Two-phase elastic axisymmetric nanoplates

Abstract

In the present work, the two-phase integral theory of elasticity developed in Barretta et al. (Phys E 97:13–30, 2018) for nano-beams is generalized to model two-dimensional nano-continua. Notably, a well-posed mixture local/stress-driven nonlocal elasticity is proposed to accurately predict size effects in Kirchhoff axisymmetric nanoplates. The key idea is to express the elastic radial curvature as a convex combination of local and nonlocal integral responses, that is a coherent choice motivated by virtue of the plate axisymmetry. The relevant structural problem is shown to be governed by a set of integro-differential equations, whose solution is computationally onerous. Thus, Helmholtz’s averaging kernel is advantageously adopted, since it enables explicit inversion of the integral constitutive law by virtue of an equivalence property. Specifically, the elastostatic problem of axisymmetry nanoplates is equivalently formulated in a differential form whose solution in terms of transverse displacement field is governed by nonlocal and mixture parameters. A parametric study is performed for case studies of applicative interest, and numerical solutions are finally provided and discussed. The presented methodology can be adopted to design and optimization of plate-based nano-electro-mechanical-systems (NEMS).