STRUCTURAL TOPOLOGY AND SHAPE OPTIMIZATION FOR A FREQUENCY-RESPONSE PROBLEM

A topology and shape optimization technique using the homogenization m ethod was developed for stiffness of a linearly elastic structure by B endsoe and Kikuchi (1988), Suzuki and Kikuchi (1990, 1991), and others . This method has also been extended to deal with an optimal reinforce ment problem for a free vibration structure by Diaz and Kikuchi (1992) . In this paper, we consider a frequency response optimization problem for both the optimal layout and the reinforcement of an elastic struc ture. First, the structural optimization problem is transformed to an Optimal Material Distribution problem (OMD) introducing microscale voi ds, and then the homogenization method is employed to determine an equ ivalent ''averaged'' structural analysis model. A new optimization alg orithm, which is derived from a Sequential Approximate Optimization ap proach (SAO) with the dual method, is presented to solve the present o ptimization problem. This optimization algorithm is different from the CONLIN (Fleury 1986) and MMA (Svanderg 1987), and it is based on a si mpler idea that employs a shifted Lagrangian function to make a convex approximation. The new algorithm is called ''Modified Optimality Crit eria method (MOC)'' because it can be reduced to the traditional OC me thod by using a zero value for the shift parameter. Two sensitivity an alysis methods, the Direct Frequency Response method (DFR) and the Mod al Frequency Response method (MFR), are employed to calculate the sens itivities of the object functions. Finally, three examples are given t o show the feasibility of the present approach.