TEST CASE 6.4 CYLINDER CONTACT PROBLEM
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/cm^{2};
Poisson’s ratio: μ = 0.3;
Stiffness of one-sided links: EA/L = 1·10^{7} 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:
Target value |
Numerical solution |
LIRA 10 |
Deviation, % |
ψ, deg |
120-125 |
122 |
0.00 |
U_{r}, cm |
1.118 |
1.1176 |
0.036 |
Contact domain
Radial displacement U_{r}, cm