Accuracy of some finite element models for arch problems

This paper presents a theoretical accuracy study of some finite element models for thin arches. As is well known, the selection of finite elements for curved members is quite a delicate problem. We obtain order estimates of errors of finite element solutions by means of the perturbation theory of mixed models and the technique of asymptotic expansion. In particular, we theoretically show that certain finite element models may suffer from the so-called locking phenomenon. Numerical results are also given to be compared with the theoretical error estimates.