Unified topology design of static and vibrating structures using multiobjective optimization

Since structural design is usually required to perform in more than one environment, the ability to consider multiple objectives has to be included within the framework of topology optimization. A unified topology design methodology is proposed to generate structures satisfying both static and vibration performance measures using the multiobjective optimization approach. The weighted sum of conflicting objectives resulting from the norm method is used to generate the optimal compromise solutions, and the decision function is set to select the preferred solution. The objective function is defined by the mean compliance and mean eigenvalue to design a flexible structure which meets both the static and vibration requirements. The optimality conditions of the bicriteria problem are derived based on the modified optimality criteria method. To substantiate this approach, illustrated examples are presented both for verification and application.