Finite Element Modeling for Buckling Analysis of Tapered Axially Functionally Graded Timoshenko Beam on Elastic Foundation
In this study, an efficient finite element model with two degrees of freedom per node is developed for buckling analysis of axially functionally graded (AFG) tapered Timoshenko beams resting on Winkler elastic foundation. For this, the shape functions are exactly acquired through solving the system...
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Semnan University
2020-11-01
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| Series: | Mechanics of Advanced Composite Structures |
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| Online Access: | https://macs.semnan.ac.ir/article_4308_260a200df7c35404c67dc65d027dcad0.pdf |
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| author | Masoumeh Soltani |
| author_facet | Masoumeh Soltani |
| author_sort | Masoumeh Soltani |
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| description | In this study, an efficient finite element model with two degrees of freedom per node is developed for buckling analysis of axially functionally graded (AFG) tapered Timoshenko beams resting on Winkler elastic foundation. For this, the shape functions are exactly acquired through solving the system of equilibrium equations of the Timoshenko beam employing the power series expansions of displacement components. The element stiffness matrix is then formulated by applying the developed shape functions to the total potential energy along the element axis. It is demonstrated that the resulting shape functions, in comparison with Hermitian cubic interpolation functions, are proportional to the mechanical features of the beam element, including the geometrical properties, material characteristics, as well as the critical axial load. An exhaustive numerical example is implemented to clarify the efficiency and simplicity of the proposed mathematical methodology. Furthermore, the effects of end conditions, material gradient, Winkler parameter, tapering ratio, and aspect ratio on the critical buckling load of AFG tapered Timoshenko beam are studied in detail. The numerical outcomes reveal that the elastic foundation enhances the stability characteristics of axially non-homogeneous and homogeneous beams with constant or variable cross-section. Moreover, the results show that the influence of non-uniformity in the cross-section and axially inhomogeneity in material characteristics play significant roles in the linear stability behavior of Timoshenko beams subjected to different boundary conditions. |
| format | Article |
| id | doaj-art-73b45c7c110242f78608b8394be1a3e8 |
| institution | OA Journals |
| issn | 2423-4826 2423-7043 |
| language | English |
| publishDate | 2020-11-01 |
| publisher | Semnan University |
| record_format | Article |
| series | Mechanics of Advanced Composite Structures |
| spelling | doaj-art-73b45c7c110242f78608b8394be1a3e82025-08-20T01:58:20ZengSemnan UniversityMechanics of Advanced Composite Structures2423-48262423-70432020-11-017220321810.22075/macs.2020.18591.12234308Finite Element Modeling for Buckling Analysis of Tapered Axially Functionally Graded Timoshenko Beam on Elastic FoundationMasoumeh Soltani0Department of Civil Engineering, University of Kashan, Kashan, IranIn this study, an efficient finite element model with two degrees of freedom per node is developed for buckling analysis of axially functionally graded (AFG) tapered Timoshenko beams resting on Winkler elastic foundation. For this, the shape functions are exactly acquired through solving the system of equilibrium equations of the Timoshenko beam employing the power series expansions of displacement components. The element stiffness matrix is then formulated by applying the developed shape functions to the total potential energy along the element axis. It is demonstrated that the resulting shape functions, in comparison with Hermitian cubic interpolation functions, are proportional to the mechanical features of the beam element, including the geometrical properties, material characteristics, as well as the critical axial load. An exhaustive numerical example is implemented to clarify the efficiency and simplicity of the proposed mathematical methodology. Furthermore, the effects of end conditions, material gradient, Winkler parameter, tapering ratio, and aspect ratio on the critical buckling load of AFG tapered Timoshenko beam are studied in detail. The numerical outcomes reveal that the elastic foundation enhances the stability characteristics of axially non-homogeneous and homogeneous beams with constant or variable cross-section. Moreover, the results show that the influence of non-uniformity in the cross-section and axially inhomogeneity in material characteristics play significant roles in the linear stability behavior of Timoshenko beams subjected to different boundary conditions.https://macs.semnan.ac.ir/article_4308_260a200df7c35404c67dc65d027dcad0.pdfpower series methodshape functionsbuckling loadtimoshenko beamfunctionally graded materials |
| spellingShingle | Masoumeh Soltani Finite Element Modeling for Buckling Analysis of Tapered Axially Functionally Graded Timoshenko Beam on Elastic Foundation Mechanics of Advanced Composite Structures power series method shape functions buckling load timoshenko beam functionally graded materials |
| title | Finite Element Modeling for Buckling Analysis of Tapered Axially Functionally Graded Timoshenko Beam on Elastic Foundation |
| title_full | Finite Element Modeling for Buckling Analysis of Tapered Axially Functionally Graded Timoshenko Beam on Elastic Foundation |
| title_fullStr | Finite Element Modeling for Buckling Analysis of Tapered Axially Functionally Graded Timoshenko Beam on Elastic Foundation |
| title_full_unstemmed | Finite Element Modeling for Buckling Analysis of Tapered Axially Functionally Graded Timoshenko Beam on Elastic Foundation |
| title_short | Finite Element Modeling for Buckling Analysis of Tapered Axially Functionally Graded Timoshenko Beam on Elastic Foundation |
| title_sort | finite element modeling for buckling analysis of tapered axially functionally graded timoshenko beam on elastic foundation |
| topic | power series method shape functions buckling load timoshenko beam functionally graded materials |
| url | https://macs.semnan.ac.ir/article_4308_260a200df7c35404c67dc65d027dcad0.pdf |
| work_keys_str_mv | AT masoumehsoltani finiteelementmodelingforbucklinganalysisoftaperedaxiallyfunctionallygradedtimoshenkobeamonelasticfoundation |