Two-scale concurrent optimization of composites with elliptical inclusions under microstress constraints within the FE2 framework

Abstract

In order to avoid the adverse effects of structural damage caused by stress concentration, the optimization problem considering stress constraints is very important in structural design. This paper aims at introducing microstress constraints within a multilevel finite element (FE2) analysis framework to perform the two-scale concurrent optimization and reduce the stress concentration while exhibiting better overall stiffness properties for composites with elliptical inclusions. In order to do that, at the macroscale, relying on the solid isotropic material with penalization (SIMP), a density-based optimization algorithm is raised for a maximum stiffness design and free material distribution optimization under a volume constraint, these displacement solutions and material distributions at the macroscopic structural scale provide kinematic constraints for microscale optimization. At the microscale, the parameterized composite microstructure (inclusion orientation and aspect ratio) is optimized under the principal strain direction constraints of the macroscale element’s Gauss integration point. The optimized microstructure in turn updates the macroscopic effective stress directly from the volume average of the microscopic stress field. The clustering strategy is used in order to improve the computation efficiency of the optimization. The novelty of the work lies in the use of microstress constraints to solve the concurrent optimization problems of two-phase composites within the FE2 framework. The effectiveness of the proposed concurrent optimization approach is validated through three numerical examples.