Maximum-entropy meshfree method for incompressible media problems
| Autor: | N. Sukumar, A. Ortiz, Michael A. Puso |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Diffuse element method
Mathematical optimization Applied Mathematics Hydrostatic pressure General Engineering Computer Graphics and Computer-Aided Design Numerical integration symbols.namesake Incompressible flow symbols Applied mathematics Meshfree methods Gaussian quadrature Analysis Weakened weak form Stiffness matrix Mathematics |
| Zdroj: | Finite Elements in Analysis and Design. 47:572-585 |
| ISSN: | 0168-874X |
| DOI: | 10.1016/j.finel.2010.12.009 |
| Popis: | A novel maximum-entropy meshfree method that we recently introduced in Ortiz et al. (2010) [1] is extended to Stokes flow in two dimensions and to three-dimensional incompressible linear elasticity. The numerical procedure is aimed to remedy two outstanding issues in meshfree methods: the development of an optimal and stable formulation for incompressible media, and an accurate cell-based numerical integration scheme to compute the weak form integrals. On using the incompressibility constraint of the standard u-p formulation, a u-based formulation is devised by nodally averaging the hydrostatic pressure around the nodes. A modified Gauss quadrature scheme is employed, which results in a correction to the stiffness matrix that alleviates integration errors in meshfree methods, and satisfies the patch test to machine accuracy. The robustness and versatility of the maximum-entropy meshfree method is demonstrated in three-dimensional computations using tetrahedral background meshes for integration. The meshfree formulation delivers optimal rates of convergence in the energy and L^2-norms. Inf-sup tests are presented to demonstrate the stability of the maximum-entropy meshfree formulation for incompressible media problems. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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