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A PARAMETRIC STUDY FOR THE DESIGN OF STIFFENED

COMPOSITE PANEL

Hao Wu and Ying Yan

School of Aeronautic Science and Engineering, Beihang University,Beijing, 100083, China

E-mail: wuhao1212@foxmail.com

Keywords stiffened composite panel, critical buckling load, specific critical buckling load, critical buckling mode,

boundary condition effect

Abstract

A parametric study is conducted for the design of stiffened composite panel (SCP). A SCP with two stiffeners, loaded

under uniaxial compression load is studied, where effects of stiffener thickness and distance on the critical buckling

behaviour of the SCP are investigated. It is illustrated that stiffener has an effect of boundary condition on the skin, andan optimal structural efficiency exists when this effect is significant enough. The boundary condition effect makes the

whole SCP buckles as local skin buckling and its critical buckling behaviour is dominated by the local skin buckling

with the lowest critical buckling load. The parametric study provides designer with comprehension of the stiffener/skin

enhancement in the buckling behaviour of the SCP, serving for the design of SCP in the future.

1 Introduction

Skin-stiffened composite structures are extensively used in aircraft and space structures to sustain the in-plane load.

Design of this structure considering linear buckling failure is generally solved through a process of optimization,

where the stiffener construction and skin stacking sequence are operated by the optimization algorithm to search for

the lightest panel under local and global buckling load constraints. Although optimization is an efficient way for the

design, it can not explain the mechanism of buckling behaviour of the stiffened composite structure. This paper aims to

explain this mechanism through a parametric study of a stiffened composite panel (SCP), where the effects of stiffener

thickness and distance on the critical buckling load (CBL) of the SCP are investigated.

2 Experimental Buckling Behaviour of SCP

A SCP used in the wing box generally consists of a skin and several stiffeners attaching on one side of the skin, while

the edges of skin together with the ends of stiffeners are fixed to the adjacent structures. In the published optimization

works1,2 of SCP subjected to buckling load constraints, the buckling modes are considered as global buckling and local

skin buckling. However, in many published experimental studies of buckling behaviour of SCP P3-5, local skin buckling

modes are shown to be dominated in the load-shortening tests. Hence, it is doubted here that the enhancement of

stiffener/skin in the buckling behaviour of a SCP is explored through the way that the skin is isolated into several local

skins by the stiffener. This assumption will be validated by the parametric study of stiffener thickness and distance in

the following sections.

3 Finite Element of SCP

A finite element model of SCP is built in MSC/PATRAN as shown in Fig. 1 (a). The panel is 0.4 m wide and 0.4 m

long with two blade stiffeners located symmetrically. The skin edge A is loaded by uniform compressive load Nx=1000

N/m while it is restrained in displacement y and z. Two longitudinal edges B and D are restrained in displacement y

and z while edge C together with attaching stiffener ends are restrained in displacements x, y and z. The material ply

thickness is 0.125 mm, and the properties of T300/5208 are used: E1=181 GPa, E2=10.3 GPa, G12=7.17 GPa, 12=0.28.

The skin has a stacking sequence of [45/-45/90/0]s while the stiffener has only 0 degree plies, and the stiffener flange

has half the stacking sequence of the blade. The stiffener ply number and stiffener distance are variables in the

parametric study. The critical buckling behaviour is simulated in MSC/NASTRAN using a linear eigenvalue analysis,

while the four-node shell element is applied based on the classical laminate plate theory (CLPT). The multi-point

constraint is utilized for skin/flange connection, also the identical displacement between edge A and the ends of two

stiffeners, as shown in Fig. 1 (b).

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(a) Finite element model (b) Multi-point constraint

Fig. 1 Finite element model of the SCP

4 Parametric Study

4.1 Effect of stiffener thickness

The effect of stiffener thickness on the CBL is investigated in three SCP with different stiffener distances Ds, which

are 0.1 m, 0.16 m and 0.2 m. Ds changes smoothly from [0]2s to [0]40s and the according CBL factor is shown in Fig. 2

(a), increasing then tending to be constant. The specific CBL factor in Fig. 2 (b), which is a structural efficiency index

meaning the CBL factor gained by per unit weight, increases and then declines. Hence the two figures indicate that, the

CBL of the SCP does not rise monotonically with the increase of stiffener thickness, while that when it is not sensitive

to the increase of stiffener thickness, an optimal structural efficiency exists.

(a) Critical buckling load factor (b) Specific critical buckling load factor

Fig. 2 Effect of stiffener thickness on the critical buckling load of SCP

In order to explain the variation of CBL in Fig. 2, the critical buckling modes (CBM) around the peak points in Fig. 2

(b) are shown in Fig. 3, the modes in the middle column being according to the peak points. For each Ds, with the

thickening of stiffener, the mode changes from simultaneous skin/stiffener buckling to only one local skin buckling.

