Тест 4.10 Stability of a circular arch under moment loading (new)

Analytical solution: С. П. Timoshenko Stability of Elastic Systems, Gostekhteorizdat, 1955, 576 pp..

Geometry:

R = 1 м;

Material characteristics: ЕIy = EIz = 1 тм², GI = 1 тм².

Boundary conditions: uA = vA = vB = wA = wB = θyA = θXB = 0.

Loads:
- 1 – в т. А Mz = -10 тм, в т. В Mz = 10 тм;
- 2 – в т. А Mz = 10 тм, в т. В Mz = -10 тм.

We used rod finite elements (FE 10), breakdown - 100 FE.
The formulas (3.3.20) from the book by A.S. Gorodetsky, I.D. Evzerov, Computer models of structures, M. "ASV" were used for constructing the stability matrix., 2009.

CALCULATION RESULTS:

Loading scheme	The desired value	Analytical solution	Calculation results (LIRA)	Uncertainty,%
1	Stability coefficient	14,8626	14,8606	0,01
2	Stability coefficient	44,8715	44,8663	0,01

Note: In the book by A. V. Perelmuter, V. I. Slivker Stability of structures and related problems, Moscow: Publishing house SCADSOFT, 2007, p. 491 gives an erroneous analytical solution that differs from the solution by S. P. Timoshenko. The given results are one more confirmation of the correctness of S. P. Timoshenko's solution.

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