Nonlocal inflected nano-beams: A stress-driven approach of bi-Helmholtz type. (15th September 2018)

• Record Type: Journal Article
• Authors: Barretta, R.; Fazelzadeh, S.A.; Feo, L.; Ghavanloo, E.; Luciano, R.
• Is Part Of: Composite structures. Volume 200(2018)
• Page Start: 239
• Page End: 245
• Publication Date: 2018-09-15
• Subjects: Nonlocal elasticity -- Stress-driven integral law -- Size effect -- Nano-beam -- Bi-Helmholtz kernel -- CNT; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2018.04.072
• Languages: English
• ISSNs: 0263-8223

Abstract

Abstract: Size-dependent bending behavior of Bernoulli-Euler nano-beams is investigated by elasticity integral theory. Eringen's strain-driven nonlocal integral formulation, providing the bending moment interaction field as output of the convolution between elastic curvature and bi-Helmholtz averaging kernel, is examined. Corresponding higher-order constitutive boundary conditions are established for the first time, showing inapplicability of strain-driven nonlocal integral law of bi-Helmholtz type to continuous nano-structures defined on bounded domains. As a remedy, an innovative stress-driven nonlocal integral elastic model of bi-Helmholtz type is presented for inflected Bernoulli-Euler nano-beams, by swapping input and output of Eringen's nonlocal integral elastic law. The proposed stress-driven nonlocal integral constitutive law is proven to be equivalent to a fourth-order linear differential equation in the elastic curvature, fulfilling suitable homogeneous constitutive boundary conditions. The corresponding elastic equilibrium problem of an inflected nano-beam is well-posed and numerically solved for statics schemes of nano-technological interest, under standard loading and kinematic boundary conditions. New benchmarks for nonlocal computational mechanics are also detected.