Designing Benchmark Tests for Shell Finite Elements

This paper on "Designing Benchmark Tests for Shell Finite Elements" was presented at the International Conference on Quality Assurance and Standards in Finite Element Analysis - 13-15 May 1987, The Grand Hotel, Brighton.

Summary

In this paper the requirements for designing a series of benchmark tests for finite element assemblies are defined and discussed in detail. The guidelines thus obtained are subsequently applied in the creation of benchmark tests for constant inextensional bending behaviour of thin shells of positive, zero and negative Gaussian curvature.
A portion of a sphere, a cylinder and a catenoid of revolution were modelled with a 2x2 mesh of 8 node Mindlin shell elements. It was confirmed that, as predicted by Morley, the stress recovery for an arbitrary point on the shell and especially at the nodes was grossly in error. It was also confirmed that the stresses recovered at the Gauss points were very nearly exact for all three types of curvature.
The same geometries were also tested with 2x2 patches of distorted elements and again it was found that the Gauss points were the most accurate points. The results for a distorted cylindrical patch of Semi-Loof shell elements were found to have the same characteristics as the Mindlin elements.