Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material
In this study, non-linear static analysis of a cantilever Timoshenko beam composed of functionally graded material (FGM) under a non-follower transversal uniformly distributed load is studied with large displacements and large rotations. Material properties of the beam change in the thickness direct...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2011-06-01
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| Series: | Science and Engineering of Composite Materials |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/secm.2011.005 |
| _version_ | 1818695552753205248 |
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| author | Kocatürk Turgut Şimşek Mesut Akbaş Şeref Doğuşcan |
| author_facet | Kocatürk Turgut Şimşek Mesut Akbaş Şeref Doğuşcan |
| author_sort | Kocatürk Turgut |
| collection | DOAJ |
| description | In this study, non-linear static analysis of a cantilever Timoshenko beam composed of functionally graded material (FGM) under a non-follower transversal uniformly distributed load is studied with large displacements and large rotations. Material properties of the beam change in the thickness direction according to a power-law function. In this study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The non-linear problem is solved by using the incremental displacement-based finite element method in conjunction with the Newton-Raphson iteration method. To use the solution procedures of the Newton-Raphson method, there is a need to linearize equilibrium equations, which can be achieved through the linearization of the principle of virtual work. In this study, the effects of large deflections, large rotations and various material distributions on displacements and normal stress and shear stress distributions through the thickness of the beam are investigated in detail. The convergence study is performed for various numbers of finite elements. In addition, some of the particular results of the present study which are obtained for the homogeneous material case are compared with the results of the SAP2000 packet program. Numerical results show that geometrical non-linearity and material distribution play very important roles in the static responses of FGM beams. |
| first_indexed | 2024-12-17T13:47:18Z |
| format | Article |
| id | doaj.art-9c5f19e86f2c42ac898b16fd92a9256e |
| institution | Directory Open Access Journal |
| issn | 0792-1233 2191-0359 |
| language | English |
| last_indexed | 2024-12-17T13:47:18Z |
| publishDate | 2011-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Science and Engineering of Composite Materials |
| spelling | doaj.art-9c5f19e86f2c42ac898b16fd92a9256e2022-12-21T21:46:07ZengDe GruyterScience and Engineering of Composite Materials0792-12332191-03592011-06-01181-2213410.1515/secm.2011.005Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded materialKocatürk Turgut0Şimşek Mesut1Akbaş Şeref Doğuşcan2Department of Civil Engineering, Yildiz Technical University, Davutpaşa Campus, 34210 Esenler-İstanbul, TurkeyDepartment of Civil Engineering, Yildiz Technical University, Davutpaşa Campus, 34210 Esenler-İstanbul, TurkeyDepartment of Civil Engineering, Yildiz Technical University, Davutpaşa Campus, 34210 Esenler-İstanbul, TurkeyIn this study, non-linear static analysis of a cantilever Timoshenko beam composed of functionally graded material (FGM) under a non-follower transversal uniformly distributed load is studied with large displacements and large rotations. Material properties of the beam change in the thickness direction according to a power-law function. In this study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The non-linear problem is solved by using the incremental displacement-based finite element method in conjunction with the Newton-Raphson iteration method. To use the solution procedures of the Newton-Raphson method, there is a need to linearize equilibrium equations, which can be achieved through the linearization of the principle of virtual work. In this study, the effects of large deflections, large rotations and various material distributions on displacements and normal stress and shear stress distributions through the thickness of the beam are investigated in detail. The convergence study is performed for various numbers of finite elements. In addition, some of the particular results of the present study which are obtained for the homogeneous material case are compared with the results of the SAP2000 packet program. Numerical results show that geometrical non-linearity and material distribution play very important roles in the static responses of FGM beams.https://doi.org/10.1515/secm.2011.005finite element analysisfunctionally graded materialsnon-linear static analysistimoshenko beam |
| spellingShingle | Kocatürk Turgut Şimşek Mesut Akbaş Şeref Doğuşcan Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material Science and Engineering of Composite Materials finite element analysis functionally graded materials non-linear static analysis timoshenko beam |
| title | Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material |
| title_full | Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material |
| title_fullStr | Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material |
| title_full_unstemmed | Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material |
| title_short | Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material |
| title_sort | large displacement static analysis of a cantilever timoshenko beam composed of functionally graded material |
| topic | finite element analysis functionally graded materials non-linear static analysis timoshenko beam |
| url | https://doi.org/10.1515/secm.2011.005 |
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