TY - JOUR

T1 - On the use of Somigliana's formula and Fourier series for elasticity problems with circular boundaries

AU - Crouch, Steven L

AU - Mogilevskaya, Sofia

PY - 2003/9/28

Y1 - 2003/9/28

N2 - 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.

AB - 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.

KW - Direct boundary integral method

KW - Elasticity

KW - Fourier series

KW - Multiple circular holes and inclusions

KW - Somigliana's formula

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U2 - 10.1002/nme.789

DO - 10.1002/nme.789

M3 - Article

AN - SCOPUS:0141682738

VL - 58

SP - 537

EP - 578

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 4

ER -