The weak patch test for nonhomogeneous materials modeled with graded finite elements

Glaucio H. Paulino, Jeong Ho Kim

Research output: Contribution to journalArticlepeer-review

Abstract

Functionally graded materials have an additional length scale associated to the spatial variation of the material property field which competes with the usual geometrical length scale of the boundary value problem. By considering the length scale of nonhomogeneity, this paper presents the weak patch test (rather than the standard one) of the graded element for nonhomogeneous materials to assess convergence of the finite element method (FEM). Both consistency (as the size of elements approach zero, the FEM approximation represents the exact solution) and stability (spurious mechanisms are avoided) conditions are addressed. The specific graded elements considered here are isoparametric quadrilaterals (e.g. 4, 8 and 9-node) considering two dimensional plane and axisymmetric problems. The finite element approximate solutions are compared with exact solutions for nonhomogeneous materials.

Original languageEnglish (US)
Pages (from-to)63-81
Number of pages19
JournalJournal of the Brazilian Society of Mechanical Sciences and Engineering
Volume29
Issue number1
DOIs
StatePublished - 2007

Keywords

  • Finite element method (FEM)
  • Functionally graded material (FGM)
  • Graded element
  • Patch test
  • Weak patch test

ASJC Scopus subject areas

  • Mechanical Engineering

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