Avoiding negative elastic moduli when using Lagrange interpolation for material grading in finite element analysis

Zhong Chen, Mehrdad Negahban

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Polynomial interpolations, one of the most common interpolations used in finite element methods (FEMs), are a workhorse of many FEM codes. These interpolations are readily available for all kinds of elements, and using them for modeling the variation of elastic moduli in graded elements is thus both convenient and natural. Yet, like all polynomial interpolations, they can be prone to oscillations that can result in regions of negative elastic modulus in the element, even with only positive nodal values of elastic moduli. The result of these negative modulus regions, even if the region is small, can be unexpected singularities in the solution. This defeats the purpose of using polynomial interpolations for capturing material grading in the element. We demonstrate the issue using three-node quadratic Lagrange interpolations of material grading in otherwise isoparametric p-type elements and show how to avoid this problem.

Original languageEnglish (US)
Pages (from-to)693-706
Number of pages14
JournalActa Mechanica
Volume227
Issue number3
DOIs
StatePublished - Mar 1 2016

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Interpolation
Elastic moduli
Finite element method
Polynomials

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanical Engineering

Cite this

Avoiding negative elastic moduli when using Lagrange interpolation for material grading in finite element analysis. / Chen, Zhong; Negahban, Mehrdad.

In: Acta Mechanica, Vol. 227, No. 3, 01.03.2016, p. 693-706.

Research output: Contribution to journalArticle

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