A Mechanical Model Based on Conformal Strain Energy and Its Application to Bending and Buckling of Nanobeam Structures

Abstract

In the present work, a nonlocal 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 classical (local) mechanical formulations. The first one specifies the amount of the integer and the noninteger 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 (nonlinear) equation has been solved by the Galerkin method and the effects of both free parameters have been shown. As a case study, the bending and buckling of nanobeam structures has been studied.