One step forward towards the full integration of BEM and CAD software: An effective adaptive approach

Abstract

The advent of Isogeometric analysis enabled advances towards the straightforward connection between geometric design and mechanical modelling phases. 3D approaches of the Isogeometric Boundary Element Method (IGABEM) stand out in this context, because it requires information only from the boundary as well as the Computer-Aided Design (CAD) models. Thus, the 3D IGABEM best fulfils the isogeometric paradigm, since the geometric representation provided by CAD packages can be interpreted directly by BEM as mesh. However, there is a lack of information regarding convergence and accurate mesh refinement for the proper mechanical fields representation in the 3D IGABEM. Although the IGA models from CAD are geometrically exact in various problems, they usually are not refined enough for the accurate mechanical fields representation. This study proposes mesh adaptivity strategies for the 3D IGABEM formulation in elastostatics, which provide accurate geometric representation and mechanical fields description and contribute towards the full coupling of BEM and CAD schemes. The proposed strategy utilises the error based upon the hypersingular residuals, which provides point-wise error estimates at the boundary. Then, errors based on displacements/tractions or strains can be assessed. The adaptive scheme utilises mesh optimality criteria for both local and global conditions. The refinement strategy applies the knot insertion process, which makes the adaptivity procedure robust and accessible since it does not require iterative communication with the CAD system. The proposed adaptive strategy based on strains error provides good convergence rates in comparison to globally uniform refinement for homogeneous and nonhomogeneous bodies. Additionally, the mesh adaptivity strategy can be applied for fibre-reinforced IGABEM formulations, for which a different error estimator is proposed accounting for the coupling 1DBEM/BEM and FEM/BEM. The strain-based error estimator identifies the required mesh refinement for minimising the oscillating adherence forces surrounding the fibre discontinuity regions. Five applications demonstrate the accuracy of the proposed adaptive schemes, in which the globally homogeneous refinement is a reference.