Various aspects of structural optimization techniques under transient loads are extensively reviewed. The main themes of the paper are treatment of time-dependent constraints, calculation of design sensitivity, and approximation. Each subject is reviewed with corresponding papers that have been published since the 1970s. The treatment of time-dependent constraints in both the direct method and the transformation method is discussed. Two ways of calculating design sensitivity of a structure under transient loads are discussed—direct differentiation method and adjoint variable method. The approximation concept mainly focuses on the response surface method in crashworthiness and local approximation with the intermediate variables. Especially, a method using the equivalent static load is discussed as an approximation method. It takes advantage of the well-established static response optimization. The structural optimization in flexible multibody dynamic systems is reviewed in the viewpoint of the above three themes.

A review of optimization of structures subjected to transient loads

Recently, an algorithm for dynamic response optimization transforming dynamic loads into equivalent static loads has been proposed. In later research, it was proved that the solution obtained by the algorithm satisfies the Karush-Kuhn-Tucker necessary conditions. In the present research, the proposed algorithm is applied to the optimization of flexible multibody dynamic systems. The equivalent static load is derived from the equations of motion for a flexible multibody dynamic system. The equivalent load is utilized in sequential static response optimization of the flexible mutibody dynamic system. In the end, the converged solution of the sequential static response optimization is the solution of the original dynamic response optimization. Some standard examples are solved to show the feasibility and efficiency of the proposed method. The control arm of an automobile suspension system is optimized as a practical problem. The results are discussed regarding the application of the proposed algorithm to flexible multibody dynamic systems.

Zhang Xianmin

Papers

Optimal design of flexible mechanisms with frequency constraints