Isogeometric boundary element methods and patch tests for linear elastic problems: Formulation, numerical integration, and applications

An Isogeometric Boundary Element Method for solving three-dimensional boundary-value problems of classical linear elasticity theory is proposed. The method is developed as a generalization of the author’s earlier work on Laplace’s equation to Navier’s equations. As a result the proposed method features (i) proper basis functions for approximating Dirichlet and Neumann data, (ii) high-order collocation schemes for weakly singular, singular, and hyper-singular integral operators, (iii) state-of-the-art numerical integration schemes capable of handling geometries with disparate dimensions, (iv) well-conditioned linear algebraic systems, with the condition number independent of the mesh size. Boundary Element Patch Tests, as extensions of concepts widely used for finite element methods, are also introduced. It is shown how these tests can be used to assess the veracity of boundary element formulations and numerical integration schemes, implementations, and geometric precision of Computer Aided Design models. The method is applied to two challenging case studies, representative of industrial applications.