Comparison of the h-, p-, hp- and rp-version of the FEM for 2D contact simulation

Even though mechanical contact simulations have been performed since more than two decades, numerous problems are still not solved completely. These problems include discontinuities at the contacting nodes, non smooth solutions, convergence problems, high numerical effort, etc. Recent investigations showed distinct differences between discretizations for contact problems with the classical h-, p-, hp-, or the rp-version of the FEM. In each case special attention has to be drawn to the contact region. Two points have to be focused on: firstly the accurate representation of curved boundaries, and secondly the change of the boundary conditions at the contact interface from contact to no contact. The investigation of the different methods will be performed for the 2D Hertzian contact model of two infinitely long cylinders coming in contact. In the presentation we consider each of the above mentioned refinement strategies and its influence on the quality of the approximation. The penalty method will be used to introduce the contact constraints and the local contact search is performed on Gauss-Legendre points along the contacting edge.     «

Even though mechanical contact simulations have been performed since more than two decades, numerous problems are still not solved completely. These problems include discontinuities at the contacting nodes, non smooth solutions, convergence problems, high numerical effort, etc. Recent investigations showed distinct differences between discretizations for contact problems with the classical h-, p-, hp-, or the rp-version of the FEM. In each case special attention has to be drawn to the contact re...     »