Nonlinear dynamic stability of an imperfect shear deformable orthotropic functionally graded material toroidal shell segments under the longitudinal constant velocity

Abstract

This study investigates the nonlinear dynamic buckling of the exponentially functionally graded orthotropic toroidal shell segments under constant loading rates under the shear deformation theory with the damping influence. The properties of the shell material are assumed to be graded according to the exponential distribution function through the shell thickness direction. The shear deformation theory with von Karman nonlinearity, Stein and McElman assumption, initial imperfection, and damping effect are adopted to create the theoretical formulations. Nonlinear dynamic stability equation is solved using Galerkin's procedure and the fourth-order Runge–Kutta technique. The dynamic buckling loads are evaluated by using Budiansky–Roth criterion. Moreover, different parameter influences such as geometrical parameters, velocity, imperfections, damping ratios, and nonhomogeneous parameters on the dynamic buckling are examined in detail. The obtained results are validated with the previous publications and the good agreements are shown.

Free Vibration Analysis of Toroidal Shell Segments Reinforced by Graded Graphene in Elastic Medium

“…They used Jacobi elliptic functions to solve the nonlinear governing differential equations. On the basis of shear deformation theory (SDT), Ali et al (9,10) investigated the nonlinear free vibration behavior and dynamic stability of orthotropic functionally graded toroidal shell segments, considering the damping effect.…”

Dynamic Pulse Buckling of Composite Stanchions in the Sub-Cargo Floor Area of a Civil Regional Aircraft

“…The so-called buckling load is the lowest of the loads for which equilibrium is indifferent. However, buckling can also be caused by loads that vary over time [ 1 , 2 , 3 ]. The application of a time-dependent axial load to a beam, which then induces lateral vibrations and can eventually lead to instability, is something that has been investigated by many authors [ 4 , 5 , 6 , 7 , 8 , 9 , 10 ].…”