Topological Shape Optimization of Multiphysics Actuators using Level Set Method

This paper proposes a topological shape optimization method for the design of multi-physics piezoelectric actuators using a level set method of piecewise constants. A level set function taking level sets of piecewise constants is applied to implicitly represent design boundaries in a multiphase design domain, in which each constant level set denotes one material phase. As a result, only one level set function consisting of different constants is required to identify multiphase interfaces by making use of its discontinuities. In the design of smart actuators with in-plane motions, the optimization problem is defined to minimize a smooth energy functional under specific constraints. Thus, the design of smart actuators is transferred into a numerical iterative process to update the piecewise constants with a semi-implicit additive operator splitting (AOS) scheme. In such a way, multiple material phases are distributed simultaneously in the design domain until the compliant host structure and the equipped piezoelectric actuators are optimized, in which the compliant structure acts as a mechanical amplifier to enlarge the small strain stroke of the piezoelectric actuators. This method can avoid numerical difficulties in most conventional level set methods, such as the CFL condition, re-initializations and the non-differentiability of the Heaviside and Delta functions. One typical numerical example is used to demonstrate the effectiveness of the proposed topological shape optimization method.