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无网格彼得洛夫伽辽金法在大变形问题中的应用 被引量：4

APPLICATION OF MLPG METHOD IN LARGE DEFORMATION ANALYSIS
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摘要 将无网格局部彼得洛夫伽辽金(MLPG)法推广应用于大变形问题。导出了非线性局部子域对称弱形式,通过对该弱形式进行线性化得到了用于非线性计算的MLPG格式,并对MLPG的计算速度进行了优化,使MLPG成为一种复杂度为O(N)的算法。几何非线性和几何与材料双重非线性的数值算例表明,相对有限元方法,MLPG在处理此类大变形问题时收敛性好,精度高,并能减小有限元分析中易遇到的网格畸变带来的困难。 The meshless local Petrov-Galerkin method （MLPG） is extended for solving large deformation problems in this paper. A nonlinear local symmetric weak form is derived and linearized to obtain the nonlinear MLPG approach, and the optimization of the efficiency of MLPG is performed to make the MLPG method to be an algorithm of O（N）. Some numerical examples on both geometrically nonlinear, and geometrically and material multiple nonlinear problems are given to verify that the MLPG handles such large deformation problems with good convergence and high accuracy as compared with the finite element method, and it can reduce the difficulty of mesh distortion, which usually encountered in the finite element analysis.
作者 张希 姚振汉
机构地区 清华大学工程力学系
出处 《工程力学》 EI CSCD 北大核心 2006年第A01期16-20,共5页 Engineering Mechanics
基金 国家自然科学基金(10472051)
关键词 无网格法 无网格局部彼得洛夫伽辽金法 几何非线性 材料非线性 超弹性材料 the meshless method MLPG method geometrically nonlinear material nonlinear hyperelastic material
分类号 O344.5 [理学—固体力学]
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参考文献15

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同被引文献39

  • 1宋康祖,张雄,陆明万.MESHLESS METHOD BASED ON COLLOCATION WITH CONSISTENT COMPACTLY SUPPORTED RADIAL BASIS FUNCTIONS[J].Acta Mechanica Sinica,2004,20(5):551-557. 被引量：3
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引证文献4

二级引证文献10

工程力学
2006年 第A01期

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