# 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.