Interface shape design of multi-material structures for delamination strength

Abstract

This paper deals with interface shape optimum design of multi-material structures for the delamination strength problem. The optimum design problem is formulated as a non-parametric shape optimization problem in which the interface variation in the normal direction is considered as a design variable. The maximum value of a delamination function, an index of the delamination strength, is defined as an objective function subject to a volume constraint. The shape sensitivity, called shape gradient function, is derived by using the material derivative method and the adjoint variable method, and is applied to the H¹ gradient method to determine the optimal interface shape. With this method, the maximum value of the delamination function can be minimized while the smooth optimal interface shape can be obtained without any shape design parametrization. Several interface shape design examples are presented to verify the validity and practical utility of the proposed method.