Structural optimization of flexible components within a multibody dynamics approach

Structural optimization techniques rely on mathematical foundations in order to reach an optimized design in a rational manner. Nowadays, these techniques are commonly used for industrial applications with impressive results but are mostly limited to (quasi-) static or frequency domain loadings. The objective of this thesis is to extend structural optimization techniques to account for dynamic load cases encountered in multibody applications.

The thesis relies on a nonlinear finite element formalism for the multibody system simulation, which needs to be coupled with structural optimization techniques to perform the optimization of flexible components in an integrated way. To tackle this challenging optimization problem, two methods, namely the fully and the weakly coupled methods, are investigated.

The fully coupled method incorporates the time response coming directly from the MBS in the optimization. The formulation of the time-dependent constraints are carefully investigated as it turns out that it drastically affects the convergence of the optimization process. Also, since gradient-based algorithms are employed, a semi-analytical method for sensitivity analysis is proposed.

The weakly coupled method mimics the dynamic loading by a series of equivalent static loads (ESL) whereupon all the standard techniques of static response optimization can be employed. The ESL evaluation strongly depends on the formalism adopted to describe the MBS dynamics. In this thesis, the ESL evaluation is proposed for two nonlinear finite element formalisms: a classical formalism and a Lie group formalism.

An original combination of a level set description of the component geometry with a particular mapping is adopted to parameterize the optimization problem. The approach combines the advantages of both shape and topology optimizations, leading to a generalized shape optimization problem.

The adopted system-based optimization framework supersedes the classical component-based approach as the interactions between the component and the system can be consistently accounted for.