Otimização topológica de aerofólios utilizando algoritmo evolucionário bidirecional

Abstract

In this work it is presented the topological optimization of an airfoil considering compliance and stress minimizations subjected to a volume constraint using bidirectional evolutionary structural optimization (BESO) method for a two-dimensional case. Initially, the compliance formulation is developed defining the minimization and constraint functions. Also the sensitivity filtering scheme is shown. Then the stress minimization is presented based on the modified P-norm stress function, which provides values below the maximum stress on the structure. For this, the constitutive and strain-displacement matrices are determined, as well as the shape functions for the four-node bilinear element. In the sequence, the methods are verified compared to a literature example and the filter radius is investigated. Finally, some simulations are performed on a NACA 2412 airfoil for different angles of attack and multiple loads. The results are discussed analyzing the main effects for each method on the optimized topologies. Varying the filter radius and comparing different mesh refinements, the compliance minimization showed more stable and similar topologies than the stress minimization.