A further study of hybrid strain-based three-node flat triangular shell elements

Abstract

This paper presents a further study of various lower-order three-node flat triangular shell elements that were based on the Hellinger–Reissner hybrid strain formulation and were developed previously by the authors. The present investigation is to examine the effects of including membrane-bending coupling feature in the shell element formulation on the performance of the hybrid strain-based three-node flat triangular shell elements. Additional features are considered. These include, for example, linear distribution of the assumed strain field of the membrane strain, and hybrid strain formulation with linear assumed membrane strains and membrane-bending coupling. A numerical study of mesh topology is also included. This relatively detailed study leads one to the conclusion that the hybrid strain-based flat triangular shell elements previously developed by the authors are attractive and promising for economical analysis of general shells. It is also found that the inclusion of features such as membrane-bending coupling is unnecessary. Numerical results presented here seem to strongly substantiate the theoretical developments that flat triangular shell elements do converge to the correct solution of deep shell problems. Finally it is observed that for deep shell problems appropriate mesh topology becomes the key to an accurate finite element solution.