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Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric Functions
Joint Authors
Ritelli, Daniele
Scarpello, Giovanni Mingari
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-09-27
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
The stress induced in a loaded beam will not exceed some threshold, but also its maximum deflection, as for all the elastic systems, will be controlled.
Nevertheless, the linear beam theory fails to describe the large deflections; highly flexible linear elements, namely, rods, typically found in aerospace or oil applications, may experience large displacements—but small strains, for not leaving the field of linear elasticity—so that geometric nonlinearities become significant.
In this article, we provide analytical solutions to large deflections problem of a straight, cantilevered rod under different coplanar loadings.
Our researches are led by means of the elliptic integrals, but the main achievement concerns the Lauricella FD(3) hypergeometric functions use for solving elasticity problems.
Each of our analytic solutions has been individually validated by comparison with other tools, so that it can be used in turn as a benchmark, that is, for testing other methods based on the finite elements approximation.
American Psychological Association (APA)
Scarpello, Giovanni Mingari& Ritelli, Daniele. 2011. Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric Functions. International Journal of Mathematics and Mathematical Sciences،Vol. 2011, no. 2011, pp.1-22.
https://search.emarefa.net/detail/BIM-502242
Modern Language Association (MLA)
Scarpello, Giovanni Mingari& Ritelli, Daniele. Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric Functions. International Journal of Mathematics and Mathematical Sciences No. 2011 (2011), pp.1-22.
https://search.emarefa.net/detail/BIM-502242
American Medical Association (AMA)
Scarpello, Giovanni Mingari& Ritelli, Daniele. Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric Functions. International Journal of Mathematics and Mathematical Sciences. 2011. Vol. 2011, no. 2011, pp.1-22.
https://search.emarefa.net/detail/BIM-502242
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-502242