Problem Description
In this example a straight cantilever beam, modeled with shell elements, is subjected to unit forces at the tip in the three orthogonal directions and unit moments at the tip about the three orthogonal directions, each in a different load case. The tip displacements in the direction of the load are compared with hand calculated results.
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The independent solution is derived using elementary beam theory that assumes no local Poisson’s effect occurs at the support. The beam is modeled in this model to match this assumption. At the fixed end, joint 1 is restrained in the Ux, Uy, Uz and Rz degrees of freedom and joint 8 is restrained in the Ux, Uy and Rz degrees of freedom. Joint 8 is not restrained in the Uz degree of freedom to avoid imposing the unwanted local Poisson’s effect into the model. Also, when the beam is loaded with in-plane shear, an in-plane force equal to half the applied tip load is applied to joint 8 in the opposite direction of the tip load. This special load at joint 8 is applied to model the reaction without the Poisson’s effect.
Tested Features
- Membrane analysis using shell elements
- Plate bending analysis using shell elements
- Effect of shell element aspect ratio
- Effect of geometrical distortion of shell element from rectangular
- Joint force loading
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