Isotropic Biased and Orthotropic Analog Plates

The purpose of this test is to validate orthotropic elements properties. You will use an isotropic biased plate and an orthotropic analog plate, computed with a 2D mesh.

Reference:

M. JONES, Mechanics of Composite Materials, Hemisphere publishing corporation, pp250-254, 1975.

ASHTON JE, An Analogy for Certain Anisotropic Plate, Journal of Composite Materials, pp355-358, April 1969.
 

Specifications

Geometry Specifications

Isotropic biased plate:

  • Length:
    L = 500 mm

  • Thickness:
    th = 10 mm

  • Angle:
    θ= 60 deg

   Isotropic plate

Orthotropic analog plate:

  • Length:
    L = 500 mm

  • Thickness:
    th = 10 mm

  • Square geometry with principal axes inclined at -45 deg  
    with respect to the lower side.

Orthotropic plate


Analysis Specifications

Isotropic plate:

  • Young Modulus (material):
    E = 1000 MPa

  • Poisson's Ratio:
    ν = 0

  • Loads (pressure):
    P1 = 1000 Pa

Orthotropic plate:

  • Young Modulus (material):
    E11 = 2250 MPa
    E22 = 250 MPa

  • Shear Modulus:
    G12 = 375 MPa

  • Poisson's Ratio:
    ν12 = 0

  • Loads (pressure):
    P2 = 562.5 Pa

Mesh Specifications:
13 x 13 nodes

Restraints (User defined):
Tx = Ty = Tz = 0 for all edges
 

Results
 

  • Analytical Solution:

    The following formula gives the analytical solution for the vertical displacement at the center of an isotropic biased plate:


    This solution is also valid for an orthotropic plate with the geometry specifications indicated below, and with characteristics given by:

 

  • Computed Results:

    The computed results (in mm) are given in the tables below.
    Normalized results (computed results divided by analytical solution) are listed.

    Plates

     Analytical
    Solution

    Linear Triangle (TR3)

    Parabolic Triangle (TR6)

    Linear Quadrangle (QD4)

    Parabolic Quadrangle (QD8)

    Computed Results

    Normalized
    Results

    Computed Results

    Normalized
    Results

    Computed Results

    Normalized
    Results

    Computed Results

    Normalized
    Results

    Biased Isotropic

    1.907

    1.988

    1.048

    2.011

    1.055

    1.933

    1.013

    1.977

    1.037

    Analog Orthotropic

    1.907

    1.900

    0.996

    1.931

    1.012

    1.908

    1.001

    1.884

    0.988

To Perform the Test:

The Isotropic_biased_plate_QD4.CATAnalysis document presents the complete analysis on an isotropic biased plate, computed with a mesh formed of linear quadrangle elements (QD4).

The Orthotropic_analog_plate_QD4.CATAnalysis document presents a complete analysis on an orthotropic analog plate, computed with a mesh formed of linear quadrangle elements (QD4).

To compute the case with other meshes (TR3, TR6 and QD8), proceed as follow:

  1. Open one of the CATAnalysis documents.

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

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