plate elements

8/20/2019 PLATE Elements

http://slidepdf.com/reader/full/plate-elements 1/21

Analysis of PlatedStructures

Flat Plate - very small thickness in comparison

to the planar dimensions

Lateral Loading - forces are perpendicular to the

plane of the plate

Resists the applied load by bending in twodirections and twisting moment - BendingBehaviour Dominates



Stress Resultants in a Plate



Stresses



Plate Theory

Plate theory is to calculate the deformation andstresses in a plate subjected to loads.

Due to very small thicness in comparison to the

planar dimensions! reduces the full three-dimensionalsolid mechanics problem to a two-dimensional

problem.

"hin Plate "heory#

• thickness to width ratio < 0.1

•

maximum deection < one tenth of thickness



!ssumptions

1. The line normal to the neutral axis "efore "endin#

remains strai#ht after "endin#.

$. The normal stress in thickness direction is

ne#lected.' ( ) *

%. The transverse shearin# strains gx& and gyz are

assumed to "e &ero.



'imitations.

1. (irchho) plate element cannot rotateindependently of the position of the mid*surface.Pro"lems occur at "oundaries where theunde+ned transverse shear stresses are

necessary especially for thick plates

$. is only applica"le for analysis of plates withsmaller deformations as hi#her order terms ofstrain*displacement relationship cannot "ene#lected for lar#e deformations.

%. ,nly for small deformations the transversesti)ness can "e assumed to "e constant



"hic Plate "heory

Reissner - indlin or indlin plate theory is applied

for analysis of thick plates where the sheardeformations are considered rotation and lateraldeections are decoupled.

/ross*sections need not "e perpendicular to the axialforces after deformation.

+ssumptions#

1. The deections of the plate are small.

$. ormal to the plate mid*surface "efore

deformation remains strai#ht "ut not necessarily

normal to it after deformation.



PL+", ,lements

+pplications

Floor Panels hear alls

"riangular elements

Four or ,ight /oded 0uadrilateral ,lements

D1F ) 2 3Displacement and "wo Rotations4 , , at

each node



ulation of Rectangular Plate Bending Element – THIC

5soparametric formulation

x



ulation of Rectangular Plate Bending Element – THIC

!. oment -/urvature Relation

6ompactForm

+nalogous to tress 7 trainRelation



23 is the strain displacement matrix

4di5 is the nodal displacement vector



/3p

6



2. Strain 7isplacement Relation



atrix8orm

8our ode 9uadrilateral case



/ompact 8orm



:xplicit form

5n general for any i/ 3p 2i3 6



The "endin# and shear terms are separated andwritten as

/ompact 8orm



Element !ti"ne## $atrix

8auss 0uadrature integration rule is used tocompute the sti&ness matri9 :;.

plate elements

Documents