Mechanical APDL Structural Analysis Guide

• Unit loads are usually sufficient (that is, actual load values need not be specified). The eigenvalues
  calculated by the buckling analysis represent buckling load factors. Therefore, if a unit load is specified,
  the load factors represent the buckling loads.All loads are scaled. (Also, the maximum permissible
  eigenvalue is 1,000,000 - you must use larger applied loads if your eigenvalue exceeds this limit.)


• It is possible that different buckling loads may be predicted from seemingly equivalent pressure and
  force loads in a eigenvalue buckling analysis. The difference can be attributed to the fact that pressure
  is considered as a “follower” load. The force on the surface depends on the prescribed pressure
  magnitude and also on the surface orientation. Forces are not considered as follower loads. As with
  any numerical analysis, it is recommended to use the type of loading which best models the in-service
  component. See Pressure Load Stiffness of the Mechanical APDL Theory Reference for more details.


• Note that eigenvalues represent scaling factors for all loads. If certain loads are constant (for example,
  self-weight gravity loads) while other loads are variable (for example, externally applied loads), you
  need to ensure that the stress stiffness matrix from the constant loads is not factored by the eigenvalue
  solution.

One strategy that you can use to achieve this end is to iterate on the eigensolution, adjusting

the variable loads until the eigenvalue becomes 1.0 (or nearly 1.0, within some convergence

tolerance).

Consider, for example, a pole having a self-weight W 0 , which supports an externally-applied load,

A. To determine the limiting value of A in an eigenvalue buckling solution, you could solve re-

petitively, using different values of A, until by iteration you find an eigenvalue acceptably close

to 1.0.

Figure 7.2: Adjusting Variable Loads to Find an Eigenvalue of 1.0

Wo Wo Wo

A=1. 0 A= 100 A= 111

λ= 1 00:

F= 100 + 100 Wo

λ=1. 1 :

F= 110 +1.1Wo

λ=0. 99 :

F= 110 +0. 99 Wo

1 2 3

• You can apply a nonzero constraint in the prestressing pass as the static load. The eigenvalues found
  in the buckling solution will be the load factors applied to these nonzero constraint values. However,
  the mode shapes will have a zero value at these degrees of freedom (and not the nonzero value
  specified).


• At the end of the solution, leave SOLUTION (FINISH).

7.5.3. Obtain the Eigenvalue Buckling Solution

This step requires file Jobname.ESAV from the static analysis. Also, the database must contain the
model data (issue RESUME if necessary). Follow the steps below to obtain the eigenvalue buckling
solution.

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Procedure for Eigenvalue Buckling Analysis