# A weak form quadrature element formulation of geometrically exact shells incorporating drilling degrees of freedom

• Run Zhang
• Hongzhi Zhong
• Xiaohu Yao
Original Paper

## Abstract

Geometrically nonlinear analysis of shell structures is conducted using weak form quadrature elements. A new geometrically exact shell formulation incorporating drilling degrees of freedom is established wherein rotation quaternions in combination with a total Lagrange updating scheme are employed for rotation description. An extended kinematic condition to serve as the drilling rotation constraint, derived from polar decomposition of modified mid-surface deformation gradient, is exactly satisfied in the formulation. Several benchmark examples are presented to illustrate the versatility and robustness of the present formulation.

## Keywords

Geometrically exact shell Drilling degrees of freedom Polar decomposition of deformation Weak form quadrature element method

## Notes

### Acknowledgements

The present investigation was performed with the support of the National Natural Science Foundation of China (No. 11702098), the Project funded by China Postdoctoral Science Foundation (No. 2017M612650) and the Fundamental Research Funds for the Central Universities (No. 2017BQ096).

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