A new analytical approach for nonlinear pressured buckling behavior of FG-GRMMC complexly curved toroidal shell segments with piezoelectric layers stiffened by spiral FG-GRMMC stiffeners

A new analytical solution is successfully developed for nonlinear pressured buckling analysis of complexly curved toroidal shell segments made from functionally graded graphene-reinforced metal matrix composite (FG-GRMMC) stiffened by spiral FG-GRMMC stiffeners and integrated with electric effects of piezoelectric layers is presented in this research. The analysis is based on Donnell’s shell theory combined with the large deflection nonlinearities, and parabolic and sinusoid shapes are considered in the longitudinal direction of shells. Additionally, an improved technique is proposed to approximate the stress function of shells in a nonlinear form. The Ritz energy method is employed to solve the governing equation system, while the smeared stiffener technique, improved to accommodate the behavior of FG-GRMMC stiffeners, is used to model the contribution of spiral stiffeners. Numerical simulations demonstrate the effects of complex curvature, material parameters, spiral stiffener distribution, and piezoelectric actuation on the buckling and postbuckling responses.