Civil Engineering Reference
In-Depth Information
(9.13)
From virtual work principle, it can be established that the element nodal
forces induced by the nodal displacements are given by
where
t
denotes the thickness of the element and hence the stiffness matrix
of the element is
(9.14)
(9.15)
Since all the terms are constant, the integral
d
x
d
y
over the whole area of
the element is just its area
D
. Hence
(9.16)
where
(9.17)
or written in terms of the sub-matrices
(9.18)
The coefficients of the stiffness sub-matrix can be expressed explicitly, e.g.
for the case of isotropic medium
(9.19)
and for the general case
(9.20)
Hence, the forces at a node i are given by
(9.21)
