Stress distribution in a plate containing a triaxial ellipsoidal cavity

Abstract

This paper presents the three-dimensional analysis of the stress distribution arising in an isotropic infinite slab with a triaxial ellipsoidal cavity, the surface of which is subjected to the three principal stresses ${\sigma }_1,{\sigma }_2,$ and ${\sigma }_3$. To satisfy both boundary conditions on the surface of slab and the cavity, harmonic functions in rectangular coordinates are used and double Fourier transform is applied. The problem is reduced to the solution of three integro-differential equations. The existence and uniqueness of the solution is investigated.

Keywords:

• Triaxial ellipsoid
• integro-differential equations
• Fourier transform
• elliptic integral

2010 Mathematics Subject Classification:

• 74B05

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No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.