Membrane plate patch test
Objective
To present and verify the results obtained by FEEA SDK for the membrane plate elements patch test proposed by
MacNeal and Harder.
This example also demonstrates the application of prescribed displacement loading in FEEA SDK.
Problem description
In this example a rectangular plate with irregularly shaped elements is subjected to prescribed displacements at the edges
that theoretically impose a constant stress field over the model.
The above Figure shows the model to be analyzed.
The boundary conditions (applied prescribed displacements) of the model are calculated by the following equations:
· u = 0.001 * (x + y/2)
· v = 0.001 * (y + x/2)
Finite element model
The finite element model consists of five 4-node quadrilateral plane stress elements. See image below:
Solution
The theoretical solution is given in MacNeal and Harder [page 10, Table 2]
and with the use of Timoshenko [page 6, equations (2)] we obtain:
Both the theoretical and the FEEA solution are listed below:
Membrane plate patch test - prescribed displacements
|
 |
 |
 |
 |
 |
 |
| Reference | 0.001 | 0.001 | 0.001 | 1333.33 | 1333.33 | 400 |
| FEEA SDK | 0.001 | 0.001 | 0.001 | 1333.33 | 1333.33 | 400 |
Conclusion
The results obtained with FEEA SDK show an exact comparison with the theoretical solution.