Nonlinear Finite Element Analysis of Concrete Structures

- 104 -
APPENDIX B
Skewed Kinematic Constraints
The finite element modelling results in the equation system
given by eq. (4.6-1). This equation system refers to the RZcoordinate
system; when nodal displacements are prescribed in
the R- and Z-direction a modification of the equation system
in accordance with eq. (4.6-2) is performed. However, if nodal
displacements are prescribed in other directions than the R-
or Z-axis, i.e., if skewed kinematic constraints are present,
then eq. (4.6-1) has to be transformed to the R'Z*-coordinate
system shown in fig. 1. After that a modification of the
equation system corresponding to eq. (4.6-2) is performed and
" V
R
Fig. B-l: Skewed kinematic constraint.
a retransformation back to the original RZ-coordinate system
is then carried out. Using a transformation matrix similar to
eq. (4.3-14) and noting the transformation formula of eq.
(4.3-15), after trivial matrix multiplications the above
procedure results in the following:
If the displacement in the R'-direction at nodal point i is pre
scribed to be Y then the following contributions should be
added to elements in the matrix K in eq. (4.6-1)