EI、Scopus 收录
中文核心期刊

一维准晶功能梯度层合圆柱壳热电弹性精确解

李杨, 秦庆华, 张亮亮, 高阳

李杨, 秦庆华, 张亮亮, 高阳. 一维准晶功能梯度层合圆柱壳热电弹性精确解[J]. 力学学报, 2020, 52(5): 1286-1294. DOI: 10.6052/0459-1879-20-126
引用本文: 李杨, 秦庆华, 张亮亮, 高阳. 一维准晶功能梯度层合圆柱壳热电弹性精确解[J]. 力学学报, 2020, 52(5): 1286-1294. DOI: 10.6052/0459-1879-20-126
Li Yang, Qin Qinghua, Zhang Liangliang, Gao Yang. EXACT THERMO-ELECTRO-ELASTIC SOLUTION OF FUNCTIONALLY GRADED MULTILAYERED ONE-DIMENSIONAL QUASICRYSTAL CYLINDRICAL SHELLS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1286-1294. DOI: 10.6052/0459-1879-20-126
Citation: Li Yang, Qin Qinghua, Zhang Liangliang, Gao Yang. EXACT THERMO-ELECTRO-ELASTIC SOLUTION OF FUNCTIONALLY GRADED MULTILAYERED ONE-DIMENSIONAL QUASICRYSTAL CYLINDRICAL SHELLS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1286-1294. DOI: 10.6052/0459-1879-20-126
李杨, 秦庆华, 张亮亮, 高阳. 一维准晶功能梯度层合圆柱壳热电弹性精确解[J]. 力学学报, 2020, 52(5): 1286-1294. CSTR: 32045.14.0459-1879-20-126
引用本文: 李杨, 秦庆华, 张亮亮, 高阳. 一维准晶功能梯度层合圆柱壳热电弹性精确解[J]. 力学学报, 2020, 52(5): 1286-1294. CSTR: 32045.14.0459-1879-20-126
Li Yang, Qin Qinghua, Zhang Liangliang, Gao Yang. EXACT THERMO-ELECTRO-ELASTIC SOLUTION OF FUNCTIONALLY GRADED MULTILAYERED ONE-DIMENSIONAL QUASICRYSTAL CYLINDRICAL SHELLS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1286-1294. CSTR: 32045.14.0459-1879-20-126
Citation: Li Yang, Qin Qinghua, Zhang Liangliang, Gao Yang. EXACT THERMO-ELECTRO-ELASTIC SOLUTION OF FUNCTIONALLY GRADED MULTILAYERED ONE-DIMENSIONAL QUASICRYSTAL CYLINDRICAL SHELLS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1286-1294. CSTR: 32045.14.0459-1879-20-126

一维准晶功能梯度层合圆柱壳热电弹性精确解

基金项目: 1)国家自然科学基金(11972365);国家自然科学基金(51704015);辽宁省教育厅科学研究经费(L2019006)
详细信息
    通讯作者:

    高阳

  • 中图分类号: O343.6

EXACT THERMO-ELECTRO-ELASTIC SOLUTION OF FUNCTIONALLY GRADED MULTILAYERED ONE-DIMENSIONAL QUASICRYSTAL CYLINDRICAL SHELLS

