A conforming point interpolation method (CPIM) by shape function reconstruction for elasticity problems
| Autor: | Guiyong Zhang, Gui-Rong Liu, Xu Xu, YuanTong Gu |
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| Rok vydání: | 2010 |
| Předmět: |
Numerical analysis
Mathematical analysis Finite element method 010300 NUMERICAL AND COMPUTATIONAL MATHEMATICS 080200 COMPUTATION THEORY AND MATHEMATICS Computational Mathematics 090600 ELECTRICAL AND ELECTRONIC ENGINEERING Quadratic equation Rate of convergence Displacement field Computer Science (miscellaneous) Meshfree methods Galerkin method Numerical method computational method finite element method meshfree methods point interpolation method convergence rates computational efficiency nonconforming Mathematics Stiffness matrix |
| Zdroj: | International Journal of Computational Methods |
| ISSN: | 2381-3652 |
| Popis: | A conforming point interpolation method (CPIM) is proposed based on the Galerkin formulation for 2D mechanics problems using triangular background cells. A technique for reconstructing the PIM shape functions is proposed to create a continuous displacement field over the whole problem domain, which guarantees the CPIM passing the standard patch test. We prove theoretically the existence and uniqueness of the CPIM solution, and conduct detailed analyses on the convergence rate; computational efficiency and band width of the stiffness matrix of CPIM. The CPIM does not introduce any additional degrees of freedoms compared to the linear FEM and original PIM; while convergence rate of quadratic CPIM is in between that of linear FEM and quadratic FEM which results in the high computational efficiency. Intensive numerical studies verify the properties of the CPIM. |
| Databáze: | OpenAIRE |
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