The optimal design of the stress state in elastic plate structures with openings is a problem of great significance in engineering practice. Achieving proper shape of hole can reduce stress concentration around the boundaries remarkably. The optimal shape of a single hole in an infinite plate under uniform stresses has been obtained by complex variable method based on different optimal criteria. The complex variable method is particularly suitable for the hole shape optimization in infinite plate, in which the continuous hole boundary can be represented by the mapping function. It can also be used to solve the shape optimization problems of two or more holes. However, because of the difficulty of finding the mapping function for multi connected domain, the holes are mapped onto slits or separately mapped onto a circle. In this article, the two symmetrical and identical holes are mapped onto an annulus simultaneously by the newly found mapping function, which has a general form. The maximum tangential stress around the boundaries is minimized to achieve the optimal hole shape. And the coefficients of mapping function which describe the boundary are calculated by differential-evolution algorithm.

具有开口的弹性板结构中应力状态的优化设计在工程实践中具有重要意义。获得合适的孔形状可以显着降低边界周围的应力集中。通过基于不同最优准则的复杂变量法，获得了在均匀应力下无限大板中单孔的最佳形状。复变量法特别适合无限板中的孔形状优化，其中连续的孔边界可以由映射函数表示。它也可以用于解决两个或多个孔的形状优化问题。但是，由于难以找到多连接域的映射函数，因此将孔映射到狭缝上或分别映射到圆上。在这篇文章中，新发现的映射函数将两个对称且相同的孔同时映射到环上，该映射函数具有一般形式。边界周围的最大切向应力被最小化以实现最佳的孔形状。利用微分进化算法计算出描述边界的映射函数系数。