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Structural Engineering and Mechanics Volume 68, Number 6, December25 2018 , pages 713-720 DOI: https://doi.org/10.12989/sem.2018.68.6.713 |
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Numerical method to determine the elastic curve of simply supported beams of variable cross-section |
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Istvan Biro, Livija Cveticanin, Peter Szuchy
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| Abstract | ||
| In this paper a new numerical method to determine the elastic curve of the simply supported beams of variable cross-section is demonstrated. In general case it needs to solve linear or small nonlinear second order differential equations with prescribed boundary conditions. For numerical solution the initial values of the slope and the deflection of the end cross-section of the beam is necessary. For obtaining the initial values a lively procedure is developed: it is a special application of the shooting method because boundary value problems can be transformed into initial value problems. As a result of these transformations the initial values of the differential equations are obtained with high accuracy. Procedure is applied for calculating of elastic curve of a simply supported beam of variable cross-section. Results of these numerical procedures, analytical solution of the linearized version and finite element method are compared. It is proved that the suggested procedure yields technically accurate results. | ||
| Key Words | ||
| elastic curve; simply supported beams of variable cross-section; initial guess for slope and deflection | ||
| Address | ||
| Istvan Biro and Peter Szuchy: University of Szeged, Faculty of Engineering, Mars ter 7, H-6724 Szeged, Hungary Livija Cveticanin: 1) University of Novi Sad, Faculty of Technical Sciences, Trg D. Obradovica 6, 21000 Novi Sad, Serbia 2) Obuda University, Donat Banki Faculty, Nepszinhaz u. 8, H-1081 Budapest, Hungary | ||