Example Description
This example uses a flat plate to test out-of-plane buckling of shell elements. The plate is 24 inches long, 24 inches wide and 1 inch thick. Unit shear and bending stresses, and σ, respectively, are applied to the plate edges in two separate load cases. The buckling loads, cr and σcr, calculated by SAP2000 are compared with independent results.
The modeling for this example is set up such that the automatic area meshing feature of SAP2000 can be used. This makes it easy to test the model with different mesh sizes. In this example both a 16x16 and a 64x64 mesh are used, in separate models.
The automatic area meshing feature has a special option to add a restraint to a degree of freedom at a new joint (created by the meshing) along the edge of the area object if both adjacent corners of the area object have that degree of freedom restrained. This special option is used in this example.
The desired restraints for this example are as follows (see figure on next page):
- Joint 1: Ux, Uy and Uz
- Joints 2, 3: Uz
- Joint 4: Ux and Uz (Ux applied as spring, see discussion that follows)
- All other edge joints created by automatic meshing: Uz
The Ux restraint at joint 4 is applied as a spring with 1E9 kip/in stiffness. This is done so that the automatic area meshing will only put a Uz restraint on the intermediate joints along edge 1-4. If the Ux restraint at joint 4 were specified as a joint restraint rather than a spring, the automatic area meshing would put both Ux and Uz restraints on the intermediate joints along edge 1-4, which is not the desired result.
Four frame objects are defined around the perimeter of the plate spanning from one corner of the plate to the next. The property modifiers for those frame objects are all set to zero so that they contribute no stiffness, mass or weight to the structure. The frame objects are specified to be automatically subdivided at intermediate joints. All of the plate edge loading is applied to these “dummy” frame objects as distributed loads. Applying the load using those beams allows the edge load to be properly distributed when the automatic area meshing is used.
Tested Features
- Buckling analysis of shells
- Automatic area meshing (NxN) with added restraints
- Joint springs
- Frame property modifiers
- Frame distributed load
- Frame automatic subdivide at intermediate joints
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