Defesa de Tese de Doutorado: Topological derivative-based topology optimization of structures into three spatial dimensions

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

Banca Examinadora:
Antônio André Novotny - Laboratório Nacional de Computação Científica - LNCC (presidente)
Marcio Arab Murad - Laboratório Nacional de Computação Científica - LNCC
Ivan Fabio Mota de Menezes - Pontifícia Universidade Católica do Rio de Janeiro - PUC-RJ
Hélio Emmendoerfer Junior - Pontifícia Universidade Católica do Paraná. - PUC-PR

Suplentes:
Gilson Antônio Giraldi - Laboratório Nacional de Computação Científica - LNCC
Eduardo Alberto Fancello - Universidade Federal de Santa Catarina - UFSC

Resumo:

The topological derivative method has been widely and succes sfully applied in many different fields over the last years and has proved to be of great relevance, especially in engineering problems. In this work, the topological derivative is applied for the topology optimization of structures into three spatial dimensions in the context of linear elasticity. More precisely, we deal with the topology optimization of structures subject to external loads and self-weight loading, as well as the design of microstructures which optimize desired properties in the macro scale. The proposed topology optimization problem is solved with the help of a topology optimization algorithm based on the topological derivative concept together with a level-set domain representation method. The algorithm is implemented in the open-source program FreeFEM, originally designed for solving partial differential equations by the finite element method. FreeFEM allows us for dealing with problems into three spatial dimensions with almost the same simplicity of two-dimensi onal applications in terms of computational implementation, a remarkable and crucial feature for this work. In addition, the parallel version of FreeFEM based on the domain decomposition method and PETSc for the linear algebra backend is also widely explored. In this sense, a comprehensive discussion of the compliance minimization problem into three spatial dimension is provided together with the complete parallel FreeFEM implementation of the proposed algorithm. Moreover, the proposed parallel FreeFEM implementation is also adapted to the challenging problem of multi-material design of three-dimensional microstructures. Finally, in order to show the effectiveness of the proposed approach, several numerical experiments are performed.