Topology optimization-based distribution design of actuation voltage in static shape control of plates

This paper investigates the optimal spatial distribution of single-channel actuation voltage in static structural shape control problem. It is pointed out that single-channel actuation voltage input for shape control applications is of practical importance due to its ease of implementation. The Mindlin plate theory is used in the finite element modeling of laminates with piezoelectric layers. The optimal distribution of the single-channel actuation voltage is formulated as a discrete optimization problem with tri-level design variables, where a least-square function measuring the structural shape error is to be minimized under a constraint on the control effort. Such a problem is then transformed into a continuous one by introducing element-wise artificial design variables defining the topological feature of the control voltage distribution. A power-law function relating the design variables and the applied voltages is proposed to penalize intermediate values of the design variables. Based on the sensitivity analysis, the problem is solved effectively using the MMA algorithm tailored for constrained least-square problems. Numerical examples presented demonstrate the validity of the proposed problem formulation and numerical approaches.