Maximum-entropy meshfree method for incompressible media problems
Abstract
A novel maximum-entropy meshfree method that we recently introduced in Ortiz et al. (2010) I 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. (C) 2010 Elsevier B.V. All rights reserved.
Más información
Título según WOS: | Maximum-entropy meshfree method for incompressible media problems |
Título de la Revista: | FINITE ELEMENTS IN ANALYSIS AND DESIGN |
Volumen: | 47 |
Número: | 6 |
Editorial: | ELSEVIER SCIENCE BV |
Fecha de publicación: | 2011 |
Página de inicio: | 572 |
Página final: | 585 |
Idioma: | English |
URL: | http://linkinghub.elsevier.com/retrieve/pii/S0168874X10002040 |
DOI: |
10.1016/j.finel.2010.12.009 |
Notas: | ISI |