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Uniformly loaded and simply supported square plate

Consider a uniformly loaded and simply supported square plate: the problem’s data are listed in the table below.

Young’s modulusE100.000.000kPa
Poisson’s ratio \(\nu\) 0,30
Uniform pressureq-10,00kPa
Flexural rigidity of the plateD247252,75kN/m

The flexural rigidity is calculated as \( {E \cdot h^3}/{12(1-\nu^2)}\)

You can find the model in our tutorials in WeStatiX. Alternatively you can build it yourself: you can read how to do it in our documentation.

Once geometry, properties and boundary conditions are defined, you just have to start the analysis to get the results.

This is the displacements’ field.

Uniformly loaded and simply supported square plate deflection

Secondly, the bending moment

Uniformly loaded and simply supported square plate bending moment

And finally, the nodal forces.

Uniformly loaded and simply supported square plate force corner

Please note that the corners of the plate have a tendency to rise up under the actions of the applied load. The concentrated forces R exist to prevent this and they are therefore directed downward. In order to catch the exact value of these forces you will need to make a finer mesh.

The analytical solution to the problem is known, and you can find it in Theory of plates and shells [1] .

Below we compare the foundamental points of the solution with the results we obtained with our FE analysis.

DescriptionParameterUMAnalytical solutionWSX – rough meshError- rough mesh
Bending moment\(M_{x_{max}}\)kNm/m-47,90-48.070,35%
Reactive forces at the cornersRkN65,0058,4511,21%

And finally the comparison with the results obteined with the finest mesh.

DescriptionParameterUMAnalytical solutionWSX – fine meshError – fine mesh
Bending moment\(M_{x_{max}}\)kNm/m -47,90 -47,910,02%
Reactive forces at the cornersRkN65,0064,870,20%

[1] TIMOSHENKO S., WOINOWSKY Y-RIEGER S., Theory of plates and shells, 2ed., McGraw-Hill, New York, 1959.