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General finite element description for non-uniform and discontinuous beam elements

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Abstract

The theory of generalized functions is used to address the static equilibrium problem of Euler–Bernoulli non-uniform and discontinuous 2-D beams. It is shown that if simple integration rules are applied, the full set of response variables due to end nodal displacements and to in-span loads can be derived, in a closed form, for most common beam profiles and arbitrary discontinuity parameters. On this basis, for finite element analysis purposes, a non-uniform and discontinuous beam element is implemented, for which the exact stiffness matrix and the fixed-end load vector are derived. Upon computing the nodal response, no numerical integration is required to build the response variables along the beam element.

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Authors and Affiliations

  1. Dipartimento di Meccanica e Materiali (MECMAT), Università “Mediterranea” di Reggio Calabria, Via Graziella, Località Feo di Vito, 89122, Reggio Calabria, Italy

    Giuseppe Failla

  2. Dipartimento di Architettura (DARC), Università di Catania, P.zza Federico di Svevia, 96100, Siracusa, Italy

    Nicola Impollonia

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  1. Giuseppe Failla
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  2. Nicola Impollonia
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Correspondence to Giuseppe Failla.

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Failla, G., Impollonia, N. General finite element description for non-uniform and discontinuous beam elements. Arch Appl Mech 82, 43–67 (2012). https://doi.org/10.1007/s00419-011-0538-8

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  • DOI: https://doi.org/10.1007/s00419-011-0538-8

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