an rp-adaptive finite element discretization applied to physically non ...

Vera Nübel, Alexander Düster and Ernst Rankadditional singularities occur, such as those due to reentrant corners. Each subdomain isthen discretized by the p-version applied on a coarse mesh, where no refinement towardsthe elastic-plastic interface is necessary. The computational domain with a non-smoothsolution is split into areas for which regular solutions do exist. As the boundary ofthe elastic-plastic interface describes an arbitrarily curved contour, element edges areaccordingly shaped. To describe such arbitrarily bounded elements we use the blendingfunction method first proposed by Gordon and Hall (see [3]). It is an important featureof the p-version that enables a large varity of element shapes.PSfrag replacementsΓ NtΩΩ eΩ puΓ DFigure 1: Domain Ω, decomposed into an elastic region Ω e and a plastic region Ω pAs position and shape of the elastic-plastic interface are not known a priori, an rpadaptivealgorithm iteratively detects the boundary of the plastic zone. Within thisadaptive cycle elements may be arbitrarily curved and strongly distorted. As the p-version is very robust with respect to distortion (see Szabó et al. [3]), these effects can becompensated with an increase of the polynomial degree of the finite element computation.3 Numerical examplesNumerical studies on the rp-adaptive approach for two-dimensional problems haveshown that the proposed discretization strategy enables an improvement of efficiencyand provides accurate results [4]. Furthermore it turned out to be superior to adaptiveh-version approaches when investigating the example of a rectangular domain with acentral hole which has been defined by Stein et al. [2] as a benchmark problem forthe joint German research project ’Adaptive Finite-Element-Methods in ComputationalMechanics’. This can be seen from Figure 2 which shows the relative error in u y in [%]at point 4, located at the upper right corner. Three of the corresponding finite-elementmeshes,arising during the rp-adaptive cycle, are presented in Figure 3.A similar behaviour of the rp-method can be observed in 3D, when investigating the threedimensionalproblem of a thick-walled hollow sphere under internal pressure. Figure 4shows the results for a uniform h-version, a p-version with a priori adjusted interface atthe plastic front and an adaptive rp-version.2