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 = 2.1·10¹¹ 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:

Buckling mode