An rp-adaptive finite element method for the deformation theory of plasticity

In this paper we present an rp-discretization strategy for physically non-linear problems based on a high order finite element formulation. In order to achieve convergence, the p-version leaves the mesh unchanged and increases the polynomial degree of the shape functions locally or globally,whereas the r-method moves nodes and edges of an existing FE-mesh. The basic idea of our rp-version approach is to adjust the finite element mesh to the shape of the elastic-plastic interface in order to take into account the loss of regularity which arises along the curve of the plastic front. Numerical examples will demonstrate that this approach leads to an exponential rate of convergence and highly accurate results.     «

In this paper we present an rp-discretization strategy for physically non-linear problems based on a high order finite element formulation. In order to achieve convergence, the p-version leaves the mesh unchanged and increases the polynomial degree of the shape functions locally or globally,whereas the r-method moves nodes and edges of an existing FE-mesh. The basic idea of our rp-version approach is to adjust the finite element mesh to the shape of the elastic-plastic interface in order to take...     »