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Critical Buckling Load Optimization of a Filament Wound Composite Cylindrical Underwater Structure

B.Acar, A.Yetgin, and E.Özaslan

Roketsan Missile Ind.

Abstract: Filament wound composite structures have high resistance to water corrosion which

makes them popular for military underwater applications besides their high strength to weight

ratio. The main loading condition for an underwater structure is hydrostatic external pressure

which generally causes structural instability or buckling rather than rupture of the structure. In

this study, a military underwater cylindrical Glass/Epoxy filament wound structure was analyzed

in terms of buckling. Abaqus/CAE and Isight tool with Response Surface Method were used.

Helical winding angle and thickness of helical and hoop layers with constant total thickness were

used as main variables to investigate the effects of them on the critical buckling pressure.

However, cylinder diameter, cylinder length, total thickness and material were kept constant as

design constraints. It is seen that the critical buckling pressure can be increased 5.5% by

changing the helical winding angle. Critical buckling pressure increases with increasing helical

winding angle from 30° to 58° and decreases with further increasing of helical winding angle

from 58° to 80°. Also, it is seen that the critical buckling pressure can be raised maximum 21% by

changing the thickness of helical layers with constant total thickness. Critical buckling pressure

increases with increasing of helical layer thickness from 2 mm to a certain value and falls after

that certain value up to 4 mm. In addition to individual effects, interaction effects of variables on

the critical buckling pressure were demonstrated. Also, optimum design point was determined,

and structural strength of optimized design was checked with Tsai-Wu failure criteria.

Keywords: Buckling, Composites, Design Optimization, Optimization

1. Introduction

Filament wound composite materials have been used in both civil and military underwater

structures due to their high strength to weight ratio and high resistance to salt water corrosion over

the past few years. The main loading condition of an underwater structure is hydrostatic pressure.

This type of loading generally causes structural instability or buckling rather than crushing of

structure [1]. When the cylindrical composite structure exposed to hydrostatic pressure load, the

buckling may be seen at a stress which is far lower than material strength. Because of this fact, the

designers should consider the buckling failure as well as crushing of structure. Dey A. et al. [2],

investigated the buckling behavior of carbon/epoxy filament wound stiffened thick walled

composite pressure vessel subjected to hydrostatic pressure. They concluded that stiffened

filament wound composite pressure vessel has higher critic buckling pressure than unstiffened

pressure vessel. Kim H.M. et al. [3], studied the finite element analysis of thick walled composite

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pressure vessel under hydrostatic pressure load. They showed that solid and shell modeling of this

type structure gives comparable results in terms of critic buckling load. Also, they concluded that

finite element model with effective properties of laminate rather than separate modeling of hoop

and helical layers may give %40 errors from the actual hydrostatic experimental value. It is

showed by many investigators that the thin composite tubes subjected to internal pressure give

optimum strength values when they wound [±55]n angle [1,4-6]. The reason of this fact is that 55-

degree angle wound gives best response to loading ratio which is 2:1 circumferential and axial

components for internal pressure loading case. Messager T. et al. [7], performed an optimization

study to improve stability limit of a thin-walled laminated composite unstiffened vessel under

hydrostatic pressure loading. They showed that optimizing the stacking sequence may increase the

critic buckling load approximately %40.

In this study, a military underwater cylindrical filament wound composite structure which was

exposed to hydrostatic pressure was performed in terms of critical buckling load optimization.

Helical winding angle and thickness of helical/hoop layers with constant total thickness were used

as main variables to optimize the critical buckling pressure. However, cylinder diameter, cylinder

length, total thickness and material were kept constant as design constraints. Also, individual

effects and interaction effects of variable parameters on the critical buckling load were

demonstrated. Also, structural strength of optimized design was checked with using Tsai-Wu

failure criteria. Abaqus/CAE 2016 [8] and Isight [9] optimization tool were used for the study.

2. Problem Description and Finite Element Analysis

2.1 Problem description

In this study, critical buckling load optimization of a deep sea cylindrical structure which exposed

to hydrostatic pressure load was performed. A schematic view of structure is shown in Figure1

where total composite section length L is 500 mm, inner diameter of composite part D is 288 mm

and total thickness of composite cylinder t is 6 mm. Both end closures are steel.

Figure 1. Schematic view of structure

Geometrical design constraints are total thickness t, cylinder length L and cylinder diameter D.

The effect of thickness ratio of helical/hoop layers (t_angle/t_hoop) with constant total thickness

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(t) and winding angle of helical layers on the critical buckling load was investigated. Also,

winding angle and helical/hoop thickness optimization was performed in terms of critical buckling

load. Constrained and variable geometric parameters were shown in Figure 2.

