A review of the recent developments in the analysis of laminated beams and plates with an emphasis on shear effects and buckling is presented. A discussion of various shear-deformation theories for plates and beams is given. The available theories are derived assuming a variation of either the in-plane displacement components or the stress components or both in the thickness coordinate. A review of the recently developed finite elements to analyze thin and thick laminated beams and plates is given next. These elements have been derived using the displacement methods, or the mixed methods or the hybrid methods. Recent studies on the buckling and postbuckling behavior of perfect and geometrically imperfect plates are described next. These behaviors have been studied using analytical, numerical, and experimental techniques. Finally, a review of the various studies on the delamination buckling and growth in beams and plates is given. Once again, the studies have been conducted using analytical, numerical, and experimental techniques. The energy release rates have been determined using closed-form solutions or using numerical differentiation. Mention also is made of studies on multiple delaminations and on dynamic response of composite laminates under impact loads.

Recent advances in analysis of laminated beams and plates. Part I - Sheareffects and buckling.

https://shellbuckling.com/abstracts/panda2/1987.abs.basic.pdf

PANDA2: Program for Minimum Weight Design of Stiffened, Composite, Locally Buckled Panels

Conditions for laminated plates to remain flat under inplane loading

Vibration and buckling of rectangular composite plates with variable fiber spacing

The influence of different parameters on the impact behavior of laminated composite plates is considered analytically. A Rayleigh-Ritz energy method was used to spatially discretize the time-varying boundary value problem and a set of coupled, ordinary differential equations in time were obtained based on the discretized system Lagrangian. The effects of shearing deformation, bending-twisting coupling, and nonlinear contact behavior were included in the model. The resulting equations were integrated using the implicit Newmark beta method without the effects of rotary inertia. The results indicate that the effective mass of the plate is often an important effect in the response to impact events. In general, the influence of the constitutive behavior dominates for very low velocity impact, whereas the target mass properties become more important as the impactor velocity increases. This importance of mass clearly shows that impactor kinetic energy is not sufficient to characterize the impactor as the impactor mass is shown to have a large influence on the resulting dynamic behavior. In addition to these parameters, the effects of preload and material properties are considered and discussed.

Transient response of graphite/epoxy and Kevlar/epoxy laminates subjected to impact

: This work summarizes the technical literature dealing with buckling and post-buckling behavior of laminated composite plates and shell panels. Emphasis is given to modern materials used in the aerospace industry having fiber-matrix constituents (e.g., glass-epoxy, boron-epoxy, graphite-epoxy, boron-aluminum), but other applications are also considered (e.g., plywood, paperboard). Geometric configurations taken up are either flat (plates) or cylindrically curved (shells), and have rectangular planform. All possible types of loading conditions and edge constraint conditions are considered. Both symmetrically and unsymmetrically laminated configurations are included, with symmetrical laminates represented by orthotropic or anisotropic plate or shell theory. Complicating effects dealt with include: internal holes, shear deformation, sandwich plates with soft cores, local instability, inelastic materials, hygrothermal effects and stiffeners. Approximately 400 references are used. Extension numerical results are presented in graphical and tabular form. Both theoretical and experimental results are summarized. Keywords: Vibrations; Unsymmetric laminates.

Arthur W. Leissa

Papers

Buckling of Laminated Composite Plates and Shell Panels