A nonlocal higher order shear deformation theory for electro-elastic analysis of a piezoelectric doubly curved nano shell

Nonlocal higher order electro-elastic bending analysis of a piezoelectric doubly curved nano shell is studied in this paper based on nonlocal elasticity theory and third order shear deformation theory. Nonlocal piezo-elasticity relations are used for size-dependent analysis of the piezoelectric structure. One can conclude that combination of important theories such as Reddy's shear deformation theory, nonlocal piezoelasticity theory to a more complicated structure such as doubly curved shells leads to an important and novel work in context of mechanical engineering. The kinematic relations are used based on third order shear deformation theory of Reddy. The doubly curved piezoelectric nano shell is subjected to transverse loads and applied voltage. In addition, the structure is resting on Winkler-Pasternak foundation. The governing equations of nonlocal electro-elastic bending are derived based on principle of virtual work. The nonlocal electro-elastic bending results of doubly curved nano shell are investigated using Navier's method. Influence of nonlocal parameter, applied electric potential, Winkler and Pasternak's parameters of foundation is studied on the mechanical and electrical components of the piezoelectric doubly curved nano shell.