黄颖青*, 肖奇志?, 冯淼林**, 陈海波,*,1)* 中国科学院材料力学行为和设计重点实验室, 中国科学技术大学近代力学系, 合肥 230027 ? LUSAS, Forge House, 66 High Street, Kingston upon Thames, KT1 1HN, UK ** 上海交通大学工程力学系, 上海 200030
THEORY AND APPLICATIONS OF INCOMPATIBLE AND HYBRID ELEMENT METHOD——IN MEMORY OF PROF. WU CHANGCHUN
Huang Yingqing*, Xiao Qizhi?, Feng Miaolin**, Chen Haibo,*,1)* CAS Key Laboratory of Mechanical behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China ? LUSAS, Forge House, 66 High Street, Kingston upon Thames, KT1 1HN, UK ** Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200030, China
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. Keywords：incompatible element;hybrid element;patch test;penalty equilibrium;elemental optimization design
PDF (181KB)元数据多维度评价相关文章导出EndNote|Ris|Bibtex收藏本文 本文引用格式 黄颖青, 肖奇志, 冯淼林, 陈海波. 非协调和杂交有限元的理论和应用——纪念恩师吴长春教授. 力学学报[J], 2021, 53(1): 293-297 DOI:10.6052/0459-1879-20-381 Huang Yingqing, Xiao Qizhi, Feng Miaolin, Chen Haibo. THEORY AND APPLICATIONS OF INCOMPATIBLE AND HYBRID ELEMENT METHOD——IN MEMORY OF PROF. WU CHANGCHUN. Chinese Journal of Theoretical and Applied Mechanics[J], 2021, 53(1): 293-297 DOI:10.6052/0459-1879-20-381
( WuChangchun . A new numerical method for analysing bent elastic thin plates——the discrete operator method Science in China, 1975,5(4):360-375 (in Chinese)) [本文引用: 1]
WuCC . Some problems of a plate bending hybrid model with shear effect International Journal for Numerical Methods in Engineering, 1982,18(5):755-764 [本文引用: 1]
WuCC, HuangMG, PianTHH . Consistency condition and convergence criteria of incompatible elements: General formulation of incompatible functions and its application Computers & Structures, 1987,27(5):639-644 [本文引用: 2]
PianTHH, WuCC . A rational approach for choosing stress terms for hybrid finite element formulations International Journal for Numerical Methods in Engineering, 1988,26(10):2331-2343 [本文引用: 2]
PianTHH . Derivation of element stiffness matrices by assumed stress distributions AIAA Journal, 1964,2(7):1333-1336 [本文引用: 1]
WuCC, CheungYK . On optimization approaches of hybrid stress elements Finite Elements in Analysis and Design, 1995,21(1-2):111-128 [本文引用: 1]
WuCC, CheungYK . Penalty-equilibrating approach and an innovative formulation of 4-noded hybrid stress elements Communications in Numerical Methods in Engineering, 1996,12(11):707-717 [本文引用: 1]
HuangYQ, HuanYK, ChenHB . 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 [本文引用: 1]
(GuoYimu, WanLi. Recommendation and introduction of 《Incompatible numerical analysis and hybrid element method》 Advances in Mechanics, 2001,31(3):475 (in Chinese)) [本文引用: 1]
PianTHH, WuCC . Hybrid and Incompatible Finite Element Methods. Boca Raton, London, New York: Chapman & Hall/CRC,Taylor & Francis Group, 2006 [本文引用: 1]
CheungYK, WuCC . The patch test condition in curvilinear coordinate system——formulation and application Science in China(Series A), 1993,36(1):62-73 [本文引用: 1]
WuCC, HuangYQ, RammE . 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 [本文引用: 1]
WuCC, CheungYK . Numerical stability and constitution analysis of $\lambda $-type incompatible elements International Journal for Numerical Methods in Engineering, 1991,31(8):1669-1682 [本文引用: 1]
WuCC . Dual zero energy modes in mixed/hybrid elements——definition, analysis and control Computer Methods in Applied Mechanics and Engineering, 1990,81(1):39-56 [本文引用: 1]
WuCC, HansB . Multivariable finite elements: consistency and optimization Science in China(Series A), 1991,34(3):284-299 [本文引用: 1]
CheungYK, WuCC . A study on the stability of 3-field finite elements by the theory of zero energy modes International Journal of Solids and Structures, 1992,29(2):215-229 [本文引用: 1]
