In this page we compare the analytical and the numerical solution for an uniformly loaded square plate supported at the corners.

You can read the data in the table below.

Young’s modulus

E

100.000.000

kPa

Thickness

h

0,30

m

Poisson’s ratio

\(\nu\)

0,30

–

Length

a

10,00

m

Uniform pressure

q

-10,00

kPa

Flexural rigidity of the plate

D

247253,75

kN/m

The flexural rigidity of the plate is computed as \( {E \cdot h^3}/{12(1-\nu^2)}\).

If you need to understand how to build the model, you can read in our documentation how we built a similar one. You just have to follow the steps except for the supports on the nodes along the edges.

Otherwiseyou can find it through our public tutorials in WeStatiX, you just need to start the calculation.

Now you can compare the results with the solution given in Theory of plates and shells [1].

Description

Parameter

UM

Analytical solution

WSX

Error

Deflections (x=0; y=0)

\(w_{max}\)

m

-1,01E-02

-1,03E-02

2%

Bending moment in the centre of the plate (x=0; y=0)

\(M_{x _{max}}\)

kNm/m

-109,00

-108,594

0%

Bending moment on the edge (x=0; y=a/2)

\(M_{y _{max}}\)

kNm/m

-140,40

-142,716

2%

Finally, we here you can see some screenshots of the results.

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