SS-V: 5020 Lateral Buckling of a Right Angle Frame

Definition

Perform analysis of buckling and post-buckling of a thin-walled frame-like structure in the shape of right angle (Figure 1). One end of the structure is clamped, and a conservative load in X-directions is applied to the other end.

The material properties are:

Properties

Value

Modulus of Elasticity

7.124e+10 pa

Poisson's Ratio

0.31

Figure 1. Geometry and loading

Results

Structure is simulated as a solid. Reference critical load found from 1D beam bending model of the structure is P = 0.820035 N. Negligible perturbation load of Pz = P*1.e-4 = 8.2e-5 N is applied in lateral Z-direction at the loaded end of the structure in order to cause a very small initial deflection of the structure from the flat. The main load was gradually increased from 0 to 1.6*P.

Figure 2 shows maximum deflections versus applied load. The load-lateral deflection curve is in a good agreement with the results reported in the reference. Transversal post-buckling behavior at first is associated with a very small transversal stiffness, but then the load carrying capacity increases (load-displacement curve flattens). In-plane behavior is almost monotonic, no capacity increase occurs in the range of load change.

3D solution predicts the critical load approximately 10% lower than 1D beam model solution. Figure 3 shows von Mises stress distribution which is substantially different from the one assumed in the beam bending model.

Figure 2. Load deflection graph

Figure 3. Deformed shape and von Mises stress plot at load 1.4 N