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.

Loads:

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: