Nonlinear Finite Element Analysis of Concrete Structures

- OD -
where
[B e . D e .,, B^-.dV^K 0 . (4.1-20)
J ija ljkl klB aS
e
v
is the symmetric stiffness tensor of the element
j N J a b. dV = Ff (4.1-21)
e
v
is the body force vector. Discrete point forces P. can be treated
by this formulation, but are conveniently treated separately by
use of eq. (22) which follows from eq. (21).
7N® P. = F pe (4.1-22)
L ia i ex
is the discrete point force vector. The tensor N.
is evaluated
at the location of the point force in question and the summation
is extended over all point forces located within the element.
N e t.dS = F te (4.1-23)
ia i a
is the traction force vector.
B S . D 6 .,, e?, dV = F L ° ,. . ...
j lja ljkl kl a (4.1-24)
e
v
is the force vector due to initial strains.
e
v
B ija °ij dV = F °f
is the force vector due to initial stresses.
(4^- 25)
By means of the fundamental equation given by eq. (19) the original
problem has been transformed into a form relating nodal displacements
linearly to forces that can be vizualized as located
at the nodal points. As previously mentioned, an equation completely
analogous to this equation and valid for the whole structure
can be set up; introduction of the geometrical boundary
conditions will then establish the final linear equation system