Level set-based multi-material topology optimization considering material and joint cost

Abstract

In vehicle body structural design, weight reduction is one of the most important issues for improving both dynamic performance and fuel efficiency. Therefore, structural design using multi-materials has been attracting attention in order to achieve weight reduction while maintaining the stiffness of the vehicle body. By employing multi-materials with different physical properties, superior designs can be obtained in various aspects such as stiffness, mass, and cost. However, these are trade-offs with each other. Therefore, it is important to develop a multi-material design method that can improve these aspects. On the other hand, multi-material design has some challenges that single-material design does not have. One of them is how to evaluate the joints of multi-material structures. The boundary between dissimilar materials must be joined by means of adhesion or welding. However, few optimal design methods exist that refer to joints. In this study, we propose a design method for optimal structures based on multi-material topology optimization. This takes into account not only the cost dependent on the quantity of materials, but also the cost of joining different materials. To evaluate this joining cost, level set method is used, since it requires a clear representation of the material boundary area. We applied the MM-LS (Multi-Material Level Set) method, which can represent the shapes of multi-materials. Numerical examples for the cost minimization problem and the cost-mass multi-objective optimization problem are presented.