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.

等几何分析的出现使几何设计和机械建模阶段之间的直接联系取得了进展。等几何边界元法 (IGABEM) 的 3D 方法在这种情况下脱颖而出，因为它只需要来自边界的信息以及计算机辅助设计 (CAD) 模型。因此，3D IGABEM 最能满足等几何范式，因为 CAD 软件包提供的几何表示可以直接由 BEM 解释为网格。然而，在 3D IGABEM 中，缺乏关于正确机械场表示的收敛和精确网格细化的信息。尽管 CAD 中的 IGA 模型在各种问题中几何上都是精确的，但它们通常不足以精确地表示机械场。本研究为弹性静力学中的 3D IGABEM 公式提出了网格自适应策略，该策略提供了准确的几何表示和机械场描述，并有助于 BEM 和 CAD 方案的完全耦合。所提出的策略利用基于超奇异残差的误差，它在边界处提供逐点误差估计。然后，可以评估基于位移/牵引力或应变的误差。自适应方案利用局部和全局条件的网格优化标准。细化策略应用了结插入过程，这使得自适应过程变得健壮且易于访问，因为它不需要与 CAD 系统进行迭代通信。与均匀和非均匀物体的全局均匀细化相比，所提出的基于应变误差的自适应策略提供了良好的收敛速度。此外，网格自适应策略可以应用于纤维增强的 IGABEM 公式，为此提出了不同的误差估计器，以考虑耦合 1DBEM/BEM 和 FEM/BEM。基于应变的误差估计器识别所需的网格细化，以最小化围绕纤维不连续区域的振荡粘附力。五个应用证明了所提出的自适应方案的准确性，其中全局同质细化是参考。提出了一个不同的误差估计器来解释耦合 1DBEM/BEM 和 FEM/BEM。基于应变的误差估计器识别所需的网格细化，以最小化围绕纤维不连续区域的振荡粘附力。五个应用证明了所提出的自适应方案的准确性，其中全局同质细化是参考。提出了一个不同的误差估计器来解释耦合 1DBEM/BEM 和 FEM/BEM。基于应变的误差估计器识别所需的网格细化，以最小化围绕纤维不连续区域的振荡粘附力。五个应用证明了所提出的自适应方案的准确性，其中全局同质细化是参考。