A novel straightforward dynamic approach for the evaluation of extensional modes within GBT 'cross-section analysys'. (May 2017) - Ferrarotti, Alberto; Piccardo, Giuseppe; Luongo, Angelo
Abstract: Within the Generalized Beam Theory, the 'cross-section analysis' is a key point to evaluate a suitable basis of modes for the elastic analysis of thin-walled beams. A new dynamic approach is proposed for the evaluation of extensional modes for any possible kind of cross-section (i.e., open, partially closed or closed), using a dual method that perfectly complements and improves the GBT dynamic approach (GBT-D). The method relies on the solution of a very limited number of constrained eigenvalue problems. The emergence of specific hybrid modes for multiply-connected cross-section is pointed out. The proposed approach is much simpler to use than the classic static one, in addition to providing even better results from the point of view of accuracy and symmetry of the displacement fields. An illustrative example shows all the steps of the novel procedure. Several additional examples illustrate the high quality of the results arising from its application. Abstract : Highlights: A novel dynamic method for the evaluation of GBT extensional modes is proposed. The proposed dynamic procedure is very competitive with respect to the static one. Dynamic modes have a physical interpretation without the need for further processing. Two eigenvalue problems are required at most to calculated extensional modes. The complete set of modes is found through a reduced number (3 or 4) of problems.