Nonlinear frequency prediction of cutout borne multi-layered shallow doubly curved shell structures

Abstract

This is the first time two different geometrical nonlinear strain–displacement relationships are adopted to model the laminated shell structure with the cutout to predict the eigenvalues considering a higher-order displacement model. The nonlinear solution for the natural frequency value is obtained using Picard's iterative method in association with the isoparametric finite element method. The present research mainly indicates the inevitability of Green-Lagrange's nonlinear strain in the framework of higher-order displacement kinematics instead of von-Karman's nonlinear strain including all of the nonlinear higher-order strain. The predicted nonlinear solution consistency is verified by solving a series of examples, as same as the source data. The influences of the cutout (shape and size) related data and the corresponding geometrical parameters of the multilayered structure are expressed in the final output form. Lastly, the inclusive inferences are highlighted to recommend the nonlinear model to analyze a flexible laminated structural component with and without cutout.