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On the formulation of elastic and electroelastic gradient beam theories

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Abstract

Variational approach for the formulation of gradient beam-type models is discussed. The second gradient elasticity and electroelasticity theories are considered. It is shown that introducing the classical Bernoulli–Euler hypotheses one should take into account the additional boundary conditions on the top and bottom surfaces of the beam to construct the correct gradient beam theory. These boundary conditions are missed in number of works; however, they straightforwardly follow from the variational formulation of the beam-type models as well as from the three-dimensional statement of the boundary value problems of considered gradient theories. Simple example of verification of the correct beam-type models by using semi-inverse analytical solution of a beam pure bending problem is given.

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This work was supported by the IAM RAS basic program AAAA-A19-119012290177-0.

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  1. Institute of Applied Mechanics of Russian Academy of Sciences, Moscow, Russia

    Sergey Lurie & Yury Solyaev

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Lurie, S., Solyaev, Y. On the formulation of elastic and electroelastic gradient beam theories. Continuum Mech. Thermodyn. 31, 1601–1613 (2019). https://doi.org/10.1007/s00161-019-00781-3

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