Assessment of various isogeometric contact surface refinement strategies

Since its inception, isogeometric analysis (IGA) has shown significant advantages over Lagrange polynomials-based finite element analysis (FEA), especially for contact problems. IGA often uses C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<^>\text {1}$$\end{document}-continuous non-uniform rational B-splines (NURBS) as basis functions, providing a smooth description of kinematic variables across the contact interface. This leads to increased accuracy and stability in the numerical solutions. However, from the existing literature on isogeometric contact analysis, it is not yet clear what interpolation order and continuity of NURBS one should employ to accurately capture the distribution of contact forces across the contact interface. The present work aims to fill this gap and provides a comparative assessment of different NURBS-based standard (conventional) refinement strategies for contact problems within the IGA framework. A recently proposed refinement strategy, known as the varying-order (VO) based NURBS discretization, has demonstrated its capability to refine geometry through the implementation of order elevation in a controlled manner. However, a detailed investigation that directly compares the VO based NURBS discretization with the standard NURBS discretization has not yet been carried out. Therefore, a thorough study of the VO based discretization strategy is also conducted, evaluating its effectiveness in comparison with the standard discretization strategy for contact problems. For this, a few examples on contact problems are solved using an in-house MATLAB (R) code. The solution to these examples shows that quadratic order standard NURBS discretization is sufficient to achieve the desired level of solution accuracy just by increasing the mesh size. It is further demonstrated that VO based discretization can achieve much higher accuracy than standard discretization, even with a coarse mesh, by generating additional degrees of freedom in the contact boundary layer. In addition, VO based discretization makes considerable savings in analysis time to achieve the same accuracy level as standard discretization.