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Semi‐analytical integration of the elastic stiffness matrix of an axisymmetric eight‐noded finite element
Author(s) -
Lozada I.J.,
Griffiths D.V.,
Cerrolaza M.
Publication year - 2010
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20512
Subject(s) - finite element method , stiffness matrix , rotational symmetry , mathematics , smoothed finite element method , partial differential equation , mixed finite element method , partial derivative , subroutine , matrix (chemical analysis) , gaussian , stiffness , mathematical analysis , computer science , boundary element method , boundary knot method , structural engineering , geometry , engineering , physics , materials science , quantum mechanics , composite material , operating system
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