A priori error for unilateral contact problems with Lagrange multiplier and IsoGeometric Analysis

TL;DR

This paper develops an isogeometric analysis method for unilateral contact problems, providing theoretical error estimates and demonstrating high accuracy through numerical experiments.

Contribution

It introduces an inf-sup stable mixed formulation with optimal a priori error estimates for unilateral contact problems using NURBS and B-Splines.

Findings

Proves inf-sup stability of the method

Derives optimal a priori error estimates

Numerical examples confirm high accuracy

Abstract

In this paper, we consider unilateral contact problem without friction between a rigid body and deformable one in the framework of isogeometric analysis. We present the theoretical analysis of the mixed problem using an active-set strategy and for a primal space of NURBS of degree $p$ and $p-2$ for a dual space of B-Spline. A inf-sup stability is proved to ensure a good property of the method. An optimal a priori error estimate is demonstrated without assumption on the unknown contact set. Several numerical examples in two- and three-dimensional and in small and large deformation demonstrate the accuracy of the proposed method.