Figure 2. Constrained and variable geometric parameters

The winding angle pattern was chosen as [(90)a / (θ)b / (90)a ] which is a typical characteristic

pattern to provide high critical buckling load and high structural strength [7]. Helical winding

angle range was given as; θ ϵ [30°……80°]. The thickness range of helical layers was given as;

t_angle ϵ [2…...4] mm.

The composite material is glass/epoxy which is used for underwater structures thanks to its high

resistance to salt water corrosion. The material properties of glass/epoxy are given in Table 1 and

Table 2.

Table 1. Material properties of Glass/Epoxy

E1 [GPa] 45.6

E2 [GPa] 16

E3 [GPa] 16

G12 [GPa] 5.88

G13 [GPa] 5.88

G23 [GPa] 5.9

v12 0.264

v13 0.264

v23 0.437

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Table 2. Strength values of Glass/Epoxy

Xt [MPa] 1264

Xc [MPa] -812

Yt [MPa] 41.6

Yc [MPa] 146.4

S [MPa] 50

2.2 Finite element analysis

Buckling analysis was performed with Abaqus/CAE 2016 [8]. Composite cylindrical structure was

modelled with Abaqus Composite Layup Manager. Helical layers were modelled as +θ/-θ to

represent filament winding nature. Boundary conditions and loading for buckling analysis are

given in Figure 3 and Figure 4.

Figure 3. Boundary conditions

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Figure 4. Loading for buckling analysis

3. DOE Procedure

In the DOE procedure, thickness of the helical layers is changed while keeping total thickness the

same. Another parameter is winding angle of helical layers. First step of the DOE process begins

with generating new input parameter as shown in Figure 5. In this study, design matrix is

generated using Latin Hypercube method. Design space is evenly divided into levels for each

parameter and design points are generated by randomly combining these levels.[9] Figure 6

illustrates, five design points that are selected from uniformly divided levels of parameters X1 and

X2. This method allows designer to select any number of design points which is greater than

parameters and more combinations can be investigated. [9]

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Figure 5. Work flow

Figure 6. Latin Hypercube

Isight provides an easy to use environment to set up DOE process and post process the results.

Another advantage is seamless utilization of simulation products such as Abaqus. Isight sim-flow

used in this work is shown in Figure 7. In the component in the flow is a simcode which combines

an input text editor, command prompter and output text parser. In this component, design

parameters are written into buckling input file, solved and critical buckling factor is extracted from

dat file. Next component calculates pressure and edge loading corresponding buckling load and

stress analysis is solved afterwards. In the final component, failure index is calculated using stress

results.

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Figure 7. Isight Sim-Flow view

4. Results

The first buckling eigenvalue of buckling analysis was accepted as critical buckling load. The

shapes of first buckling modes were shown in Figure 8. Characteristic buckling shapes for

laminated cylinders were obtained as expected.

Figure 8. First buckling shapes for analysis

Firstly, the effects of the geometric variables (helical winding angle and thickness of helical layer

with constant total thickness) on the critical buckling load were investigated with using Response

Surface Method (RSM).

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From the helical winding angle main effect plot (Figure 9), it is seen that the helical angle variance

changes the critical buckling load maximum %5.5 for the winding angle range of 30° to 80°. The

critical buckling load increases with increasing of helical winding angle from 30° to a certain

value. From this certain winding angle, the critical buckling load decreases with increasing the

helical winding angle until 80°. This fact can be expressed as the stiffness contribution of helical

layers to axial and hoop directions is optimum at a certain winding angle. When the helical

winding angle is less than optimum value, the helical layers give less stiffness contribution to

hoop direction than optimum winding angle. Similarly, when the helical winding angle is more

than optimum value, the helical layers give less stiffness contribution to axial direction than

optimum winding angle.

Figure 9. Main effect plot of helical winding angle

From the helical layer thickness main effect plot (Figure 10), it is seen that the thickness of helical

layers with constant total thickness changes the critical buckling load maximum %21 for the

helical thickness range of 2 mm to 4 mm. The critical buckling load increases with increasing of

helical layer thickness from minimum value to a certain value. The critical buckling load decrease

from this certain value to maximum thickness value. This behavior is similar to helical winding

angle behavior. When the helical layer thickness is less than the optimum value, the helical layers

give less stiffness contribution to axial direction than optimum thickness value. Similarly, when

the helical winding angle is more than optimum value, the total hoop direction stiffness is less than

optimum thickness value.

