Objective
To determine the buckling factor of a cantilever strip with a rectangular cross-section subjected to a uniformly distributed transverse load applied to its free end.
Reference
L.D. Landau, E.M. Lifshitz, Theory of elasticity, M.: Nauka, 1987, p. 123.
Problem statement
To determine the buckling factor of the cantilever strip.
Design model
A cantilever strip with a rectangular cross-section is subjected to a uniformly distributed transverse load applied to its free end.
Geometry
Cross-section height b = 0,5 m
Cross-section width h = 0,1 m
Strip length L = 10 m
Material properties
Modulus of elasticity Е = 2*107 tf/m2
Poisson's ratio ν = 0,3
Boundary conditions
The left end is restrained in all degrees of freedom (DOF).
Loads
f = 20 tf/m
Note
The problem is solved in 3D formulation (model type 5).
The model is generated with FE type 44 – arbitrary quadrilateral FE of shell.
Nodes: 2211. Elements: 2000.
Output data
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Design model
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Buckling shape
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Comparison of calculation results
| Load | The unknown | Analytical solution | LIRA-FEM | Error, % |
| f | Buckling factor | 4,39 | 4,23018 | 3,644 |
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