کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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514126 | 866701 | 2011 | 14 صفحه PDF | دانلود رایگان |
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 L2-norms. Inf–sup tests are presented to demonstrate the stability of the maximum-entropy meshfree formulation for incompressible media problems.
Journal: Finite Elements in Analysis and Design - Volume 47, Issue 6, June 2011, Pages 572–585