Two techniques are available for predicting the buckling load and buckling mode shape of a structure: nonlinear buckling analysis (see (a) in Figure 7.1: Buckling Curves), and eigenvalue (or linear) buckling analysis (see (b) in Figure 7.1: Buckling Curves). Because the two methods can yield dramatically different results, it is necessary to first understand the differences between them.
Figure 7.1: Buckling Curves
(a) Nonlinear load-deflection curve, (b) Linear (Eigenvalue) buckling curve
Nonlinear buckling analysis is usually the more accurate approach and is therefore recommended for design or evaluation of actual structures. This technique employs a nonlinear static analysis with gradually increasing loads to seek the load level at which your structure becomes unstable, as depicted in Figure 7.1: Buckling Curves (a).
Using the nonlinear technique, your model can include features such as initial imperfections, plastic behavior, gaps, and large-deflection response. In addition, using deflection-controlled loading, you can even track the post-buckled performance of your structure (which can be useful in cases where the structure buckles into a stable configuration, such as "snap-through" buckling of a shallow dome).
Eigenvalue buckling analysis predicts the theoretical buckling strength (the bifurcation point) of an ideal linear elastic structure. (See Figure 7.1: Buckling Curves (b).) This method corresponds to the textbook approach to elastic buckling analysis: for example, an eigenvalue buckling analysis of a column will match the classical Euler solution. However, imperfections and nonlinearities prevent most real-world structures from achieving their theoretical elastic buckling strength. Thus, eigenvalue buckling analysis often yields unconservative results, and should generally not be used in actual day-to-day engineering analyses.
There are two methods to apply prestress effects in an eigenvalue buckling analysis:
Linear perturbation analysis (preferred) — The preferred method uses linear perturbation analysis because it accommodates linear or nonlinear, static or full transient prestressed cases in the prior base analysis. See:
| General Procedure for Linear Perturbation Analysis - general description of linear perturbation analysis |
| Second Phase - Eigenvalue Buckling Analysis - description of the procedure for a linear perturbation eigenvalue buckling analysis |
| Eigenvalue Buckling Analysis Based on Linear Perturbation in the Theory Reference - description of the theory and governing equations for linear perturbation eigenvalue buckling analysis |
| Example 9.6: Using Linear Perturbation to Predict a Buckling Load - example using linear perturbation to predict a buckling load, considering a linear (case 1) and nonlinear (case 2) base analysis |
You can include inertia relief to simulate a minimally restrained structure in a linear perturbation eigenvalue buckling analysis. For details and the commands used to include inertia relief calculations, see Inertia Relief in a Linear Perturbation Static Analysis in the Basic Analysis Guide.
PSTRES command (legacy procedure) — An alternative legacy procedure that is limited to a linear prestress analysis uses the PSTRES command to obtain a static solution for the prior base analysis. See:
| Eigenvalue Buckling Analysis Process- detailed description of the procedure using PSTRES |
| Example: Eigenvalue Buckling Analysis (GUI Method)- example using PSTRES to predict a buckling load |