A fully coupled level set-based topology optimization of flexible components in multibody systems

Abstract

A fully coupled level set-based topology optimization of flexible components in multibody systems is considered. Thereby, using the floating frame of reference approach, the flexible components are efficiently modeled and incorporated in multibody systems. An adjoint sensitivity analysis is utilized to obtain the gradient of the objective function with respect to a set of density-like design variables assigned to elements included in the underlying finite element model. The utilized adjoint sensitivity analysis provides a gradient, which is within numerical limits exact. In this process, the parametrization of material properties of finite elements has a significant influence on the calculated gradient, in particular for poorly filled elements. These influences are studied in detail. As an application example, the compliance minimization problem of a flexible piston rod in a transient slider-crank mechanism is considered. For this model, the influence of different parametrization methods on the obtained gradient is discussed, and a gradient strategy is proposed to overcome numerical issues included in different parametrization laws. Using this gradient strategy within a level set-based algorithm, a topology optimization of the flexible piston rod is performed. The corresponding results are then compared with optimization results provided by the method of moving asymptotes (MMA). Moreover, the computational effort of the sensitivity analysis is high and scales with the number of design variables. In this work, a gradient approximation is introduced using radial basis functions (RBFs). This helps to develop an appropriate gradient for a level set-based topology optimization of the flexible components in multibody systems, where the RBF-based design space reduction decreases the computational effort of the utilized sensitivity analysis. Finally, the efficiency gain obtained by the introduced design space reduction is demonstrated by optimization examples.