Improving the MITC3 shell finite element by using the Hellinger–Reissner principle

The objective of this study is to improve the performance of the MITC3 shell finite element. The Hellinger–Reissner (HR) variational principle is modified in the framework of the MITC method, and a special approximated transverse shear strain field is proposed. The MITC3-HR shell finite element improved by using the Hellinger–Reissner functional passes all the basic tests (zero energy mode test, patch test, and isotropic element test). Convergence studies considering a fully clamped plate problem, a sixty-degree skew plate problem, cylindrical shell problems, and hyperboloid shell problems demonstrate the improved predictive capability of the new 3-node shell finite element.