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Figure 10. Main effect plot of helical layer thickness

From the interaction plot (Figure 11), the effect of both parameters on the critical buckling load

can be seen instead of individual effects of parameters. It is obviously seen that 30° helical

winding angle gives higher critical buckling load than 80° for minimum helical layer thickness.

The reason of this fact is the high axial stiffness contribution of 30° helical winding angle to axial

direction. Oppositely, 80° helical winding angle gives higher critical buckling load than 30° for

maximum helical layer thickness. The reason of this fact is the high hoop stiffness contribution of

80° helical winding angle to hoop direction. Also, 30° and 80° helical winding angles give same

critical buckling load at a certain helical layer thickness value.

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Figure 11. Interaction plot

The effect ratio of individual and interaction parameters to critical buckling load is shown in

Figure 12 Pareto chart. From this chart, it is seen that the quadratic form of helical layer thickness

parameter (t_angle) has the maximum effect on the critical buckling load. The second effective

parameter is the interaction of helical winding angle (angle) and helical layer thickness. Next

effective parameter is linear form of helical layer thickness. Finally, the least effective parameter

on the critical buckling load is linear form of helical winding angle.

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Figure 12. Pareto chart

All these effects also can be seen in surface plot (Figure 13) in 3D space.

Figure 13. Surface plot

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After the investigation of the effect of the parametric variables on the critical buckling load,

optimum design point in terms of maximum buckling load was studied. The optimum design

values were found as 2.06 mm helical layer thickness and 39.6° helical winding angle to maximize

the critical buckling load. The critical buckling load is 4.2 MPa for optimum helical layer

thickness and helical winding angle. Static analysis was performed to control of structural strength

at the optimum buckling load point, 4.2 MPa. Tsai-Wu failure index distribution was shown in

Figure 14. Tsai-Wu failure index was found as less than 1 for entire structure which means that the

composite structure is safe in terms of structural integrity.

Figure 14. Tsai-Wu failure index distribution for 4.2 MPa load

5. Conclusion

A military underwater cylindrical filament wound composite structure which was exposed to

hydrostatic pressure was performed in terms of critical buckling load optimization. Helical

winding angle and thickness of helical/hoop layers with constant total thickness were used as main

variables to optimize the critical buckling pressure. However, cylinder diameter, cylinder length,

total thickness and material were kept constant as design constraints. It is seen that the critical

buckling pressure can be increased 5.5% by changing the helical winding angle and the critical

buckling pressure can be raised maximum 21% by changing the thickness of helical layers with

constant total thickness. Also, individual effects and interaction effects of changeable parameters

on the critical buckling load were demonstrated.

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6. References

[1] Kaddour, A.S, and Soden, P.D., “Failure of 55 Degree Filament Wound Glass/Epoxy

Composite Tubes Under Biaxial Compression,” Journal of Composite Materials, Vol. 32, No.

18/1998.

[2] Dey, A, Pandey, K.M, and Choudhury, P.L., “A Comparison Study of Filament Wound

Composite Cylindrical Shell Used in Under Water Vehicle Application by Finite Element

Method,” 5th International & 26th All India Manufacturing Technology, Design and Research

Conference (AIMTDR 2014) December 12th–14th, 2014, IIT Guwahati, Assam, India.

[3] Kim, H.M., Et al. “Buckling Analysis of Filament-Wound Thick Composite Cylinder Under

Hydrostatic Pressure,” International Journal of Precision Engineering and Manufacturing Vol. 11,

No. 6, Pp. 909-913, 2010.

[4] Davies, P, Chauchot P., “Composites for marine applications––part 2: underwater structures,”

In: Mechanics of composite materials and structures. Dordrecht: Kluwer Academic Publishers;

1999, p. 249–60.

[5] Soden, P.D., Kitching, R. and Tse, P.C., “Experimental Failure Stress [±55]° Filament Wound

Glass Fiber Reinforced Plastic Tubes Under Biaxial Loads,” Composites, 1989. Vol.20, p.125-

135.

[6] Soden, P.D., Et al. “The Strength of a Filament Wound Composite Under Biaxial Loading,”

Composites, 1978. Vol.9, p.247-250.

[7] Messager, T., Et al. “Optimal laminations of thin underwater composite cylindrical vessels,”

Composite Structures 58 (2002) 529–537.

[8] Abaqus Users Manual, Version 2016-1, Dassault Systémes Simulia Corp., Providence, RI.

[9] Isight Users Manual, Version 2017. Dassault Systémes Simulia Corp., Providence, RI.

7. Acknowledgment

This study is fully supported by Roketsan Missiles Ind. Inc., a major Turkish defense and

energetic systems manufacturer.