THEORY AND APPLICATIONS OF INCOMPATIBLE AND HYBRID ELEMENT METHOD——IN MEMORY OF PROF. WU CHANGCHUN
-
摘要: 本纪念文介绍了吴长春教授在计算力学领域的主要学术贡献, 重点介绍了他在非协调和杂交有限元的理论和应用方面的开创性工作, 他发展的构造非协调插值函数的一般公式以及杂交应力元优化方法至今仍是发展高性能有限元的重要工具, 经常被同行引用.Abstract: This memorial paper gives an overview of Prof. Wu Changchun's main contributions to computational mechanics, especially his pioneering work on the incompatible and hybrid element method and its applications. The general formula for the incompatible shape functions and the optimization design method for hybrid stress elements proposed by Prof. Wu are still important means to develop high performance finite elements and are cited by peers constantly.
-
-
[1] Wu CC . A new numerical method for analysing bent elastic thin plates——the discrete operator method. Scientia Sinica, 1975,18(5):628-650 [2] 吴长春 . 受弯弹性薄板数值分析的新方法——离散算子法. 中国科学, 1975,5(4):360-375. (Wu Changchun . A new numerical method for analysing bent elastic thin plates——the discrete operator method. Science in China, 1975,5(4):360-375 (in Chinese))
[3] Wu CC . Some problems of a plate bending hybrid model with shear effect. International Journal for Numerical Methods in Engineering, 1982,18(5):755-764 [4] Wu CC, Huang MG, Pian THH . Consistency condition and convergence criteria of incompatible elements: General formulation of incompatible functions and its application. Computers & Structures, 1987,27(5):639-644 [5] Pian THH, Wu CC . A rational approach for choosing stress terms for hybrid finite element formulations. International Journal for Numerical Methods in Engineering, 1988,26(10):2331-2343 [6] Pian THH . Derivation of element stiffness matrices by assumed stress distributions. AIAA Journal, 1964,2(7):1333-1336 [7] Wu CC, Cheung YK . On optimization approaches of hybrid stress elements. Finite Elements in Analysis and Design, 1995,21(1-2):111-128 [8] Wu CC, Cheung YK . Penalty-equilibrating approach and an innovative formulation of 4-noded hybrid stress elements. Communications in Numerical Methods in Engineering, 1996,12(11):707-717 [9] Huang YQ, Huan YK, Chen HB . An incompatible and unsymmetric four-node quadrilateral plane element with high numerical performance. International Journal for Numerical Methods in Engineering, 2020,121(15):3382-3396 [10] 吴长春, 卞学鐄 . 非协调数值分析与杂交元方法. 北京: 科学出版社, 1997. (Wu Changchun, Pian THH. Incompatible Numerical Analysis and Hybrid Element Method. Beijing: Science Press, 1997 (in Chinese))
[11] 郭乙木, 万力 . 《非协调数值分析与杂交元方法》推介. 力学进展, 2001, 31(3): 475. (Guo Yimu, Wan Li. Recommendation and introduction of 《Incompatible numerical analysis and hybrid element method》. Advances in Mechanics, 2001,31(3):475 (in Chinese))
[12] Pian THH, Wu CC . Hybrid and Incompatible Finite Element Methods. Boca Raton, London, New York: Chapman & Hall/CRC,Taylor & Francis Group, 2006 [13] Cheung YK, Wu CC . The patch test condition in curvilinear coordinate system——formulation and application. Science in China(Series A), 1993,36(1):62-73 [14] Wu CC, Huang YQ, Ramm E . A further study on incompatible models: revise-stiffness approach and completeness of trial functions. Computer Methods in Applied Mechanics and Engineering, 2001,190(45):5923-5934 [15] Wu CC, Cheung YK . Numerical stability and constitution analysis of $lambda $-type incompatible elements. International Journal for Numerical Methods in Engineering, 1991,31(8):1669-1682 [16] Wu CC . Dual zero energy modes in mixed/hybrid elements——definition, analysis and control. Computer Methods in Applied Mechanics and Engineering, 1990,81(1):39-56 [17] Wu CC, Hans B . Multivariable finite elements: consistency and optimization. Science in China(Series A), 1991,34(3):284-299 [18] Cheung YK, Wu CC . A study on the stability of 3-field finite elements by the theory of zero energy modes. International Journal of Solids and Structures, 1992,29(2):215-229 [19] Wu CC, Liu XY, Pian THH . Incompressible-incompatible deformation modes and plastic finite elements. Computers & Structures, 1991,41(3):449-453 [20] Cheung YK, Wu CC . Incompatible numerical simulation of the axisymmetric cracked body made of ideally elastic-plastic material. Engineering Fracture Mechanics, 1993,45(3):399-405 [21] Wu CC, Yuan L, Furukawa T . Deviatoric hybrid model and multivariable elimination at element level for incompressible medium. International Journal for Numerical Methods in Engineering, 1999,46(5):729-745 [22] Dong YF, Wu CC, De Freitas JAT . The hybrid stress model for Mindlin-Reissner plates based on a stress optimization condition. Computers & Structures, 1993,46(5):877-897 [23] Cheung YK, Jiao ZP, Wu CC . General formulation of C$^{0}$ bending models based on the rational $w$-$ heta $ constraint. Computational Mechanics, 1995,16(1):53-61 [24] Huang YQ, Liu M, Wu CC . Bimaterial interface hybrid element for piezoelectric laminated analysis. Journal of Strain Analysis for Engineering Design, 1999,34(2):97-106 [25] Huang YQ, Di SL, Wu CC , et al. Bending analysis of composite laminated plates using a partially hybrid stress element with interlaminar continuity. Computers & Structures, 2002,80(5-6):403-410 [26] 袁振, 吴长春, 庄守兵 . 