TEST CASE 3.5 STABILITY OF RING DISC WITH A HARD CORE UNDER THE ACTION OF TORQUE
Reference:
Dean W. R. The elastic stability of an annular plate. Proc. Roy. Soc. London, Ser. A, 1924, pp. 268-284; E. Ore, D. Dur-ban. Elastoplastic Buckling of Annular Plates in Pure Shear // Journal of Applied Mechanics. Vol 56. September 1989, pp. 644-651.
Problem description:
The annular disk with a hard core is loaded with torque М at point O. Determine the critical value of torque M_{cr}.
Problem sketch:
Type of created problem:
Spatial structure (X, Y, Z, UX, UY, UZ).
Geometric characteristics:
R = 4.18 m; r = 1 m;
Disk thickness: t = 0.1 m.
Material characteristics:
Elastic modulus: E = 2.1·10^{11} Pa;
Poisson’s ratio: μ = 0.3.
Boundary conditions:
Point O: X = Y = Z = UX = UY = 0;
Outer circle edge: X = Y = Z = UX = UY = UZ = 0;
All disk nodes are restrained in the radial direction;
All disk nodes are restrained in the UZ direction (axe Z is perpendicular to the disk plane).
Loads:
М = 1000 МN·m.
Model description:
The system is modeled using 600 finite elements of thin shell (FE type is 44). The nodes of the inner circle edge are combined into an absolutely rigid body with a leading node in the center of the circle (point O). The number of nodes in the calculation scheme is 661.
Calculation results:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
M_{cr}, МN·m |
5334.7^{} |
5601.9 |
4.77 |
Buckling mode