Topology Optimization of fiber reinforced structures considering stress constraint and optimized penalization

Abstract

The use of materials reinforced with fibers has been increasing due to their advantages, for example, the ratio between its mass and strength. For this reason, new additive manufacturing technologies have been developed for this material type. Some technologies allow tailoring fiber orientation, creating space for applying optimization techniques. On this account, many works dedicated to optimizing fiber orientation have been currently published. However, the critical issue of the stress yield criteria should be addressed. Thus, this work proposes to solve the Topology Optimization problem of minimizing the volume of the structure considering local stress constraints, determining the material distribution and the fiber orientation by using a proposed method named NDFO-adapt. The penalization used in the method is a field optimized together with the material distribution and the fiber angle. The same approach is extended to the penalization of SIMP and β parameters of threshold projection. This strategy enlarges the solution space and facilitates the discovery of previously unachievable local minima while eliminating the need for a heuristic selection of continuation methods. The Augmented Lagrangian method is used to deal with the local stress constraints. A mesh refinement scheme developed in the FEniCS project is proposed. Numerical examples are presented to illustrate the performance of the proposed method.