 
 
 
 
 
 
 
  
To calculate buckling loads routine arpackbu.c is called. The following steps are needed in a buckling calculation:
 of the previous static step
  (including large deformation stiffness and stress stiffness) and the stress
  stiffness matrix
 of the previous static step
  (including large deformation stiffness and stress stiffness) and the stress
  stiffness matrix  
 of the buckling load [18].
 of the buckling load [18].
 
 
 buckling factor
   buckling factor exit loop, else set
 exit loop, else set
  
 buckling factor
   buckling factor and cycle
 and cycle
The buckling mode in ARPACK (Mode 4, cf [41]) is used to solve a system of the form
|  | (454) | 
where 
 is symmetric and positive definite and
 is symmetric and positive definite and 
 is symmetric but indefinite. The iterative
procedure to find the eigenvalues requires routines to solve
 is symmetric but indefinite. The iterative
procedure to find the eigenvalues requires routines to solve
and to calculate
Similar to the frequency calculations, the LU decomposition (SPOOLES) to solve Equation (455) is performed before the loop determining the buckling factor, since the left hand side of the equation does not vary. The matrix multiplication in Equation (456) is taken care of by routine op.f.
A major difference with the frequency calculations is that an additional
iteration loop is necessary to guarantee that the value of the buckling
factor is right. Indeed, experience has shown that the value of  matters
here and that the inequality
 matters
here and that the inequality 
 buckling factor
   buckling factor should be satisfied. If it is not, the whole procedure starting with the LU
decomposition is repeated with a new value of
should be satisfied. If it is not, the whole procedure starting with the LU
decomposition is repeated with a new value of 
 buckling
factor
buckling
factor . If necessary, up to four such iterations are allowed.
. If necessary, up to four such iterations are allowed. 
 
 
 
 
 
 
