On the use of Somigliana's formula and Fourier series for elasticity problems with circular boundaries

Steven L Crouch, Sofia Mogilevskaya

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

This paper considers the problem of an infinite, isotropic elastic plane containing an arbitrary number of non-overlapping circular holes and isotropic elastic inclusions. The holes and inclusions are of arbitrary size and the elastic properties of all of the inclusions can, if desired, be different. The analysis is based on the two-dimensional version of Somigliana's formula, which gives the displacements at a point inside a region V in terms of integrals of the tractions and displacements over the boundary S of this region. We take V to be the infinite plane, and S to be an arbitrary number of circular holes within this plane. Any (or all) of the holes can contain an elastic inclusion, and we assume for simplicity that all inclusions are perfectly bonded to the material matrix. The displacements and tractions on each circular boundary are represented as truncated Fourier series, and all of the integrals involved in Somigliana's formula are evaluated analytically. An iterative solution algorithm is used to solve the resulting system of linear algebraic equations. Several examples are given to demonstrate the accuracy and efficiency of the numerical method.

Original languageEnglish (US)
Pages (from-to)537-578
Number of pages42
JournalInternational Journal for Numerical Methods in Engineering
Volume58
Issue number4
DOIs
StatePublished - Sep 28 2003

Keywords

  • Direct boundary integral method
  • Elasticity
  • Fourier series
  • Multiple circular holes and inclusions
  • Somigliana's formula

Fingerprint Dive into the research topics of 'On the use of Somigliana's formula and Fourier series for elasticity problems with circular boundaries'. Together they form a unique fingerprint.

Cite this