An Approximate Solution of the Bending of Beams on a Nonlinear Elastic Foundation with the Galerkin Method
The analysis of beam deformation on elastic foundation is very important in engineering applications, and studies of beams on linear elastic foundations are abundant and accurate. For practical problems, it is always demanded that the influence of the nonlinear effect of the foundation on the analy...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Shahid Chamran University of Ahvaz
2025-04-01
|
| Series: | Journal of Applied and Computational Mechanics |
| Subjects: | |
| Online Access: | https://jacm.scu.ac.ir/article_19265_d7325bc18af2146399e66db5e1adbbd7.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849392898112487424 |
|---|---|
| author | Junlong Jiang Chencheng Lian Baochen Meng Huimin Jing Xiang Fang Ji Wang |
| author_facet | Junlong Jiang Chencheng Lian Baochen Meng Huimin Jing Xiang Fang Ji Wang |
| author_sort | Junlong Jiang |
| collection | DOAJ |
| description | The analysis of beam deformation on elastic foundation is very important in engineering applications, and studies of beams on linear elastic foundations are abundant and accurate. For practical problems, it is always demanded that the influence of the nonlinear effect of the foundation on the analytical methods and results must be considered. This study treats the static bending problem of an elastic beam resting on the nonlinear elastic foundation by solving the nonlinear differential equations with the Galerkin method, converting the nonlinear differential equations to a system of nonlinear algebraic equations for approximate solutions. The nonlinear equations are solved with a series expansion of the deflection satisfying the boundary conditions, and coefficients of the series are obtained with usual techniques including the iterative method. The accuracy of the approximate solution with the Galerkin method is verified through examples from earlier studies. The procedure and results show that the Galerkin method is effective in solving static nonlinear differential equations in addition to the nonlinear vibrations with the extended Galerkin method in earlier studies. |
| format | Article |
| id | doaj-art-c56b44a64e4047f5a3c94995ca6fd74c |
| institution | Kabale University |
| issn | 2383-4536 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Shahid Chamran University of Ahvaz |
| record_format | Article |
| series | Journal of Applied and Computational Mechanics |
| spelling | doaj-art-c56b44a64e4047f5a3c94995ca6fd74c2025-08-20T03:40:40ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362025-04-0111228529310.22055/jacm.2024.46952.463319265An Approximate Solution of the Bending of Beams on a Nonlinear Elastic Foundation with the Galerkin MethodJunlong Jiang0Chencheng Lian1Baochen Meng2Huimin Jing3Xiang Fang4Ji Wang5Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, 315211 Zhejiang, ChinaPiezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, 315211 Zhejiang, ChinaPiezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, 315211 Zhejiang, ChinaPiezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, 315211 Zhejiang, ChinaPiezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, 315211 Zhejiang, ChinaPiezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, 315211 Zhejiang, ChinaThe analysis of beam deformation on elastic foundation is very important in engineering applications, and studies of beams on linear elastic foundations are abundant and accurate. For practical problems, it is always demanded that the influence of the nonlinear effect of the foundation on the analytical methods and results must be considered. This study treats the static bending problem of an elastic beam resting on the nonlinear elastic foundation by solving the nonlinear differential equations with the Galerkin method, converting the nonlinear differential equations to a system of nonlinear algebraic equations for approximate solutions. The nonlinear equations are solved with a series expansion of the deflection satisfying the boundary conditions, and coefficients of the series are obtained with usual techniques including the iterative method. The accuracy of the approximate solution with the Galerkin method is verified through examples from earlier studies. The procedure and results show that the Galerkin method is effective in solving static nonlinear differential equations in addition to the nonlinear vibrations with the extended Galerkin method in earlier studies.https://jacm.scu.ac.ir/article_19265_d7325bc18af2146399e66db5e1adbbd7.pdfnonlinear foundationbeamdeflectiongalerkin method |
| spellingShingle | Junlong Jiang Chencheng Lian Baochen Meng Huimin Jing Xiang Fang Ji Wang An Approximate Solution of the Bending of Beams on a Nonlinear Elastic Foundation with the Galerkin Method Journal of Applied and Computational Mechanics nonlinear foundation beam deflection galerkin method |
| title | An Approximate Solution of the Bending of Beams on a Nonlinear Elastic Foundation with the Galerkin Method |
| title_full | An Approximate Solution of the Bending of Beams on a Nonlinear Elastic Foundation with the Galerkin Method |
| title_fullStr | An Approximate Solution of the Bending of Beams on a Nonlinear Elastic Foundation with the Galerkin Method |
| title_full_unstemmed | An Approximate Solution of the Bending of Beams on a Nonlinear Elastic Foundation with the Galerkin Method |
| title_short | An Approximate Solution of the Bending of Beams on a Nonlinear Elastic Foundation with the Galerkin Method |
| title_sort | approximate solution of the bending of beams on a nonlinear elastic foundation with the galerkin method |
| topic | nonlinear foundation beam deflection galerkin method |
| url | https://jacm.scu.ac.ir/article_19265_d7325bc18af2146399e66db5e1adbbd7.pdf |
| work_keys_str_mv | AT junlongjiang anapproximatesolutionofthebendingofbeamsonanonlinearelasticfoundationwiththegalerkinmethod AT chenchenglian anapproximatesolutionofthebendingofbeamsonanonlinearelasticfoundationwiththegalerkinmethod AT baochenmeng anapproximatesolutionofthebendingofbeamsonanonlinearelasticfoundationwiththegalerkinmethod AT huiminjing anapproximatesolutionofthebendingofbeamsonanonlinearelasticfoundationwiththegalerkinmethod AT xiangfang anapproximatesolutionofthebendingofbeamsonanonlinearelasticfoundationwiththegalerkinmethod AT jiwang anapproximatesolutionofthebendingofbeamsonanonlinearelasticfoundationwiththegalerkinmethod AT junlongjiang approximatesolutionofthebendingofbeamsonanonlinearelasticfoundationwiththegalerkinmethod AT chenchenglian approximatesolutionofthebendingofbeamsonanonlinearelasticfoundationwiththegalerkinmethod AT baochenmeng approximatesolutionofthebendingofbeamsonanonlinearelasticfoundationwiththegalerkinmethod AT huiminjing approximatesolutionofthebendingofbeamsonanonlinearelasticfoundationwiththegalerkinmethod AT xiangfang approximatesolutionofthebendingofbeamsonanonlinearelasticfoundationwiththegalerkinmethod AT jiwang approximatesolutionofthebendingofbeamsonanonlinearelasticfoundationwiththegalerkinmethod |