Nonlinear static and dynamic buckling analysis of GPL-reinforced spherical caps and circular plates with porous core and stepped spiderweb stiffeners

• Nonlinear buckling of spherical caps with stepped spiderweb stiffeners is presented. • The stiffened caps are made from GPL-reinforced face sheets and porous core. • The improved smeared stiffener technique of stepped spiderweb stiffener is proposed. • Energy method, Donnell shell theory , and nonlinear foundation model are applied. • Effects of stepped spiderweb stiffeners are investigated and discussed in detail. This paper analyzes the nonlinear static and dynamic buckling responses of graphene platelet (GPL) reinforced shallow spherical caps and circular plates with porous core and stepped spiderweb stiffeners. The new design of stepped spiderweb stiffeners is proposed by adding meridian stiffeners near the edge region, and three regions are created as the edge region, the middle region, and the top region. Different GPL distribution laws, including U, X, O, A, and V laws are considered for GPL-reinforced face sheets, and the U, X, O, V, and A GPL distribution laws for spiderweb stiffeners are respectively chosen, while the trigonometric distribution law of porosity is designed for the porous core. The smeared stiffener technique is improved for stepped spiderweb stiffeners, combining with nonlinear Donnell shell theory , and nonlinear foundation model to derive the static and dynamic responses of the structures. The energy method is employed to perform the equilibrium equations for static problems, and the motion equation for dynamic problems. The static postbuckling responses are explicitly obtained, and the Runge-Kutta method is applied to investigate the nonlinear dynamic buckling behavior of the considered plates and shell caps. The numerical examples of nonlinear static and dynamic buckling of spherical caps and circular plates can predict the significant effects of spiderweb stiffeners, geometrical and material parameters, and nonlinear foundation. The results show that the spiderweb stiffeners largely enhance the buckling strength of spherical caps, while a higher porosity coefficient reduces mechanical but increases thermal postbuckling strength.