Topology Optimization of Smart Structures Using a Homogenization Approach

Engineers are often required to design mechanical structures to meet specific loading conditions. Topology optimization automates the process of finding an optimal structural design, allowing for size, shape, and topology variations. For a given set of boundary conditions and design specifications, an optimal structure is computed, based on a formulated cost function. In this paper, the optimization considers not only the distribution of conventional material, but also simultaneously the distribution of active piezoelectric material within the domain. 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 individually at each point. This enables us 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 are provided to demonstrate the application of the method to find structures that maximize the deflection at a point when the piezoelectric material is activated.