TEST CASE 4.5 CONSOLE BENDING TO CYLINDER SURFACE FORMING
Reference:
L.D. Landau, E.M. Lifshitz. Course of Theoretical Physics. In 10 Volumes. Vol. VII. Theory of Elasticity – 4th edition. – М.: Nauka, 1987, p. 106
Problem description:
Console bar is loaded by bending moment М_{у} at point B. Determine vertical displacement value w and horizontal displacement value u at point B. Find also horizontal displacement value u at the centre of bar span.
Problem sketch:
Type of created problem:
Spatial structure (X, Y, Z, UX, UY, UZ).
Geometric characteristics:
L = 10 m; b = 1 m; h = 0.01 mm.
Material properties:
Elastic modulus: E = 1.2·10^{8} tf/m^{2}.
Boundary conditions:
Point А: X = Y = Z = UX = UY = UZ = 0.
Loads:
M_{y} = 2π tf·m.
Model description:
The system is modeled via 100 geometrically nonlinear elements of tight bend bar (FE type is 309). Automatic selection of step of loading applying for nonlinear problem solution is used.
Calculation results:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
w_{В}, m |
0.00 |
-0.0433 |
– |
u_{В}, m |
-10.00 |
-10.042 |
0.42 |
u_{L}_{/2}, m |
-5.00 |
-5.0001 |
0.002 |
Vertical displacements distribution w, m
Horizontal displacements distribution u, m