  • 摘要: 两种或多种不同性质材料组成的层状结构可以满足工业发展的需求. 然而, 材料属性在接触面的突变问题, 容易导致层间界面处产生应力集中、裂纹以及分层等问题. 功能梯度材料利用连续变化的组分梯度来代替突变界面, 可以消除界面处的物理性能突变, 提高结构的粘结强度. 本文以一维准晶功能梯度层合圆柱壳为研究对象, 利用类Stroh公式和传递矩阵方法, 建立了材料参数沿径向呈现幂函数变化的层合圆柱壳模型, 获得了简支边界条件对应的一维准晶功能梯度层合圆柱壳的热电弹性精确解. 数值算例中讨论了层合圆柱壳内外表面承受温度载荷时, 功能梯度指数因子对温度场、电场、声子场和相位子场的影响, 尤其是对层合圆柱壳内外表面的影响. 结果表明, 指数因子改变了材料参数的空间分布情况, 进而对温度场、电场、声子场和相位子场都有影响; 增加功能梯度指数因子, 可减小温度载荷引起的内表面变形, 进而提升结构强度. 本文得到的结果可以为功能梯度准晶层合圆柱壳的设计和制造提供可靠的理论依据.
    Abstract: Layered structures made of two and more materials with different properties can meet the needs of industrial development. However, the abrupt change of material properties at the interface of the laminated structures can easily cause some interface problems, such as stress concentration, interface cracks, and interface delamination phenomena. Functionally graded materials refer to utilize a continuously changing component gradient instead of the original sudden change interface, which can eliminate or weaken the abrupt change of the physical properties and then increase the bonding strength of the layered structures. In this paper, the research object is the functionally graded multilayered one-dimensional quasicrystal cylindrical shells. By virtue of the pseudo-Stroh formalism and the propagator matrix method, we establish the layered one-dimensional quasicrystal cylindrical shells model with the material parameters following the power-law type distribution along its radius direction, and obtain the exact thermo-electro-elastic solution of the functionally graded layered one-dimensional quasicrystal cylindrical shells with simply supported boundary condition. Numerical examples are carried out to investigate the influences of the exponential factor on temperature, electric, phason and phonon fields of the functionally graded layered one-dimensional quasicrystal cylindrical shells subjected to both inner and outer surfaces temperature variations, especially the effects on physical quantities at the inner and outer surfaces of the layered one-dimensional quasicrystal cylindrical shells. The obtained results indicate that: the exponential factor can change the distribution characteristic of material parameters, which can cause a significant influence on the physical quantities in the temperature, electric, phason, and phonon fields; by increasing the exponential factor, the deformation at the internal surface induced by temperature stimuli is reduced and the strength of the layered one-dimensional quasicrystal cylindrical shells is improved. The results obtained in this paper can provide a reliable theoretical basis for the design and manufacture of functionally graded layered one-dimensional quasicrystal cylindrical shells.
  • [1] 叶天贵, 靳国永, 刘志刚. 多层复合壳体三维振动分析的谱--微分求积混合法. 力学学报, 2018,50(4):847-852
    [1] ( Ye Tiangui, Jin Guoyong, Liu Zhigang. A spectral-differential quadrature method for 3-d vibration analysis of multilayered shells. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(4):847-852 (in Chinese))
    [2] 仲政, 吴林志, 陈伟球. 功能梯度材料与结构的若干力学问题研究进展. 力学进展, 2010,40(5):528-541
    [2] ( Zhong Zheng, Wu Linzhi, Chen Weiqiu. Progress in the study of mechanics problems of functionally graded materials and structures. Advances in Mechanics, 2010,40(5):528-541 (in Chinese))
    [3] 柯燎亮, 汪越胜. 功能梯度材料接触力学若干基本问题的研究进展. 科学通报, 2015,60(17):1565-1573
    [3] ( Ke Liaoliang, Wang Yuesheng. Progress in some basic problems on contact mechanics of functionally graded materials. Chin Sci Bull, 2015,60:1565-1573 (in Chinese))
    [4] 郑保敬, 梁钰, 高效伟 等. 功能梯度材料动力学问题的POD模型降阶分析. 力学学报, 2018,50(4):787-797
    [4] ( Zheng Baojing, Liang Yu, Gao Xiaowei, et al. Analysis for dynamic response of functionally graded materials using pod based reduced order model. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(4):787-797 (in Chinese))
    [5] 杨健鹏, 王惠明. 功能梯度球形水凝胶的化学力学耦合分析. 力学学报, 2019,51(4):1054-1063
    [5] ( Yang Jianpeng, Wang Huiming. Chemomechanical analysis of a functionally graded spherical hydrogel. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(4):1054-1063 (in Chinese))
    [6] Yang QQ, Gao CF. Reduction of the stress concentration around an elliptic hole by using a functionally graded layer. Acta Mechanica, 2016,227(9):2427-2437
    [7] Yang B, Chen WQ, Ding HJ. Approximate elasticity solutions for functionally graded circular plates subject to a concentrated force at the center. Mathematics and Mechanics of Solids, 2014,19(3):277-288
