Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory |
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Authors: | Bekir?Akg?z Email author" target="_blank">?mer?CivalekEmail author |
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Institution: | (1) Department of Mechanics, Huazhong University of Science and Technology, Wuhan, 430074, China;(2) Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan, 430074, China; |
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Abstract: | Bending analysis of micro-sized beams based on the Bernoulli-Euler beam theory is presented within the modified strain gradient
elasticity and modified couple stress theories. The governing equations and the related boundary conditions are derived from
the variational principles. These equations are solved analytically for deflection, bending, and rotation responses of micro-sized
beams. Propped cantilever, both ends clamped, both ends simply supported, and cantilever cases are taken into consideration
as boundary conditions. The influence of size effect and additional material parameters on the static response of micro-sized
beams in bending is examined. The effect of Poisson’s ratio is also investigated in detail. It is concluded from the results
that the bending values obtained by these higher-order elasticity theories have a significant difference with those calculated
by the classical elasticity theory. |
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Keywords: | |
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