Analytical method for studying stress concentration around arbitrary shape cavity is proposed. The method is based on the assumption that it is possible to simulate the influence of cavity on the redistribution of internal forces by including fictitious forces in the solution. To determine the stress-strain state, additional forces acting on cavity surface are used. The magnitude of these forces is chosen on the basis of the value of stress tensor flow through the examined surfaces limiting cavity volume. Research of stress-strain state for the most general three-dimensional case is done: an elastic half-space with a cubic shape cavity under action of a concentrated force applied to a free surface. The obtained results are comprehensively compared with the solution of a similar problem by the finite element method. Distributions of the stress tensor components in the vicinity of these cavities are constructed. The estimation of accuracy and efficiency of the proposed calculation model is made; the boundary of applicability of the proposed solution is determined. It seems promising to use the resource of structural materials advantageously, namely, creating in the bodies of the cavity system the required shape and size, to obtain stress reduction at critical points, thereby increasing the strength of the product.

中文翻译：

---

具有任意形状空腔的弹性半空间的应力应变状态

提出了一种研究任意形状空腔周围应力集中的解析方法。该方法基于以下假设：可以通过在解决方案中包含虚拟力来模拟空腔对内部力重新分布的影响。为了确定应力应变状态，使用了作用在型腔表面上的附加力。这些力的大小基于流经检查表面的应力张量的值来选择，从而限制了腔体的体积。对最普通的三维情况进行了应力-应变状态的研究：在施加到自由表面的集中力的作用下，具有立方体形腔体的弹性半空间。将获得的结果与通过有限元法解决类似问题的方法进行了全面比较。在这些腔附近构造应力张量分量的分布。对所提出的计算模型的准确性和效率进行了估计；确定所提出解决方案的适用范围。似乎有利地利用结构材料的资源，即在型腔系统的主体中产生所需的形状和尺寸，以获得在临界点处的应力减小，从而增加产品的强度，似乎是有希望的。