基于杂交元和变密度法的连续体结构拓扑优化设计. 中国科学技术大学学报, 2001,31(6):694-699. (Yuan Zhen, Wu Changchun, Zhuang Shoubing . Topology optimization of continuum structure using hybrid elements and artificial material model. Journal of University of Science and Technology of China, 2001,31(6):694-699 (in Chinese))
[27] Yuan Z, Wu CC, Li H . Homogenization-based topology design for pure torsion of composite shafts. Acta Mechanica Sinica, 2003,19(3):241-246 [28] Sun HY, Di SL, Zhang N , et al. Micromechanics of composite materials using multivariable finite element method and homogenization theory. International Journal of Solids and Structures, 2001,38(17):3007-3020 [29] Feng ML, Wu CC . A study of three-dimensional four-step braided piezo-ceramic composites by the homogenization method. Composites Science and Technology, 2001,61(13):1889-1898 [30] Wu CC, Xiao QZ, Yagawa G . Dual analysis for path integrals and bounds for crack parameter. International Journal of Solids and Structures, 1998,35(14):1635-1652 [31] Wu CC, Xiao QZ, Yagawa G . Finite element methodology for path integrals in fracture mechanics. International Journal for Numerical Methods in Engineering, 1998,43(1):69-91 [32] Sze KY, Wu CC, Huang YQ . Upper and lower bounds for evaluation of nonlinear fracture parameters. Engineering Fracture Mechanics, 1999,62(2-3):185-201 [33] Wu CC, Xiao QZ . Electro-mechanical crack systems: Bound theorems, dual finite elements and error estimation. International Journal of Solids and Structures, 2005,42(20):5413-5425 [34] Li ZR, Lim CW, Wu CC . Bound theorem and implementation of dual finite elements for fracture assessment of piezoelectric materials. Computational Mechanics, 2005,36(3):209-216 [35] Liu M, Wu CC . Numerical analysis of crack-tip fields of piezoelectric media by hybrid finite element. Chinese Science Bulletin, 1999,44(11):995-1000 [36] Wu CC, Sze KY, Huang YQ . Numerical solutions on fracture of piezoelectric materials by hybrid element. International Journal of Solids and Structures, 2001,38(24-25):4315-4329 [37] Wu CC, He PX, Li ZR . Extension of J integral to dynamic fracture of functional graded material and numerical analysis. Computers & Structures, 2002,80(5-6):411-416 [38] 何沛祥, 吴长春, 李子然 等. 无网格Galerkin法与非协调元方法的耦合. 计算力学学报, 2004,21(4):455-458, 480. (He Peixiang, Wu Changchun, Li Ziran, et al. Coupling of element-free Galerkin method and incompatible element method. Chinese Journal of Computational Mechanics, 2004,21(4):455-458, 480 (in Chinese))
[39] 李子然, 吴长春 . 基于局部间断Galerkin方法的p型有限元. 中国科学技术大学学报, 2003,33(3):324-329. (Li Ziran, Wu Changchun . New $p$-version finite element by local discontinuous Galerkin method. Journal of University of Science and Technology of China, 2003,33(3):324-329 (in Chinese))
[40] 李子然, 吴长春 . 弹性力学问题中的间断Galerkin有限元法. 上海交通大学学报, 2003,37(5):770-773. (Li Ziran, Wu Changchun . Local discontinuous Galerkin method in elastic mechanics. Journal of Shanghai Jiao Tong University, 2003,37(5):770-773 (in Chinese))
[41] 黄若煜, 吴长春 . 应用Pian-Sumihara杂交列式的板弯曲模拟元. 工程力学, 2005,22(2):16-21. (Huang Ruoyu, Wu Changchun . A plate bending element as the counterpart of Pian-Sumihara hybrid element. Engineering Mechanics, 2005,22(2):16-21 (in Chinese))
[42] 黄若煜, 吴长春 . 应力函数及其对偶理论在有限元中的应用. 力学学报, 2004,36(4):419-426. (Huang Ruoyu, Wu Changchun . Application of stress functions and its dual theory to finite element. Acta Mechanica Sinica, 2004,36(4):419-426 (in Chinese))
[43] 黄若煜, 吴长春, 钟万勰 . 基于平面偶应力-Reissner/Mindlin板比拟的偶应力有限元. 力学学报, 2004,36(3):272-280. (Huang Ruoyu, Wu Changchun, Zhong Wanxie . Finite element of elasticity with couple-stress using the analogy between plane couple-stress and Reissner/Mindlin plate bending. Acta Mechanica Sinica, 2004,36(3):272-280 (in Chinese))
-
期刊类型引用(0)
其他类型引用(1)
计量
- 文章访问数: 1064
- HTML全文浏览量: 194
- PDF下载量: 174
- 被引次数: 1
下载:
