Reference:

П. Панагиотопулос, Неравенства в механике и их приложения, Москва: «Мир», 1989, стр. 387.

Problem description:

Cylindrical pipe is anchored to concrete. The concrete is considered as absolutely rigid. Pipe is loaded via trapezoidal distributed changed along the height pressure with maximal ordinate P_max. Determine rotational angle ψ, at which contact is maintained. Find also maximal radial displacement U_r.

Problem sketch:

Type of created problem:

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

Geometric characteristics:

Cylinder radius: R = 1.315 m;

Cylinder wall thickness: t = 0.04 m;

h_w = 1.18 m.

Material properties:

Elastic modulus: E = 60 kN/cm²;

Poisson’s ratio: μ = 0.3;

Stiffness of one-sided links: EA/L = 1·10⁷ kN/m.

Boundary conditions:

All circuit nodes: Z = UX = UY = 0;

Points О and А: X = Y = Z = UX = UY = UZ = 0;

Point В: X = Z = UX = UY = UZ = 0.

Loads:

P_max = 5.8·(h_w + 2·R) kN/m.

Model description:

The system is modeled by 180 general finite elements of spatial bar (FE type is 10) and 181 physically nonlinear bar FE of one-sided inelastic links (FE type is 265). Because of symmetry only a half of construction is considered. For nonlinear solution, iterative process is used (number of steps is 1, minimum number of iterations is 2334).

Calculation results:

Contact domain

Radial displacement U_r, cm