Optimal Design of Topology and Gradient Orthotropic Material

Abstract

The goal of this research is to optimize an object’s macroscopic topology and gradient material properties subject to multiple loading conditions. The gradient material is modeled as an orthotropic material where the elastic modulus in the x and y directions can change in addition to rotating the orthotropic material to align with the loading condition at each point. This orthotropic material is similar to a fiber-reinforced material where the number of fibers in the x and y-directions can change at each point as well as the overall rotation of the material at each point. 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 celluar materials. The mesostructures are an order of magnitude smaller than the macro structure which then allows small variations in strain and stress to be averaged out. The average (homogenized) properties of a group of these mesostructures can be customized by carefully designing the topology of the repeating unit cell used to make the mesostructure. In the past, gradient material optimization coupled to optimal fiber optimization has been used to design material properties within a single part. By combining topology optimization with gradient material optimization and fiber orientation optimization, the algorithm significantly decreases the objective, which is to minimize the strain energy of the object. Additive manufacturing techniques enable the fabrication of these designs by selectively placing reinforcing fibers or by printing different mesostructures in each region of the design. Finally, this work shows a comparison of simple topology optimization, topology optimization with isotropic gradient materials, and topology optimization with orthotropic gradient materials.