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| Analytical solutions in terms of the quadrilateral area coordinates for pure bending state and the finite element model overcoming the limitation of MacNeal's theorem |
| Received:May 04, 2016 Revised:June 18, 2016 |
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| DOI：10.7511/jslx201604006 |
| KeyWord:analytical solutions the second form of the quadrilateral area coordinate method (QACM-Ⅱ) pure bending state unsymmetric element MacNeal's theorem |
| Author | Institution |
| 岑松 |
清华大学 航天航空学院工程力学系, 北京 |
| 周培蕾 |
清华大学 航天航空学院工程力学系, 北京 |
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| Abstract: |
| In order to improve the performance of finite element models,analytical solutions of problems in theory of elasticity (the general solutions of the homogeneous equations) were often used as the element trial functions.However,the number of the element DOFs usually does not match the number of the complete analytical solutions,and such incomplete trial functions may lead to direction dependence of the finite elements.In this paper,a new local natural coordinate method,i.e.,the second form of the quadrilateral area coordinate method QACM-Ⅱ (S,T),was employed to formulate the analytical solutions (the linear combination of S3 and T3) of the Airy stress function for pure bending state along arbitrary directions.And corresponding analytical solutions for stresses,strains or displacements were also derived out.Then,by utilizing above solutions,a new unsymmetric 4-node,8-DOF plane quadrilate-ral element,denoted by USQ4,was successfully created.The new element can pass both the constant strain/stress patch test and the pure bending test,which means that the limitation defined by the MacNeal's theorem is overcome. |
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