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| An efficient finite element of spatial curved beams |
| Revised:April 14, 2003 |
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| DOI：10.7511/jslx20051017 |
| KeyWord:spacial curved beam elements,shape functions,small strains, finite elements |
| TAN Mei-lan~ |
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| Abstract: |
| Stress analysis of a drill-string, usually thousands meters long slender steel tube with circular cross-section, is a complex problem in a general three-dimensional well bore. Thus numerical method, such as commonly used finite element method, has to be resorted to. When carrying out finite element analysis, the element size of the existing beam elements should be small enough to capture the curve shape on geometry of drill string in three-dimensional well bore as well as to ensure the accuracy of the calculated results. This in turn results in considerably long computational time. A special three-dimensional curved and twisted beams with circular cross-section, which posses 12 degrees of freedom, is proposed herein. The key to success for the proposed element is that shape functions are obtained by ensuring all rigid body displacements and rotations as well as the constant strain state, thus the convergence is guaranteed. The natural (curvilinear) coordinate system is used in the derivations and detailed formulations are given. To verify the formulations, several examples are analyzed by using the proposed element for the static situation. Numerical results are compared well with existing theoretical and/or numerical data in the literature. Based on the results reported herein, one may conclude that the proposed curved element may be used for the analysis of three-dimensional curved beam structures. |
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