The shape functions defining the bilinear element used in the Mindlin plate
are:
(1)
or, in terms of local coordinates:
(2)
It is also useful to write the shape functions in the
Belytschko-Bachrach
1 mix form:
(3)
with
is the area of the element.
The velocity of the element
at the mid-plane reference point is found using the relations:
(4)
(5)
(6)
Where,
are the nodal velocities in the x, y, z directions.
In a
similar fashion, the element rotations are found by:
(7)
(8)
Where,
and
are the nodal rotational velocities about the x and y
reference axes.
The velocity change with respect to the coordinate change is given
by:
(9)
(10)