| 弹性大变形问题的复变量无单元Galerkin方法 |
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| 引用本文： | 李冬明,彭妙娟,程玉民.弹性大变形问题的复变量无单元Galerkin方法[J].中国科学:物理学 力学 天文学,2011(8):1003-1014. |
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| 作者姓名： | 李冬明 彭妙娟 程玉民 |
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| 作者单位： | 上海大学土木工程系;上海大学上海市应用数学和力学研究所; |
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| 基金项目： | 国家自然科学基金(批准号:10871124,11026223); 上海市教育委员会科研创新项目(编号:09ZZ99)资助 |
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| 摘 要： | 基于复变量移动最小二乘法,建立了适合于大位移、大转动等弹性大变形问题的复变量无单元Galerkin方法.复变量移动最小二乘法的优点是采用一维基函数构造二维问题的试函数.将复变量移动最小二乘法应用于弹性大变形平面问题,结合大变形问题的Galerkin积分弱形式,采用罚函数法施加本质边界条件,建立了全Lagrange格式下的弹性大变形问题的复变量无单元Galerkin方法,推导了相应的计算公式,数值实现中采用了Newton-Raphson迭代法.最后通过数值算例证明了该方法的有效性.
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| 关 键 词： | 无网格方法 移动最小二乘法 复变量移动最小二乘法 无单元Galerkin方法 复变量无单元Galerkin方法 大变形问题 |
The complex variable element-free Galerkin(CVEFG) method for elastic large deformation problems |
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| LI DongMing,PENG MiaoJuan & CHENG YuMin.The complex variable element-free Galerkin(CVEFG) method for elastic large deformation problems[J].Scientia Sinica Pysica,Mechanica & Astronomica,2011(8):1003-1014. |
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| Authors: | LI DongMing PENG MiaoJuan & CHENG YuMin |
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| Institution: | LI DongMing1,PENG MiaoJuan1 & CHENG YuMin2* 1 Department of Civil Engineering,Shanghai University,Shanghai 200072,China,2 Shanghai Institute of Applied Mathematics and Mechanics |
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| Abstract: | On the basis of the moving least-squares(MLS) approximation,the complex variable element-free Galerkin(CVEFG) method for two-dimensional elastic large deformation problems,such as large displacement and large rotation,is presented in this paper.The advantage of the CVMLS approximation is that the trial function of a two-dimensional problem is formed with one-dimensional basis function.Then the CVMLS approximation is applied to solve two-dimensional large deformation problems.The Galerkin weak form is employ... |
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| Keywords: | Meshless method moving least-squares(MLS) approximation complex variable moving least-squares(CVMLS) approximation element-free Galerkin(EFG) method complex variable element-free Galerkin(CVEFG) method large deformation problem |
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