260]	Blackman BRK, Hadavinia H, Kinloch AJ, et al. The use of a cohesive zone model to study the fracture of fibre composites and adhesivelybonded joints. International Journal of Fracture, 2003, 119(1):25-46 doi: 10.1023/A:1023998013255
[261]	Pike MG, Oskay C. XFEM modeling of short microfiber reinforced composites with cohesive interfaces. Finite Elements in Analysis and Design, 2015, 106:16-31 doi: 10.1016/j.finel.2015.07.007
[262]	Ouyang ZY, Li GQ. Cohesive zone model based analytical solutions for adhesively bonded pipe joints under torsional loading. International Journal of Solids and Structures, 2009, 46(5):1205-1217 doi: 10.1016/j.ijsolstr.2008.10.021
[263]	Lorenzis LD, Zavarise G. Cohesive zone modeling of interfacial stresses in plated beams. International Journal of Solids and Structures, 2009, 46(24):4181-4191 doi: 10.1016/j.ijsolstr.2009.08.010
[264]	Yuan H, Teng JG, Seracino R, et al. Full-range behavior of FRPto-concrete bonded joints. Engineering Structure, 2004, 26(5):553-565 doi: 10.1016/j.engstruct.2003.11.006
[265]	Yuan H, Lu XS, Hui D, et al. Studies on FRP-concrete interface with hardening and softening bond-slip law. Composite Structures, 2012, 94(19):3781-3792 http://site.icce-nano.org/Clients/iccenanoorg/hui%20pub/2012%20studies%20on%20frp-concrete%20interface%20with%20hardening%20and%20softening%20bond-slip%20law%20(1).pdf
[266]	Chen JF, Yuan H, Teng JG. Debonding failure along a softening FRP-to-concrete interface between two adjacent cracks in concrete members. Engineering Structures, 2007, 29:259-270 doi: 10.1016/j.engstruct.2006.04.017
[267]	赵玉萍, 袁鸿, 韩军.基于弹性-塑性内聚力模型的纤维拔出界面宏观行为分析.力学学报, 2015, 47(1):127-134 doi: 10.6052/0459-1879-14-165 Zhao Yuping, Yuan Hong, Han Jun. Analysis of the macroscopic interfacial behaviour of the fibre pullout using elastic-plastic cohesive model. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(1):127-134 (in Chinese) doi: 10.6052/0459-1879-14-165
[268]	刘三星, 袁鸿. FRP抗剪加固混凝土梁中间裂缝的扩展过程.暨南大学学报, 2014, 35(1):104-112 doi: 10.11778/j.jdxb.2014.01.019 Liu Sanxing, Yuan Hong. Process of middle crack propagation in concrete beams shear-strengthened with FRP strips. Journal of Jinan University, 2014, 35(1):104-112(in Chinese) doi: 10.11778/j.jdxb.2014.01.019
[269]	关天发, 袁鸿. CFRP加固钢筋混凝土曲梁的抗弯性能试验研究.中山大学学报(自然科学版), 2008, 47(增刊2):109-113 http://www.cnki.com.cn/Article/CJFDTOTAL-ZSDZ2008S2025.htm Guan Tianfa, Yuan Hong. Experimental study on bending properties of RC curved beam strengthened with CFRP. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2008, 47 (Sup.2):109-113(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZSDZ2008S2025.htm
[270]	袁鸿, 李庆, 萧澎伟等.侧面黏贴纤维复合材料的抗剪加固梁破坏机理.暨南大学学报(自然科学版), 2012, 33(4):463-467 http://www.cnki.com.cn/Article/CJFDTOTAL-JNDX201205005.htm Yuan Hong, Li Qing, Xiao Pengwei, et al. Failure mechanism of shear strengthened beam with side-bonded FRP. Journal of Jinan University (Natural Science), 2012, 33(4):463-467 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JNDX201205005.htm
[271]	向红, 傅衣铭, 洪力.受面内双向载荷蜂窝材料的弹性屈曲模式及其影响因素.应用力学学报, 2009, 26(2):321-324 http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX200902022.htm Xiang Hong, Fu Yiming, Hong Li. Elastic buckling mode and influence factors of hexagonal honeycombs under biaxial loading. Chinese Journal of Applied Mechanics, 2009, 26(2):321-324 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX200902022.htm
[272]	向红, 傅衣铭, 洪力.不规则蜂窝材料在单向载荷作用下的蠕变屈曲分析.固体力学学报, 2008, 29(2):181-186 http://www.cnki.com.cn/Article/CJFDTOTAL-GTLX200802012.htm Xiang Hong, Fu Yiming, Hong Li. Creep-buckling of irregular hexagonal honeycombs under uniaxial loading. Chinese Journal of Solid Mechanics, 2008, 29(2):181-186 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GTLX200802012.htm
[273]	Wang YJ, Wang ZM. Creep buckling of cross-ply symmetric laminated cylindrical panels. Applied Mathematics and Mechanics, 1993, 14(3):313-318 https://www.researchgate.net/publication/245265499_Creep_buckling_of_cross-ply_symmetric_laminated_cylindrical_panels
[274]	Xue JH, Luo QZ, Han F, et al. Two dimensional analyses of delamination buckling of symmetrically cross-ply, rectangular laminates. Applied Mathematics and Mechanics, 2013, 34(4):597-612 https://www.researchgate.net/publication/257517666_Two-dimensional_analyses_of_delamination_buckling_of_symmetrically_cross-ply_rectangular_laminates
[275]	Xue JH, Zi L, Yuan H, et al. Contact analysis for fiber reinforced, delaminated laminates with kinematic nonlinearity. Acta Mechanica Solida Sinica, 2013, 26(3):388-402 https://www.researchgate.net/publication/259134034_Contact_analysis_for_fiber-reinforced_delaminated_laminates_with_kinematic_nonlinearity
