Finite element and experimental modeling of composite plates with initial transversal imperfection

1.2 Presentation

In this part, the buckling behavior of the plates with initial transversal deformation, placed between two pairs of stiffeners of the ship hull structure is analyzing. The results obtained on buckling analysis of ship hull plates made of composite materials taking into account the imperfection due to fabrication, are presented. Due to the special behavior of the layered composite plates, the nonlinear analysis of the buckling behavior of the plates is done. The buckling load is determined according to the first failure occurring in an element, based on the Tsai-Wu failure criterion.

The most used framing construction types for the ship deck plates made of composite materials are transversal or mixed. So, the following case of plate placed in the ship deck structure is analyzed: the plate placed between two pairs of parallel stiffeners (two transversal web frames and two longitudinal frames – longitudinal framing construction system).

The geometry of the plate is square one, having the side length of 320mm, and total thickness of 4.96mm. The layers were grouped into the macro-layers (group of layers having the same characteristics: thickness (t), direction of fibers (a) and type of material).

The imperfections of plates are considered the initial transversal deformations. The shape of the deformation is just the first form of the buckling of perfect plate clamped on the sides. The analysis presented in this part is done for the most usual magnitudes of the transversal deformation of the imperfections (versus side length of the plate) occurred in the ship deck plates after fabrication.

The following cases (in numerical and experimental ways) are presented: compressive buckling, shear buckling, mixed compressive and shear buckling. The results (for linear and
nonlinear model) are presented as variation of the buckling loads function of maximum transversal displacement (buckling and post-buckling behaviour).

The simplest stiffened plate consists of only orthogonal stiffeners (stiffened orthogrid) such as longitudinals and transversal girders. Other type of stiffener arrangement is the transversal framing system.

The characteristics of the material used in this chapter are:

Ex=46 GPa, Ey=13 GPa, Ez=13 GPa, Gxy=5 GPa, Gxz=5 GPa, Gyz = 4.6 GPa, pxy=0.3, PyZ=0.42, pxz=0.3,

– traction strengths Rx=1.062 GPa, Ry=0.031 GPa,

– compression strength Ry=0.118 GPa,

– shear strength Rxy=0.72 GPa.

Finite element and experimental modeling of composite plates with initial transversal imperfection

Fig. 17.2. Plate cross section in plane xz

Finite element and experimental modeling of composite plates with initial transversal imperfection

Fig. 17.3. Imperfect plate

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. These analytical tools developed are divided into three major categories. 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 plate, and the pre-buckling deformation and stress in the plate have an insignificant effect on the predicted bifurcation buckling load of the shell (Ambarcumyan, 1991, Thurley & Marshall, 1995). The second kind of bifurcation analysis takes into consideration the nonlinear pre-buckling deformation and stresses and results in a much more accurate buckling load (Adams & all, 2003, Chirica & all, 2008).

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 (Adams & all, 2003). A lot of work has been done in finite elements analysis pertaining to the investigation of buckling of stiffened panels (Beznea, 2008, Chirica & all, 2008). One of the major drawbacks associated with this tool is the tedious model-building phase involved and the subsequent inconvenient parametric study. Following to these considerations, in this chapter the results of the buckling behavior analysing of the plates placed between two pairs of stiffeners of the ship hull structure are analysed. In the following pages only the results obtained after buckling analysis of ship hull plates made of composite materials taking into account the imperfection due to fabrication will be presented. Due to the special behavior of the layered composite plates, the nonlinear analysis of the buckling behavior of the plates is to do (Altenbach, 2004, Hilburger, 2001).