Topology optimization of smart structures using a homogenization approach

Engineers are often required to design mechanical structures to meet specific loading conditions. Topological optimization automates the process of finding an optimal structural design, allowing for size, shape and topological variations. For a given set of boundary conditions and design specifications (constraints), a structure, optimal in terms of a formulated cost function, is computed. As the cost function, static properties such as the mean compliance, as well as dynamic properties such as the eigenfrequencies of the structure can be chosen. In this paper, the optimization considers not only the placement of conventional material, but also, simultaneously, the placement of smart PZT material. In the formulation of the topology optimization problem, a microstructure consisting of smart as well as conventional material is used. Instances of the microstructure occur in a rectangular grid and cover the design domain. Since the microstructure is defined parametrically, the density of each material can be controlled independently at each point. This enables one to formulate the problem of finding an optimal material distribution as a parameter optimization problem. A homogenization approach is used to find and use effective material properties for the limiting case of an infinitely small microstructure. Several numerical examples demonstrate the use of this method.