This paper attempts to perform the optimal topology design of plate
structures subject to an external excitation with excitation frequency in a frequency domain. The major goal of the study is to study the applicability and essential characteristics of a variety of proposed objective functions,including the dynamic mean compliance, the norm of the frequency response vector, the kinetic energy and the strain energy. To formulate the topology optimization problems, a homogenization
algorithm proposed in Suzuki and Kikuchi23 together with finite element methods (FEM) are employed, and solution of the optimization problems is sought by using an optimality criterion method and a generalized stress based approach. To substantiate the proposed optimization algorithms and formulations, the optimum topology design of reinforcements of a simply-supported plate structure subject to various external excitations is performed.The derived results show that if the first eigenfrequency of the
intermediate design could not exceed the specified external excitation
frequency during the optimization process, a convergent solution would be
unavailable, which is also the main cause for the last three objective
functions incapable of providing optimal solutions. However, it is shown
that the proposed approach by means of a simple adjustment and
modification of these objective functions turns out to be quite effective to ease the difficulty.