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Smart Structures and Systems Volume 13, Number 4, April 2014 , pages 637-657 DOI: https://doi.org/10.12989/sss.2014.13.4.637 |
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A dynamic analysis of three-dimensional functionally graded beams by hierarchical models |
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Gaetano Giunta, Yao Koutsawa, Salim Belouettar and Adriano Calvi
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| Abstract | ||
| This paper presents a dynamic analysis of three-dimensional beams. Structures made of functionally graded materials are considered. Several higher-order as well as classical theories are derived by means of a compact notation for the a-priori expansion order of the displacement field over the beam cross-section. The governing differential equations and boundary conditions are obtained in a condensed nuclear form that does not depend on the kinematic hypotheses. The problem is, then, exactly solved in space by means of a Navier-type solution, whereas time integration is performed by means of Newmark\'s solution scheme. Slender and short simply supported beams are investigated. Results are validated towards three-dimensional FEM results obtained via the commercial software ANSYS. Numerical investigations show that good accuracy can be obtained through the proposed formulation provided that the appropriate expansion order is considered. | ||
| Key Words | ||
| three-dimensional beam structures; functionally graded materials; dynamic analysis | ||
| Address | ||
| Gaetano Giunta, Yao Koutsawa and Salim Belouettar: Centre de Recherche Public Henri Tudor, 29, av. John F. Kennedy, L-1855, Luxembourg-Kirchberg, Luxembourg Adriano Calvi: ESTEC - European Space Agency, P.O. Box 299, 2200 AG, Noordwijk, The Netherlands | ||