Gang LEI，Shu-song YANG

(Chongqing University of Technology，Key Laboratory of Advanced Manufacturing Technology for Automobile Parts，Ministry of Education，Chongqing 400054，China)

A study on the buckling of stiffened composite fuselage panel

Gang LEI*，Shu-song YANG

(Chongqing University of Technology，Key Laboratory of Advanced Manufacturing Technology for Automobile Parts，Ministry of Education，Chongqing 400054，China)

Local buckling load and overall buckling load of stiffened composite fuselage panel were analyzed by both FEM and engineering method.In engineering method，local buckling of the stiffened panel was simplied as plate supported on four sides，and overall buckling was considered as the transverse shear effects.Eigenvalue analysis method was used for local buckling of stiffened panel，and non-linear arc-length method was used for overall buckling of stiffened panel in finite element method.The results of two methods are consistent.

Composite materials，Buckling，Engineering method，F(xiàn)inite element method

1 Introduction

Structural stability is an important issue for the thinwalled structures of plane.Buckling is one of the most common failure modes of instability，when the thinwalled structures suffered the load，such as，in-plane compression and shearing.In recent years，many scholars did substantial researches on the stability of structures using approximate analytical method，numerical method，and test method，etc.SHI Xudong［1］researched the structural stability of composite plates and shells.ZHANG Guofan［2］researched the post-buckling of stiffened plate with finite element method.

As itself particularity of the plane wall plate structure and the complexity of composites materials，there are many unresolved issues in the field of structural stability of composite materials.Based on the seniors’researches，the paper explores the local buckling andoverall buckling of composite fuselage panel using the finite element method(FEM)and engineering method.The whole process of buckling with compressive load is simulated through two calculations.

2 Structural buckling analysis

There are many kinds of failure modes for stiffened composite panels in engineering，such as local buckling of stiffened stringer skin or stringer，overall buckling of stiffened panel，compressive damage of stiffened panel，complex buckling mode coupling，and delaminating buckling，etc.Failure modes happened depended on the aspect ratio of stiffened panel in practice.Generally，the stiffened panel which has a big aspect ratio emerges overall buckling with ultimate load.On the contrary，the stiffened panel which has a small aspect ratio emerges compressive damage with ultimate load.

When the skin structure between stiffened girder occurred buckling，the stiffened composite panel structures of aircraft mostly have load-bearing capacity and the local buckling of panel is allowed.In this paper，the longer stiffened fuselage panel is studied.Under the compressive load applied，the panel finally appeared overall buckling after local buckling happened.

3 Local buckling analysis of panel

In this paper，two methods were applied to research the local buckling of stiffened composite panel:①eigenvalue analysis was carried out on the finite element model of stiffened composite panel using commercial software abaqus.The eigenvalues，eigenvectors，and buckling modes of panel can be obtained by the method;②local buckling load of stiffened panel was calculated using analytical method which be deduced by Shen Guanlin［4］.

3.1 Finite element analysis

Fig.1 shows the finite element model of stiffened composite panel.Skin，stringer and fuselage frame structure were discretized using 2D elements.The connections between them are simulated by beam elements.Bonding between skin and stringer are simulated by tie contactor.The model consists of 121357 nodes and 117648 elements.

Fig.1 FE model of stiffened composite panel

The thickness of single plate of the composite material is 0.19 mm.Basic mechanical property included: E11=174 600，E12=8 700，G12=6 400，v12=0.33.Skin and stringer are［45/-45/0/0/45/90/-45/0］s，The material of fuselage frame is aluminium alloy，and rivet is titanium alloy.The structure of stiffened composite panel is shown in Fig.2.

Fig.2 Structure of stiffened composite panel

Table 1 Structure parameters of cap stringer

The fuselage frame separation distance is 580 mm and the stringer separation distance is 218 mm.The structure parameters of hat stringer were shown in Table 1.Based on lanczos method in buckling mode of ABAQUS software，the modal of stiffened composite panel is analyzed under the boundary condition(the simply supported is established on one end in reinforcement direction of the stiffened panel.The compressive load of 1.0E+6N is applying at the other end based on equal displacement method).Fig.3 shows the 1st order buckling mode of stiffened composite panel.The buckling critical load coefficient is λ=1.51，i.e.the buckling load is 1.51E+6 N and unit buckling load should be 609.8 N/mm.The instability form of stiffened composite panel is the local buckling of skins between stringers.

Fig.3 First order buckling mode of stiffened composite panel

3.2 Calculation method in engineering

The buckling of skin between adjacent stringers of stiffened composite panel is analyzed according to symmetric orthotropic laminated rectangular plate.The axial compressive load is applied on stiffened panel，the skin surrounded by ribs is the simply supported，and the buckling load can be described as［4］:

Where，Nxis axial compressive buckling load per unit length;m is numbers of buckling half wave;b is loading edge length of rectangular plate;a is the other side length of rectangular plate;D is bending stiffness co-efficient of laminated board.

