Shape design optimization of 2-dimensional inlaid structures

Abstract

Owning to the different mechanical behaviors of the instinct materials, inlaid structures composed of dissimilar materials have potential for industrial application, such as vibration suppression. The shape and position of inlaid components strongly affect the mechanical behaviors of inlaid structures. Thereby, we propose a shape optimization method for designing inlaid structures in terms of stiffness problem in the present work. This study focuses on the design optimization of 2-dimensional structures with inlaid components for enhancing their stiffness by optimizing the shape and position of inlaid components. We use compliance as the objective function and minimize it under the area constraint of inlaid components. The proposed shape optimization method is a type of gradient method that was named as the H¹ gradient method. We derive the shape gradient function based on the material derivative method and apply it to the proposed shape optimization method for determining the optimal shape and position of the inlaid components. Design examples of 2-dimensional inlaid structures are presented in this study to verify the effectiveness and feasibility of the proposed optimization method, and the results show that stiffness of inlaid structures can be significantly enhanced according to the shape design optimization, especially for a inlaid structure with a higher differential Young's modulus of the instinct materials.