Topology Optimization of Structures with High Spatial Definition Considering Minimum Weight and Stress Constraints

Resumen

The first formulation of Topology Optimization was proposed in 1988. Since then, many contributions have been presented with the purpose of improving its efficiency and extending its applicability. In this thesis, a topology optimization algorithm that allows to obtain the structure of minimum weight that is able to support different loads is developed. For this purpose, the requirement that stresses have to be lower than a maximum value has been considered in its development. Although the structural topology optimization problem with stress constraints have been previously formulated with several different approaches, a Damage Constraint approach is developed in this thesis to incorporate them in a different way. The main objective of this modification is to reduce the CPU time required in the solution of the topology optimization problem. This reduction will allow to solve problems with a higher number of design variables what enables the attainment of solutions with high spatial definition. Moreover, two different approaches are used to define the material distribution in the domain: uniform density per element formulation and material density distribution by means of isogeometric interpolation. In the first approach the Finite Element Method (FEM) is used to solve the structural analysis and the relative density in each element of the mesh is chosen as design variable, while the second one uses the Isogeometric Analysis (IGA) for solving the structural analysis and the values of the relative density at a certain number of control points are used as design variables. On the other hand, the optimization is addressed by using Sequential Linear Programming, that requires a first order sensitivity analysis. All the sensitivities are obtained through analytic derivatives by using both, direct differentiation and the adjoint variable method. Finally, some application examples are solved by means of both methods (FEM and IGA) in the two-dimensional and three-dimensional space.