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.
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 |
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 |
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 |
9,25 |
9,233 |
0,18 |
My/L |
2p |
6,284 |
0,01 | |
fL |
23,3 |
23,3 |
0 |
Preview image: Array
Verification examples
- Section 1 Linear static problems for rod systems, plates and shells, three-dimensional problems
- Section 2 Physically nonlinear problems
- Section 3 Geometrically nonlinear problems for threads, cable-stayed trusses, rods, membranes and plates
- Section 4 Задачи устойчивости, в основном изгибно-крутильные формы потери устойчивости
- Section 5 Modal analysis
- Section 6 Linear dynamic problems
- Section 7 Static and dynamic problems with one-sided constraints
- Section 8 Geometric characteristics of the section
- Section 9 Procritical calculations
- Section 10 Problems of stationary and non-stationary heat conduction
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