Maximum-entropy meshfree method for incompressible media problems

Ortiz A.; Puso, M.A.; Sukumar, N.

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