Skew-symmetric Nitsche's formulation in isogeometric analysis: Dirichlet and symmetry conditions, patch coupling and frictionless contact

TL;DR

This paper introduces a skew-symmetric Nitsche's formulation within isogeometric analysis to effectively handle boundary conditions, patch coupling, and contact problems, demonstrating stability and accuracy through various numerical tests.

Contribution

It presents a parameter-free, stable, and accurate skew-symmetric Nitsche's formulation for IGA applicable to multiple problem types, including contact and coupling scenarios.

Findings

Stable and accurate for a wide range of stabilization parameters

Effective in simulating contact problems with complex boundary conditions

Demonstrated good convergence and stability in numerical tests

Abstract

A simple skew-symmetric Nitsche's formulation is introduced into the framework of isogeometric analysis (IGA) to deal with various problems in small strain elasticity: essential boundary conditions, symmetry conditions for Kirchhoff plates, patch coupling in statics and in modal analysis as well as Signorini contact conditions. For linear boundary or interface conditions, the skew-symmetric formulation is parameter-free. For contact conditions, it remains stable and accurate for a wide range of the stabilization parameter. Several numerical tests are performed to illustrate its accuracy, stability and convergence performance. We investigate particularly the effects introduced by Nitsche's coupling, including the convergence performance and condition numbers in statics as well as the extra "outlier" frequencies and corresponding eigenmodes in structural dynamics. We present the Hertz test, the block test, and a 3D self-contact example showing that the skew-symmetric Nitsche's formulation is a suitable approach to simulate contact problems in IGA.