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| US-FE-LSPIM QUAD4 element and its application in the geometrically nonlinear problems |
| Received:November 30, 2010 Revised:January 04, 2011 |
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| DOI：10.7511/jslx201105023 |
| KeyWord:geometrically nonlinear problem US-FE-LSPIM QUAD4 element updated Lagrangian formulation mesh distortion |
| Author | Institution |
| 贾程 |
盐城工学院 土木工程学院,盐城 ;河海大学 工程力学系,南京 |
| 陈国荣 |
河海大学 工程力学系,南京 |
| 陈卉卉 |
盐城工学院 土木工程学院,盐城 |
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| Abstract: |
| In order to improve precision of numerical calculation for distorted meshes, the US-FE-LSPIM QUAD4 element is developed based on the concept of unsymmetric finite element formulation. This element is formed by using two different sets of shape functions for the trial and test functions, viz. sets of FE-LSPIM QUAD4 element shape functions and sets of classical isoparametric shape functions. The former is used for requirements of intra-element and inter-element continuity in displacement field, and the latter is for requirements of completeness in displacement field. This element combines the strengths of finite element and meshfree methods, and could easily fulfil exact essential boundary condition along the entire length of the edge. In the analysis of the geometrically nonlinear problems, the formulation is derived based on the updated Lagrangian formulation. An incremental and iterative solution procedure using Newton-Raphson iterations is used to solve the problems. FORTRAN programme is made. Numerical examples show that the US-FE-LSPIM QUAD4 element exhibits superiority to classical four node isoparametric element and QM6 element, and possesses good precision for both regular and distorted meshes, insensitiveness to mesh distortion. |
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