| Título: | An independent basis isogeometric boundary element formulation |
| Autor: | Guilherme Henrique Teixeira |
| Programa: | Engenharia de Infraestrutura Aeronáutica |
| Área de Concentração: | Infraestrutura Aeroportuária |
| Orientador : | Sérgio Gustavo Ferreira Cordeiro |
| Coorientador : | Francisco Alex Correia Monteiro |
| Ano de Publicação : | 2023 |
| Curso : | Mestrado Acadêmico |
| Assuntos : | Métodos de elementos de contornos |
| t | Projeto auxiliado por computador |
| t | Desenho geométrico |
| t | Equações integrais |
| t | Condições de contorno |
| t | Projetos |
| t | Geometria |
| t | Engenharia estrutural |
| Resumo : | The integration between Computer-Aided Design (CAD) models and boundary element analysis can be achieved with isogeometric formulations and has great potential for reducing the engineers efforts during the design phase in several projects. In this work, an Isogeometric Boundary Element Method (BEM) formulation is presented using independent basis for geometry description and unknown boundary fields approximation. Three types of boundary value problems are investigated, which are governed by Laplace, Helmholtz and Navier-equations. B-splines are considered as basis for the boundary fields and Lagrange polynomials, with equally spaced roots, are used in order to compare the results. The geometry description is based on Non-Uniform Rational B-splines (NURBS) obtained directly from CAD. The independence between geometry and boundary fields allows refinement strategies without requiring changes in the CAD geometric model. The exact boundary conditions are accounted into the boundary integral equations and their contributions are computed directly in the right-hand side vector. This approach leads to a single-matrix formulation, improving the memory storage requirements of the method. Continuity between prescribed and non-prescribed boundary fields is ensured by an auxiliary function when necessary. P-refinement is applied for the Lagrange polynomial basis while both knot insertion and k-refinement are employed for the B-spline basis. Convergence analysis in terms of the L-2 norm of the boundary fields errors are carried out for benchmark problems with known analytical solutions. The results indicate that p-refinement with Lagrange polynomial is susceptible to the Runge's phenomenon. On the other hand, the knot insertion produces convergence rates p+1 for B-splines basis of order p. K-refinement performed even better resulting in hypergeometric convergence. Applications such as nuclear reactor heat transfer analysis, airplane acoustic radiation analysis and structural analysis of an open spanner are presented for illustrative purposes. |
| Data de Defesa : | 20/07/2023 |
| Texto na íntegra : | [Visualizar] |