Objective
To determine the buckling factor of a cantilever bar subjected to a uniformly distributed axial compressive load.
Reference
L.D. Landau, E.M. Lifshitz. Theory of elasticity. Moscow: Nauka, 1987, p. 122.
Problem statement
To determine the buckling factor of the cantilever bar.
Design model
A cantilever bar subjected to a uniformly distributed axial compressive load.
Geometry
Length L = 10 m
Area F = 5*10-5 m2
Moment of inertia I = 5*10-5 m4
Material properties
Modulus of elasticity Е = 2*107 tf/m2
Boundary conditions
All degrees of freedom are restrained at Point A.
Loads
f = 1 tf/m
Notes
The problem is solved in 2D formulation (model type 2 – XOZ-plane).
To describe behaviour of the bar, the model is generated with FE type 2 – FE of 2D frame.
Nodes: 101. Elements: 100.
Output data
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Design model
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Buckling mode
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Comparison of calculation results
| Load | The unknown value | Analytical solution | LIRA-FEM | Error, % |
| f | Buckling factor | 7,843 | 7,72111 | 1,55 |
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