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论文类型： 期刊论文

发表时间： 2014-08-01

发表刊物： COMPUTATIONAL MECHANICS

收录刊物： SCIE、EI、Scopus

卷号： 54

期号： 2

页面范围： 353-368

ISSN号： 0178-7675

关键字： Meshfree/meshless; EFG; Nodal integration; Hourglass; Hu-Washizu variational principle

摘要： Robust and efficient integration of the Galerkin weak form only at the approximation nodes for second order meshfree Galerkin methods is proposed. The starting point of the method is the Hu-Washizu variational principle. The orthogonality condition between stress and strain difference is satisfied by correcting nodal derivatives. The corrected nodal derivatives are essentially linear functions which can exactly reproduce linear strain fields. With the known area moments, the stiffness matrix resulting from these corrected nodal derivatives can be exactly evaluated using only the nodes as quadrature points. The proposed method can exactly pass the quadratic patch test and therefore is named as quadratically consistent nodal integration. In contrast, the stabilized conforming nodal integration (SCNI) which prevails in the nodal integrations for meshfree Galerkin methods fails to pass the quadratic patch test. Better accuracy, convergence, efficiency and stability than SCNI are demonstrated by several elastostatic and elastodynamic examples.