Stress analysis of a flat plate with holes

Update: June 1, 2017
OpenFOAM 4.x

Case directory

$FOAM_TUTORIALS/stressAnalysis/solidDisplacementFoam/plateHole

Summary

This is a stress analysis of a loaded flat plate with a circular hole. Only the upper right quarter is modeled and we use symmetry conditions to estimate the overall deformation. We will set (10000, 0, 0) Pa for region right and (0, 0, 0) Pa for region up and region hole. Symmetry conditions will be set for region left and region down, and the calculation is performed as a two-dimensional problem with a single mesh in the Z direction.

Model geometry Model geometry

After the calculation, the values on the region left are sampled to create a graph of the XX component of the stress. The sampling settings are specified in the file system/singleGraph as follows.

singleGraph
{
    start   (0 0.5 0.25);
    end     (0   2 0.25);
    fields  (sigmaxx);

    #includeEtc "caseDicts/postProcessing/graphs/sampleDict.cfg"

    setConfig
    {
        axis    y;
    }

    // Must be last entry
    #includeEtc "caseDicts/postProcessing/graphs/graph.cfg"
}		

The meshes are as follows, and the number of mesh is 1000.

Mesh Meshes

The calculation result is as follows.

Displacement (D, multiplied by 2.5 million times and reflected in the shape) Displacement (D, multiplied by 2.5 million times and reflected in the shape)
von Mises stress (sigmaEq) von Mises stress (sigmaEq)
Relationship between the Y-coordinate and the stress XX component on the region left (sigmaxx) Relationship between the Y-coordinate and the stress XX component on the region left (sigmaxx)

Commands

cp -r $FOAM_TUTORIALS/stressAnalysis/solidDisplacementFoam/plateHole plateHole
cd plateHole

blockMesh
solidDisplacementFoam

postProcess -func "components(sigma)"
postProcess -func singleGraph

paraFoam

gnuplot
gnuplot>plot "postProcessing/singleGraph/100/line_sigmaxx.xy"

Calculation time

0.2 seconds *Single, Inter(R) Core(TM) i7-2600 CPU @ 3.40GHz 3.40GHz

Reference