Tóm tắt Luận án Researching on the structural and processing solutions of winding the internally - Pressurized composite shells of revolution

MINISTRY OF EDUCATION AND TRAINING MINISTRY OF DEFENSE 
ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY 
TRAN THI THANH VAN 
RESEARCHING ON THE STRUCTURAL AND 
PROCESSING SOLUTIONS OF WINDING THE 
INTERNALLY- PRESSURIZED COMPOSITE 
SHELLS OF REVOLUTION 
Specialization: Dynamics and Mechanical Engineering 
Code: 9520116 
SUMMARY OF PHD DISERTATION IN ENGINEERING 
HANOI – 2021 
2 
The work was completed at: 
Academy of Military Science and Technology 
Scientific supervisiors: 
1. Assoc.Prof.Dr Tran Ngoc Thanh 
2. Assoc.Prof.Dr Pham Tien Dat 
Reviewer 1: Prof.Dr Hoang Xuan Luong 
Reviewer 2: Assoc.Prof.Dr Vu Ngoc Pi 
Reviewer 3 : Assoc.Prof.Dr Nguyen Trang Minh 
The dissertation has been be defended the Doctoral Evaluatning 
Committee held at Academy of Military Science and Technology 
at , , 2021. 
This disertation can be found at: 
- Vietnam National Library 
- The Library of Academy of Military Science and Technology 
3 
LIST OF PUBLISHED SCIENTIFIC WORKS 
1. Tran Ngọc Thanh, Tran Thi Thanh Van “Design of automated 4-axes wrapping 
machine for manufacturing of composite cylinderd with closed ends”. Journal 
of Viet Nam mechanical Engineering. No 1+2, (131-135), 2016. 
2. Tran Thi Thanh Van, Tran Ngoc Thanh, Pham Ngoc Vương, Nguyen Duong 
Nam: “Calculation of cylindrical products made of composite meterials using 
wrap technology”. Journal of Mechanical Engineering Research and 
Developments; Volume 42(2), pp. 76 – 78, 2019,. 
3. Tran Ngoc Thanh, Pham Tien Dat, Tran Thi Thanh Van, Nguyen Duong 
Nam:“Research using composite meterials in manufacturing pressureresistant 
circular details with the two spherical bottom by winding technology”. Journal 
of Mechanical Engineering Research and Developments; Volume 42(5), pp. 74 
– 78, 2019. 
4. Tran Thi Thanh Van, Tran Ngoc Thanh: “Researching to model and calculate 
technology to manufacture for Emergency Escape breathing device (EEBD) on 
a ship made of composite materials by wrap technology ”. Journal of transport, 
No 7, (81-85), 2020. 
5. Tran Thi Thanh Van1, Le Van Hao2, Tran Ngoc Thanh2: “Design of automatic 
polar filament winding machine for composite hight – pressure vassels 
manufacturing process”. Journal of Viet Nam mechanical Engineering, No 4 
(133-137), 2020. 
6. Tran Thi Thanh Van, Tran Ngoc Thanh, Đinh Van Hien: “ Design of shape 
model for composite pressure vessels based on non – geodesic trajectories”. 
journal of marine science and technology. No 8 (9-11), 2020. 
7. Dinh Van Hien, Tran Ngoc Thanh, Vu Tung Lam, Tran Thi Thanh Van, Le Van 
Hao: “Design of planar wound composite vessel based on preventing slippage 
tendency of fibers”, Journal of Composite Structures, pp(1-14), 2020. 
8. Dinh Van Hien, Tran Ngoc Thanh, Vu Tung Lam, Le Van Hao, Tran Thi Thanh 
Van: “The dome contour ò the cylindrical composite shell with the opened polar 
hole fabricted by the planar winding method”, Journal of Military Science and 
Technology - Academy of Military Science and Technology , pp.274-281, 2020,
1 
INTRODUCTION 
Necessity of this dissertation: Research on developing forced structures 
in general and structures of shells of revolution in particular made of high-
strengh filament-reinforced composite materials received by winding 
methods has been being a growing trend in the world due to the outstanding 
advantage of high-strength fiber-reinforced composites is that they have the 
higher specific strength and elastic modulus than traditional structural 
materials, resulting in more durable, stiffer, lighter and safer composites. 
A characteristic of composite materials is that "Material - Structure - 
Technology" has a close and inseparable relationship, which means that in 
order to master the material and product process, it is necessary to master the 
structural design. 
Around the world, research and design of internally pressurized shell 
structures of revolution from composite materials by winding process is quite 
diversified and plentiful, but due to the characteristic "Material-Structure-
Technology" relationship of composite materials and the popularity in the 
application of shell structures of revolution, so the research on establishing 
structural and processing solutions of these types of structures continues to 
attract many scientists and it is necessary to set out in the current period, 
especially when the research to master the design and manufacturing 
technology of composite shell structures of revolution in Vietnam is at an 
early stage. Therefore, the implementation of the thesis “Research structural 
and processing solutions of winding the internally-pressurized composite 
shells of revolution” is a necessary task. 