    [8] Pan E, Han F. Exact solution for functionally graded and layered magneto-electro-elastic plates. International Journal of Engineering Science, 2005,43(3-4):321-339
    [9] Shechtman D, Blech I, Gratias D, et al. Metallic phase with long-range orientational order and no translational symmetry. Physical Review Letters, 1984,53(20):1951-1953
    [10] 范天佑. 准晶数学弹性力学和缺陷力学. 力学进展, 2000,30(2):161-174
    [10] ( Fan Tianyou. Mathematical theory of elasticity and defects of quasicrystals. Advances in Mechanics, 2000,30(2):161-174 (in Chinese))
    [11] Bak P. Symmetry, stability, and elastic properties of icosahedral incommensurate crystals. Physical Review B, 1985,32(9):5764-5772
    [12] Gao Y, Ricoeur A. Three-dimensional Green's functions for two-dimensional quasi-crystal bimaterials. Proceedings of the Royal Society A, 2011,467(2133):2622-2642
    [13] Jaric M. Introduction to Quasicrystals. Elsevier, 2012
    [14] Fan TY. A study on the specific heat of a one-dimensional hexagonal quasicrystal. Journal of Physics-Condensed Matter, 1999,11(45):513-517
    [15] Dubois JM. Properties- and applications of quasicrystals and complex metallic alloys. Chemical Society Reviews, 2012,41(20):6760-6777
    [16] Maugin GA. A note on the thermo-mechanics of elastic quasi-crystals. Archive of Applied Mechanics, 2016,86(1):245-251
    [17] Li XY, Wang YW, Li PD, et al. Three-dimensional fundamental thermo-elastic field in an infinite space of two-dimensional hexagonal quasi-crystal with a penny-shaped/half-infinite plane crack. Theoretical and Applied Fracture Mechanics, 2017,88:18-30
    [18] Guo JH, Yu J, Xing YM, et al. Thermoelastic analysis of a two-dimensional decagonal quasicrystal with a conductive elliptic hole. Acta Mechanica, 2016,227(9):2595-2607
    [19] Li Y, Qin QH, Zhao MH. Analysis of 3D planar crack problems in one-dimensional hexagonal piezoelectric quasicrystals with thermal effect. part I: Theoretical formulations. International Journal of Solids and Structures, 2020, 188-189:269-281
    [20] Li Y, Qin QH, Zhao MH. Analysis of 3D planar crack problems of one-dimensional hexagonal piezoelectric quasicrystals with thermal effect. part II: Numerical approach. International Journal of Solids and Structures, 2020, 188-189:223-232
    [21] Zhang L, Guo JH, Xing YM. Bending deformation of multilayered one-dimensional hexagonal piezoelectric quasicrystal nanoplates with nonlocal effect. International Journal of Solids and Structures, 2018,132:278-302
    [22] Yang LZ, Li Y, Gao Y, et al. Three-dimensional exact thermo-elastic analysis of multilayered two-dimensional quasicrystal nanoplates. Applied Mathematical Modelling, 2018,63:203-218
    [23] Waksmanski N, Pan E, Yang LZ, et al. Free vibration of a multilayered one-dimensional quasi-crystal plate. Journal of Vibration and Acoustics, 2014,136(4):041019
    [24] Li Y, Yang LZ, Zhang LL, et al. Exact thermoelectroelastic solution of layered one-dimensional quasicrystal cylindrical shells. Journal of Thermal Stresses, 2018,41(10-12):1450-1467
    [25] 杨世铭, 陶文铨. 传热学. 北京:高等教育出版社, 2006
    [26] Pan E. Exact solution for simply supported and multilayered magneto-electro-elastic plates. Journal of Applied Mechanics, 2001,68(4):608-618
    [27] Li XY, Wang T, Zheng RF, et al. Fundamental thermo-electro-elastic solutions for 1D hexagonal QC. Zeitschrift für Angewandte Mathematik und Mechanik, 2015,95(5):457-468
    [28] Ootao Y, Ishihara M. Exact solution of transient thermal stress problem of a multilayered magneto-electro-thermoelastic hollow cylinder. Journal of Solid Mechanics and Materials Engineering, 2011,5(2):90-103
    [29] Li Y, Yang LZ, Gao Y. Thermo-elastic analysis of functionally graded multilayered two-dimensional decagonal quasicrystal plates. Zeitschrift für Angewandte Mathematik und Mechanik, 2018,98(9):1585-1602
    [30] Waksmanski N, Pan E, Yang LZ, et al. Harmonic response of multilayered one-dimensional quasicrystal plates subjected to patch loading. Journal of Sound and Vibration, 2016,375:237-253
  • 期刊类型引用(2)

    1. 邢时超,翁晨,戴明,高存法. 含空心纤维热电复合材料的能量转换效率及力学性能. 固体力学学报. 2022(03): 257-270 . 百度学术
    2. 金晨淞,李佩栋,李翔宇. 一维六方准晶中椭圆裂纹问题的三维热-弹性解. 四川轻化工大学学报(自然科学版). 2022(06): 42-49 . 百度学术

    其他类型引用(1)

计量
  • 文章访问数:  1253
  • HTML全文浏览量:  212
  • PDF下载量:  216
  • 被引次数: 3
出版历程
  • 收稿日期:  2020-04-17
  • 刊出日期:  2020-10-09

目录

    /

    返回文章
    返回