 English
English
Documentation
> > Validation Case: Circular Plate with a Localized Distributed Load

# Validation Case: Circular Plate with a Localized Distributed Load

In this case, we consider the deformation of a thin, circular plate subject to a distributed load at its center. This test case focuses on the entire edge surface of the plate being fixed against both translation and rotation (Fixed support).

Analysis results are compared against hand calculations per Roark’s Formulas for Stress and Strain, Eighth Edition, Table 11.2, Row 17 (p 515,) and Row 16 (p 514.) to determine the displacement as a result of the prescribed load and geometry. ## • Geometry Dimensions
• Plate Radius (a) = 150 mm
• Plate Thickness = 1.5 mm

## Material:

• Structural Steel
• Young’s Modulus (E) = 200 GPa
• Poisson’s Ratio (ν) = 0.29
• Density (ρ) = 7750 kg/m3

## Physics:

• Restraints (Fixture of all degrees of freedom) on the circumference edge surface
• Apply to: Part 1 Face 2
• Force Load (W) can be calculated using the W = q.π.ro2
• Apply to: Part 2 Face 3
• q = 1 N/mm2 = 1MPa
• W = 314.16 N

Note, q and W are equivalent loads – assigning either load type will yield the same result.

## Meshing:

OnScale Solve automatically generated a 3D second-order tetrahedral mesh. The meshing statistics are:

Mesh Quality: Medium

## Reference Solution:

The displacement (δ) of the circular plate is given by: At the center of the circular plate (r = 0) where deflection will be the greatest, it simplifies the equation to: Where D can be calculated from the Young’s Modulus, Poisson’s ratio and thickness of the plate with this equation: yielding a value of  61.415.

The analytical maximum displacement (δmax) therefore, is calculated to be -2.29 mm.

## Results Comparison:

The table below compares the values obtained using the analytical methods described above and the FEA analysis performed using OnScale Solve.

Outputs Analytical Method OnScale Solve
Displacement at r = 0 (mm) -2.29 -2.24 