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A Bernoulli–Euler
beam model based on the local gradient theory of
elasticity
Olha Hrytsyna |
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Vol. 15 (2020), No. 4, 471–487
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Abstract |
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Using the total energy balance equation and principle of the frame indifference, a fundamental set of relations of the local gradient continuum model of elastic solids is formulated. The model is based on taking account of non-convective and non-diffusive mass flux related to the changes in the material microstructure. Linear stationary governing equations of the local gradient theory and corresponding boundary conditions are also derived by variational principle. In order to investigate the size-dependent behavior of nano-scale structures, this model is combined with the Bernoulli–Euler beam theory. Deflection of the cantilever beam subjected to the end-point loading under the plane stress conditions is evaluated and compared to the corresponding ones provided by the classical theory and by the strain gradient theory. It is shown that the beam deflection within the local gradient theory is smaller than that predicted by the classical Bernoulli–Euler beam theory. This work may be of special interest for designing the devices utilizing the micro/nano-beam elements. |
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Keywords
gradient-type theory, continuum mechanics modeling, local
gradient elasticity, Bernoulli–Euler beam,
micro/nano-beams, size effect
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Milestones
Received: 10 January 2020
Revised: 13 May 2020
Accepted: 27 June 2020
Published: 19 October 2020
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Authors |
| Olha Hrytsyna | |
| Institute of Construction and
Architecture Slovak Academy of Sciences 84503 Bratislava 45 Slovakia |
Center of Mathematical
Modeling Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine 79005 Lviv Ukraine |
