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A quadrilateral hybrid‐Trefftz plate bending element for the inclusion of warping based on a three‐dimensional plate formulation
Author(s) -
Piltner R.
Publication year - 1992
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.1620330210
Subject(s) - bending of plates , image warping , quadrilateral , isotropy , finite element method , plate theory , polygon mesh , geometry , transverse shear , structural engineering , shear (geology) , bending , mathematical analysis , transverse plane , boundary value problem , mathematics , materials science , physics , engineering , composite material , computer science , quantum mechanics , artificial intelligence
A plate formulation, for the inclusion of warping and transverse shear deformations, is considered. From a complete thick and thin plate formulation, which was derived without ad hoc assumptions from the three‐dimensional equations of elasticity for isotropic materials, the bending solution, involving powers of the thickness co‐ordinate z , is used for constructing a quadrilateral finite plate bending element. The constructed element trial functions, for the displacements and stresses, satisfy, a priori , the three‐dimensional Navier equations and equilibrium equations, respectively. For the coupling of the elements, independently assumed functions on the boundary are used. High accuracy for both displacements and stresses (including transverse shear stresses) can be achieved with rather coarse meshes for thick and thin plates.