An Evaluation of Some Alternative Formulations for Transient Dynamic Response Optimization

Some alternative formulations for transient dynamic response optimization are described and analyzed. A critical review and comparative study of the formulations are presented. The key feature of the formulations is that the state variables, in addition to the real design variables, are treated as independent variables in the optimization process. The state variables include different combinations of generalized displacements, velocities and accelerations. Formulations based on different discretization techniques for first-order and second-order differential equations are presented. Finite difference, Newmark’s method and some methods based on collocation are all discussed. Similar to the simultaneous analysis and design (SAND) approach used for optimization of static structures and the direct collocation/transcription method for optimal control, the state governing equations are treated as equality constraints. A major advantage of these formulations is that special design sensitivity analysis methods are no longer needed. However, the formulations have larger numbers of variables and constraints. Therefore sparsity of the problem functions must be exploited in all the calculations. Advantages and disadvantages of the formulations are discussed. The results of a numerical example and performance features of the formulations are compared.