A modified element‐free Galerkin method with essential boundary conditions enforced by an extended partition of unity finite element weight function
A modified element‐free Galerkin method with essential boundary conditions enforced by an extended partition of unity finite element weight function
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DOI：
10.1002/nme.730
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发表时间：
2003-07
影响因子：
2.9
通讯作者：
M. Alves;Rodrigo Rossi
中科院分区：
文献类型：
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作者：
M. Alves;Rodrigo Rossi
本文提出了一种将无单元伽辽金法（EFG）与扩展单元划分有限元法（PUFEM）相结合的方法，该方法能够在某种极限意义上强制执行有限元法（FEM）中所做的基本边界条件。所提出的扩展PUFEM基于移动最小二乘逼近（MLSA），由于考虑了线性和高阶基函数，能够克服全局形状函数中的奇异性问题。以避免奇异点的存在为目标，扩展PUFEM考虑了经典PUFE权函数支持的扩展。由于扩展PUFEM与EFG方法密切相关，因此不需要具有复杂实现过程的特殊近似函数，也不需要使用惩罚和/或乘数方法来近似施加基本边界条件。因此，需要一个相对简单的程序来结合这两种方法。为了验证该方法的性能，我们考虑了一个解析弹性问题的解和一些弹塑性损伤耦合问题的解。版权所有©2003 John Wiley & Sons， Ltd
In this work we propose a method which combines the element‐free Galerkin (EFG) with an extended partition of unity finite element method (PUFEM), that is able to enforce, in some limiting sense, the essential boundary conditions as done in the finite element method (FEM). The proposed extended PUFEM is based on the moving least square approximation (MLSA) and is capable of overcoming singularity problems, in the global shape functions, resulting from the consideration of linear and higher order base functions. With the objective of avoiding the presence of singular points, the extended PUFEM considers an extension of the support of the classical PUFE weight function. Since the extended PUFEM is closely related to the EFG method there is no need for special approximation functions with complex implementation procedures, and no use of the penalty and/or multiplier method is required in order to approximately impose the essential boundary condition. Thus, a relatively simple procedure is needed to combine both methods. In order to attest the performance of the method we consider the solution of an analytical elastic problem and also some coupled elastoplastic‐damage problems. Copyright © 2003 John Wiley & Sons, Ltd.