Details

Title

An Improved XFEM for the Poisson Equation with Discontinuous Coefficients

Journal title

Archive of Mechanical Engineering

Yearbook

2017

Numer

No 1

Keywords

Mechanical Engineering ; Mechanics of Materials

Divisions of PAS

Nauki Techniczne

Abstract

<jats:title>Abstract</jats:title><jats:p>Discontinuous coefficients in the Poisson equation lead to the weak discontinuity in the solution, e.g. the gradient in the field quantity exhibits a rapid change across an interface. In the real world, discontinuities are frequently found (cracks, material interfaces, voids, phase-change phenomena) and their mathematical model can be represented by Poisson type equation. In this study, the extended finite element method (XFEM) is used to solve the formulated discontinuous problem. The XFEM solution introduce the discontinuity through nodal enrichment function, and controls it by additional degrees of freedom. This allows one to make the finite element mesh independent of discontinuity location. The quality of the solution depends mainly on the assumed enrichment basis functions. In the paper, a new set of enrichments are proposed in the solution of the Poisson equation with discontinuous coefficients. The global and local error estimates are used in order to assess the quality of the solution. The stability of the solution is investigated using the condition number of the stiffness matrix. The solutions obtained with standard and new enrichment functions are compared and discussed.</jats:p>

Publisher

Polish Academy of Science, Committe of Machine Design

Date

2017

Identifier

ISSN 0004-0738, e-ISSN 2300-1895

DOI

10.1515/meceng-2017-0008

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