The stress concentration at the interface between two dissimilar materials is a serious problem in designing adhesive joints and composite structures. Numerous studies have been conducted with the aim of reducing the stress concentration at the interface between dissimilar materials. In most of these works it was achieved by changing the geometry or properties of one of the materials at the edges of the interface. In this paper we propose a method of determining the values of elastic constants of the interlayer material and its geometry near the edges of the interfaces, to reduce the stress concentration. The method is based on the results of solving the problem of stress optimisation in the vicinity of singular points, according to which the optimal variants determine the boundary between the solutions with and without stress singularity. The paper presents the results of the construction of eigensolutions in the vicinity of singular points, which allow us to determine the ranges of parameters responsible for the appearance of solutions with and without stress singularity. The main advantage of the proposed method is the possibility of finding the range of optimal configurations for the interlayer, which is made of homogeneous or functionally graded material and used to bond materials having similar or dissimilar properties. A number of model problems are solved to demonstrate the capabilities of the proposed method in a search for the optimal mechanical characteristics of the elastic interlayer between two similar or dissimilar materials and its geometric parameters, in order to minimise the stress concentration at their interface.

两种不同材料界面处的应力集中是胶接接头和复合结构设计中的一个严重问题。为了减少异种材料之间界面处的应力集中，已经进行了大量研究。在大多数这些工作中，它是通过改变界面边缘材料之一的几何形状或属性来实现的。在本文中，我们提出了一种确定界面边缘附近的夹层材料及其几何形状的弹性常数值的方法，以减少应力集中。该方法基于奇异点附近应力优化问题的求解结果，根据该结果，最优变体确定了有应力奇异性和无应力奇异性的解之间的边界。本文介绍了在奇异点附近构造特征解的结果，这使我们能够确定负责具有和不具有应力奇异性的解的出现的参数范围。所提出的方法的主要优点是可以找到中间层的最佳配置范围，中间层由均质或功能梯度材料制成，用于粘合具有相似或不同特性的材料。解决了许多模型问题，以证明所提出的方法在寻找两种相似或不同材料之间的弹性夹层的最佳机械特性及其几何参数方面的能力，以最大限度地减少它们界面处的应力集中。