Doutorado em Engenharia Mecânica

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Navegando Doutorado em Engenharia Mecânica por Assunto "Boundary element method"

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    Dinâmica em meios setorialmente homogêneos com o método dos elementos de contorno usando as técnicas de interpolação direta e de superposição de domínios
    (Universidade Federal do Espírito Santo, 2019-12-12) Barbosa, Joao Paulo; Neto, Carlos Friedrich Loeffler; https://orcid.org/0000-0002-5754-6368; http://lattes.cnpq.br/3102733972897061; https://orcid.org/; http://lattes.cnpq.br/; Santiago, Jose Antonio Fontes; https://orcid.org/0000-0003-3089-954X; http://lattes.cnpq.br/6891803842511248; Mansur, Webe Joao; https://orcid.org/0000-0001-6033-9653; http://lattes.cnpq.br/9499429606822923; Telles, Jose Claudio de Faria; https://orcid.org/; http://lattes.cnpq.br/9055052467152337; Lara, Luciano de Oliveira Castro; https://orcid.org/0000000313292957; http://lattes.cnpq.br/1675675424615229; Bulcao, Andre; Cezario, Flavio
    The Domain Superposition Technique (DST) is a new alternative to the Boundary Element Method (BEM) for solving piecewise homogeneous problems where the complete domain is divided into a surrounding homogeneous domain and other complementary subdomains with different constitutive properties. In this work, the DST is coupled to the direct interpolation technique with radial basis functions (DIBEM) to solve problems governed by the Helmholtz equation, by properly transforming the domain integral, relative to the inertia of the system, into a boundary integral. Thus, we generate a dynamic model capable of calculating the natural frequency spectrum in piecewise homogeneous domains with non-regular boundaries and internal inclusions, for both two-dimensional and three-dimensional cases. In the treatment of two-dimensional problems, linear isoparametric elements are used, while in three-dimensional cases the discretization is done by flat triangular isoparametric elements, of linear variation, with multiple nodes at the edges. To assess the numerical consistency of the more general model, simpler problems such as the three-dimensional homogeneous problems governed by the Laplace and Helmholtz equations were previously examined. Piecewise homogeneous three dimensional cases governed by the Laplace Equation were solved as well, in which the DST was also applied, including examples with geometric irregularities in the contour. The methodology proposed here provides a new model based on a BEM formulation simpler and faster than the previous related formulations, with satisfactory accuracy and convergence ensured with the mesh refinement. The work is also justified considering the use of the well-known advantages of BEM, such as its greater flexibility in mesh redefinition, its natural extension to open domain cases and suitability to fracture and contact problems, provided that the computational cost in these applications is not prohibitive.
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    O método dos elementos de contorno com interpolação direta aplicado aos problemas escalares de onda em meios homogêneos
    (Universidade Federal do Espírito Santo, 2024-12-16) Santos, Gyslane Aparecida Romano dos; Lara, Luciano de Oliveira Castro ; https://orcid.org/0000-0003-1329-2957; http://lattes.cnpq.br/1675675424615229; Loeffler Neto, Carlos Friedrich; https://orcid.org/0000-0002-5754-6368; http://lattes.cnpq.br/3102733972897061; https://orcid.org/0009-0008-0138-3556; http://lattes.cnpq.br/0314997680090929; Bulcão, André ; https://orcid.org/0000-0002-9871-9683; http://lattes.cnpq.br/2273897370773348; Chacaltana, Julio Tomás Aquije ; https://orcid.org/0000-0003-2488-6232; http://lattes.cnpq.br/9108224414966705; Campos, Lucas Silveira ; https://orcid.org/; http://lattes.cnpq.br/0275751616450131; Mansur, Webe João ; https://orcid.org/0000-0001-6033-9653; http://lattes.cnpq.br/9499429606822923
    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