Semi-analytical sensitivity analysis approach for fully coupled optimization of flexible multibody systems

Abstract

Flexible multibody systems have high geometric nonlinearity, which makes it very difficult to solve the dynamic response optimization problem. If mathematical programming tools are used, two main optimization methods are weakly coupled methods and fully coupled methods. The latter must consider the full dynamics of the system. When the objective function and constraint function are related to velocity vector or multicomponent-based constraints are involved in the optimization problem, only fully coupled optimization methods can be used. In this case, dynamic sensitivity analysis is necessary, but the solution is relatively difficult. In this paper, a semi-analytical sensitivity analysis approach for fully coupled optimization of flexible multibody systems is proposed. This approach combines the advantages of finite difference method and analytic method, and solves the bottleneck problem of the sensitivity calculation for fully coupled optimization methods. The formulas of the semi-analytical sensitivity analysis approach at the system and element levels are given. And the correctness and effectiveness are verified by two numerical examples. The results show that fully coupled optimization of flexible multibody system dynamics has good engineering application value.