A novel nonlocal strain gradient Quasi-3D bending analysis of sigmoid functionally graded sandwich nanoplates

Abstract

This manuscript aims to examine and investigate the bending deflection and stress distribution of sandwich functionally graded nanoplates rested on variable Winkler elastic foundation based on new quasi 3D hyperbolic shear theory in conjoint with nonlocal strain gradient theory. The sandwich sigmoidal function graded material (SFGM) is proposed with three different configurations through thickness direction. New 3D hyperbolic shear theory is exploited to satisfy parabolic variation of shear through thickness direction and zero shear at the bottom and top surfaces. Modified continuum nonlocal strain gradient theory is used to include the material and geometrical nanosize length scales. Variable Winkler foundation model is proposed to the first time to include the variable elastic environmental under the nanoplate. The comprehensive model and governing equilibrium equations of SFG nanoplates is derived in detail with principle of virtual work and solved analytically by Galerkin method. The developed model is verified with previous work and parametric studies are presented to illustrate influences of the elastic foundation models, sigmoidal distribution index constant, configuration of sandwich plate, material and length nanoscales, boundary conditions on the static deflection and stress distributions of FG sigmodal nanoplate. The proposed model can be applied in design and analysis of NEMS structure under static load, such as nanocapacitor and nanoswitch.