REISSNER-MINDLIN EXTENSIONS OF KIRCHHOFF ELEMENTS FOR PLATE BENDING

2005 ◽  
Vol 02 (01) ◽  
pp. 127-147 ◽  
Author(s):  
FUMIO KIKUCHI ◽  
KEIZO ISHII ◽  
HIDEYUKI TAKAHASHI
Keyword(s):  
Transverse Shear ◽  
Degrees Of Freedom ◽  
Plate Thickness ◽  
Special Technique ◽  
Test Problems ◽  
Element Approximation ◽  
Plate Bending ◽  
Wide Range ◽  
Shear Strains ◽  
Transverse Shear Strains

A method of extending various existing Kirchhoff elements to Reissner-Mindlin elements for plate bending is developed and tested. The essential idea is to use independent transverse shear strains and a special mixed formulation. The Nedelec edge element is effective for assuming the shear strains. Furthermore, the displacements are carefully constructed so that the strain-displacement relations are strictly satisfied for the transverse shear strains. We present our approach for displacement-based three-node triangular elements including both conforming and non-conforming ones as the base Kirchhoff elements. It is also possible to reduce the shear variables from the element degrees of freedom by means of a special technique called the beam element approximation. Numerical results are obtained for some fundamental test problems and are generally reasonable over wide range of plate thickness. In particular, it is observed that the tested elements actually reduce to the base Kirchhoff element in the thin plate range and are free from transverse shear locking.

The Transverse Shear Effect of a New Plate Bending Finite Element Based on the Strain Approach

2018 ◽  
Vol 35 ◽  
pp. 1-10
Author(s):  
Sifeddine Abderrahmani ◽  
Toufik Maalem ◽  
Djamal Hamadi
Keyword(s):  
Finite Element ◽  
Numerical Analysis ◽  
Transverse Shear ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Plate Bending ◽  
Shear Effect ◽  
Thin Plate Bending ◽  
Kirchhoff Theory ◽  
Three Degrees Of Freedom

In this paper, we present a comparative study of the transverse shear effect on the plate bending. The element used is a rectangular finite element called SBRPK (Strain Based Rectangular Plate-Kirchhoff Theory-), it used for the numerical analysis of thin plate bending, and it based on the strain approach. This element has four nodes and three degrees of freedom per node (w, θx, θy). Through the numerical applications with different loading cases and boundary conditions; the numerical results obtained are in close agreement with the analytical solution.

BENDING OF FGM PLATES BY A SIMPLIFIED FOUR-UNKNOWN SHEAR AND NORMAL DEFORMATIONS THEORY

2013 ◽  
Vol 05 (02) ◽  
pp. 1350020 ◽  
Author(s):  
ASHRAF M. ZENKOUR
Keyword(s):  
Virtual Work ◽  
Plate Thickness ◽  
Present Theory ◽  
Normal Strain ◽  
Principle Of Virtual Work ◽  
Governing Equations ◽  
Shear Strains ◽  
Transverse Normal Strain ◽  
Transverse Shear Strains ◽  
Bending Response

The bending response of FGM plates is presented based upon a simplified shear and normal deformations theory. The present simplified theory is accounted for an adequate distribution of transverse shear strains through the plate thickness and tangential stress-free on the plate surfaces. The effect of transverse normal strain is also included. The number of unknown functions involved here is only four as against six in case of other shear and normal deformations theories. The principle of virtual work is employed to derive the governing equations. A comparison with the corresponding results is made to check the accuracy and efficiency of the present theory. Additional results for all stresses are investigated through-the-thickness of the FGM plate.

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