A nonlinear buckling analysis is a static analysis with large deflection active (NLGEOM,ON), extended to a point where the structure reaches its limit load or maximum load. Other nonlinearities such as plasticity may be included in the analysis. The procedure for a static analysis is described in Structural Static Analysis, and nonlinearities are described in Nonlinear Structural Analysis.
The basic approach in a nonlinear buckling analysis is to constantly increment the applied loads until the solution begins to diverge. Be sure to use a sufficiently fine load increment as your loads approach the expected critical buckling load. If the load increment is too coarse, the buckling load predicted may not be accurate. Turn on bisection and automatic time stepping (AUTOTS,ON) to help avoid this problem.
With automatic time stepping on, the program automatically seeks out the buckling load. If automatic time stepping is ON in a static analysis having ramped loading and the solution does not converge at a given load, the program bisects the load step increment and attempts a new solution at a smaller load. In a buckling analysis, each such convergence failure is typically accompanied by a "negative pivot" message indicating that the attempted load equals or exceeds the buckling load. You can usually ignore these messages if the program successfully obtains a converged solution at the next, reduced load. The program normally converges to the limiting load as the process of bisection and resolution continues 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.
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 unconverged 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.
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 select appropriate locations for applying perturbations to stimulate the desired buckling response.) 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.
If the predictor option is used, the solution could miss some critical buckling points even though the solution converges to a given tolerance. Therefore, Ansys, Inc. recommends turning the predictor off (PRED,OFF) for a nonlinear buckling analysis.