TEST CASE 3.2 STABILITY OF CANTILEVER
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·m^{2}.
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:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
Safety factor |
2.4674^{} |
2.4674 |
0.00 |
Buckling mode