WuCC, LiuXY, PianTHH . Incompressible-incompatible deformation modes and plastic finite elements Computers & Structures, 1991,41(3):449-453 [本文引用: 1]
CheungYK, WuCC . Incompatible numerical simulation of the axisymmetric cracked body made of ideally elastic-plastic material Engineering Fracture Mechanics, 1993,45(3):399-405
WuCC, YuanL, FurukawaT . Deviatoric hybrid model and multivariable elimination at element level for incompressible medium International Journal for Numerical Methods in Engineering, 1999,46(5):729-745 [本文引用: 1]
DongYF, WuCC, De FreitasJAT . The hybrid stress model for Mindlin-Reissner plates based on a stress optimization condition Computers & Structures, 1993,46(5):877-897 [本文引用: 1]
CheungYK, JiaoZP, WuCC . General formulation of C$^{0}$ bending models based on the rational $w$-$\theta $ constraint Computational Mechanics, 1995,16(1):53-61
HuangYQ, LiuM, WuCC . Bimaterial interface hybrid element for piezoelectric laminated analysis Journal of Strain Analysis for Engineering Design, 1999,34(2):97-106
HuangYQ, DiSL, WuCC , 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 [本文引用: 1]
( YuanZhen, WuChangchun, ZhuangShoubing . 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)) [本文引用: 1]
YuanZ, WuCC, LiH . Homogenization-based topology design for pure torsion of composite shafts Acta Mechanica Sinica, 2003,19(3):241-246 [本文引用: 1]
SunHY, DiSL, ZhangN , 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 [本文引用: 1]
FengML, WuCC . A study of three-dimensional four-step braided piezo-ceramic composites by the homogenization method Composites Science and Technology, 2001,61(13):1889-1898 [本文引用: 1]
WuCC, XiaoQZ, YagawaG . Dual analysis for path integrals and bounds for crack parameter International Journal of Solids and Structures, 1998,35(14):1635-1652 [本文引用: 1]
WuCC, XiaoQZ, YagawaG . Finite element methodology for path integrals in fracture mechanics International Journal for Numerical Methods in Engineering, 1998,43(1):69-91
SzeKY, WuCC, HuangYQ . Upper and lower bounds for evaluation of nonlinear fracture parameters Engineering Fracture Mechanics, 1999,62(2-3):185-201 [本文引用: 1]
WuCC, XiaoQZ . Electro-mechanical crack systems: Bound theorems, dual finite elements and error estimation International Journal of Solids and Structures, 2005,42(20):5413-5425 [本文引用: 1]
LiZR, LimCW, WuCC . Bound theorem and implementation of dual finite elements for fracture assessment of piezoelectric materials Computational Mechanics, 2005,36(3):209-216
LiuM, WuCC . Numerical analysis of crack-tip fields of piezoelectric media by hybrid finite element Chinese Science Bulletin, 1999,44(11):995-1000
WuCC, SzeKY, HuangYQ . Numerical solutions on fracture of piezoelectric materials by hybrid element International Journal of Solids and Structures, 2001,38(24-25):4315-4329 [本文引用: 1]
WuCC, HePX, LiZR . Extension of J integral to dynamic fracture of functional graded material and numerical analysis Computers & Structures, 2002,80(5-6):411-416 [本文引用: 1]
(HePeixiang, WuChangchun, LiZiran, 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)) [本文引用: 1]
( LiZiran, WuChangchun . 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)) [本文引用: 1]
( HuangRuoyu, WuChangchun . A plate bending element as the counterpart of Pian-Sumihara hybrid element Engineering Mechanics, 2005,22(2):16-21 (in Chinese)) [本文引用: 1]
( HuangRuoyu, WuChangchun . Application of stress functions and its dual theory to finite element Acta Mechanica Sinica, 2004,36(4):419-426 (in Chinese)) [本文引用: 1]
( HuangRuoyu, WuChangchun, ZhongWanxie . 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)) [本文引用: 1]
,*,1)* 
