Nonlinear Finite Element Analysis of Concrete Structures

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now be directed towards nanerical aspects related to the implementation
of these matters.
The AXIPLANE-program is written in Algol and runs at Rise's
Burrough B-6700 computer using single precision that considers
11 significant digits. Now, essentially the finite element modelling
described in the previous sections results in an equation
system with 2n degrees of freedom where n is the number of nodal
points, i.e.
R a = f (4.6-1)
Here K denotes the total symmetric stiffness matrix, the vector
a contains all the nodal displacements, while the vector F contains
the nodal forces. This equation refers to the RZ-coordinate
system. However, in accordance with the discussion in section
4.1 the geometric boundary conditions still remain to be
considered.
Suppose that the nodal displacement a. in either the R- or Z-
direction is prescribed as a. = y. In accordance with the method
described by Zienkiewicz and Cheung (1S67) p. 233 the corresponding
j-th equation in the equation system (1) is then modified by
multiplying the diagonal stiffness term K.. with the factor 10
and by replacing the right hand side with the quantity then
obtained multiplied by y. This means that equation j in the
equation system (1) is replaced by
K jl a 1+ K. 2 a 2+ ... + K jj .lO 10 a j+ ... + K. /2n . 1 a 2n _ 1
+K j,2n a 2n- K jj' lol °*
(4 ' 6 " 2)
where no summation convention is utilized. As all other terms
than that containing a. contribute insignificantly, this equation
yields as a very close approximation the attempted expression
a. = y. The advantages of the method are that symmetry of
the coefficient matrix continues and no rearrangements of the
equations are involved.