Development of a Topology Optimization Algorithm with Additive Manufacturing Constraints
Topology Optimization (TO) is a systematic method widely applied to structural optimization. TO combines optimization algorithms with finite element method algorithms, in order to provide an optimal material distribution inside a design domain (Ω), aiming to attend a specified objective function and to satisfy the constraints on the optimization problem. Additive Manufacturing (AM) is a generalized term utilized to designate the manufacturing techniques, that employ the principle of fabrication by adding material layer by layer to obtain the final geometry of a product. This principle is powerful for manufacturing geometries of higher complexity when compared to traditional manufacturing techniques, such as machining, forging and others. TO is a fully developed design tool and is already utilized in mechanical, automotive and aerospace industry. With the present state of development of AM techniques, and its capability of creating complex geometries, AM can complement TO, in the sense of potentially being the most efficient technique to manufacture the geometries obtained by TO. Although AM techniques have high capacity of producing TO geometries, without compromising to much its optimality, these techniques still have inherent manufacturing constraints. Feasible AM geometries have associated requirements such as minimum member size, minimum overhang angle and minimum hole size, for instance. The aim of this work is to develop a structural optimization algorithm, including in the formulation of the TO problem a based-projection filter which implicitly applies a manufacturing constraint imposed by the AM process known as FDM (Fused Deposition Modelling), whose technique possess a critical overhang angle at which the structure does not self-supports. In this case, a projection function and variable mappings are defined to impose the maximum overhang constraint. Specifically, it aims to avoid or eliminate the support material utilized in the FDM process and, consequently, reducing the fabrication costs of the process. Some results are presented to demonstrate the potential of the proposed TO algorithm.