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009017
2020-06-27

VE 0017 | Zginanie plastyczne - obciążenie ciągłe

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.


Odniesienia
  1. Lubliner, J. (1990). Teoria plastyczności. Nowy Jork: Macmillana.


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