Тест 4.4 Stability of the flat cantilever bend form

Verification of the LIRA-FEM software / Тест 4.4 Stability of the flat cantilever bend form / Analytical solution: L. D. Landau, E. M. Lifshitz Theory of Elasticity, M.: Nauka, 1987, p. 123.



Тест 4.4  Stability of the flat cantilever bend form

Analytical solution: L. D. Landau, E. M. Lifshits Theory of Elasticity, M: Nauka, 1987, p. 123.

Geometry:


L = 1 м.

Material characteristics: ЕIy = 300 тм2, EIz = GI = 1 тм2.

Boundary conditions: Point A is pinched.
Point B:
1. without fixings;
2. θX = 0;
3. v = θX = 0;
4. θX = θZ = 0.

Loads: f = 1 т/м, F = 1 т, My = 1 тм.

Rod finite elements (FE 10) were used, the partition is 100 FE. Formulas (3.3.20) from Appendix 1 were used for constructing the stability matrix. A.S. Gorodetsky, I.D. Evzerov Computer models of structures, K. "Fact", 2007.

CALCULATION RESULTS:

Loads

The desired value

Analytical solution

Calculation results (LIRA)

Uncertainty,%

Boundary condition 1

F

Resistance reserve coefficient
stability

4,012

4,013

0,02

My/L

p/2

1,571

0

fL

12,86

12,85

0,08

Boundary condition 2

F

Resistance reserve coefficient

5,54

5,552

0,22

My/L

p

3,142

0,01

fL

15,9

15,95

0,31

Boundary condition 3

F

Stock Factor
устойчивости

10,3

10,31

0,1

My/L

4,5

4,494

0,13

fL

33,15

33,132

0,05

Boundary condition 4

F

Resistance reserve coefficient
stability

9,25

9,233

0,18

My/L

2p

6,284

0,01

fL

23,3

23,3

0


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