Objective
To determine the buckling factor of a cantilever bar subjected to a compressive load applied at its free end.
Reference
L.D. Landau, E.M. Lifshitz, Theory of elasticity, M.: Nauka, 1987, p. 120.
Problem statement
To determine the buckling factor of the cantilever bar.
Design model
A cantilever bar subjected to an axial compressive load applied at its free end.
Geometry
Length L = 10 m
Area F = 5*10-6 m2
Moment of inertia I = 5*10-6 m4
Material properties
Modulus of elasticity Е = 2*107 tf/m2
Boundary conditions
The beam is restrained in all degrees of freedom at point A.
Loads
F = 1 tf
Note
The problem is solved in 2D formulation (model type 2 – XOZ-plane).
The model is generated with FE type 2 – FE of 2D frame.
Nodes: 11. Elements: 10.
Output data
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Design model
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Buckling mode shape
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Comparison of calculation results
| Load | The unknown | Analytical solution | LIRA-FEM | Error, % |
| F | Buckling factor | 2,4674 | 2,4674 | 0,000 |
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