WOLFRAM|DEMONSTRATIONS PROJECT

Partially Loaded Rectangular Plate

​
display
problem
result
load point [m]
first corner
second corner
length [m]
first side
2
second side
2
load bysquare meter N/
2
m
​
1000
material
steel
thickness ofplate [mm]
10
accuracy ofsolution
4
axes
This Demonstration shows an approximate method for determining the deflection of a rectangular plate, freely supported at the boundary (so that the momentum on the boundary is zero). With regard to the material, the calculation is based on Young's modulus and the Poisson ratio. To understand the problem more easily, the graphic shows the load as a cuboid whose height corresponds to a unit load if the cuboid is made of iron.
The governing differential equation is
E
3
h
12(1-
2
ν
)
4
δ
w
δ
4
x
+2
4
δ
w
δ
2
x
2
δy
+
4
δ
w
δ
4
y
=
q
m,n
sin
mπx
a
sin
nπy
b
.