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An effective hybrid displacement function element method for solving the edge effect of Mindlin–Reissner plate
Author(s) -
Shang Yan,
Cen Song,
Li ChenFeng,
Huang JunBin
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4843
Subject(s) - finite element method , displacement (psychology) , enhanced data rates for gsm evolution , boundary knot method , boundary (topology) , boundary element method , mathematical analysis , function (biology) , mixed finite element method , boundary value problem , geometry , extended finite element method , mathematics , structural engineering , engineering , psychology , telecommunications , evolutionary biology , psychotherapist , biology
Summary 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.