Analysis of Elastic Beams on Linear and Nonlinear Foundations Using Finite Difference Method
An approximate method is developed to analyze the deflection in beams and beam-column by solving the differential equation for the elastic deformation of beam and beam-column. The analysis is performed using the central difference of finite difference method for the Euler-Bernoulli beam and beam-col...
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| Format: | Article |
| Language: | English |
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Tishk International University
2018-06-01
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| Series: | Eurasian Journal of Science and Engineering |
| Subjects: | |
| Online Access: | http://eajse.org/wp-content/uploads/2018/05/Analysis-of-Elastic-Beams-on-Linear-and-Nonlinear-Foundations-.pdf |
| _version_ | 1797723118085603328 |
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| author | Saad Essa |
| author_facet | Saad Essa |
| author_sort | Saad Essa |
| collection | DOAJ |
| description | An approximate method is developed to analyze the deflection in beams and beam-column by solving the differential equation for the elastic deformation of beam and beam-column. The analysis is performed using the central difference of finite difference method for the Euler-Bernoulli beam and beam-column supported on an elastic, nonlinear foundation with rigid or elastic discrete supports. To make a verification of the results, Laplace Transformation method was used to solve the elastic differential equation of beam and beam-column based on linear elastic supports and the results were compared with the finite difference method. Two types of beams were selected, simply supported and fixed-fixed with five elastic supports of an idealized soil. In the nonlinear idealization, the division of force into many levels were assumed and based on these forces, the equivalent displacements were obtained from an assumed power law equation by using the finite difference method. Central finite difference scheme, which has a second order, was used throughout the numerical analysis with five nonlinear behavior of springs separated by an equal distance between them. |
| first_indexed | 2024-03-12T09:58:19Z |
| format | Article |
| id | doaj.art-470d071f27c448c69352efe124628841 |
| institution | Directory Open Access Journal |
| issn | 2414-5629 2414-5602 |
| language | English |
| last_indexed | 2024-03-12T09:58:19Z |
| publishDate | 2018-06-01 |
| publisher | Tishk International University |
| record_format | Article |
| series | Eurasian Journal of Science and Engineering |
| spelling | doaj.art-470d071f27c448c69352efe1246288412023-09-02T11:59:26ZengTishk International UniversityEurasian Journal of Science and Engineering2414-56292414-56022018-06-01339210110.23918/eajse.v3i3p92Analysis of Elastic Beams on Linear and Nonlinear Foundations Using Finite Difference MethodSaad EssaAn approximate method is developed to analyze the deflection in beams and beam-column by solving the differential equation for the elastic deformation of beam and beam-column. The analysis is performed using the central difference of finite difference method for the Euler-Bernoulli beam and beam-column supported on an elastic, nonlinear foundation with rigid or elastic discrete supports. To make a verification of the results, Laplace Transformation method was used to solve the elastic differential equation of beam and beam-column based on linear elastic supports and the results were compared with the finite difference method. Two types of beams were selected, simply supported and fixed-fixed with five elastic supports of an idealized soil. In the nonlinear idealization, the division of force into many levels were assumed and based on these forces, the equivalent displacements were obtained from an assumed power law equation by using the finite difference method. Central finite difference scheme, which has a second order, was used throughout the numerical analysis with five nonlinear behavior of springs separated by an equal distance between them.http://eajse.org/wp-content/uploads/2018/05/Analysis-of-Elastic-Beams-on-Linear-and-Nonlinear-Foundations-.pdfFinite Difference MethodEuler-Bernoulli BeamLaplace Transformation |
| spellingShingle | Saad Essa Analysis of Elastic Beams on Linear and Nonlinear Foundations Using Finite Difference Method Eurasian Journal of Science and Engineering Finite Difference Method Euler-Bernoulli Beam Laplace Transformation |
| title | Analysis of Elastic Beams on Linear and Nonlinear Foundations Using Finite Difference Method |
| title_full | Analysis of Elastic Beams on Linear and Nonlinear Foundations Using Finite Difference Method |
| title_fullStr | Analysis of Elastic Beams on Linear and Nonlinear Foundations Using Finite Difference Method |
| title_full_unstemmed | Analysis of Elastic Beams on Linear and Nonlinear Foundations Using Finite Difference Method |
| title_short | Analysis of Elastic Beams on Linear and Nonlinear Foundations Using Finite Difference Method |
| title_sort | analysis of elastic beams on linear and nonlinear foundations using finite difference method |
| topic | Finite Difference Method Euler-Bernoulli Beam Laplace Transformation |
| url | http://eajse.org/wp-content/uploads/2018/05/Analysis-of-Elastic-Beams-on-Linear-and-Nonlinear-Foundations-.pdf |
| work_keys_str_mv | AT saadessa analysisofelasticbeamsonlinearandnonlinearfoundationsusingfinitedifferencemethod |