非线性大变形问题的边界元分析法
Analysis of Nonlinear Large Deformation Problems by Boundary Element Method
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摘要: 本文采用有限变形理论的拖带坐标描述法导出了瞬时位形上的速率形式非线性影响函数(近似速率型基本解),从而导出以瞬时位形为基准的非线性大变形的边界积分方程.由编制的NBEM计算程序的算例表明本文建立的非线性边界元方法是可行的.Abstract: In this paper, the author deduces an approximate solution of nonlinear influence function in rate form for two-dimensional elastic problems on current configuration by the method of comoving coordinate system.Here BEM formulation of large deformation based on Chen's theory[1] is given. The computational processes of nonlinear boundary integral equation is discussed. The author also compiles a nonlinear computing program NBEM. Numerical examples show that the results presented here is available to the solution of engineering problems.
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[1] 陈至达,《有理力学》,中国矿业学院北京研究生部(1980, 1983). [2] Mukhejee, S., Boundary Element Method in Creep and Fracture, Applied Science Publishers, Beibing, U.K. (1982). [3] Jelles, J.C.F., The Boundary Element Method Applied to Inelastic Problem, Lecture Notes in Eng., New York (1983). [4] Chandra, A. and S. Mukhejee, Boundary element formulation for large strain-large deformations of viscoplasticity, Int. J. Solids Structures, 30, 1 (1984), 41-53. [5] Sneddon, I.N., Fourier Transforms, Scotland (1950). [6] Xie He-ping and Chen Zhi-da, Nonlinear finite element analysis of large deformation for continua in gravity field, Int. Conf. on Nonlinear Mech., Shanghai, China, Oct. (1985), 1337. [7] Xie He-ping and Chen Zhi-da, Nonlinear computing program NEPR for large deformation of underground openings in rock and its application, Proc. of Int. Symp. on Mining Tech. and Science, Xuzhou, China, Sept. (1985), 23-1. [8] Novati, G. and C.A. Brebbia, Boundary element formulation for geometrically nonlinear elastostatics, Appl. Math. Modelling, 6 (1982), 136-138. -
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