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.

中文翻译：

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包含三轴椭球腔的板中的应力分布

本文介绍了具有三轴椭圆体空腔的各向同性无限板中应力分布的三维分析，其表面受到三个主应力${\sigma }_{\mathrm{1个}},{\sigma }_{\mathrm{2个}},$和${\sigma }_{\mathrm{3个}}$. 为了满足板坯表面和空腔的边界条件，使用直角坐标调和函数并应用双傅里叶变换。问题简化为求解三个积分微分方程。研究解的存在性和唯一性。