Contact Modelling in Isogeometric Analysis: Application to Sheet Metal Forming Processes

Rui P.R Cardoso,O.B Adetoro,D. Adan

doi:10.1088/1742-6596/734/3/032123

Abstract

Isogeometric Analysis (IGA) has been growing in popularity in the past few years essentially due to the extra flexibility it introduces with the use of higher degrees in the basis functions leading to higher convergence rates. IGA also offers the capability of easily reproducing discontinuous displacement and/or strain fields by just manipulating the multiplicity of the knot parametric coordinates. Another advantage of IGA is that it uses the Non-Uniform Rational B-Splines (NURBS) basis functions, that are very common in CAD solid modelling, and consequently it makes easier the transition from CAD models to numerical analysis. In this work it is explored the contact analysis in IGA for both implicit and explicit time integration schemes. Special focus will be given on contact search and contact detection techniques under NURBS patches for both the rigid tools and the deformed sheet blank.

Highlights

The constant drive for change in computational methods has created an increased demand for new computational tools as are the cases of meshless methods and, more recently, Isogeometric Analysis (IGA) based on Non-Uniform Rational B-Splines (NURBS)
Non-Uniform Rational B-Splines (NURBS) and IsoGeometric Analysis (IGA) Detailed overview of B-Spline curves, B-Splines surfaces and NURBS can be found in Piegl and Tiller [2] and Cottrell et al [3]
An open knot vector is a set of non-negative parametric coordinates which are repeated p + 1 times at the beginning and at the end of the vector (p is the order of the polynomial basis functions)

Summary

Introduction

The constant drive for change in computational methods has created an increased demand for new computational tools as are the cases of meshless methods and, more recently, Isogeometric Analysis (IGA) based on Non-Uniform Rational B-Splines (NURBS). Besides many other advantages of IGA, numerical analysis directly on NURBS objects avoids the time consuming step of mesh generation, providing in this way a more competitive approach for numerical simulations in general. In this work the contact analysis is implemented under the IGA framework and NURBS geometric approximation functions are going to be defined for contact analysis for both the rigid tools and the deformable blank sheet. 2. Non-Uniform Rational B-Splines (NURBS) and IsoGeometric Analysis (IGA) Detailed overview of B-Spline curves, B-Splines surfaces and NURBS can be found in Piegl and Tiller [2] and Cottrell et al [3]

Knot vectors

Conclusions