Nonlocal strain gradient exact solutions for functionally graded inflected nano-beams. (1st May 2019)

• Record Type: Journal Article
• Authors: Apuzzo, A.; Barretta, R.; Faghidian, S.A.; Luciano, R.; Marotti de Sciarra, F.
• Is Part Of: Composites. Number 164(2019)
• Page Start: 667
• Page End: 674
• Publication Date: 2019-05-01
• Subjects: Integral elasticity -- Modified nonlocal strain gradient theory -- Constitutive boundary conditions -- Higher-order boundary conditions -- Size effects -- Nanobeams; Composite materials -- Periodicals; Materials science -- Periodicals; Composite materials; Periodicals; Electronic journals; 620.118
• DOI: 10.1016/j.compositesb.2018.12.112
• Languages: English
• ISSNs: 1359-8368

Abstract

Abstract: The size-dependent bending behavior of nano-beams is investigated by the modified nonlocal strain gradient elasticity theory. According to this model, the bending moment is expressed by integral convolutions of elastic flexural curvature and of its derivative with the special bi-exponential averaging kernel. It has been recently proven that such a relation is equivalent to a differential equation, involving bending moment and flexural curvature fields, equipped with natural higher-order boundary conditions of constitutive type. The associated elastostatic problem of a Bernoulli-Euler functionally graded nanobeam is formulated and solved for simple statical schemes of technical interest. An effective analytical approach is presented and exploited to establish exact expressions of nonlocal strain gradient transverse displacements of doubly clamped, cantilever, clamped-simply supported and simply supported nano-beams, detecting thus also new benchmarks for numerical analyses. Comparisons with results of literature, corresponding to selected higher-order boundary conditions are provided and discussed. The considered nonlocal strain gradient model can be advantageously adopted to characterize scale phenomena in nano-engineering problems.