Тест 9.5 Large displacements and loss of stability of a pinched circular arch (new)

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.

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