Fundamental Study of Optimal Shape Design of Bimetallic Composite Structures for Time-Response Problem

Abstract

The optimal shape design of solid structures must satisfy two key objectives: high mechanical performance and low volume or mass. For machines in motion, vibration behavior is crucial for machine life and reliability, requiring optimal time response characteristics depending on the objective function. Time response problems arise not only in solid structures made of single materials but also in composite structures composed of heterogeneous materials. Heterogeneous composite structures can exhibit excellent mechanical behavior that is unattainable with single-material structures. For example, by using dissimilar materials with different thermal expansion coefficients, it is possible to control thermal displacement through optimal shape design. Optimal shape design is also beneficial for reducing the dynamic compliance of solid structures within a limited volume. Bimetals are a type of composite structure consisting of two different adhered metals. In recent years, metal additive manufacturing technology has rapidly advanced, allowing for precise fabrication of metal parts. This study aims to develop a gradient-based optimal shape design method for minimizing the dynamic compliance of 3D bimetallic composite structures. First, we formulate the design problem, where the time-dependent dynamic compliance is set as the objective function to be minimized, with the volume constraint serving as the constraint condition. Then, we theoretically derive the shape gradient function (i.e., the sensitivity function) and construct the optimal shape design system. Furthermore, the effectiveness and feasibility of the proposed optimal shape design method are validated through design examples.