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\title{A Computational Study of Buckling Analysis of Filament Wound Composite Pressure Vessel Subjected to Hydrostatic Pressure}
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\begin{document}

             \author[1]{  K.M.Pandey}

             \affil[1]{  National Institute of Technology}

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\date{\small \em Received: 14 December 2013 Accepted: 2 January 2014 Published: 15 January 2014}

\maketitle


\begin{abstract}
        


In this present study the post buckling cha-racteristics of moderately thick-walled filament-wound carbonâ??" epoxy composite cylinders under external hydrostatic pressure were investigated through finite element analysis for under water vehicle applications. The winding angles were [±30/90] FW, [±45/90] FW and [±60/90] FW. Finite element software ANSYS 14.0 were used to predicted the buckling pressure of filament-wound composite cylinders. For the finite element modeling of a composite cylinder, an eight-node shell element is used. To verify the finite element results for comparison, three finite element software, MSC/NASTRAN , MSC/MARC and an in-house program ACOS were used. Among these software?s, the finite element software ANSYS predicts the buckling loads within 1.5% deviation. The analysis and test results showed that the cylinders do not recover the initial buckling pressure after buckling and that this leads directly to the collapse. Major failure modes in the analysis were dominated by the helical winding angles. The finite element analysis shows global buckling modes with four waves in the hoop direction.

