A well-posed Euler-Bernoulli beam model incorporating nonlocality and surface energy effect

doi:10.1007/s10483-019-2541-5

Abstract

Abstract: This study shows that it is possible to develop a well-posed size-dependent model by considering the effect of both nonlocality and surface energy, and the model can provide another effective way of nanomechanics for nanostructures. For a practical but simple problem (an Euler-Bernoulli beam model under bending), the ill-posed issue of the pure nonlocal integral elasticity can be overcome. Therefore, a well-posed governing equation can be developed for the Euler-Bernoulli beams when considering both the pure nonlocal integral elasticity and surface elasticity. Moreover, closed-form solutions are found for the deflections of clamped-clamped (C-C), simply-supported (S-S) and cantilever (C-F) nano-/micro-beams. The effective elastic moduli are obtained in terms of the closed-form solutions since the transfer of physical quantities in the transition region is an important problem for span-scale modeling methods. The nonlocal integral and surface elasticities are adopted to examine the size-dependence of the effective moduli and deflection of Ag beams.

Key words: nonlocal integral elasticity, bending, size-dependence effect, surface elasticity

2010 MSC Number:

74K10
74S30

Xiaowu ZHU, Li LI. A well-posed Euler-Bernoulli beam model incorporating nonlocality and surface energy effect. Applied Mathematics and Mechanics (English Edition), 2019, 40(11): 1561-1588.

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