Multi-patch isogeometric Kirchhoff-Love shell analysis for post-buckling of functionally graded graphene platelets reinforced composite shells

This paper develops a multi-patch isogeometric Kirchhoff-Love shell method for post-buckling of functionally graded graphene platelets reinforced composite (FG-GPLRC) cylindrical, spherical, and conoidal shell structures, which are built with single or multiple NURBS patches. A penalty strategy is employed to weakly couple nonconforming interfaces between adjacent patches. The coupling work induced by enforcing displacement continuity and rotational continuity is added to the equilibrium equation, and the corresponding stiffness matrix is derived in detail. A simplified arc-length method is utilized to capture the complex equilibrium paths including snap-through and snap-back behaviors. Five distribution patterns of the shells including uniform (UD), V-type, A-type, O-type, and X-type are considered. The cylindrical and spherical shells are subjected to concentrated loadings at central points while for conoidal shells the concentrated loadings are enforced at the center points of an edge. The post-buckling of isotropic and laminated shell structures is first studied to validate the developed formulations by comparing the obtained results with those given in existing literature. Then a series of numerical examples considering nonlinear FG-GPLRC shell problems are conducted to explore the effect of various parameters like geometric dimensions, GPL distribution patterns, and shell thickness on the mechanical performance. Finally, the post-buckling of a cylindrical shell subjected to an offset concentrated load, with extremely complicated equilibrium paths, is modeled and analyzed by using the developed multi patch isogeometric method. The numerical results reveal that the X-type GPL distribution pattern demonstrates better performance in load-deflection responses and provides the largest buckling critical load among the five patterns. Additionally, the increase in height ratio could deteriorate the stability performance of FG-GPLRC conoidal shells.