Análise de sensibilidade topológica de segunda ordem / Second order topological sensitivity analysis
AUTOR(ES)
Jairo Rocha de Faria
DATA DE PUBLICAÇÃO
2008
RESUMO
The topological derivative provides the sensitivity of a given shape functional with respect to an infinitesimal non-smooth domain pertubation (insertion of hole or inclusion, for instance). Classically, this derivative comes from the second term of the topological asymptotic expansion, dealing only with inifinitesimal pertubations. However, for pratical applications, we need to insert pertubations of finite sizes.Therefore, we consider other terms in the expansion, leading to the concept of higher-order topological derivatives. In a particular, we observe that the topological-shape sensitivity method can be naturally extended to calculate these new terms, resulting in a systematic methodology to obtain higher-order topological derivatives. In order to present these ideas, initially we apply this technique in some problems with exact solution, where the topological asymptotic expansion is obtained until third order. Later, we calculate first as well as second order topological derivative for the total potential energy associated to the Laplace equation in two-dimensional domain pertubed with the insertion of a hole, considering homogeneous Neumann or Dirichlet boundary conditions, or an inclusion with thermal conductivity coefficient value different from the bulk material. With these results, we present some numerical experiments showing the influence of the second order topological derivative in the topological asymptotic expansion, which has two main features:it allows us to deal with pertubations of finite sizes and provides a better descent direction in optimization and reconstruction algorithms.
ASSUNTO(S)
equacoes diferenciais parciais derivada topológica topological rerivative derivada topológica de segunda ordem second order topological derivative análise assintótica análise de sensibilidade topológica topological sensitivity analysis asymptotic analysis
ACESSO AO ARTIGO
http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=141Documentos Relacionados
- Análise de Sensibilidade Topológica
- Análise de sensibilidade topológica em modelos constitutivos multi-escalas
- Análise de segunda ordem global em edifícios com estrutura de concreto armado
- Estrategias de segunda ordem para problemas de complementaridade
- Análise dos efeitos de segunda ordem em pilares solicitados a flexão oblíqua composta.