Тест 9.3 Hinged rod system 3. Large displacements and loss of stability (new)

Analytical solution: А. V. Perelmuter, V. I. Slivker Stability of structures and related issues, М.: SKADSOFT Publishers, 2007, p. 585.

Geometry::

a = 9 м; b =10 м.

Material characteristics: ЕA1 = ЕA2 = 1000000 т, ЕA3 = 1000 т;

linear weight: q1 = 0.25 т/м, q2 = 0.00025 т/м.

Boundary conditions: u_C = w_C = w_A = w_B = 0, u_B = u_D.

Loads: P = 80 т.

The system was modeled by three finite elements of the filament (FE 310- filament).

CALCULATION RESULTS:

Loading	The desired value	Analytical solution	Calculation results (LIRA)	Uncertainty,%
	N1, т	-112,21	-111,88	0,3
	N2, т	118,35	118,22	0,1
	N3, т	-8,532	-8,95	0,5
A	uA, м	18,014	18,017	0,016
B	uB, м	18,096	18,111	0,003
D	wD, м	-0,0853	-0,0895	1,1

Note: The structure loses stability under load P = 57,450 т, movesu_A = 6,665м, u_B = 3,602 м, w_D = 2,324м. The stable equilibrium state is at u_A = 18,013 м, u_B = -18,085 м, w_D = -0,0663м.

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