Objectives of this dissertation: Build a scientific and technological basis 
for the design and manufacture of the two-dome-cylindrical shells subjected 
to internal pressure from monotropic composite materials according to the 
planar wound schema. 
Contents of this dissertation 
1. Research on structure, material and processing technology of filament 
wound composite shells of revolution. 
2. Mathematical model of the closed-dome cylindrical composite 
pressure shell recieved by winding method 
3. Build the mathematical model of the planar filament-wound closed-
dome of the cylindrical composite pressure shell 
2 
4. Experiment of fabricating the closed-dome cylindrical composite 
vessel recieved by winding method 
Object of this investigation: The relationship of structural and processing 
parameters of the internally-pressured composite cylindrical shell and the 
planar winding parameters. 
Scope of this investigation: two-dome cylindrical composite shells with 
the closed domes received from the planar winding method. Vessel samples 
and winding machine were designed and fabricated at the laboratory scale. 
Methods of this investigation: On the basis of physical and geometrical 
model, building a mathematical model describing the relationship between 
the structural parameters and processing parameters of the planar wound 
two-dome cylindrical composite shell and experimental validation. 
Meaningfulness in science: Supplementing the theoretical basis for the 
calculation and design of two-dome cylindrical shell subjected to internal 
pressure from monotropic composites using planar wound technique. 
Meaningfulness in reality: The results of the dissertation can be used in 
research, design, fabrication and computational development of structural 
designs for internal pressure cylinders made of composite materials 
fabricated by winding technique used in the civil and military purpose. 
Lay-out of this dissertation: In addition to the introduction and general 
conclusion, the basic content of the dissertation is presented in 4 chapters 
and a list of references. 
CHAPTER 1. STRUCTURE, MATERIAL AND MANUFACTURE OF 
FILAMENT WOUND COMPOSITE SHELLS OF REVOLUTION 
1.1. Structure and materials for fabricating internally-pressured composite 
shells of revolution 
1.1.1. General introduction of internally-pressured shells of revolution 
Internally-pressured shell structures are widely used in civil and defense, in 
which, the type of structure of revolution subjected to internal pressure is a 
fairly common structural type such as cylindrical shells with domes, 
spherical shell or toroidal shell, typical types as the high-pressure vessel in 
the underwater oxygen system, the shell of the solid or liquid fuel rocket 
motor, ... For these structures, in the past, it was usually made of metal 
structural materials such as high-strength steel, titanium alloy ... However, 
the vital disadvantage of these materials is that their specific strength is not 
high, so it makes structures heavier but in some specific structures as the 
3 
high-pressure vessel in the underwater oxygen system or the forced shell of 
the flying object ..., light weight is a priority. With the advent of high-
strength and low-density fibers such as glass fiber, organic fiber, carbon 
fiber, ... thus forced composite structures, especially composite structures of 
revolution fabricated by winding method has been gradually replaced for 
metal shell structures. 
1.1.2. General structure of internally-pressured shells of revolution 
General structure includes: 1- forced shell of fiber-reinforced polymer 
composite is formed by widing method; 2- liner (sealing shell) is made of 
thermoplastic polymers or metal such as aluminum alloy, stainless steel; 3- 
functional flanges that include the boss and the base flange (Figure 1.4 to 
Figure 1.6). 
Figure 1.4. Structure of two-dome 
clindrical pressure vessel. 
Fige 1.5. Structure of pherical pressure 
shell. 
Figure 1.6. Structure of toroidal pressure shell. 
In the group of internally-pressurized composite shell structures of 
revolution, two-dome cylindrical shells are the most commonly used 
structures due to the simplicity of technology and variety of applications. 
According to the working function, the two-dome cylindrical composite 
shell is classified into 2 groups: (1) - the cylindrical composite shells with 
the closed polar holes are called the closed pole pressure composite vessels, 
they are often used to contain high pressure compressed air; (2) - an opened 
polar hole cylindrical composite shell (also known as an opened polar hole 
4 
composite pressure vessel), the typical type of this structure is the shell of 
rocket motor. 
1.1.2. Fiber-reinfored composite materials for fabricating the composite 
shell of revolution 
- Composite materials of the forced shell: Due to the specific shape and 
forced requirements, high-strength fiber-reinforced composite materials 
such as fiberglass, organic fibers and carbon fibers/polymer matrix (usually 
epoxy) received by winding method for fabricating internally-pressurized 
shells of revolution are usually used. The mechanical properties of some 
high-strength fiber-reinforced composites compared with metal structural 
materials used for making pressure vessels are shown in Table 1.3. 
