Isogeometric nonlinear bending and instability analysis of cylindrical composite shells reinforced with graphene platelets

Abstract

In the present study, by using IGA (isogeometric analysis) method, the nonlinear bending and instability behavior of cylindrical composite shells embedded with GPLs (graphene platelets) having functional gradation is investigated. In IGA, NURBS functions are employed both to construct the geometry and to approximate the field variables. Advantages of adopting IGA include: the exact geometrical description, high accuracy and efficacy, higher-order smoothness. The nonlinear equations of equilibrium are derived via the virtual work principle on the basis of a higher-order shell theory with the large deflection. A solution procedure in which the arc length method is modified and exploited in combination with the modified Newton-Raphson method for the highly nonlinear problem is designed to trace accurately the nonlinear equilibrium path that encompasses the snap-through and snap-back phenomena. Four patterns of the GPL dispersions are prepared: uniform, O-type, X-type and A-type, and evenly distributed and central point loadings are considered. The proposed IGA approach is evidenced to successfully capture the complete nonlinear equilibrium path of the composite shell under flexure. The further parametric examinations that follow to highlight the impacts of the loading and constraint conditions, GPL weight fraction, reinforcement schemes and shell geometric parameter on the nonlinear bending and instability responses.