Non-linear response and buckling of imperfect laminated composite plates under in-plane pulse forces

Abstract

This study presents a semi-analytical solution of the non-linear dynamic response, shock spectrum, and dynamic buckling of an imperfect angle-ply laminated composite plate under various types of in-plane pulse forces. The laminated composite plate is modeled using a higher-order shear deformation theory and von-Kármán geometric nonlinearity. The non-linear governing partial differential equations (PDEs) of imperfect laminated composite plates are derived via Hamilton’s principle. Using Galerkin’s method, the non-linear PDEs are transformed into non-linear algebraic equations for the static stability problems and non-linear ordinary differential equations for the dynamic problem such as dynamic response, shock spectrum, and dynamic buckling. The buckling load of the plate is obtained through the associated eigenvalue problem. The static failure load of the composite plate is evaluated using the post-buckling analysis based on the Tsai-Wu failure criterion. The dynamic response and shock spectrum of the composite plate are determined via Newmark’s method. The dynamic failure load of the plate is evaluated using Newmark’s method based on the Tsai-Wu failure criterion. Dynamic buckling is to be characterized by dynamic load factor (DLF), which is represented as the ratio of the dynamic failure load to the static failure load. Based on the pulse/shock duration time, the pulse forces are divided into three loading regimes known as impulsive, dynamic, and quasi-static. The study revealed that the DLF values are > 1, < 1, and [Formula: see text]1 respectively for the case of impulsive, dynamic, and quasi-static loading regimes of pulse force. The influences of various types of in-plane pulse forces, amplitude and time duration of pulse forces, and amplitude of initial geometric imperfections on the non-linear dynamic response, shock spectrum, and dynamic buckling behavior of the laminated composite plate are addressed in detail. The results will help in the appropriate design of the laminated composite plate against dynamic buckling.

Transient nonlinear responses of a sandwich plate with micro-cellular auxetic core based on modified strain gradient theory under impact loads

“…In the second step, to make the micro-cellular auxetic samples, a nanosecond laser system was used on the 50 μm-thick stainless steel sheets (Figure 5). The dimensions of micro-cellular auxetic samples are as follows: L ¼ 370 ðμmÞ, h ¼ 900 ðμmÞ, t c ¼ 71ðμmÞ, l 0 ¼ 7:9 ðμmÞ, θ ¼ À0:9ðradÞ, h c ¼ 50ðμmÞ (22) Finally, Young's modulus of the micro-cellular auxetic structure was acquired through a tensile test. Table 1 compares the numerical, experimental, and analytical (MSGT) results, indicating an excellent agreement among the findings.…”

“…Substituting Navier’s relations in governing equations (Equations (28a) and (28b)) and applying Galerkin’s method 22 leads to the micro-cellular auxetic sandwich structure’s equations of motion:…”

“…(Bubnov-Galerkin method). 22 Step 3) The Algebraic equations system is solved, and the results are substituted into the differential equations. Finally, the nonlinear ordinary differential equations of motion for the micro-cellular auxetic sandwich plate are obtained as equations (28a) and (28b).…”