Buckling and Post-buckling Analysis of Composite Plates

Elena-Felicia Beznea and Ionel Chirica

University Dunarea de Jos of Galati Romania

1. Introduction

Thin walled stiffened composite panels are among the most utilized structural elements in ship structures. The composite layered panels with fibers are the most usually used in shipbuilding, aerospace industry and in engineering constructions as well. These structures possess the unfortunate property of being highly sensitive to geometrical and mechanical imperfections. These panels, unfortunately, have one important characteristic connected to big sensitivity on geometrical imperfections (different dimensions comparative with the design ones). The defects are of following types: different directions of fibers design, variations in thickness, inclusions, delaminations or initial transversal deformations.

Ship structure plates are subjected to any combination of in plane, out of plane and shear loads during application. Due to the geometry and general load of the ship hull, buckling is one of the most important failure criteria of these structures.

This is why it is necessary to develop the appropriate methodologies able to correctly predict the behavior of a laminated composite plate in the deep postbuckling region, at the collapse load, which is characterized by separation between the skin and the stiffeners, delaminations, crack propagations and matrix failure, as well as to understand its behavior under repeated buckling.

During its normal service life, a ship hull, which is composed of many curved laminated composite stringer stiffened panels, may experience a few hundreds of buckling – postbuckling cycles. Although it is well recognized that CFRP stiffened structures are capable of withstanding very deep post-buckling, yielding collapse loads equal to three – four times their buckling load (Bisagni & Cordisco, 2004, Knight & Starnes, 1988), there exists scarce knowledge in the literature about the effects of repeated buckling on the global behavior of the laminated composite panels under combined loading influences.

According to the studies, it is possible to predict on how far into the post-buckling region it is possible to increase loading without loosing structural safety.

Buckling failure mode of a stiffened plate can further be subdivided into global buckling, local skin buckling and stiffener crippling. Global buckling is collapse of the whole structure, i. e. collapse of the stiffeners and the shell as one unit.

Local plate buckling and stiffeners crippling on the other hand are localized failure modes involving local failure of only the skin in the first case and the stiffener in the second case. A grid stiffened panel will fail in any of these failure modes depending on the stiffener configuration, plate thickness, shell winding angle and type of applied load.

Over the past four decades, a lot of research has been focused on the buckling, collapse and post buckling behavior of composite shells. The simplest stiffened panel consists of only orthogonal stiffeners (stiffened orthogrid) such as longitudinal and transversal girders. Another type of stiffener arrangement is the transversal framing system.

Different analytical tools have so far been developed by researches to successfully predict the three buckling failure modes associated with stiffened panels subjected to different loading conditions.

The use of finite-elements analysis for investigation of buckling problem of composite panels is becoming popular due to the improvement in computational hardware and emergence of highly specialized software. Depending on the degree of accuracy desired and limit of computational cost, three types of buckling analysis can be carried out. Linear bifurcation analysis is the basic analysis type which does not take into consideration the pre­buckling deformation and stresses. This analysis can accurately predict the buckling load of a geometrically perfect compression loaded panel, and the pre-buckling deformation and stress in the panel have an insignificant effect on the predicted bifurcation buckling load of the shell. The second kind of bifurcation analysis takes into consideration the nonlinear pre­buckling deformation and stresses and results in a much more accurate buckling load.

The third analysis, the nonlinear buckling analysis, allows for large nonlinear geometric deflections. Unlike the previous two bifurcation analyses that are eigenvalue problems, the nonlinear analysis is iterative in nature. In this analysis the load is steadily increased until the solution starts to diverge.

In this chapter, layered composite plates with imperfections are analysed.