Dinâmica em meios setorialmente homogêneos com o método dos elementos de contorno usando as técnicas de interpolação direta e de superposição de domínios - Barbosa, Joao Paulo (2019)
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.