Reference:

L.D. Landau, E.M. Lifshitz. Course of Theoretical Physics. In 10 Volumes. Volume VII. Theory of Elasticity. – 4th ed., revised and expanded. – M.: «Nauka», 1987, p. 120.

Problem description:

The cantilever rod is loaded with axial force F at its free end (point B). Determine the safety factor coefficient k.

Problem sketch:

Type of created problem:

Plane frame (X, Z, UY).

Geometric characteristics:

L = 10 m.

Material properties:

Bending stiffness: EI_y = 100 tf·m².

Boundary conditions:

Point А: X = Z = UY = 0.

Loads:

F = 1 tf.

Description model:

The system is modeled using 100 universal finite elements of a spatial bar (FE type is 10). To ensure geometric invariance, the minimal axial stiffness EA = 1 tf was introduced. The number of nodes in the calculation scheme is 101.

Analytical solution:

Calculation results:

Buckling mode