Acta Mechanica

, Volume 230, Issue 10, pp 3571–3591

# Nonlinear dynamic analysis of shell structures by the formulation based on a discrete shear gap

• She Li
• Jingfei Zhang
• Xiangyang Cui
Original Paper

## Abstract

In this work, a shear locking-free three-node shell element based on Mindlin–Reissner theory is presented for a nonlinear dynamic analysis including sheet metal forming. In the present formulation, only displacement and rotational degrees of freedom are utilized, and the discrete shear gap of each field node is deduced using rotations of all three field nodes in a local coordinate system by the integral from the fictitious central point to the corresponding field node, which makes it alleviate the shear locking phenomenon. In order to validate the availability in solving nonlinear dynamic problems, several benchmark problems and sheet metal forming applications are employed. The results show potentiality in application to practical problems because of the simple implementation.

## Notes

### Acknowledgements

The support of National Key R & D Program of China (2017YFB1002704), National Science Foundation of China (11872177), Hunan Provincial Innovation Foundation for Postgraduate of China (CX2018B202), and the China Scholarship Council (201806130094) is gratefully acknowledged.

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