Clamped Square Plate Under a Uniformly Distributed Load

Let us consider a clamped square plate under a pressure.
Only a quarter of the plate is analyzed due to symmetry conditions on the corresponding edges (restrained displacements in the direction of axis of the coordinate system normal to the face plane).

Clamped Square Plate Under a Uniformly Distributed Load, the finite element model with applied loads and restraints

The finite element model with applied loads and restraints

Analytical solution for the deflection in the center of the plate is given by formula:
.
Let us use the following data: the length and width of the plate a = 500 mm, plate thickness is h = 3 mm, applied pressure is q = 800 Pa.
Elastic properties of the material are taken as: E = 2.1E+011 Pa, ν = 0.28.
Analytical solution can be expressed as: w = 1.2288E-004 m.
After carrying out calculations with the help of AutoFEM, the following results are obtained:

Table 1.Parameters of finite element mesh

Finite Element Type	Number of Nodes	Number of Finite Elements
quadratic tetrahedron	3698	10584

Table 2.Result "Displacement, magnitude"*

Numerical Solution Displacement w*, m	Analytical Solution Displacement w, m	Error δ = 100% * \|w* - w\| / \|w\|
1.2295E-004	1.2288E-004	0.06

Clamped Square Plate Under the Uniform Load, Result "Displacement, magnitude"

Conclusions:

The relative error of the numerical solution compared to the analytical solution is equal to 0.06% for quadratic finite elements.

*The results of numerical tests depend on the finite element mesh and may differ slightly from those given in the table.