Abstract

An exact formulation and a solution of the stability problem for a three-dimensional elastic body containing distributed dislocations are given. The buckling phenomenon for a hollow nonlinear elastic sphere of the semi-linear (harmonic) material with edge dislocations is studied. The study is carried out within the framework of the continuum theory of continuously distributed dislocations using the bifurcation method of buckling analysis. The bifurcation method is to find the equilibrium positions of an elastic body, which differ little from the subcritical (unperturbed) state. The perturbed equilibrium state is described by a linearized boundary value problem. By solving a homogeneous linear boundary value problem, the minimum critical value of the external pressure at which the sphere loses stability is found. The influence of dislocations on the buckling of both thin and thick spherical shells is analyzed.

中文翻译：

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分布位错的非线性弹性球的平衡稳定性。

摘要

给出了包含位错的三维弹性体的精确公式和稳定性问题的解决方案。研究了具有边缘错位的半线性（调和）材料的空心非线性弹性球体的屈曲现象。该研究是在屈曲分析的分叉方法的基础上，在连续分布的位错的连续理论的框架内进行的。分叉方法是找到弹性体的平衡位置，该平衡位置与亚临界（无扰动）状态相差不大。扰动的平衡状态由线性边界值问题描述。通过解决齐次线性边界值问题，找到了球体失去稳定性的外部压力的最小临界值。