Nonlinear Response and Buckling of Imperfect Plates Under In-Plane Pulse Forces: A Semi-analytical Investigation

Abstract

This study presents a semi-analytical solution of the nonlinear dynamic response, shock spectrum, and dynamic buckling of a simply supported imperfect plate under various types of in-plane pulse forces. Here, the plate is modelled based on higher-order shear deformation theory (HSDT) considering the von-Kármán geometric nonlinearity. The governing nonlinear partial differential equations (NLPDEs) of the imperfect plates are developed via Hamilton’s principle. Using Galerkin’s method, the NLPDEs are converted into sets of nonlinear algebraic equations (NLAEs) for static stability problems and nonlinear ordinary differential equations (NLODEs) for dynamic problems. The critical buckling load of the plate is obtained through the associated eigenvalue problem. The static failure load of the plate is evaluated using nonlinear static stability analysis based on the yield stress failure criterion. The dynamic response and shock spectrum of the plates are plotted via Newmark’s method. The dynamic failure load of the plate is evaluated using Newmark’s method based on the yield stress failure criterion. Dynamic load factor (DLF) is the ratio of dynamic failure load to static failure load. Based on the pulse duration time, the pulse forces are divided into three categories known as impulsive, dynamic, and quasi-static. In the case of impulsive, dynamic, and quasi-static loading regimes, DLF > 1, DLF < 1, and DLF 1, respectively. The results obtained from the current works will help in the appropriate design of the imperfect plates against dynamic buckling.