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On the use of Somigliana's formula and Fourier series for elasticity problems with circular boundaries
Author(s) -
Crouch S. L.,
Mogilevskaya S. G.
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.789
Subject(s) - isotropy , mathematical analysis , mathematics , fourier series , elasticity (physics) , fourier transform , geometry , linear elasticity , series (stratigraphy) , boundary (topology) , series expansion , boundary value problem , plane (geometry) , algebraic number , classical mechanics , physics , finite element method , paleontology , quantum mechanics , biology , thermodynamics
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. Copyright © 2003 John Wiley & Sons, Ltd.