to the point at which the minimum time step increment (specified by DELTIM or NSUBST) is achieved.
The minimum time step will directly affect the precision of your results.
7.3.3. Unconverged Solution
An unconverged solution does not necessarily mean that the structure has reached its maximum load.
It could also be caused by numerical instability, which might be corrected by refining your modeling
technique. Track the load-deflection history of your structure's response to decide whether an uncon-
verged load step represents actual structural buckling, or whether it reflects some other problem. Perform
a preliminary analysis using the arc-length method (ARCLEN) to predict an approximate value of
buckling load. Compare this approximate value to the more precise value calculated using bisection to
help determine if the structure has indeed reached its maximum load. You can also use the arc-length
method itself to obtain a precise buckling load, but this method requires you to adjust the arc-length
radius by trial-and-error in a series of manually directed reanalyses.
7.3.4. Hints and Tips for Performing a Nonlinear Buckling Analysis
If the loading on the structure is perfectly in-plane (that is, membrane or axial stresses only), the out-
of-plane deflections necessary to initiate buckling will not develop, and the analysis will fail to predict
buckling behavior. To overcome this problem, apply a small out-of-plane perturbation, such as a modest
temporary force or specified displacement, to begin the buckling response. (A preliminary eigenvalue
buckling analysis of your structure may be useful as a predictor of the buckling mode shape, allowing
you to choose appropriate locations for applying perturbations to stimulate the desired buckling re-
sponse.) The imperfection (perturbation) induced should match the location and size of that in the real
structure. The failure load is very sensitive to these parameters.
Consider these additional hints and tips as you perform a nonlinear buckling analysis:
- Forces (and displacements) maintain their original orientation, but surface loads will "follow" the changing
geometry of the structure as it deflects. Therefore, be sure to apply the proper type of loads. - Carry your stability analysis through to the point of identifying the critical load in order to calculate the
structure's factor of safety with respect to nonlinear buckling. Merely establishing the fact that a structure
is stable at a given load level is generally insufficient for most design practice; you will usually be required
to provide a specified safety factor, which can only be determined by establishing the actual limit load. - For those elements that support the consistent tangent stiffness matrix, activate the consistent tangent
stiffness matrix (KEYOPT(2) = 1 and NLGEOM,ON) to enhance the convergence behavior of your nonlinear
buckling analyses and improve the accuracy of your results. This element KEYOPT must be defined before
the first load step of the solution and cannot be changed once the solution has started. - Many other elements (such as BEAM188,BEAM189,SHELL181,REINF264,SHELL281, and ELBOW290) provide
consistent tangent stiffness matrix with NLGEOM,ON.
7.4. Performing a Post-Buckling Analysis
A post-buckling analysis is a continuation of a nonlinear buckling analysis. Aft er a load reaches its
buckling value, the load value may remain unchanged or it may decrease, while the deformation con-
tinues to increase. For some problems, after a certain amount of deformation, the structure may start
to take more loading to keep deformation increasing, and a second buckling can occur. The cycle may
even repeat several times.
Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationPerforming a Post-Buckling Analysis