【摘 要】
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Recently,the smoothed point interpolation method(S-PIM)regarded as weakened weak W2 formulation method has been developed in solving engineering mechanics p
【机 构】
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College of Mathematics,Taiyuan University of Technology,Taiyuan,Shanxi,030024,China
【出 处】
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第7届Trefftz工程计算方法(ICTM2015)暨第3届基本解工程应用方法(MFS)
论文部分内容阅读
Recently,the smoothed point interpolation method(S-PIM)regarded as weakened weak W2 formulation method has been developed in solving engineering mechanics problems,and works well with distorted meshes.The G space theory offers the theoretical base for all W2 methods that use smoothing operations.In this paper,we first prove that if a function w(x)is of Lipschitz continuity and its interpolation function wI(x)is established using PIM shape functions,then the function wI(x)belongs to a Gsh,0 space on the node-based,cell-based and the mixture of both smoothing domains(SDs).In addition,when the nodes are refined,functions of Lipschitz continuity can be approximated by its interpolation function wI(x),i.e.the error norm approaches to zero.Mathematically,the stability and convergence of W2 methods using PIM shape functions and G space theory can be ensured.
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