Nonlocal Elasticity Response of Doubly-Curved Nanoshells

• Published in: Symmetry (Basel) 2020-03, Vol.12 (3), p.466
• Main Authors: Dindarloo, Mohammad Hassan, Li, Li, Dimitri, Rossana, Tornabene, Francesco
• Format: Article
• Language: English
• Subjects: doubly-curved nanoshells; high-order shear deformation theory; nonlocal elasticity theory; static analysis
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym12030466

In this paper, we focus on the bending behavior of isotropic doubly-curved nanoshells based on a high-order shear deformation theory, whose shape functions are selected as an accurate combination of exponential and trigonometric functions instead of the classical polynomial functions. The small-scale effect of the nanostructure is modeled according to the differential law consequent, but is not equivalent to the strain-driven nonlocal integral theory of elasticity equipped with Helmholtz’s averaging kernel. The governing equations of the problem are obtained from the Hamilton’s principle, whereas the Navier’s series are proposed for a closed form solution of the structural problem involving simply-supported nanostructures. The work provides a unified framework for the bending study of both thin and thick symmetric doubly-curved shallow and deep nanoshells, while investigating spherical and cylindrical panels subjected to a point or a sinusoidal loading condition. The effect of several parameters, such as the nonlocal parameter, as well as the mechanical and geometrical properties, is investigated on the bending deflection of isotropic doubly-curved shallow and deep nanoshells. The numerical results from our investigation could be considered as valid benchmarks in the literature for possible further analyses of doubly-curved applications in nanotechnology.