Numerical Shape Optimization in Structural Acoustics

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This dissertation presents a numerical method to optimize the thickness distribution of threedimensional structures with respect to various vibrational and structural properties. A combination of a commercially available finite element software package and additional user-written programs is used to modify the shape (but not the number of nodes and elements) of finite element models of the structures to be optimized. This is done iteratively and without manual intervention so as to achieve significant improvements of the objective function. The optimization process continues automatically until some predefined convergence criterion is met or until some prespecified maximum number of iterations is reached. The design variables are the structure's local thickness values at selected surface nodes. Possible objectives of the optimization include the minimization of the mean level of structure borne sound (a measure of the vibrational sensitivity of a structure), the minimization of the structural mass, the maximization of the fundamental frequency, and the maximization of the difference between two arbitrarily chosen natural frequencies. In addition, suitable constraints must be specified that restrict the number of acceptable solutions to the optimization problem. Possible candidates for constraints are the structural mass, the mean level of structure borne sound, and the fundamental frequency. Furthermore, the allowable range of design variable values is restricted by prescribed upper and lower limits. The optimization procedure is tested on the finite element models of four different three-dimensional structures made of steel, namely, a rectangular plate, two rectangular plates joined at 90°, a half-cylinder, and a gearbox.