Computational contact mechanics based on the rp-version of the Finite Element Method

In this paper we present an rp-adaptive discretization strategy to perform unilateral two-dimensional mechanical contact simulations by combining the r and p-version of the finite element method (FEM). The p-version leaves the finite element mesh unchanged and increases the shape function's polynomial degree in order to obtain convergence towards the exact solution of the underlying mathematical model. The r-method relocates nodes of an existing FE-mesh to improve the discretization of a given problem without introducing additional degrees of freedom, therefore keeping the problem size fixed. The rp-version, which is a combination of the two aforementioned methods, is used in our study to move a node of the FE-mesh to the end of the contact zone to account for the loss of regularity which arises due to the change from contact to non-contact along the edge. It will be shown that highly accurate results can be obtained by using highorder (p) finite elements in combination with the penalty method and a relocation (r) of element nodes.     «

In this paper we present an rp-adaptive discretization strategy to perform unilateral two-dimensional mechanical contact simulations by combining the r and p-version of the finite element method (FEM). The p-version leaves the finite element mesh unchanged and increases the shape function's polynomial degree in order to obtain convergence towards the exact solution of the underlying mathematical model. The r-method relocates nodes of an existing FE-mesh to improve the discretization of a given p...     »