Varying-order NURBS discretization: An accurate and efficient method for isogeometric analysis of large deformation contact problems

Abstract

A novel varying-order based NURBS discretization method is proposed to enhance the performance of isogeometric analysis (IGA) technique within the framework of computational contact mechanics. The method makes use of higher-order NURBS for the contact integral evaluations. The minimum orders of NURBS capable of representing the complex geometries exactly are employed for the bulk computations. The proposed methodology provides a possibility to refine the geometry through controllable order elevation for isogeometric analysis. To achieve this, a higher-order NURBS layer is used as the contact boundary layer of the bodies. The NURBS layer is constructed using different surface refinement strategies such that it is accompanied by a large number of additional degrees of freedom and matches with the bulk parameterization.The capabilities and benefits of the proposed method are demonstrated using the two-dimensional frictionless and frictional contact problems, considering both small and large deformations. The results with the existing fixed-order based NURBS discretizations are used for comparisons. Numerical examples show that with the proposed method, a much higher accuracy can be achieved even with a coarse mesh as compared to the existing NURBS discretization approach. It exhibits a major gain in the numerical efficiency without the loss of stability, robustness, and the intrinsic features of NURBS-based IGA technique for a similar accuracy level. The simplicity of the proposed method lends itself to be conveniently embedded in an existing isogeometric contact code after only a few minor modifications.