[276]	Tang MQ, Xue JH, Yuan H, et al. Macro-micro analysis for antipenetrating postbuckling of T300/QY8911 carbon fiber reinforced, deboned laminates with contact effects. International Journal of Applied Mechanics, 2014, 6(4):1450044 doi: 10.1142/S1758825114500446
[277]	Zhu F, Fu Y, Chen D. Analysis of fatigue delamination growth for piezoelectric laminated cylindrical shell considering nonlinear contact effect. International Journal of Solids and Structures, 2008, 45:5381-5396 doi: 10.1016/j.ijsolstr.2008.05.031
[278]	杨金花, 傅衣铭.具脱层复合材料层合圆柱壳的屈曲分析.湖南大学学报(自然科学版), 2005, 32(4):25-30 http://cdmd.cnki.com.cn/Article/CDMD-10532-2007020390.htm Yang Jinhua, Fu Yiming. Buckling analysis of composite laminated cylindrical shell with delamination. Journal of Hunan University (Natural Sciences), 2005, 32(4):25-30 (in Chinese) http://cdmd.cnki.com.cn/Article/CDMD-10532-2007020390.htm
[279]	杨金花, 傅衣铭.具脱层轴对称层合圆柱壳的振动模态分析.应用力学学报, 2007, 24(3):509-513 http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX200704004.htm Yang Jinhua, Fu Yiming. Modal analysis of axisymmetrical laminated cylindrical shell with delamination. Chinese Journal of Applied Mechanics, 2007, 24(3):509-513 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX200704004.htm
[280]	傅衣铭, 李升, 姜叶洁.具界面损伤压电智能层合板的非线性自由振动分析.应用数学和力学, 2009, 30(2):127-141 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX200902004.htm Fu Yiming, Li Sheng, Jiang Yejie. Non-linear free vibration analysis of piezoelastic laminated plates with interfacial damage. Applied Mathematics and Mechanics, 2009, 30(2):127-141 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX200902004.htm
[281]	陈得良, 傅衣铭.考虑接触效应的具脱层轴对称层合圆板的非线性动力响应.固体力学学报, 2007, 28(3):406-410 http://www.cnki.com.cn/Article/CJFDTOTAL-GTLX200704013.htm Chen Deliang, Fu Yiming. Nonlinear dynamic response of an axisymmetriclydelaminated circular plate with considering contact effect. Acta Mechanica Solida Sinic, 2007, 28(3):406-410 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GTLX200704013.htm
[282]	Chen HR, Wang M, Bai RX. The effect of nonlinear contact upon natural frequency of delaminated stiffened composite plate. Composite Structures, 2006, 76(1-2):28-33 doi: 10.1016/j.compstruct.2006.06.005
[283]	Chen HR, Hong M, Liu YD. Dynamic behavior of delaminated plates considering progressive failure process. Composite Structures, 2004, 66(1-4):456-466 http://linkinghub.elsevier.com/retrieve/pii/S0263822304001606
[284]	Schwarts-Givli H, Rabinovitch O, Frostig Y. High-order nonlinear contact effects in the dynamic behavior of delaminated sandwich panels with a flexible core. International Journal of Solids and Structures, 2007, 44(1):77-99 doi: 10.1016/j.ijsolstr.2006.04.016
[285]	Wang J, Tong L. A study of the vibration of delaminated beams using a nonlinear anti-interpenetration constraint model. Composite Structures, 2002, 57(1-4):483-488 doi: 10.1016/S0263-8223(02)00117-4
[286]	Kwon YW, Aygunes H. Dynamic finite element analysis of laminated beams with delamination cracks using contact-impact conditions. Computers and Structures, 1996, 58(6):1161-1169 doi: 10.1016/0045-7949(95)00202-2
[287]	Whitcomb JD. Analysis of a laminate with a postbuckled embedded delamination, including contact effects. Journal of Composite Materials, 1992, 26(8):1523-1535 doi: 10.1177/002199839202601008
[288]	Yeh MK, Fang LB, Kao MH. Bending behavior of delaminated composite plates with contact effects. Composite Structures, 1997, 39(3-4):347-356 doi: 10.1016/S0263-8223(97)00127-X
[289]	Yeh MK, Fang LB. Contact analysis and experiment of delaminated cantilever composite beam. Composites:Part B-Engineering, 1999, 30(4):407-414 doi: 10.1016/S1359-8368(99)00008-6
[290]	Luo H, Hanagud S. Dynamics of delaminated beams. International Journal of solid and structures, 2000, 37(8):1501-1519 https://www.researchgate.net/publication/222044827_Dynamics_of_delaminated_beams
[291]	Chen H, Bai R. Postbuckling behavior of face/core debonded composite sandwich plate considering matrix crack and contact effect. Composite Structures, 2002, 57(1-4):305-313 doi: 10.1016/S0263-8223(02)00098-3
[292]	Hu N, Fukunaga H, Sekine H, et al. Compressive buckling of laminates with an embedded delamination. Composite Science and Technology, 1999, 59(8):1247-1260 doi: 10.1016/S0266-3538(98)00166-3
[293]	Bruno D, Greco F, Lonetti P. A coupled interface-multilayer approach for mixed mode delamination and contact analysis in laminated composites. International Journal of Solids and Structures, 2003, 40(26):7245-7268 doi: 10.1016/j.ijsolstr.2003.09.006