Optimizing Topology and Gradient Orthotropic Material Properties Under Multiple Loads

Abstract

The goal of this research is to optimize an object's macroscopic topology and localized gradient material properties (GMPs) subject to multiple loading conditions simultaneously. The gradient material of each macroscopic cell is modeled as an orthotropic material where the elastic moduli in two local orthogonal directions we call x and y can change. Furthermore, the direction of the local coordinate system can be rotated to align with the loading conditions on each cell. This orthotropic material is similar to a fiber-reinforced material where the number of fibers in the local x and y-directions can change for each cell, and the directions can as well be rotated. Repeating cellular unit cells, which form a mesostructure, can also achieve these customized orthotropic material properties. Homogenization theory allows calculating the macroscopic averaged bulk properties of these cellular materials. By combining topology optimization with gradient material optimization and fiber orientation optimization, the proposed algorithm significantly decreases the objective, which is to minimize the strain energy of the object subject to multiple loading conditions. Additive manufacturing (AM) techniques enable the fabrication of these designs by selectively placing reinforcing fibers or by printing different mesostructures in each region of the design. This work shows a comparison of simple topology optimization, topology optimization with isotropic gradient materials, and topology optimization with orthotropic gradient materials. Finally, a trade-off experiment shows how different optimization parameters, which affect the range of gradient materials used in the design, have an impact on the final objective value of the design. The algorithm presented in this paper offers new insight into how to best take advantage of new AM capabilities to print objects with gradient customizable material properties.