The p-version of the finite element method for three-dimensional curved thin walled structures

In this paper we present an implementation of a three-dimensional p-version for structural problems of solids with almost arbitrarily curved surfaces. Applying the blending function method, complex structures can often be modelled by a few p-elements, being the basis for a higher order approximation. Numerical examples will demonstrate, that the p-version with anisotropic Ansatz spaces allows to predict the structural behaviour of three-dimensional plates and shells with approximately the same amount of degrees of freedom as in the two-dimensional case, yet signi+cantly more accurate due to the threedimensional model. Furthermore, it is advantageous to compute complex structures exclusively with three-dimensional discretizations as no special elements are needed to model the transition from dimensionally reduced formulations like plates or shells to fully three-dimensional solid elements. Using the p-version with anisotropic Ansatz spaces the whole structure can be e=ciently discretized with solid elements, even if the aspect ratio of the elements becomes very large.