Benchmark Computations of stresses in a spherical dome with shell finite elements

TL;DR

This paper introduces a finite element computational framework for analyzing stresses in spherical shell structures, demonstrating its effectiveness on the Girkmann benchmark problem with improved accuracy over previous methods.

Contribution

The paper develops a mesh-dependent shell model from elasticity laws and evaluates the accuracy of reduced strain four-node shell elements on a benchmark problem.

Findings

Reasonable accuracy achieved with bilinear shell elements

Mesh quality significantly affects performance

Improved results compared to earlier general shell element methods

Abstract

We present a computational framework for analysing thin shell structures using the finite element method. The framework is based on a mesh-dependent shell model which we derive from the general laws of three-dimensional elasticity. We apply the framework for the so called Girkmann benchmark problem involving a spherical shell stiffened with a foot ring. In particular, we compare the accuracy of different reduced strain four-node elements in this context. We conclude that the performance of the bilinear shell finite elements depends on the mesh quality but reasonable accuracy of the quantities of interest of the Girkmann problem can be attained in contrast to earlier results obtained with general shell elements for the problem.