Static Analysis of a Round Plate Clamped along the Contour (surface)

Static Analysis of a Round Plate Clamped Along the Contour (surface)

We need to find the maximum deflection of a round plate of radius R and thickness h, which is clamped (fixed) along the contour and is loaded with a uniform pressure q distributed on the top face of the plate.

Static Analysis of a Round Plate Clamped Along the Contour

Because of the symmetry of this study, we will work with one quarter of the plate.
Input data can be viewed here.
Next, we need to apply boundary conditions. The side surface of the plate will be fully restrained, whereas the free faces introduced after discarding 3/4 of the plate are subjected to partial restraints in the normal to the faces direction, because the points in the sections cannot have extra displacements in the normal direction and have only rotations around the normal due to the symmetry.

Static Analysis of a Round Plate Clamped Along the Contour, the finite element model with applied loads and restraints

The finite element model with applied loads and restraints

An analytical solution for this study can be sought here.

After carrying out calculation with the help of AutoFEM, the following results are obtained:

Table 1.Parameters of the finite element mesh

Finite Element Type	Number of Nodes	Number of Finite Elements
linear triangle	991	1859

Table 2.Result "Displacement, magnitude"*

Numerical Solution Displacement w*, m	Analytical Solution Displacement w, m	Error δ = 100%* \|w* - w\| / \|w\|
4.8354E-004	4.8762E-004	0.84

Static Analysis of a Round Plate Clamped Along the Contour, Result "Displacement, magnitude"

Table 3.Result "Normal Stress OX"*

Numerical Solution Stress σX, Pa	Analytical Solution Stress σ, Pa	Error δ = 100%* \|σX - σ\| / \|σ\|
3.3642E+007	3.3333E+007	0.93

Static Analysis of a Round Plate Clamped Along the Contour, Result "Normal Stress OX"

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