3.3 Result of analysis

Based on the model has been created，keeping the separation distance of fuselage frame as 580 mm，the five different cases were calculated using engineering method and finite element method through changing the separation distance of stringer.The results show that buckling occurred at the skin between adjacent stringers in each case.The unit loads，analyzed by FE method，are bigger than the results of engineering method in Table 2.Fig.4 shows that the results of the two methods is similarity.

Table 2 Results of FE method and engineering method

Fig.4 Relative deviation of FEM method and engineering method

4 Overall buckling analysis of panel

The load distribution of stiffened panels is uneven when the axial load is sequentially applied after local buckling of the skin occurred due to loads mainly passed through stringers.Overall buckling of stiffened panel finally appeared.With compressive load，the overall buckling of stiffened panel is appearing after the local buckling of the skin happened.The process of overall buckling of stiffened panel can be simulated well by Riks method in ABAQUS software.The loadbearing capacity of the stiffened panel with 4 redundant stringers can be obtained according to the modified euler’s formula with considering the transverse shear effects in paper［5］.

4.1 Finite element analysis

With keeping the stringer separation distance as 218 mm，the non-linear geometric equilibrium process of stiffened panel was simulated by Riks method in ABAQUS software.The contact between stringer and fuselage frame was established because of the geometric large deformation considered and the contact used to simulate the force transfer between the compressive panels.Consequently，the stress concentration can be reduced.The boundary condition is applied just like above.In order to improve the computational convergence of the model，the compressive displacement is applied to instead of compressive load.

Riks method was used in this paper.The initial imperfection is determined according to the local buckling mode calculated above.Then based on Hashin criterion［6］，the progressive damage process of stiffened panel is simulated.With applying the load on the FE model gradually during the analysis，the distribution of stress and strain in the structure were determined according to stress-strain relationships of material［7］.The elements’damage are estimated according to the damage criterion.The load wound be increased if the elements is well，and the load is decreased if the damage happened.Cycling the steps above until the curve of load vs.time appeared a plunge and the compressive buckling ultimate load of the test sample we obtained.

Fig.5 Integral buckling sketch of stiffened panel

Fig.5 shows the non-linear analysis result of stiffened composite panel，the result indicated that the local buckling happened both in skin and stringer and the stiffened panels appeared overall buckling.Fig.6 shows the reacting force of loading point has been changed according to time.The local buckling load of skin was labeled in the Fig.6.

Fig.6 Load curve of buckling process of stiffened panel

4.2 Method in engineering calculation

For the stiffened panel with more than 4 stringers，the stiffened panel is treated as column by ignoring the supporting effects of both sides.Based on considering the transverse shear effects，the buckling load of stiffened panel can be obtained from the following formula［5］.

Where:c is supporting coefficient of stiffened panel tip;EI is bending stiffness of stiffened panel;L is length of stiffened panel.λ is shape factor;G is equivalent shear modulus of vertical webs of stringers and A is sectional area of vertical webs of stringers.

4.3 Results and discussions

The overall buckling load of stiffened panel analyzed by engineering method is 2.03E+06 N.The relative deviation between engineering method and FE method is about 23.2%.

5 Conclusions

The buckling of stiffened composite fuselage panel is reached by FE method and engineering method in this paper.The conclusions are obtained as follow:

1)The local buckling load and overall buckling load of stiffened composite fuselage panel were achieved by FE method and engineering method，the relative deviation of these two methods is slightly differ.

2)The local buckling of stiffened composite fuselage panel happened firstly.The overall buckling occurred when the axial load was applied continuously.

3)The result analyzed by engineering method is lower than FE method.It indicates that the engineering method is conservative.The engineering method can be used well in phase of the preliminary design.

Acknowledgements

This paper is supported by Open Fund of Key Laboratory of Advanced Manufacturing Technology for Automobile Parts，Ministry of Education，Chongqing University of Technology.

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復(fù)合材料機身加筋壁板結(jié)構(gòu)穩(wěn)定性分析

雷剛*，楊述松

重慶理工大學(xué)汽車零部件先進制造技術(shù)教育部重點實驗室，重慶 400054

針對復(fù)合材料機身壁板結(jié)構(gòu)局部失穩(wěn)和總體失穩(wěn)，分別運用工程計算方法和有限元方法進行計算。工程方法計算局部失穩(wěn)把結(jié)構(gòu)簡化為四邊簡支板的失穩(wěn)，總體失穩(wěn)把結(jié)構(gòu)簡化為考慮橫向剪切的歐拉失穩(wěn);有限元法運用特征值分析法計算加筋板局部失穩(wěn)，運用非線性弧長法計算加筋板的總體失穩(wěn)。最后，兩種方法得到的結(jié)果一致。

復(fù)合材料;失穩(wěn);工程方法;有限元法

10.3969/j.issn.1001－3881.2015.06.018 Document code:A

U270.1+1

Hydromechatronics Engineering

http://jdy.qks.cqut.edu.cn

E-mail:jdygcyw@126.com

17 November 2014;revised 20 December 2014; accepted 11 January 2015

*Corresponding author:Gang LEI，Professor.

E-mail:ganglei4786@126.com