Opis prac
Cienka płyta jest w pełni zamocowana na lewym końcu i poddana równomiernemu naciskowi. Small deformations are considered and the self-weight is neglected in this example. The problem is described by the following set of parameters. Determine the maximum deflection uz,max.
Material | Elastic-Plastic | Moduł E | E | 210000.000 | MPa |
współczynnik Poissona | ν | 0.000 | - | ||
Moduł ścinania | G | 105000.000 | MPa | ||
Granica plastyczności | fy | 40.000 | MPa | ||
Geometry | Plate | obwiednia | L | 1.000 | m |
Szerokość | w | 0.050 | m | ||
Grubość | t | 0.005 | m | ||
Load | Uniform Pressure | p | 2.750 | kPa |
Analytical Solution
The quantities of the load are discussed at first. The moment Me when the first yield is occurred and the ultimate moment Mp when the structure becomes plastic hinge are calculated as follows:
The plate is brought into the elastic-plastic state by the pressure p. The bending stress is defined according to the following formula:
where κ is the curvature. The elastic-plastic zone length is described by the parameter xp. The bending stress quantity on the surface is equal to the plastic strength fy at the point xp, see the following schema.
The elastic-plastic moment Mep (internal force) has to equal to the bending moment M (external force). The curvature κp in the elastic-plastic zone results from this equality.
RFEM Settings
- Modeled in RFEM 5.26 and RFEM 6.01
- The element size is lFE=0.020 m
- In case of solid models mesh refinement across the thickness is used (6 elements per thickness)
- Geometrically linear analysis is considered
- The number of increments is 5
- Shear stiffness of the members is neglected
Wyniki
Model | Analytical Solution | RFEM 5 | RFEM 6 | ||
uz,max [mm] | uz,max [mm] | Ratio [-] | uz,max [mm] | Ratio [-] | |
Izotropowy Plastyczny 1D | 166.234 | 166.214 | 1.000 | 166.018 | 0.999 |
Isotropic Plastic 2D/3D, Plate | 162.987 | 0.980 | 162.960 | 0.980 | |
Isotropic Nonlinear Elastic 2D/3D, Plate, von Mises | 165.730 | 0.997 | 165.700 | 0.997 | |
Isotropic Nonlinear Elastic 2D/3D, Plate, Tresca | 166.998 | 1.005 | 166.969 | 1.004 | |
Isotropic Plastic 2D/3D, Solid | 160.601 | 0.966 | 162.429 | 0.977 | |
Isotropic Nonlinear Elastic 2D/3D, Solid, von Mises | 163.003 | 0.981 | 165.593 | 0.996 | |
Isotropic Nonlinear Elastic 2D/3D, Solid, Tresca | 168.725 | 1.015 | 169.691 | 1.021 | |
Izotropowy, nieliniowy, sprężysty 1D | 166.214 | 1.000 | 166.018 | 0.999 |
Uwaga: The results deviation is also caused by the difference between the analytical and numerically calculated torsional constant.