Study of topological optimization techniques applied to the design of aeronautical structures.

Study of topological optimization techniques applied to the design of aeronautical structures. This thesis deals with the study of di˙erent topology optimization techniques in which the aim of the optimization procedure is to maximize the sti˙ness of a typical structural component subject to a given reduction of volume. Specifically, three di˙erent topology optimization techniques are analysed and com-pared. The techniques that are treated in this dissertation are: (1) SIMP approach,(2) Topological derivative methodology, and (3) variational approach, which has been developed by the COMP-DES-MAT research group. These three techniques are compared in terms of computational cost, mass distribution and compliance function. The comparison is carried out in a set of benchmarking tests. The proposed optimization methodology described in this thesis was deeply analysed with a set of numerical experiments. In order to simulate those examples, an in-house code within MATLAB framework was implemented, in which two- and three-dimensional problems could be executed using triangular, quadrilateral, tetrahedral or hexahedral elements. Moreover, a set of loads and boundary conditions could be applied, such as concentrated, distributed or volumetric loads. Nevertheless, the code is limited to linear elements. Finally, the potential of the variational method is analysed optimizing the internal structure of a rib. The aerodynamics loads have been obtained from the open source program Xfoil. The optimization of the structure is carried out in a 2D wing profile by the use of quadrilateral elements