Lightweight Engineering Design of Nonlinear Dynamic Systems with Gradient-Based Structural Design Optimization

Reducing the weight of a system leads to lower forces being exerted, which in turn allows for lower requirements and an even lighter system. This “virtuous circle of lightweight engineering design” can especially be present when designing dynamic systems. Design optimization is a tool to enable and exploit this favorable phenomenon. This work introduces a unified approach to reap the benefits of optimally designed lightweight systems in structural dynamics and multibody dynamics. An efficient gradient-based optimization framework has been implemented and this is explained and demonstrated. The centerpiece of this optimization methodology is the design sensitivity analysis applied to the time integration with a nonlinear solver. A semi-analytical approach is chosen to balance computational effort and implementation effort, where the sensitivities are derived via direct differentiation with numerical differences for the sensitivities of the system parameters. Nomenclature is introduced to simplify these equations for a more lucid description showing the intrinsic equivalence of the solving routines of structural dynamics and multibody dynamics. The method is shown on the practical example for the optimal design of a hydraulic engineering mechanism.