Scale resolution, locking, and high-order finite element modelling of shells Original Research Article

We demonstrate, both by theory and experiment, the benefits of using standard finite elements of relatively high degree in shell problems. The difficulty of shell problems lies in their asymptotic diversity at zero thickness and in the multiple-scale character of the deformation field when the thickness is small. Due to these characteristics, standard finite elements of low degree often resolve the length scales of practical shell deformation very poorly unless extremely fine meshes are used. However, with standard finite elements of sufficiently high degree, say cubic or quartic at least, the quality of numerical scale resolution improves remarkably. We show by simple error analysis that this effect is not problem-specific but rather robust among the diversity of shell problems. As numerical test cases, we analyze two challenging problems in cylindrical shell geometry.