A meshfree b-spline finite element formulation for unilateral contact problems

The integrated, accurate and robust analysis of unilateral structural contact problems at all scales is a prerequisite for a comprehensive CAE process which accommodates the design of assemblies. In addition, such an integration must reduce any manual intervention to a bare minimum. The current reliance on legacy mesh-based finite element software for such analysis instead leads to excessive manual mesh construction and modification. Although the adoption of a meshfree formulation would seem to hold the answer, the current state-of-the-art in nodebased formulations suffers from a lack of stability and/or consistency for such applications. This investigation demonstrates that there exists a meshfree B-Spline formulation which is consistent, stable, and demonstrates accuracy comparable to that of mesh-based approaches for simple frictionless Hertzian problems in two dimensions. Together with the Solution Structure Method (SSM) of boundary condition enforcement, it is argued that this approach may provide a more robust finite element framework within existing CAE pipelines.