On the equivalent static load method for flexible multibody systems described with a nonlinear finite element formalism

The equivalent static load (ESL) method is a powerful approach to solve dynamic response structural optimization problems. The method transforms the dynamic response optimization into a static response optimization under multiple load cases. The ESL cases are defined based on the transient analysis response whereupon all the standard techniques of static response optimization can be used. In the last decade, the ESL method has been applied to perform the structural optimization of flexible components of mechanical systems modeled as multibody systems (MBS). The ESL evaluation strongly depends on the adopted formulation to describe the MBS and has been initially derived based on a floating frame of reference formulation. In this paper, we propose a method to derive the ESL adapted to a nonlinear finite element approach based on a Lie group formalism for two main reasons. Firstly, the finite element approach is completely general to analyze complex MBS and is suitable to perform more advanced optimization problems like topology optimization. Secondly, the selected Lie group formalism leads to a formulation of the equations of motion in the local frame, that turns out to be a strong practical advantage for the ESL evaluation. Examples are provided to validate the proposed method.