Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Convergence studies in elasticity with an independent basis isogeometric boundary element formulation
Submission Author:
Sérgio Cordeiro , SP
Co-Authors:
Sérgio Cordeiro, Francisco Alex Monteiro, Guilherme Henrique Teixeira
Presenter: Sérgio Cordeiro
doi://10.26678/ABCM.COBEM2023.COB2023-1518
Abstract
This work presents an independent basis isogeometric boundary element method (IGABEM). The geometry description is based on Non-Uniform Rational B-splines (NURBS) and independent B-splines basis are used for the unknown boundary fields. Lagrange polynomial basis are also applied for the boundary fields for comparative purposes. The boundary conditions are exactly considered and its contribution computed directly in the right-hand side vector of the linear system. This approach results a single-matrix formulation, improving storage requirements. The independence between geometry and boundary fields allows refinement strategies without changes in the geometry. Both knot insertion and k-refinement are applied for B-spline basis while p-refinement is applied for Lagrange polynomial basis. Convergence studied in terms of the L-2 norm of boundary fields are carried out in benchmark problems with available analytical solution. The results pointed-out that p-refined with equally spaced Lagrange polynomials suffers with the Runge Effect and diverges quickly. On the other hand, the p-refinement has convergence rates p+1 for b-splines basis of order p. As expected, the k- Refinement performed even better, with hypergeometric convergence. An open spanner problem is also presented for illustrative purposes.
Keywords
Isogeometric Analysis, Boundary Element Method, Independent basis, convergence studies
