Тест 4.5 Stability of a flat bend shape of an articulated beam
Verification of the LIRA-FEM software / Тест 4.5 Stability of a flat bend shape of an articulated beam / Analytical solution: L. D. Landau, E. M. Lifshitz Theory of Elasticity, M.: Science, 1987, p. 123.
Analytical solution: L. D. Landau, E. M. Lifshits Theory of Elasticity, Moscow: Science, 1987, p. 123.
Geometry:
 |
L = 1 м. |
Material characteristics: ЕIy = 300 тм2, EIz = GI = 1 тм2.
Boundary conditions:
1. uA = uB = vA = vB = wA = wB = θXA = θXB = 0;
2. uA = uB = vA = vB = wA = wB = θXA = θXB = θZA = θZB = 0.
Loads: f is applied along the entire length of the rod f=1 t/m and on its left half f=2 т/м, F=1 т,
My = 1 тм.
Rod finite elements ( FE 10) were used, the breakdown is 100 FE.
Formulas (3.3.20) from the book by A.S. Gorodetsky and I.D. Evzerov, Computer Modeling of Structures, Moscow, ASV, were used for constructing the stability matrix.», 2009.
CALCULATION RESULTS:
|
Loads |
The desired value |
Analytical solution |
Calculation results (LIRA) |
Uncertainty,% |
|
Boundary condition 1 | ||||
|
F |
Resistance reserve coefficient |
16,914 |
16,936 |
1,9 |
|
My |
p |
3,142 |
0,01 | |
|
fL |
28,27 |
28,32 |
0,18 | |
|
fL/2 |
27,32 |
27,31 |
0,04 | |
|
Граничное условие 2 | ||||
|
F |
Stock Factor |
25,9 |
25,9 |
0 |
|
My |
2p |
6,284 |
0,01 | |
|
fL |
47,6 |
47,59 |
0,02 | |
|
fL/2 |
45,3 |
45,23 |
0,15 | |
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