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Structural Engineering and Mechanics Volume 54, Number 3, May10 2015 , pages 393-417 DOI: https://doi.org/10.12989/sem.2015.54.3.393 |
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Higher-order assumed stress quadrilateral element for the Mindlin plate bending problem |
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Tan Li, Zhaohui Qi, Xu Ma and Wanji Chen
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| Abstract | ||
| In this paper an 8-node quadrilateral assumed stress hybrid Mindlin plate element with 39B is presented. The formulation is based on complementary energy principle. The proposed element is free of shear locking and is capable of passing all the patch tests, especially the non-zero constant shear enhanced patch test. To accomplish this purpose, special attention is devoted to selecting boundary displacement interpolation and stress approximation in domain. The arbitrary order Timoshenko beam function is successfully used to derive the boundary displacement interpolation. According to the equilibrium equations, an appropriate stress approximation is rationally derived. Particularly, in order to improve element\'s accuracy, the assumed stress field is derived by employing 39B rather than conventional 21B. The resulting element can be adopted to analyze both moderately thick and thin plates, and the convergence for the very thin case can be ensured theoretically. Excellent element performance is demonstrated by a wide of experimental evaluations. | ||
| Key Words | ||
| hybrid stress element; Mindlin plate; arbitrary order Timoshenko beam function; enhanced patch test | ||
| Address | ||
| Tan Li, Zhaohui Qi, Xu Ma: 1State Key Laboratory for Structural Analysis of Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116023, China Wanji Chen: 2Key Laboratory of Liaoning Province for Composite Structural Analysis of Aero craft and Simulation, Shenyang Aerospace University, Shenyang 110136, China | ||