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

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.

Robust Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition

This work proposes a new methodology for robust design optimization (RDO) of complex engineering systems. The method, capable of solving large-scale RDO problems, involves (1) an adaptive-sparse polynomial dimensional decomposition (AS-PDD) for stochastic moment analysis of a high-dimensional stochastic response, (2) a novel integration of score functions and AS-PDD for design sensitivity analysis, and (3) a multi-point design process, facilitating standard gradient-based optimization algorithms. Closed-form formulae are developed for first two moments and their design sensitivities. The method allow that both the stochastic moments and their design sensitivities can be concurrently determined from a single stochastic simulation or analysis. Precisely for this reason, the multi-point framework of the proposed method affords the ability of solving industrial-scale problems with large design spaces. The robust shape optimization of a three-hole bracket was accomplished, demonstrating the efficiency of the new method to solve industry-scale RDO problems.