An effective hybrid displacement function element method for solving the edge effect of Mindlin–Reissner plate |
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Authors: | Yan Shang Song Cen Chen‐Feng Li Jun‐Bin Huang |
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Affiliation: | 1. Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing, 100084, China;2. High Performance Computing Center, School of Aerospace Engineering, Tsinghua University, Beijing, 100084, China;3. Key Laboratory of Applied Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing, 100084, China;4. Zienkiewicz Centre for Computational Engineering & Energy Safety Research Institute, College of Engineering, Swansea University, Swansea, SA2 8PP, UK |
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Abstract: | In bending problems of Mindlin–Reissner plate, the resultant forces often vary dramatically within a narrow range near free and soft simply‐supported (SS1) boundaries. This is so‐called the edge effect or the boundary layer effect, a challenging problem for conventional finite element method. In this paper, an effective finite element method for analysis of such edge effect is developed. The construction procedure is based on the hybrid displacement function (HDF) element method [1], a simple hybrid‐Trefftz stress element method proposed recently. What is different is that an additional displacement function f related to the edge effect is considered, and its analytical solutions are employed as the additional trial functions for the first time. Furthermore, the free and the SS1 boundary conditions are also applied to modify the element assumed resultant fields. Then, two new special elements, HDF‐P4‐Free and HDF‐P4‐SS1, are successfully constructed. These new elements are allocated along the corresponding boundaries of the plate, while the other region is modeled by the usual HDF plate element HDF‐P4‐11 β [1]. Numerical tests demonstrate that the present method can effectively capture the edge effects and exactly satisfy the corresponding boundary conditions by only using relatively coarse meshes. Copyright © 2015 John Wiley & Sons, Ltd. |
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Keywords: | finite element methods edge effect hybrid displacement function (HDF) element hybrid‐Trefftz stress element analytical solution plate bending |
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