Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

Abstract

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

Multi-Objective Topology Optimization of Multi-Functional Components in a Multibody Dynamics System

“…It is concluded that the iterative sensitivity analysis method gives the sensitivity same as the AVM method and the time integration incorporated method based on the Generalized-α algorithm. 14,17,18 Figure 5 shows the time history of sensitivities of first eight interactive members. It can be seen that the sensitivities calculated by the iterative method is same as the time integration incorporated method and the AVM method in all the time duration.…”