Variational Derivation of Truncated Timoshenko-Ehrenfest Beam Theory
Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_JACM-8-3_017
تاریخ نمایه سازی: 18 اسفند 1400
Abstract:
The beam theory allowing for rotary inertia and shear deformation and without the fourth order derivative with respect to time as well as without the slope inertia, as was developed by Elishakoff through the dynamic equilibrium consideration, is derived here by means of both direct and variational methods. This formulation is important for using variational methods of Rayleigh, Ritz as well as the finite element method (FEM). Despite the fact that literature abounds with variational formulations of the original Timoshenko-Ehrenfest beam theory, since it was put forward in ۱۹۱۲-۱۹۱۶, until now there was not a single derivation of the version without the fourth derivative and without the slope inertia. This gap is filled by the present paper. It is shown that the differential equations and the corresponding boundary conditions, used to find the solution of the dynamic problem of a truncated Timoshenko-Ehrenfest via variational formulation, have the same form to that obtained via direct method. Finally, in order to illustrate the advantages of the variational approach and its adaptability to the finite element formulation, some numerical examples are performed. The calculations are implemented through a software developed in Mathematica language and results are validated by comparison with those available in the literature.
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Authors
Maria De Rosa
School of Engineering, University of Basilicata, Via dell’Ateneo Lucano, Potenza, ۸۵۱۰۰, Italy
Maria Lippiello
Department of Structures for Engineering and Architecture, University of Naples “Federico II”, Via Forno Vecchio, Naples, ۸۰۱۳۴, Italy
Isaac Elishakoff
Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, ۳۳۴۳۱-۰۹۹۱, USA
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