A Topology Optimization Approach Using Explicit Stress Tensor Analysis and NURBS Curves

Abstract

Topology optimization (TO) aims at defining the ideal layout of structures in order to minimize the use of material within a given design space. Such goal is pursued by applying an optimization strategy, where the possible solutions are the feasible geometries, and the functional to minimize is the mass structure. Obtaining high performance in terms of mass reduction depends on many factors. The most well-known and widespread topological optimization approaches can be divided into two main categories: microscopic and macroscopic. In microscopic approaches, such as SIMP and BESO, the feasible domain available for the solid material is divided in a finite number of discrete elements (FEM). The density of the material of each element represents the design variables, which may vary with continuity in SIMP method (density approach) or being binary in BESO Method (evolutionary approach). In macroscopic approaches, such as Level Set, the parameters describing the evolution of the boundaries of the solid domain of the structure are the design variables. Again, a discretization of the design domain is required, even if the implementation of this strategy in the optimization algorithm doesn’t intrinsically need the decomposition in a finite number of elements.