On design sensitivities in the structural analysis and optimization of flexible multibody systems

Abstract

The structural analysis and optimization of flexible multibody systems become more and more popular due to the ability to efficiently compute gradients using sophisticated approaches such as the adjoint variable method and the adoption of powerful methods from static structural optimization. To drive the improvement of the optimization process, this work addresses the computation of design sensitivities for multibody systems with arbitrarily parameterized rigid and flexible bodies that are modeled using the floating frame of reference formulation. It is shown that it is useful to augment the body describing standard input data files by their design derivatives. In this way, a clear separation can be achieved between the body modeling and parameterization and the system simulation and analysis.

Topology Optimization for Dynamic Flexible Multibody Systems Using the Flexible Natural Coordinates Formulation

“…The formulation's reduced mass, stiffness and damping matrices are independent of the system states, and only dependent on the topology parameters. This is in contrast to prior work where other multibody formulations are employed that lead to state dependent mass matrices and/or nonlinear internal forces [8,9]. The AVM-FNCF approach results in the Jacobian matrices ∂M ∂ρ , ∂K ∂ρ and ∂C ∂ρ being constant for each design iteration.…”

“…Furthermore, the deformations of the structural components in this work are assumed to be small such that multibody formulations relying on the small-deformation assumption can be used. Nevertheless, interesting works on structural optimization that are described using the Absolute Nodal Coordinates Formulation (ANCF) have been published [6,7,8,9,10].…”

“…The advantage of this self-adjoint expression is that the sensitivity analysis is straight-forward, computationally efficient and can be evaluated with readily computed solution variables. Further developments extended the methodology for static structural cases towards transient dynamic loading applications [12,13,14] and subsequently the field of multibody system dynamics [15,16,8].…”

Analytical Sensitivity Analysis of Dynamic Problems with Direct Differentiation of Generalized-α Time Integration

“…Therefore, direct differentiation is chosen in this work. The reader is referred to the following literature for the adjoint variable method: [19][20][21][22][23][24][25][26][27][28][29][30].…”