Nonlinear Finite Element Analysis of Concrete Structures

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Here r is the mean radius of the element and, as previously
mentioned, the matrix B is evaluated at the centroid of the triangle.
The index T denotes the transpose of a natrix. Body forces
b due to gravity in the direction of the Z-axis may be dealt with
in the program, i.e..
b = 0
b r
Using eq. (4.1-21) and eq. (4) we obtain
F. = I N '
T b dV = N T L 2TT
b J
r
m
A
el.vol
2irr
m
Ab„
Z
where the matrix N is evaluated at the centroid of the triangle.
Nodal forces due to prescribed discrete point forces P located
within the element are given by eq. (4.1-22) and eq. (4), i.e.,
- =T -
F = I N P
P
(4.2-13)
where the summation extends over the number of discrete point
forces P and where the matrix N is evaluated at the location of
the point force in question. Nodal forces due to prescribed
traction forces t are given by eq. (4.1-23) and eq. (4), i.e.
; t - f « T t ds
S - area of
the element
and nodal forces due to temperature expansion are given by eq.
(4.1-24), i.e.
l
• I
D é dV
o
= B T 5 e 2Trr A
o m
el.vol