Análise de sensibilidade topológica do problema semi-acoplado termo-mecânico

• Autor(a) principal: Rodrigues, José Edmundo Esparta
• Data de Publicação: 2013
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/139
• topic: Equações diferenciais parciais; Differential equations, Partial.; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE::EQUACOES DIFERENCIAIS PARCIAIS

The topological derivative measures the sensitivity of a given shape functional when an infinitesimal singular domain perturbation is introduced in an arbitrary point of the domain of the problem. According to the specialized literature, the topological derivative has been fully developed for a wide range of one single physical phenomenon modeled by partial differential equation. The purpose of the present work is to carry out the topological sensitivity analysis in a semi-coupled model. In particular, is considered the classical mechanical problem of elasticity with initial thermal stress. The linear elasticity problem is modeled by the Navier equation and it's coupled with the steady-state heat conduction problem (modeled by the Laplace equation). The mechanical coupling term comes out from the thermal stress induced by the temperature field. Since this term is non-local, is necessary to introduce a non-standard adjoint state, which allows to obtain a closed form for the topological derivative. Finally, is provided a full mathematical justification for the derived formulas and develop precise estimates for the remainders of the topological asymptotic expansion.