Inverse design of three-dimensional fiber reinforced composites with spatially-varying fiber size and orientation using multiscale topology optimization

Abstract

This paper presents three-dimensional topology optimization for the inverse design of unidirectional fiber reinforced composite (FRC) structures. Specifically, a multiscale topology optimization scheme is proposed for the co-design of the composite macrostructure, spatially-varying fiber size and fiber orientation. A FRC with spatially tailored fiber distribution may perform better than a conventional FRC with a fixed fiber structure. A composite macrostructure is designed using the well-established three-field density approach based on Helmholtz filtering and regularized Heaviside function. For the design of spatially-varying fiber size and orientation, a homogenization-based multiscale approach using an orientation tensor variable is proposed. As a post-processing procedure, optimized fiber microstructures are restored at a macroscopic scale. For this, a projection based de-homogenization scheme is proposed for the restoration of a circular fiber structure. The effectiveness of the proposed design scheme is validated through three design examples for compliance minimization and compliant mechanism problems.