Tensor-based Gauss-Jacobi numerical integration for high-order mass and stiffness matrices

Autor(es)

Bittencourt, M. L. ^[1] ; Vazquez, T. G. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Fac Mech Engn, Dept Mech Design DPM, BR-13083970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING; v. 79, n. 5, p. 599-638, JUL 30 2009.
• Citações Web of Science: 2

Resumo

In this work, we choose the points and weights of the Gauss-Jacobi, Gauss-Radau-Jacobi and Gauss-Lobatto-Jacobi quadrature rules that optimize the number of operations for the mass and stiffness matrices of the high-order finite element method. The procedure is particularly applied to the mass and stiffness matrices using the tensor-based nodal and modal shape functions given in (Int. J. Numer. Meth. Engng , 2007; 71(5):529-563). For square and hexahedron elements, we show that it is possible to use tensor product Of the 1D mass and stiffness matrices for the Poisson and elasticity problem. For the triangular and tetrahedron elements, all analogous analysis given in (Int. J. Numer. Meth. Engng 2005; 63(2):1530-1558), was considered for the selection of the optimal points and weights for the stiffness matrix coefficients for triangles and mass and stiffness matrices for tetrahedra. Copyright (C) 2009 John Wiley \& Sons, Ltd. (AU)

• Processo FAPESP: 02/13601-8 - Consórcio setorial em engenharia assistida por computador
• Beneficiário: Marco Lucio Bittencourt
• Modalidade de apoio: Auxílio à Pesquisa - Consórcios Setoriais para Inovação Tecnológica - CONSITEC