集中载荷作用下弹性平面刚性夹杂的形状优化

SHAPE OPTIMIZATION OFARIGID INCLUSIN INAN ELATIC PLANE UNDER CONCENTRATED LOADS

当夹杂的弹性模量比基体的弹性模量大得多时,可将其看成刚性夹杂。对于这类硬夹杂与软基体的复合材料,采用复变函数方法中的保角映射技术和推广的 Schwarz 延拓原理,并结合对复应力函数的奇性主部分析,导出了焊接任意形状刚性夹杂的全场基本奇异解,求解了集中力与集中力偶作用下弹性平面刚性夹杂的形状优化问题,描绘出了夹杂界面应力最大值、界面主应力最大值随夹杂形状的变化规律,精确地定位出了界面应力最大值、界面主应力最大值的作用位置。通过对这些不同形状夹杂的界面主应力最大值的比较,确定了夹杂的最优形状。

The shape optimization of a rigid inclusion in an elastic plane under concentrated loads is considered. The conformal mapping technique and extended Schwarz principle integrated with the analysis of singularity of complex stress functions are adopted. A number of examples of the rigid inclusion with different shapes, such as elliptical, triangular and square inclusion, to account for a wide range of shape variations are discussed. Numerical results and graphs are presented, showing that the maximum interface stresses vary with the shape of inclusion. The shape resulting in minimum interface principal stress is obtained. Some suggestions are made in regard to the design of the shape of rigid inclusion.