\end{abstract}


\keywords{buckling, thick-wall, composite, hydrostatic pressure.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
ilament-wound composite materials have been successfully used in underwater vehicles and ocean structures over the past few years, especially as composite pressure vessels \hyperref[b0]{[1]}\hyperref[b1]{[2]}\hyperref[b2]{[3]}; the use of composite materials in civil and military aircraft has also expanded considerably over the past few decades due to their light weight and high resistance to salt wat-er corrosion \hyperref[b3]{[4]}. Particularly, small underwater veh-icles can be manufactured in one piece with composite materials. Both the filament winding and tape lay-up methods can be used to manufacture a small vehicle without sub-assembly \hyperref[b6]{[6]}.\par
Although decades of R\&D in composite materials have focused on aerospace engineering, new applications are opening up in various fields where weight or resistance to corrosion is critical. Particularly, caron composites are considered promising materials for future underwater vehicles and ocean structures due to their corrosion resistance \hyperref[b5]{[5,}\hyperref[b7]{7]}.\par
Buckling has become a dominant failure mechanism when compressive stresses generated by the external hydrostatic pressure reach elevated levels for subsea composite pressure vessel. For an underwater vehicle operated in deep sea, hydrostatic pressure-induced buckling tends to dominate structural performance. Furthermore, a cylindrical structure generally experiences unstable buckling, where the loadcarrying capability of the structure decreases after the buckling \hyperref[b7]{[7,}\hyperref[b8]{8]}.\par
Generally, high external pressure vessels such as submarine structures have been manufactured of high strength steel, titanium and aluminum alloy. Large buoyancy is required for the structural weight. Accordingly, the weight-sensitive structures are expected to reduce weight for faster and more efficient peformance. It was observed that the use of composite materials for underwater vehicles can reduce their total weight and expand the depth of operation because the reduced weight can allow for greater structural reinforcement  {\ref [7, 9, and 10]}.\par
In the present work, relatively thick-walled composite cylinders (radius-to-thickness ratio, R/t = 18.8) were manufactured by a filament winding process to reduce the material and geometric imperfections for a high depth underwater vehicle \hyperref[b7]{[7]}. The main objective of this paper is to investigate the buckling, post buckling behavior and failure mode of moderately thickwalled composite cylinders with various winding angles under external hydrostatic pressure for underwater vehicle applications. The helical winding and hoop reinforcement ([±30/90] FW, [±45/90] FW and [±60/90] FW) were used for the composite cylinders.\par
e-mail: kmpandey2001@yahoo.com  
\section[{Specimen Modeling}]{Specimen Modeling}\par
The specimens were manufactured by a filament winding process using T 700-24 K carbon fiber and Bisphenol A type epoxy resin. All of the cylinders have a 300-mm nominal inner diameter; a 695-mm nominal axial length and an 8-mm nominal thickness (see Fig. \hyperref[fig_0]{1}). The cylinders have three different winding angles: [±30/ 90] FW, [±45/90] FW and [±60/90] FW. The parameters ±30, ±45 and ±60 denote the helical winding angle, while 90 is the hoop winding. For creating the finite element model, ACOS \hyperref[b15]{[15]}, an inhouse program, was used. The carbon composite cylinders were fabricated by a filament winding process and tested in a water pressure chamber. Two commercial software's, MSC.NASTRAN and MSC.MARC, were also used for comparison of the buckling pressure and mode shape. The nominal thickness of the hoop winding is 10\% of the total thickness. This value was chosen because the best buckling pressures are obtained when the hoop ratio does not exceed 50\% of the total thickness. When the hoop ratio exceeds 50\%, the cylinders become very weak with respect to static strength. In this present work the finite element model of composite pressure vessel is made by ANSYS 14.0 APDL, finite element software.\par
Two commercial software, Msc. Nastran and Msc.Marc and Acos, an in-house program were used to create the model. The cylinders have a 300mm nominal inner diameter, 695mm nominal axial length and an 8 mm nominal thickness. The nominal thickness of the hoop winding is 10\% of the total Thickness. In ANSYS  
\section[{Finite Element Analysis}]{Finite Element Analysis}\par
Finite element analysis was used to predict not only the buckling loads but also the post buckling behavior. Failure analysis was performed using the inhouse software ACOSwin, which makes possible nonlinear and progressive failure analysis. The commercial programs MSC/NASTRAN (linear analysis) and MSC/ MARC (nonlinear analysis) were used to validate the buckling loads. The theoretical background for ACOSwin is given in \hyperref[b13]{[13]}. In the finite element models, four node elements, CQUAD4 in MSC.NASTRAN and Element 75 in MSC.MARC, were used. The ACOS program used an 8-node laminate shell element that had 5 degrees of freedom at each node. In Ansys 14.0 APDL laminate shell element 8 node 281 having 6 degree of freedom at each node were used to predict the critical buckling pressure. For non-linear, post buckling behavior, progressive failure analysis was conducted by ACOS using complete unloading as the stiffness degradation method \hyperref[b16]{[16,}\hyperref[b17]{17]}. The stacking sequence of different composite laminate with different orientation of fibers has shown in fig. \hyperref[fig_1]{2}. The enlarge view of stacking sequence and different composite laminate with various thickness have been shown in fig.  {\ref 3}.  
\section[{Simulation}]{Simulation}\par
The composite structure that used in under water vehicle application, only hydrostatic pressure will consider which can apply redialy inward direction over the outer surface of the body. The equipment can apply pressures up to 10 MPa, which is equal to the pressure at a depth of 1000 meter of water. At the left end of the composite cylinder all degree of freedom can be restricted and at the right end only two degree of freedom has restricted (x direction \& y direction), so that the system will undergo only axial deformation.\par
The finite element modeling, meshing and simulation of carbon-epoxy composite filament wound pressure vessel have shown in figure  {\ref 4}. V. 
\section[{Results and Discussion}]{Results and Discussion}\par
The buckling analysis has done by Ansys APDL. It has observed that the result for critical buckling is good matched with the existing experimental results. The figures are describing the comparison study of the composite pressure vessels. Table  {\ref 3} shows the experimental and finite element buckling pressure. The ANSYS 14.0 APDL results as well as the linear and nonlinear analysis results by MSC/NASTRAN, MSC/MARC and ACO Swin are presented. In ANSYS non-linear buckling analysis has been done.     
\section[{Conclusion}]{Conclusion}\par
The buckling behavior of moderately thick walled, filament-wound, carbon-epoxy cylinders subjected to hydrostatic pressure was investigated. A total 9 no. of composite laminates has been considered for finite element analysis. The different orientation of the composite layers has been taken [±45/90] FW. considering the initial imperfections of the cylinders. The results show that finite element analysis with shell elements can be used to evaluate the buckling load of moderately thick-walled, filament-wound composite cylinders under external hydrostatic pressure.\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}FigureFigure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{44}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Figure 4 Figure 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-5.png}
\caption{\label{fig_3}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{45}\includegraphics[]{image-6.png}
\caption{\label{fig_4}Figure 4 :Figure 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{67}\includegraphics[]{image-7.png}
\caption{\label{fig_5}Figure 6 :Figure 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-8.png}
\caption{\label{fig_6}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.21366120218579235\textwidth}P{0.05573770491803279\textwidth}P{0.11612021857923498\textwidth}P{0.19972677595628416\textwidth}P{0.08360655737704918\textwidth}P{0.12540983606557377\textwidth}P{0.05573770491803279\textwidth}}
\tabcellsep \tabcellsep \tabcellsep Poisson's\tabcellsep ?12\tabcellsep 0.253\tabcellsep -\\
\tabcellsep \tabcellsep \tabcellsep ratio\tabcellsep ?13\tabcellsep 0.253\tabcellsep -\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep ?23\tabcellsep 0.421\tabcellsep -\\
\tabcellsep \tabcellsep \tabcellsep Shear\tabcellsep G12\tabcellsep 4.14\tabcellsep GPa\\
\tabcellsep \tabcellsep \tabcellsep modulus\tabcellsep G13\tabcellsep 4.14\tabcellsep GPa\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep G23\tabcellsep 3.31\tabcellsep GPa\\
\tabcellsep \tabcellsep \tabcellsep III.\\
\multicolumn{2}{l}{a) Mechanical Properties}\tabcellsep \tabcellsep \\
Property\tabcellsep Symbol\tabcellsep Rule of\tabcellsep Unit\\
\tabcellsep \tabcellsep mixture\tabcellsep \\
Elastic\tabcellsep E1\tabcellsep 149\tabcellsep GPa\\
modulus\tabcellsep E2\tabcellsep 10.6\tabcellsep GPa\\
\tabcellsep E3\tabcellsep 10.6\tabcellsep GPa\end{longtable} \par
 
\caption{\label{tab_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.37835365853658537\textwidth}P{0.25914634146341464\textwidth}P{0.2125\textwidth}}
RESULT OBTAINED\tabcellsep BUCKLING PRESSURE\tabcellsep PERCENTAGE OF ERROR (\%)\\
\tabcellsep UNIT(MPa)\tabcellsep \\
EXPERIMENTAL TEST\tabcellsep 0.60\tabcellsep -\\
ANSYS 14.0 APDL\tabcellsep 0.591\tabcellsep 1.5\\
MSC.NASTRAN\tabcellsep 0.677\tabcellsep 12.08\\
MSC.MARC\tabcellsep 0.691\tabcellsep 15.2\\
ACOSwin\tabcellsep 0.671\tabcellsep 11.8\end{longtable} \par
 
\caption{\label{tab_1}Table 1 :}\end{figure}
 			\footnote{© 2014 Global Journals Inc. (US)} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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\end{bibitemlist}
 			 		 	 
\end{document}
