Optimizing Topology and Fiber Orientations With Minimum Length Scale Control in Laminated Composites

Abstract

Abstract Discrete material optimization (DMO) has proven to be an effective framework for optimizing the orientation of orthotropic laminate composite panels across a structural design domain. The typical design problem is one of maximizing stiffness by assigning a fiber orientation to each subdomain, where the orientation must be selected from a set of discrete magnitudes (e.g., 0 deg, ±45 deg, 90 deg). The DMO approach converts this discrete problem into a continuous formulation where a design variable is introduced for each candidate orientation. Local constraints and penalization are then used to ensure that each subdomain is assigned a single orientation in the final solution. The subdomain over which orientation is constant is most simply defined as a finite element, ultimately leading to complex orientation layouts that may be difficult to manufacture. Recent literature has introduced threshold projections commonly used in density-based topology optimization into the DMO approach in order to influence the manufacturability of solutions. This work takes this idea one step further and utilizes the Heaviside projection method within DMO to provide formal control over the minimum length scale of structural features, holes, and patches of uniform orientation. The proposed approach is demonstrated on benchmark maximum stiffness design problems, and numerical results are near discrete with strict length scale control, providing a direct avenue to controlling the complexity of orientation layouts. This ultimately suggests that projection-based methods can play an important role in controlling the manufacturability of optimized material orientations.