O método dos elementos de contorno com interpolação direta aplicado aos problemas escalares de onda em meios homogêneos

• Ano de defesa: 2024
• Autor(a) principal: Santos, Gyslane Aparecida Romano dos
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Espírito Santo; BR; Doutorado em Engenharia Mecânica; Centro Tecnológico; UFES; Programa de Pós-Graduação em Engenharia Mecânica
• Palavras-chave em Português: Método dos elementos de contorno; Problemas de propagação de onda; Técnica de interpolação direta; Funções de base radial; Boundary element method; Scalar wave propagation problems; Direct interpolation technique; Radial basis functions; Engenharia Mecânica
• Link de acesso: http://repositorio.ufes.br/handle/10/18317

The search for a consistent and accurate method for transforming domain integrals composed of non-self-adjoint operators into contour integrals, strictly following the philosophy of the Boundary Element Method, is still a challenge to be overcome. The Direct Interpolation of the Contour Element Method (DIBEM) technique is among the most recent proposals to achieve this goal. After being successful in solving scalar problems governed by the Poisson, Helmholtz and Advection Diffusion equations, this work presents the results of the DIBEM procedure in approaching acoustic wave propagation problems in homogeneous media. The main objective is to achieve greater stability of the discrete model, particularly examining the numerical characteristics of the mass matrix or acoustic inertia, which is generated approximately through a sequence of radial basis functions. Some of the best-known full support radial functions were tested, several matrix conditioning standards were verified, the degrees of positivity of the matrix related to the modal content were evaluated and the minimum time steps achieved with the refinement of the mesh were investigated. contouring and insertion of interpolating internal points. The time advance scheme used was the Houbolt algorithm, whose fictitious damping eliminates spurious modal contents, related to high frequencies, producing greater stability and accuracy. Several typical wave propagation problems in bars and membranes were solved, using linear boundary elements with DIBEM to compare with the analytical solutions of displacement and stresses in several cases