Skip to end of metadata
Go to start of metadata

Step 9: Validate the results

We checked in the previous step that the BC's have been applied correctly and the deflection looks plausible.

Comparison With Plate Theory

An FEA analyst displays his mettle by going head-to-head with theory. The theoretical solution for a clamped plate subjected to pressure is presented by Timoshenko and Woinowsky-Krieger, page 202. This solution can be modified to account for the presence of stiffeners using the parallel axis theorem. This calculation and the resulting stress and displacement values have been generously provided by Prof. Alan Zehnder and are sumarized in this pdf document. Do take the time to review this document.

The head-to-head comparison of the analytical values with the FEA values from Step 8 at the center of the structure is presented in the following table.

Entity

Location

FEA

Theory

w

 

3.8 mm

3.6 mm

σxx

Bottom

-56 MPa

-50 MPa

σxx

Top

312 MPa

350 MPa

σyy

Bottom

-28 MPa

-20 MPa

σyy

Top

38 MPa

105 MPa

The deflection at the center is about 8% larger than the theoretical value due to shear deformation in the FEA model that is not accounted for in the analytical result. Correlation of stresses in the center is reasonably good. It might improve if solution for anisotropic plate were used. Also, the stiffeners are not at the centerline of the model, while maximum stresses in theory are calculated at the center.

The head-to-head comparison of the edge stresses is given in the following table.

Entity

Location

FEA

Theory

σxx

Bottom

116 MPa

100 MPa

σxx

Top

-653 MPa

-704 MPa

σyy

Bottom

77 MPa

78 MPa

σyy

Top

-300 MPa

-403 MPa

There is good correlation of the edge stress on the bottom of facesheet but the edge stress at the top of the stiffeners is overestimated by the theory. This is possibly due to the stiffeners not being at the centerline of the model while the maximum stresses in theory are calculated at the center.

Back to Problem Specification

See and rate the complete Learning Module

Go to all ANSYS Learning Modules

  • No labels