Plates - Mechanics of Structures: Variational and Computational Methods - page 774

FIGURE 13.9
Edge conditions.

shear force V x

+ ∂

m xy
∂

V x dy = q x dy dy

y

or

K ∂ w

+ ∂

m xy
∂

V x =

x y

q x

y =−

w + ( 2 − ν)∂ ∂ (13.48)

x

This is the equivalent shear force per unit length along a particular value of x , which is
parallel to the y axis.
Along a prescribed y value, which is parallel to the x axis, the equivalent shear force
would be

K ∂ w + ∂

m xy
∂

V y =

y x

q y

x =−

w + ( 2 − ν)∂ ∂ (13.49)

y

The boundary conditions for the fundamental edge conditions are now evident. For a
boundary at x

=

a :