Тест 5.5 Hovgaard's task

Analytical solution: W. Hovgaard, “Stress in three dimensional pipe-bends”, Transactions of ASME, vol. 57, FSP 75 – 12, p. 401 – 416.

Geometry:

Circular cross-section: Square: A = 0.3439 x 10-2 м2 bending radius: R = 0.922 м thickness: e = 0.00612 м outer radius: Re = 0.0925 м inner radius: Ri = 0.08638 м moments of inertia: IY = IZ = 0.1377 x 10-4 м4 (straight elements) IY = IZ = 0.5887 x 10-5 м4 (curved elements)

Point coordinates, м

	A	B	C	D
x	0	1.96	0	0
y	-2.75	0	-2.75	0
z	-3.69	0	0	0

Material characteristics: Е = 1.658 х 10¹¹ Па, v = 0.3, ρ = 13404.106 кг/м³ (pipe filled with water).

Boundary conditions: Points A and B are pinched.

Loads: For modal analysis.

CALCULATION RESULTS:

Order of form	Frequency, Hz		Uncertainty,%
	Analytical solution	Calculation results (LIRA)
1	10,18	10,25	0,7
2	19,54	20,02	2,46
3	25,47	25,171	1,17
4	48,09	48,073	0,03
5	52,86	52,676	0,35
6	75,94	85	11,93
7	80,11	87,19	8,84
8	122,34	129,29	5,68
9	123,15	132,552	7,63

Preview image: Array

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