Simply-supported Sandwich Plate

The purpose of this test is to check the elements on a non-isotropic plate structure. Transverse shear effects are necessary, but Kirchoff elements must not be used.

The reference is the mesh formed of parabolic hexahedron elements (HE20).
You will use a 2D meshes.

Reference:

Modélisation des structures par éléments finis, BATOZ J.L., DHATT G., Vol.2, p.341; Hermès Edition, Paris 1990.
 

Specifications

Geometry Specifications

Length:
L = 100 mm

Thickness:
th = 10 mm

Sandwich:
0/0/0 deg


Analysis Specifications

Face Sheets:

  • Young Modulus (material):

    • E11 = 341.56 MPa

    • E22 = 179.3 MPa

  • Shear Modulus:

    • G12 = 100 MPa

    • G13 = 60.8 MPa

    • G23 = 101.5 MPa

  • Poisson's Ratio:
    ν = 0.44


Transverse shear stress

Core:

  • Young Modulus (material):

    • E11 = 34.156 MPa

    • E22 = 17.93 MPa

  • Shear Modulus:

    • G12 = 10.0 MPa

    • G13 = 6.08 MPa

    • G23 = 10.15 MPa

  • Poisson's Ratio:
    ν12 = 0.44


Translational Displacement

Mesh Specifications:
Size of elements = 5 mm


Load and restraints

Restraints (User defined):

  • Edge AB: Tx = Ty = Tz = Ry = 0

  • Edge BC: Tx = Ty =  Ry = Rz= 0

  • Edge CD: Tx = Ty = Rx = Rz = 0

  • Edge AD: Tx = Ty = Tz = Rx = 0

Loads:
Pressure P = 1e+006 N_m2
 

Results

The results correspond to:

  • the displacement in the z-direction at point C
  • the stress σxx at point C in the middle of the upper layer
  • the stress σxz at point D in the middle of the core.

The computed results are given in the table below.

Quantity

 Point of localization

Reference Solution:

Parabolic Hexahedron (HE20)

Linear Triangle (TR3)

Parabolic Triangle (TR6)

Linear Quadrangle (QD4)

Parabolic Quadrangle (QD8)

W [mm]

Point C

41.83

41.088

41.306

42.072

41.987

σxx [MPa]

Point C

57.17

57.357

57.964

56.753

56.984

σxz [MPa]

Point D

4.128

4.08

4.64

4.04

4.32

To Perform the Test:

The simply_supported_sandwich_plate_he20.CATAnalysis document presents the complete analysis of this case, computed with a mesh formed of parabolic hexahedron elements (HE20). These results are the reference.

The simply_supported_sandwich_plate_tr6.CATAnalysis document presents a complete analysis on an orthotropic analog plate, computed with a mesh formed of parabolic triangle elements (TR6).

To compute the case with other meshes, proceed as follow:

  1. Open the simply_supported_sandwich_plate_tr6.CATAnalysis document.

  2. In the Advanced Meshing Tools workbench, replace the mesh specifications.

  3. In the Generative Structural Analysis workbench, compute the case.