Objective
To determine the stress-strain state of a cylindrical tank with a wall of constant thickness subjected to liquid pressure.
Reference
S.Timoshenko, S. Woinowsky-Krieger. Plates and shells. M.: Nauka, 1963.
Problem statement
To determine the maximum radial displacement w of the tank wall, as well as the bending moment М0 acting at the rigid support.
Design model
A cylindrical tank rigidly fixed at the bottom is subjected to liquid pressure p, varying linearly with height.
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Geometry
Radius R(а) = 1 m
Thickness h = 0,005 m
Height H(d) = 5 m
Material properties
Modulus of elasticity Е = 2 * 108 kPa
Poisson's ratio ν = 0,3
Boundary conditions
Restraints in all degrees of freedom (DOF) are applied along the lower edge of the cylinder.
Loads
Pressure varying linearly with height, γ = 10000 kN/m3 (lower ordinate of the pressure diagram q = γH = 50000 kN/m2).
Note
The problem is solved in a 3D formulation (model type 5).
The model is generated with FE type 44 – arbitrary quadrilateral FE of shell.
The finite element mesh consists of 200 elements along the height of the cylinder and 64 elements along the circumference.
A local coordinate system is assigned to the nodes of the model (the local X1-axes of nodes are directed outward from the centre of the cylinder).
Nodes: 12864. Elements: 12800.
Output data
Analytical solution
Comparison of calculation results
Without additional side nodes:
| Parameter | Analytical solution | LIRA-FEM | Error, % |
| Max deflection w, m | 0,05043 | 0,05004 | 0,7733 |
| Bending moment at fixation M0, kN*m | 74,82 | 74,442 | 0,5052 |
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Note: М0 is calculated as the ratio of nodal reaction to the distance between nodes: М0 = 7,305 / 0,09813 = 74,442 kN*m |
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With additional side nodes:
| Parameter | Analytical solution | LIRA-FEM | Error, % |
| Max deflection w, m | 0,05043 | 0,05044 | 0,0198 |
| Bending moment at fixation M0, kN*m | 74,82 | 75,9696 | 1,5132 |
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Note: М0 is calculated as the ratio of nodal reaction to the distance between nodes: М0 = 7,4549 / 0,09813 = 75,9696 kN*m |
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