Semi‐analytical integration of the elastic stiffness matrix of an axisymmetric eight‐noded finite element |
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| Authors: | I.J. Lozada D.V. Griffiths M. Cerrolaza |
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| Affiliation: | 1. Departamento de Ciencias Básicas, Decanato de Ingeniería Civil, Universidad Centroccidental Lisandro Alvarado, Apto. Postal 3001, Barquisimeto, Venezuela;2. Geomechanics Research Center, Colorado School of Mines, Golden, Colorado 80401, USA;3. Instituto Nacional de Bioingeniera, Universidad Central de Venezuela, Ciudad Universitaria S/N, Caracas, Venezuela |
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| Abstract: | The finite element method (FEM) is a numerical method for approximate solution of partial differential equations with appropriate boundary conditions. This work describes a methodology for generating the elastic stiffness matrix of an axisymmetric eight‐noded finite element with the help of Computer Algebra Systems. The approach is described as “semi analytical” because the formulation mimics the steps taken using Gaussian numerical integration techniques. The semianalytical subroutines developed herein run 50[percnt] faster than the conventional Gaussian integration approach. The routines, which are made publically available for download,1 should help FEM researchers and engineers by providing significant reductions of CPU times when dealing with large finite element models. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 |
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| Keywords: | axisymmetric quadrilateral finite elements semi‐analytical integration stiffness matrix symbolic manipulation |
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