Numerical optimization of the thickness distribution of three-dimensional structures with respect to their structural acoustic properties

This paper describes a numerical method to optimize the thickness distribution of three-dimensional structures with respect to various vibrational and structural properties. A combination of a commercially available finite element (FE) software package and additional user-written programs is used to modify the shape (but not the number of nodes and elements) of FE models of the structures to be optimized. The design variables are the structure's local thickness values at selected surface nodes. Possible objectives of the optimization include the minimization of the vibration level, the minimization of the structural mass, the maximization of the fundamental frequency, and the maximization of the difference between two arbitrarily chosen natural frequencies. The optimization procedure is applied to three example structures, namely, a rectangular plate, two plates joined at 90°, and a gearbox. Depending on the particular structure and on the choice of the objective function and constraints, the vibrational and structural properties can be substantially improved.