SoftFEM: The Soft Finite Element Method

While the finite element method (FEM) has now reached full maturity both in academy and industry, its use in optimization pipelines remains either computationally intensive or cumbersome. In particular, currently used optimization schemes leveraging FEM still require the choice of dedicated optimization algorithms for a specific design problem, and a black box approach to FEM-based optimization remains elusive. To this end, we propose here an integrated finite element-soft computing method, ie, the soft FEM (SoftFEM), which integrates a finite element solver within a metaheuristic search wrapper. To illustrate this general method, we focus here on solid mechanics problems. For these problems, SoftFEM is able to optimize geometry changes and mechanistic measures based on geometry constraints and material properties inputs. From the optimization perspective, the use of a fitness function based on finite element calculation imposes a series of challenges. To bypass the limitations in search capabilities of the usual optimization techniques (local search and gradient-based methods), we propose, instead a hybrid self adaptive search technique, the multiple offspring sampling (MOS), combining two metaheuristics methods: one population-based differential evolution method and a local search optimizer. The formulation coupling FEM to the optimization wrapper is presented in detail and its flexibility is illustrated with three representative solid mechanics problems. More particularly, we propose here the MOS as the most versatile search algorithm for SoftFEM. A new method for the identification of nonfully determined parameters is also proposed.