 Register   #### TEST CASE 6.3 CIRCULAR PLATE ON A SINGLE-SIDED ELASTIC FOUNDATION

Reference:

П. Панагиотопулос, Неравенства в механике и их приложения, Москва: «Мир», 1989, стр. 384.

Problem description:

Circular linear-elastic plate was motionless and supported by single-sided elastic foundation. Then this plate was loaded by uniformly area-distributed load q and by edge-distributed bending moment M. Determine rotational angle of plate edge ψ and domain with contact of plate and foundation at coefficient а value 1; 2; 3; 4; 5; 5.1.

Problem sketch: Type of created problem:

The spatial structure (X, Y, Z, UX, UY, UZ).

Geometric characteristics:

Plate radius: R = 6 m;

Plate thickness: t = 0.06 m.

Material properties:

Elastic modulus: E = 2.1·1011 Pa;

Poisson’s ratio: μ = 0.

Boundary conditions:

All plate nodes: X = Y = UX = UZ = 0;

Plate central assembly: UY = 0;

Plate boundary nodes: Z = 0.

q = 600 N/m2;

M = a·q·R2/32.

Model description:

The system is modeled by 95 finite elements of thin shell (FE type is 44). Because of symmetry only a sector of circular plate is considered. For nonlinear solution iterative process is used.

Analytical solution:

Rotational angle of plate edge is an angle between the perpendiculars of deformed and nondeformed plate surface. It is defined via expression ψ = dw/dn - derivative of plate displacement along normal to the boundary (along radius).

Calculation results:

 а Target value Number of iterations Analytical solution Numerical solution LIRA 10 Deviation, % 1 ψ·10-5, rad 5700 7.50 7.29 7.119 5.35 2 7100 23.00 22.236 21.872 5.16 3 12000 43.90 43.80 43.407 1.14 4 14600 71.50 72.379 71.503 0.004 5 16400 107.14 107.176 106.52 0.58 5.1 26000 126.50 126.117 121.40 4.03 1 Contact domain, m 5700 3.70 / 3.78 3.70 3.70 0.00 2 7100 2.58 / 2.64 2.58 2.58 0.00 3 12000 1.56 / 1.62 1.56 1.56 0.00 4 14600 0.54 / 0.60 0.54 0.60 0.00 5 16400 0.00 0.00 0.00 0.00 5.1 26000 No contact No contact No contact 0.00