Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric Functions
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 aer...
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| Format: | Article |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/838924 |
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| author | Giovanni Mingari Scarpello Daniele Ritelli |
| author_facet | Giovanni Mingari Scarpello Daniele Ritelli |
| author_sort | Giovanni Mingari Scarpello |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-88fea0e8b19f43cda0bb2c0306114d55 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-88fea0e8b19f43cda0bb2c0306114d552025-08-20T03:38:05ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/838924838924Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric FunctionsGiovanni Mingari Scarpello0Daniele Ritelli1Via Negroli, 6, 20136 Milan, ItalyDipartimento di Matematica per le Scienze Economiche e Sociali, Viale Filopanti, 5, 40126 Bologna, ItalyThe 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.http://dx.doi.org/10.1155/2011/838924 |
| spellingShingle | Giovanni Mingari Scarpello Daniele Ritelli Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric Functions International Journal of Mathematics and Mathematical Sciences |
| title | Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric Functions |
| title_full | Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric Functions |
| title_fullStr | Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric Functions |
| title_full_unstemmed | Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric Functions |
| title_short | Exact Solutions of Nonlinear Equation of Rod Deflections Involving the Lauricella Hypergeometric Functions |
| title_sort | exact solutions of nonlinear equation of rod deflections involving the lauricella hypergeometric functions |
| url | http://dx.doi.org/10.1155/2011/838924 |
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