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| Algorithm for deriving explicitly the analytical expression of geometric stiffness matrix of the 4-node,24 degrees of freedom flat shell element |
| Received:May 30, 2012 Revised:October 30, 2012 |
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| DOI：10.7511/jslx201306008 |
| KeyWord:quadrilateral flat shell element geometric stiffness matrix rigid body motion rule geometric nonlinearity analytical expression |
| Author | Institution |
| 文颖 |
中南大学 土木工程学院, 长沙 |
| 曾庆元 |
中南大学 土木工程学院, 长沙 |
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| Abstract: |
| The derivation of geometric stiffness matrix is an essential and difficult stage in conducting the finite element analysis of geometrically nonlinear structural problems.Any attempt to obtaining explicitly the analytical expression of geometric stiffness matrix is of great importance for simplifying the formulation,and in particular for improving efficiency and effectiveness of the overall procedure.In the context of co-rotational formulation,an algorithm analytically leading to the geometric stiffness matrix of the 4-node quadrilateral flat shell element with a total of 24 degrees of freedom was presented based on the rigid body motion rule and consecutively subject to discussion.Two benchmark problems,namely the large rotation problem of a cantilever beam and the large deflection behaviour of a hinged semi-cylindrical roof with two typical thicknesses subjected to a central pinching force,were analyzed for demonstrating the reliability and robustness of the proposed procedure.The results of numerical study reveal that:(1)The explicit formula derived herein provides a great deal of convenience while preserving acceptable accuracy of solution;(2)The derived analytical geometric stiffness matrix is element-type independent and (3)As compared with numerical integration,the analytical approach is featured by a significant improvement in computational efficiency. |