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.

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