System-wise equivalent static loads for the design of flexible mechanisms

Structural optimization of flexible multibody systems (MBS) is a challenging design problem which has received increased attention in the last decade. The weakly coupled method is a powerful method to solve this design problem as it transforms the underlying dynamic response optimization problem into a static response optimization problem subject to multiple load cases. These load cases can be conveniently defined using the so-called Equivalent Static Load (ESL) method. With the usual ESL method, ESLs are defined at a component-level assuming that each component is isolated from the rest of the system. Thus, this method cannot account for design functions involving the global response of the system but it is restricted to optimization problems that are solely formulated in terms of local responses within the components. In order to get rid of this restriction, a system-wise extension of the ESL method is proposed. It is shown that the solutions of the equivalent static optimization problem and of the initial MBS optimization problem are equivalent and that the ESL formulation naturally leads to a weakly coupled solution algorithm. Standard benchmarks exemplify the proposed method.