Three-dimensional varying-order NURBS discretization method for enhanced IGA of large deformation frictional contact problems

Abstract: We introduce a varying-order (VO) NURBS discretization method to enhance the performance of the IGA technique for three-dimensional large deformation frictional contact problems. Based on the promising results obtained with the previous work on the 2D isogeometric contact analysis, the present work extends the capability of the method for tri-variate NURBS discretization. The proposed method enables independent employment of the user-defined higher-order NURBS for the discretization of the contact surface and the minimum order of NURBS for the remaining solid volume. Such a method provides the possibility to refine a NURBS solid with the controllable order elevation-based approach while preserving its volume parametrization at a fixed mesh. The advantages of the method are twofold. First, the higher-order NURBS for the evaluation of contact integral enhances the accuracy of the contact responses at a fixed mesh, hence fully exploiting the advantage of higher-order NURBS specifically for contact computations. Second, the minimum order of NURBS for the computations in the remaining volume considerably reduces the computational cost associated with the uniform order NURBS-based isogeometric contact analyses. The capabilities of the proposed method are demonstrated using various contact problems with or without considering friction between deformable solids. The results with the standard uniform order of NURBS-based discretization are also included to provide a comparative assessment. We show that to attain similar accuracy results, the VO NURBS discretization uses a much coarser mesh resolution than the standard NURBS-based discretization, leading to a major gain in computational efficiency for isogeometric contact analysis. The convergence study demonstrates the consistent performance of the method for efficient IGA of three-dimensional (3D) frictional contact problems.