A mechanical model based on conformal strain energy and its application to bending and buckling of nano-beam structures

[+] Author and Article Information
Zaher Rahimi

Department of Mechanical Engineering, Urmia University, Urmia, Iran

Wojciech Sumelka

Institute of Structural Engineering, Poznan University of Technology, Piotrowo 5 Street, 60-965 Poznan, Poland

Dumitru Baleanu

Department of Mathematics, Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele, Romania

1Corresponding author.

ASME doi:10.1115/1.4043085 History: Received August 23, 2018; Revised February 26, 2019


In the present work, a non-local model based on the conformal strain energy, utilizing the conformable derivative definition, has been obtained. The model has two additional free parameters compared to the classicalal (local) mechanical formulations. The first one specifies the amount of the integer and the non-integer gradient of strain in the strain energy relation and the second one controls the order of the strain derivatives in the conformable energy relation. The obtained governing (non-linear) equation has been solved by the Galerkin method and the effects of both free parameters have been shown. As a case study, bending and buckling of nano-beam structures has been studied.

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