Solid patch test

Image of brick

Objective

To present and verify the results obtained by FEEA SDK for the solid patch test proposed by MacNeal and Harder. This example also demonstrates the application of prescribed displacement loading in FEEA SDK.

Problem description

This is an extension patch test in three dimensions. A unit cube made up of seven irregularly shaped solid elements is subjected to prescribed displacements at the edges that theoretically impose a constant stress field over the model. The geometry, properties and loading are as described in MacNeal and Harder. 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 * (2x + y + z)/2
· v = 0.001 * (x + 2y + z)/2
· w = 0.001 * (x + y + 2z)/2

Finite element model

A model consisted of eight 8-node hexahedral elements is considered. See images below:

Image of the model  Image of the model

Solution

The theoretical solution is given in MacNeal and Harder [page 10, Table 2] and we finally obtain:

Solid patch test - strains
Reference0.0010.0010.0010.0010.0010.001
FEEA SDK0.0010.0010.0010.0010.0010.001

Solid patch test - stresses
Reference200020002000400400400
FEEA SDK200020002000400400400

Conclusion

The results obtained with FEEA SDK show an exact comparison with the theoretical solution.