On the effect of the contact surface definition in the Cartesian grid finite element method

José Manuel Navarro-Jiménez,Juan José Ródenas,Francisco Javier Fuenmayor,Manuel Tur

doi:10.1186/s40323-018-0108-5

Abstract

The definition of the surface plays an important role in the solution of contact problems, as the evaluation of the contact force is based on the measure of the gap between the solids. In this work three different methods to define the surface are proposed for the solution of contact problems within the framework of the 3D Cartesian grid finite element method. A stabilized formulation is used to solve the contact problem and details of the kinematic description for each surface definition are provided. The three methods are compared solving some numerical tests involving frictionless contact with finite and small deformations.

Highlights

In recent years some alternatives to standard Finite Element methods have been developed under the category of immersed boundary methods [1,2,3], known as fictitious or embedded domain methods
The main differentiating features of Cartesian grid finite element method (cgFEM) with respect to other immersed boundary methods are that the cgFEM is able to consider the CAD geometry for the numerical integration and the use of a stabilized Lagrange multiplier method for the imposition of Dirichlet boundary conditions
This paper can be considered as an extension of [26], where we study the effect of the surface definition when solving frictionless contact problems with cgFEM

Summary

Introduction

In recent years some alternatives to standard Finite Element methods have been developed under the category of immersed boundary methods [1,2,3], known as fictitious or embedded domain methods. In addition to the previous approaches, linear facets and a combination of FE solution and NURBS surface, in this work we propose a new method in which the deformed configuration is defined as a NURBS surface, i.e., the control points of the original CAD surface are updated such that the new configuration fits the finite element displacement field of the contact surface.

Results

Conclusion