Numerical manifold method based on the method of weighted residuals

被引:66
作者
Li, S
Cheng, Y [1 ]
Wu, YF
机构
[1] Shanghai Univ, Shanghai Inst Appl Math & Mech, Shanghai 200072, Peoples R China
[2] City Univ Hong Kong, Dept Bldg & Construct, Hong Kong, Hong Kong, Peoples R China
关键词
numerical manifold method; method of weighted residuals; Galerkin method; manifold element; finite covers;
D O I
10.1007/s00466-004-0636-3
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Usually, the governing equations of the numerical manifold method (NMM) are derived from the minimum potential energy principle. For many applied problems it is difficult to derive in general outset the functional forms of the governing equations. This obviously strongly restricts the implementation of the minimum potential energy principle or other variational principles in NMM. In fact, the governing equations of NMM can be derived from a more general method of weighted residuals. By choosing suitable weight functions, the derivation of the governing equations of the NMM from the weighted residual method leads to the same result as that derived from the minimum potential energy principle. This is demonstrated in the paper by deriving the governing equations of the NMM for linear elasticity problems, and also for Laplace's equation for which the governing equations of the NMM cannot be derived from the minimum potential energy principle. The performance of the method is illustrated by three numerical examples.
引用
收藏
页码:470 / 480
页数:11
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