Size effects of small-scale beams in bending addressed with a strain-difference based nonlocal elasticity theory. (February 2019) - Fuschi, P.; Pisano, A.A.; Polizzotto, C.
Highlights: A strain-difference nonlocal model is applied to small-scale Euler-Bernoulli beams in bending. Three mutually independent governing Fredholm equations of second kind are set up. Five beams samples are solved and discussed against well known nonlocal approaches. Paradoxes arising with the milestone Eringen differential model are overcome. Size effect of stiffening type (agreeing with smaller-is-stiffer ) are predicted. Graphical abstract: Abstract: A strain-difference based nonlocal elasticity model devised by the authors elsewhere (Polizzotto et al., Int. J. Solids Struct. 25 (2006) 308–333) is applied to small-scale homogeneous beam models in bending under static loads in the purpose to describe the inherent size effects. With this theory —belonging to the strain-integral nonlocal model family, but exempt from anomalies typical of the Eringen nonlocal theory— the relevant beam problem is reduced to a set of three mutually independent Fredholm integral equations of the second kind (each independent of the beam's ordinary boundary conditions, only one depends on the given load), which can be routinely solved numerically. Applications to five cases of beam samples (usually addressed in the literature) are performed, the obtained results are graphically illustrated and compared with analogous results from the literature. Size effects of stiffening type are found for all beam samples, in agreement with the analogous results obtained with the well-known and widely accepted strain gradient elasticity model. Analogous size effects are expected to be predicted for other multi-dimensional structures, all of which seems to confirm the smaller-is-stiffer phenomenon.