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Composite Structures

Fiber-reinforced composite cylindrical vessel with lugs

Abstract

The use of fiber-reinforced composites has steadily increased over the last few decades. Although the use of composites allows designers to optimize material usage, the analysis becomes fairly complex.

The present work deals with the analysis of composite vessels subjected to concentrated moments applied at discrete lug positions. Finite element (FE) formulation has been used to study the stress variation in composite vessels with lug attachments. Stress indices have been developed for two different load conditions, namely, longitudinal and circumferential moments. Numerical data have been generated for rectangular lugs of varying sizes. Although the numerical results presented here include one case of relatively thick shell, they are particularly important for thin shells. Discussion related to rotations at the interface is not presented here.

Introduction

More and more new materials are being designed for a variety of uses ranging from strength-critical to stiffness-critical applications. Some of the application areas include containment vessels for chemical storage and processing, compressed gas storage, rocket fuel storage, etc.

ASME Boiler and Pressure Vessel Code [1] for composite pressure vessels recognizes that designers have little guidance when determining the stresses and deformations caused by support loads at integral lug attachments. For steel pressure vessels, several numerical approaches have been developed to evaluate the load-carrying capacity of the lugs. However, recent research of new materials and processes has introduced fiber-reinforced composites to the industry once dominated by steel. Steel had been mainly the material of choice for industrial pressure vessels but the many beneficial qualities of composites such as a higher strength-to-weight ratio and better corrosion resistance has warranted their use in many applications.

For cylindrical pressure vessels of isotropic materials a fair amount of research has been conducted to understand local stress concentrations near rectangular lugs. Bijlaard [2] developed a method to obtain the stresses and deformations by representing the thrust, and longitudinal and circumferential moments as a double Fourier series. Results from this method are contained in WRC Bulletin 107 [3]. Dodge [4] introduced the concept of the stress index, defining it as the maximum stress intensity in the pipe to the nominal stress in the pipe. Rodabaugh [5] used the same approach but defined the stress index as the maximum stress intensity in the pipe to the nominal stress in the lug. Several authors performed finite element analyses (FEA), such as Mirza and Gupgopoglu [6], [7], who compared FEA results to the previous methods to gain insight on the effects of lug and cylinder geometry. Basavaraju [8] calculated reduction factors from the FEA studies to be applied to WRC-107 results. Several researchers have studied the problem of cylindrical composite shells [9]. These works have not included the effects of localized loads which are predominantly present when dealing with integral lug attachments. Some authors have used the finite element (FE) approach. These studies have concentrated on the basic formulation, element types, treatment of shear, etc. [11], [12], [13] Some of the commercial software packages reflect these developments.

This study is based on finite element analysis investigating composite-filament-wound cylindrical pressure vessels, in particular with rectangular lug attachments on the vessel wall (Fig. 1). Local stresses due to loads applied to the lugs can be expressed in the form of stress indices. The results may also be useful as a benchmark for other numerical or analytical procedures.

Results in this paper have been obtained for two different load conditions. The lugs transfer longitudinal (M L) and circumferential (M c) moments to the composite vessel. The effect of other parameters, namely the geometry of the lugs as well as the variation of radius-to-thickness ratio (a/t) that ranges from thin to border-line thick shells, has been studied. The results generated in this paper have been compared with those obtained by other authors specially for isotropic shells.

The computations show the stress intensity factor (C *) generated in the circumferential direction is larger than that in the longitudinal direction (C). This variation is more pronounced for thinner vessels.

Section snippets

Finite element model

The FE model was generated using four-node isoparametric elements which include both membrane and bending effects. Since both membrane and bending modes are included these elements are a special case of a shell element which has zero curvature. Because of this the elements used are referred to as plate elements or plate/shell elements. It is noted that the shell structure exhibits coupling between membrane and bending. The elements used do not couple these modes within the element but this

Moment loads

The first load case considered was that of an applied longitudinal moment M L. The cylinder was modeled with a longitudinal moment applied to four equally spaced lugs 90° apart. The moment loads were generated by equal and opposite forces on either side of the center of the lug, producing distributed couples on elements. The same technique was used to create the circumferential moment distributed couples that were generated by equal and opposite forces along the circumference. As the size of the

Material characteristics

For the development of the FE model the material is assumed to be an orthotropic laminate which has three orthogonal planes of material property symmetry. The material properties used in this work were obtained from [10] and are based on experimental testing. The stress–strain relationships used for each lamina were assumed to obey generalized Hooke's law for plane stress and they behave as linear elastic material.

The composite cylindrical vessel was initially modeled with three laminae

Mesh density and stress convergence

Four different models with different mesh densities were prepared. The model consisting of one quarter vessel was generated with, (1) 536, (2) 3600, (3) 8900 and (4) 13   776 elements. Using the longitudinal moment load case, the stress indices were calculated for each of the four cases. It was seen that the model with 8900 elements shows excellent convergence and it was decided to complete all other results using this particular mesh density.

A similar study for convergence was also done using the

Boundary conditions

The lugs were placed sufficiently away from the ends of the cylinder to avoid edge effects. As discussed by other authors [6], [7], the lugs were placed at least one diameter away from the end of the cylinder. One edge of the vessel was restricted such that no translation was allowed in the axial direction.

Due to the fact that the finer model contained a very large number of elements it was decided to make use of axial symmetry conditions. Thus only a quarter of the cylindrical vessel was

Numerical computations and results

Two parameters, β 1=C 1/a and β 2=C 2/a, defining the non-dimensional geometry of the lugs, were varied. Several values, namely, β 1 =0.05, 0.1, 0.4 and β 2 =0.1, 0.2 were chosen to study the effect of lug size. The radius-to-thickness ratio γ of the vessel was given three different values – 5, 20 and 80. These values simulate from thick to very thin vessels.

The stress indices C * and C represent the indices in the circumferential and longitudinal directions. The subscripts `L' and `c' used with the

Conclusions

It is important to point out that, although the results have been generated for specific fiber orientations, the solution technique presented here is quite general. The numerical data for other fiber orientations and/or other material properties can be easily developed by modifying the reduced stiffness [Q] k in Eq. (1a).

The results presented in this study represent benchmark data which may be used in further developmental work. Stress indices were calculated for rectangular lugs of varying size

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