A new analytical approach for nonlinear thermo-mechanical postbuckling of FG-GPLRC circular plates and shallow spherical caps stiffened by spiderweb stiffeners.

• FG-GPLRC circular plates and spherical caps are stiffened by spiderweb stiffeners. • Five distribution laws of GPLs of plate/cap and stiffeners are suggested. • Lekhnitskii's smeared stiffener technique is expanded for spiderweb stiffeners. • Donnell theory and the Ritz energy method are employed to obtain explicit results. • The postbuckling behavior of stiffened plates/caps is numerically investigated. For the first time, the problem of nonlinear postbuckling of circular plates and shallow spherical caps reinforced by meridian, parallel stiffeners, and spiderweb stiffeners based on the Donnell shell theory (DST) and von Kármán geometric nonlinearities is presented. The caps/plates and stiffeners are made from functionally graded graphene platelet-reinforced composite (FG-GPLRC). These stiffened structures are subjected to uniformly distributed external pressure or/and uniformly distributed thermal loads and are rested on a nonlinear elastic foundation. By expanding Lekhnitskii's smeared stiffener technique and employing the Ritz method of energy, the formulas to determine the postbuckling curves of the external pressure–deflection and thermal load-deflection relations of stiffened plates/spherical caps are derived. Meaningful discussions of the various influences of FG-GPLRC stiffeners, material distributions of plate/cap and stiffeners, and geometrical, material, and foundation parameters are shown in the content of the numerical investigations. [ABSTRACT FROM AUTHOR]