This indicates the increasingly larger difference of CBL among local skins, illustrating that the stiffener plays a role as

boundary condition on the local skins. Hence the variation of CBL in Fig. 2 can be explained that, with the thickening

of stiffener, the local skins are becoming isolated by their edges are increasingly firmly constrained by stiffener, so

their CBL rise and gradually differ among them. Then when the boundary condition effect is significant enough and isnot sensitive to the stiffener thickening, CBL of local skins do not change much and the CBM of the lowest CBL is

dominated in the critical buckling behavior of the SCP. Meanwhile, the optimal structural efficiency occurs and then

declines because the CBL does not change with thickening of stiffener.

However in Fig. 2 (b), the stiffener thickness according to the optimal structural efficiency differs among different Ds,

so does the CBM in Fig. 3, therefore it is necessary to investigate the effect of Ds on the critical buckling behaviour of

the SCP.

[0]4s [0]10s [0]40s

(a) Ds = 0.1 m

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[0]4s [0]14s [0]40s

(b) Ds = 0.16 m

[0]4s [0]12s [0]40s

(c) Ds = 0.2 m

Fig.3 Effect of stiffener thickness on the critical buckling mode of SCP

4.2 Effect of stiffener distance

In order to study the effect of stiffener distance Ds on the critical buckling behaviour of the SCP, SCP of four stiffener[0]4s, [0]10s, [0]16s and [0]24s are investigated in 12 Ds and according CBL factors are show in Fig. 4. It observes that

CBL factor for each stiffener climbs and then declines, while each peak occurs at around Ds=0.16 m. Besides, in

thicker stiffener, the CBL factor is larger and closer to the adjacent factor, indicating the boundary condition effect is

less sensitive to the thickening of stiffener in thicker stiffener.

Fig. 4 Effect of stiffener distance on the critical buckling load of SCP

Fig. 5 shows the CBM around the peak points in Fig.4 for stiffener [0]10s, [0]16s and [0]24s, the modes in the middle

column being according to the peak points. It observes that the boundary condition effects of stiffener in (b) and (c) are

more remarkable than in (a), since in (b) and (c) critical buckling only happens in one local skin. It also should benoticed that in (b) and (c), the CBM transfers from side skin to bay (the skin portion between adjacent stiffeners).

Although in (a) local skins buckle simultaneously, the trend can be seen that buckling is vanishing in side skin while

deep in bay. Actually, from CBM of all the points in Fig. 4 most of which are not displayed here for brevity, it observes

that side skin buckling is dominated before the peak point, while bay buckling is dominated after the peak point.

Hence, it can be concluded that the variation of CBL with the change of Ds is due to the change of CBM.

Ds = 0.12 m Ds = 0.14 m Ds = 0.16 m(a) [0]10s

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Ds = 0.14 m Ds = 0.16 m Ds = 0.18 m

(b) [0]16s

Ds = 0.14 m Ds = 0.16 m Ds = 0.18 m

(c) [0]24s

Fig. 5 Effect of stiffener distance on the critical buckling mode of SCP

The analytical solution of CBL of a four-edge simply supported laminate loaded by uniaxial compression load is as

CBL = 22 [ (D11 D22)1/2 + D12 + 2D66 ] / b

2. (4.1)

where b is the width of the loaded edge, and Dij is component of laminate bending stiffness matrix. Although this

analytical solution is applicable to the symmetric laminate which has no extension/bending coupling and

bending/twisting coupling, it can be used to explain the CBL here qualitatively. Since in Eq. (1), CBL increases when

b decreases and decreases when b increases, similarly in the present study, CBL of side skin increases while that of bay

decreases when Ds increases. Consequently the variation of critical buckling behavior with the change of Ds of the

present SCP can be explained that, when Ds is little, the CBL of side skin is lower than that of bay so side skin

buckling is dominated. Then with the increase of Ds, CBL of side skin goes up while that of bay goes down, and the

dominating CBL gets its peak when two CBL in the local skins are similar. After that when the CBL of side skin

becomes higher than that of bay, bay buckling is dominated. Further with the increase of Ds, the CBL of bay continues

decreasing.

5 Conclusion

The mechanism of stiffener/skin enhancement in the buckling behaviour of a SCP is studied through a parametric

study. The study indicates the boundary condition effect that stiffener plays on the skin, and the effect makes the SCP

buckles as several local skin buckling and the local buckling mode of the lowest critical buckling load is dominated in

the critical buckling behaviour of the SCP. The enhancement of this effect raises the CBL of local skins further that of

the whole SCP while the optimal structural efficiency occurs when this effect is not sensitive to the thickening of

stiffener. The mechanism explained in this paper provides designer with the comprehension of stiffener/skin

enhancement in the buckling behaviour of the SCP, and it might be used for the expert knowledge of design of SCP in

the future.

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