Gradient elasticity solutions of 2D nano-beams
In this study, the exact analytical solutions of a two-dimensional linear homogeneous isotropic nano-beam in gradient elasticity are studied. Four different types of two-dimensional cantilever beams and related boundary conditions are considered. The cases are a cantilever beam under a concentrated...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-09-01
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| Series: | Applications in Engineering Science |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666496823000158 |
| _version_ | 1797671990012674048 |
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| author | Teoman Özer |
| author_facet | Teoman Özer |
| author_sort | Teoman Özer |
| collection | DOAJ |
| description | In this study, the exact analytical solutions of a two-dimensional linear homogeneous isotropic nano-beam in gradient elasticity are studied. Four different types of two-dimensional cantilever beams and related boundary conditions are considered. The cases are a cantilever beam under a concentrated force at the end, a cantilever beam under a uniform load, a propped cantilever beam under a uniform load, and a fixed-end beam under a uniform load. The two-dimensional stress gradient fields are investigated and obtained from the analytical solutions of a linear second-order partial differential equation written in terms of the classical and the gradient Airy stress functions. Additionally, the micro-size effects in the displacement components for different loads and support conditions for the two-dimensional cantilever beams by using strain gradient elasticity theory are investigated. Furthermore, for one-dimensional Euler–Bernoulli beam model, the associated stress and strain elasticity solutions are obtained from two-dimensional analytical solutions. The graphical presentations of the exact closed-form solutions are provided and discussed. |
| first_indexed | 2024-03-11T21:23:33Z |
| format | Article |
| id | doaj.art-1002ec09aba54c5eb3b59ab89bdb1934 |
| institution | Directory Open Access Journal |
| issn | 2666-4968 |
| language | English |
| last_indexed | 2024-03-11T21:23:33Z |
| publishDate | 2023-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Applications in Engineering Science |
| spelling | doaj.art-1002ec09aba54c5eb3b59ab89bdb19342023-09-28T05:26:31ZengElsevierApplications in Engineering Science2666-49682023-09-0115100140Gradient elasticity solutions of 2D nano-beamsTeoman Özer0İstanbul Technical University, Faculty of Civil Engineering, Division of Mechanics, Maslak, 34469 İstanbul, TurkeyIn this study, the exact analytical solutions of a two-dimensional linear homogeneous isotropic nano-beam in gradient elasticity are studied. Four different types of two-dimensional cantilever beams and related boundary conditions are considered. The cases are a cantilever beam under a concentrated force at the end, a cantilever beam under a uniform load, a propped cantilever beam under a uniform load, and a fixed-end beam under a uniform load. The two-dimensional stress gradient fields are investigated and obtained from the analytical solutions of a linear second-order partial differential equation written in terms of the classical and the gradient Airy stress functions. Additionally, the micro-size effects in the displacement components for different loads and support conditions for the two-dimensional cantilever beams by using strain gradient elasticity theory are investigated. Furthermore, for one-dimensional Euler–Bernoulli beam model, the associated stress and strain elasticity solutions are obtained from two-dimensional analytical solutions. The graphical presentations of the exact closed-form solutions are provided and discussed.http://www.sciencedirect.com/science/article/pii/S2666496823000158One and two-dimensional nano-beamsNonlocal elasticityStress and strain gradient elasticityAnalytical solutionsCantilever beamsMicro-size effects |
| spellingShingle | Teoman Özer Gradient elasticity solutions of 2D nano-beams Applications in Engineering Science One and two-dimensional nano-beams Nonlocal elasticity Stress and strain gradient elasticity Analytical solutions Cantilever beams Micro-size effects |
| title | Gradient elasticity solutions of 2D nano-beams |
| title_full | Gradient elasticity solutions of 2D nano-beams |
| title_fullStr | Gradient elasticity solutions of 2D nano-beams |
| title_full_unstemmed | Gradient elasticity solutions of 2D nano-beams |
| title_short | Gradient elasticity solutions of 2D nano-beams |
| title_sort | gradient elasticity solutions of 2d nano beams |
| topic | One and two-dimensional nano-beams Nonlocal elasticity Stress and strain gradient elasticity Analytical solutions Cantilever beams Micro-size effects |
| url | http://www.sciencedirect.com/science/article/pii/S2666496823000158 |
| work_keys_str_mv | AT teomanozer gradientelasticitysolutionsof2dnanobeams |