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Problem Description
This example is the example shown on page 376 in Roark and Young 1975. It is an annular plate with an inner radius of 1.4 inches, an outer radius of 2 inches and a thickness of 0.5 inch. The plate is simply supported at the inner edge and is loaded with a circular line load at a radius of 1.8 inches. The deflection at the free outer edge is compared with results published in Roark and Young 1975.
The results published in Roark and Young 1975 give both the bending and the shear contribution to the edge deflection. Three models are created for the example. The first model (Example 2-012a-thin) uses the thin plate option for the shell elements. Because the thin plate formulation does not include the effects of shear deformations, the results of the thin plate model are expected to compare with the published bending deflection.
The second model (Example 2-012a-thick) uses the thick plate option. Because the thick plate formulation does include the effects of shear deformations, the results of the thick plate model are expected to compare with the sum of the published bending and shear deflections.
The third model (Example 2-012b-thick) again uses the thick plate option but includes area object shear stiffness modifiers v13 = 1,000 and v23 = 1,000. Those stiffness modifiers make the shell element 1,000 times stiffer in shear and thus make the shear deflection negligible. The results of the thick plate model with shear stiffness modifiers are expected to compare with the published bending deflection.
The annular plate is meshed 6x96 (radial by tangential).
The circular line load is applied as a distributed load to dummy frame elements. All of the property modifiers for the dummy frame elements are set equal to zero. Thus, the dummy frame elements have no stiffness.
Tested Features
- Plate bending analysis of shell elements when shear deformations are significant
- Area object stiffness modifiers
- Frame distributed loads
App
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Link:
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https://openbrim.org/objidwgcdyzyogtf4u1jjtoyi.project
Library
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Link:
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https://openbrim.org/objid3d8sfz694uzrl2jdpetgh8.libobj
| Model | Output Parameter | OpenBrIM | SAP2000 | Independent | Percent Difference (SAP2000 vs Independent) | Percent Difference (OpenBrIM vs Independent) |
|---|---|---|---|---|---|---|
A Thin plate | Uz at outer edge Bending Deflection in | −0.00521 | -0.00522 | -0.00521 | 0.2% | 0% |