Тест 9.5 Large displacements and loss of stability of a pinched circular arch (new)
Verification of the LIRA-FEM software / Тест 9.5 Large displacements and loss of stability of a pinched circular arch (new) / Analytical solution: L. D. Landau, E. M. Lifshits Theory of Elasticity, M.: Science, 1987, p. 107. 107.
Analytical solution: L. D. Landau, E. M. Lifshitz Theory of Elasticity, М.: «Science», 1987, pg. 107.
Geometry::
 |
R = 41 м; cross-section of the arch - bar b = 50 см, h = 100 см. |
Material characteristics: Е =3 х 107 т/м2, specific weight R0 = 2 т/м3.
Boundary conditions: Points A and B are pinched.
Loads: P = 2000 т.
Rod finite elements of strong bending (FE 309) were used, the breakdown is 180 FE.
The formulas (3.3.20) from Appendix 1 were used to construct the stiffness matrix
A.S. Gorodetsky, I.D. Evzerov Computer models of constructions, K. "Fact", 2007.
CALCULATION RESULTS:
|
The desired value |
Analytical solution |
Calculation results (LIRA) |
Uncertainty,% |
|
w3, м |
66.07 |
66,103 |
0,02 |
Note: The structure becomes unstable under load P = 1950 t, displacement w3 = 19.7 m. Stable equilibrium state – at w3 = 65.889 m.
Preview image: Array
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