Summary
The paper gives a short introduction to the free formulation theory for finite elements, and indicates how this theory also can be used for structural analysis including geometric and material nonlinearities. Some new flat, triangular shell elements have been developed using this theory. These elements are non-conforming, but satisfy the patch test. A novel feature is that these elements include the normal rotation as well as the conventional three translational and two rotations for flexure at the corner nodes. The drilling freedoms improve the membrane behaviour significantly and are particularly useful in making a complete set of rotational freedoms for shells. The high accuracy of the shell elements are documented through a series of linear and nonlinear examples.
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References
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Nygård, M.K., Bergan, P.G. (1987). An Unconventional Class of Elements for Nonlinear Shell Analysis. In: De Roeck, G., Quiroga, A.S., Van Laethem, M., Backx, E. (eds) Shell and Spatial Structures: Computational Aspects. Lecture Notes in Engineering, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83015-0_34
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DOI: https://doi.org/10.1007/978-3-642-83015-0_34
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