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TitleFinite Element Method
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Page 67

Finite Elements Method Plates and Shells page 67


2

2. .xy
u v w

z
y x x y

δ δ δ
γ

δ δ δ δ
= + = −




0== yzxz γγ


7.1.5 Thick-Plate (Mindlin) Theory
This theory takes into account the shear deformation. The right angles are thus not preserved
anymore in cross sections. Thus γyz ≠ 0 and γzx ≠ 0 (fig. 8.4).



Fig. 8.4




x

z
x

u y
x δ

δθ
δ
δ

ε .== → deformations εx linear in z direction.




y

z
y

v x
y δ

δθ
δ
δ

ε .−== → deformations εy linear in z direction.













−=+=

xy
z

x

v

y

u xy
xy δ

δθ
δ

δθ
δ
δ

δ
δ

γ .


In summary :

Element Type


Beam Plate


Shear deformation
neglected

BERNOULLI KIRCHHOFF
Right angles are preserved in

cross-sections

Shear deformation
taken into account

TIMOSHENKO MINDLIN
Right angles are NOT preserved

in cross-sections

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