A unified buckling formulation for linear and nonlinear analysis of laminated plates using penalty based [formula omitted] FEM-HSDT model

Abstract

In this paper, the effect of pre-buckling boundary conditions and the type of nonlinearity for stress stiffening used in different linear and nonlinear buckling approaches is studied for laminated composite plates. The study is conducted using a C0 finite element (FE) plate model, employing a unified C1 higher-order shear deformation theory (HSDT). The set of governing equations is derived using the principle of virtual displacement and solved using the tangent-based arc-length method in conjunction with a simple branch switching technique. The performance of the present C0 FE model is assessed through a validation exercise and comparison with results obtained via the use of ANSYS and, for linear analysis, Navier solution, as well as solutions available in the literature. The influence of the different in-plane loads, boundary conditions, side-to-thickness ratio, fiber orientation, types of imperfection and penalty stiffness matrix are also examined. The results show that the same boundary conditions must be utilized in both pre-buckling and linear eigenvalue analyses for accurate and realistic predictions of critical buckling loads, as confirmed from the nonlinear buckling analyses. Furthermore, the critical buckling loads obtained using Green–Lagrange nonlinearity are observed to be more conservative than those obtained using von Kármán nonlinearity. The nonlinear buckling approach is a generalized approach while the nonlinear eigenvalue approach has a limited range of application.