Morley's Problem

The purpose of this test is to evaluate the sensitivity of a plate element to the direction (angular orientation) of the mesh on a plate in bending, in a context of a static case. You will use 2D meshes.

Reference:

  • MORLEY L.S.D., Skew Plates and Structures, Pergamon Oxford 1963.
  • RAZZAQUE A., Program for Triangular Bending Elements with Derivative Smoothing, IJNME Vol 6, pp333-343, 1973.

Specifications

Geometry Specifications

Length:
L = 1 mm

Thickness:
th = 0.01 mm

Angle:
Ø = 80, 60, 40, 30 deg  

Analysis Specifications

Young Modulus (material):
E = 3 x 107 MPa

Poisson's ratio (material):
ν = 0.3

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

Loads:
Pressure load of 1 MPa on the plate
 

Results

The vertical displacements at the center for various mesh directions are given in the following tables.

Output Results (7 x 7 nodes)

Angle
 

 Theoretical value
[mm]

Computed value [mm]

 Linear triangle
(TR3)

 Parabolic triangle
(TR6) 

 Linear quadrangle
(QD4)

 Parabolic quadrangle
(QD8)

 80 deg  

1.409 x 10-3

1.359 x 10-3

1.414 x 10-3

1.42 x 10-3

1.425 x 10-3

 60 deg

0.9318 x 10-3

0.925 x 10-3

0.9334 x 10-3

0.935 x 10-3

0.901 x 10-3

 40 deg

0.3487 x 10-3

0.3455 x 10-3

0.3592 x 10-3

0.3538 x 10-3

0.2923 x 10-3

 30 deg

0.1485 x 10-3

0.1474 x 10-3

0.1483 x 10-3

0.1538 x 10-3

0.1106 x 10-3

Output results (13 x 13 nodes)

Angle
 

Theoretical value
[mm]

Computed value [mm]

 Linear triangle
(TR3)

 Parabolic triangle
(TR6) 

 Linear quadrangle
(QD4)

 Parabolic quadrangle
(QD8)

 80 deg  

1.409 x 10-3

1.409 x 10-3

1.431 x 10-3

1.422 x 10-3

1.422 x 10-3

60 deg

0.9318 x 10-3

0.9403 x 10-3

0.9412 x 10-3

0.937 x 10-3

0.9306 x 10-3

40 deg

0.3487 x 10-3

0.3566 x 10-3

0.3558 x 10-3

0.3493 x 10-3

0.3271 x 10-3

30 deg

0.1485 x 10-3

0.153 x 10-3

0.1537 x 10-3

0.1497 x 10-3

0.1307 x 10-3

To Perform the Test:

The Morley_60degree_TR6_7nodes.CATAnalysis document presents a complete analysis of this case, computed with a mesh formed of 7 nodes per edge and parabolic triangle elements (TR6).

The Morley_80degree_QD8_13nodes.CATAnalysis document presents a complete analysis of this case, computed with a mesh formed of 13 nodes per edge and parabolic quadrangle elements (QD8).

To compute cases with other element types, angular orientation, and number of nodes, 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.