Exame de Qualificação: Topological Derivative-Based Topology Optimization of Structures Into Three Spatial Dimensions

Orientadores:
Antônio André Novotny - Laboratório Nacional de Computação Científica - LNCC

Banca Examinadora:
Pablo Javier Blanco - Laboratório Nacional de Computação Científica - LNCC (presidente)
Marcio Arab Murad - Laboratório Nacional de Computação Científica - LNCC
Ivan Menezes - Pontifícia Universidade Católica do Rio de Janeiro - PUC/RJ

Suplentes:
Marcio Rentes Borges - Laboratório Nacional de Computação Científica - LNCC

Resumo:

The concept of the topological derivative has been widely and successfully used on a variety of applications over the last years and proved to be of great relevance specially in engineering problems. In this work, the topological derivative is applied in the context of topology optimization of structures in two and three spatial dimensions subject to both external and self-weight loading. The proposed topology optimization problem is solved with the aid of a topology optimization algorithm based on the topological derivative method together with a level-set domain representation. The algorithm is implemented in the open source program FreeFEM, originally designed for solving partial differential equations by the finite element method. Here, one of the main features of FreeFEM is widely explored, which is performing the conversion of implementations written for two-dimensional problems into three with few adjustments to the original one. In this sense, a rich discussion of the compliance minimization problem in two spatial dimensions is provided together with the FreeFEM implementation of the proposed algorithm. From this starting point, a non-trivial extension of the compliance minimization problem of structures to three spatial dimensions subject to external loads and also to self-weight loading are performed. Finally, in order to show the effectiveness of the proposed approach, several numerical experiments are performed.