Table 1.1. Comparison of mechanical properties of some fiber-reinforced composites 
and some metals. 
Materials 
Density, 
 (g/cm3) 
Elastic 
Modulus, 
E (GPa) 
Tensile 
strength, 
Rm (MPa) 
Specific elastic 
Modulus, E/ 
(106 Nm/kg) 
Specific 
Strength, 
Rm/ (103 
Nm/kg) 
Aluminum alloy 6061-T6 2.7 68.9 310 25.7 115 
Cold worked steel SAE 1010 7.87 207 365 26.3 46.4 
Titanium alloy Ti-6Al-4V 4.43 110 1171 25.3 264 
High strength carbon 
fiber/epoxy composite 
1.55 138 1150 88.9 1000 
E-glass fiber/epoxy 
composite 
1.85 39.3 965 21.2 522 
Armid fiber/epoxy 
composite 
1.38 75.8 1378 54.9 999 
Isotropic carbon fiber/epoxy 
composite 
1.55 45.5 579 29.3 374 
- Materials of the liner: For internally-pressurized cylindrical shells, to 
ensure pressure resistance without leaking, it is necessary to use a liner. 
The most popular materials for fabricating liners are metals such as 
aluminum alloy, stainless steel ..., or polymers such as HDPE, rubber  
1.2. Winding technology 
1.2.1. Concept and classification 
Winding technology is technology for forming membrane Shell structures 
by winding resin soaked fibers on a mandrel according to a given trajectory 
to form the composite shell. After hardening the matrix-resin naturally or by 
5 
heating, the composite Shell is completed. Based on the stage of resin and 
fiber in the wound fiber tape is liquid and visco-plastic, the winding method 
will be clasified to two types: wet and dry winding. 
1.2.2. Winding pattern schemes for fabricating shells of revolution 
 There are different types of Winding pattern schemes serving to different 
winding designs and technologies. For two-dome cylindrical structures, in 
fact, the basic winding schemes consisting of hoop winding, helical winding 
and planar winding are commonly used (Figure 1.22). 
a- hoop winding b- helical winding c- planar winding 
Figure 1.22. basic patterns for fabricating cylidrical composite shells 
 Another classification of the winding process is based on the 
mathematical description of the winding trajectory, it is divided into two 
winding types: 
Geodetic winding: it is the process of striping fibers onto the mandrel surface, 
where the fiber tension is in equilibrium and the fiber is not slipped. 
Non-geodetic winding: it is the process of striping fibers onto the mandrel 
surface, where the fiber tension is not in equilibrium and the fiber is in 
slippage tendency. 
1.2.3. Winding machine for fabricating shells of revolution 
 There are many types of filament winding machines for fabricating 
various composite shells of revolution, but the most versatile is the lathe 
winding machine that allows a combination of helical and hoop winding. 
Another simple type of winding machine, the planar winding machine, is 
also used, which has a winding scheme as shown in Figure 1.22c. 
1.3. Several theorical achievements of designing the two-dome composite shell 
1.3.1. Related studies in the world 
 To focus, this section only focuses on summarizing and analyzing some 
of the main achievements in designing cylindrical composite shells. 
Through summary, the problem of designing cylindrical composite shell 
refers to 3 main problems: (1) - The problem of designing the dome profile; (2) 
6 
- The problem of determining the layer thickness to satisfy the strength 
condition; (3) - The problem of determining the geometric parameters according 
to given volumetric conditions. In which, the problem of designing the dome 
profile is the main problem, also the most difficult problem. 
To solve the above problems, there are 2 directions based on 2 theories: 
Netting theory: In this direction, the composite material is assumed to 
be monotropic material and the strength criterion is the maximum main stress 
criterion (axial stress) less than the ultimate tensile strength of the material. 
In years, the studies on the design of the two-dome cylindrical composite 
subjected to internal pressure have been quite complete. 
In terms of the planar wound cylindrical composite shell, there are some 
related studies, but there are still some defects as follows: 
- The mathematical model for building the dome profile is incomplete 
when it has not justly proposed the fitting solution of the dome profile due 
to the inflection of the basic dome profile curve; 
- The limited range of geometric parameters has not been given. 
Theory of Composite Mechanics: In this direction, polymer-based 
fiber-reinforced composites are replaced by materials with anisotropic 
properties. The study of the design of the geodetic and non-geodetic wound 
cylindrical composite shell based on the theory of composite mechanics was 
also performed. It can be said that theo ... ith closed polar holes. 
a. Composite layer thickness on the dome 
 In dimesional coordinate: 
- Thickness at the equator: 
  eqc
beq
eq
p
R
h
h
 2cos..2
 (2.58) 
- Thickness distribution on the dome: 
eq
eq
r
h
R
h
h


cos.
cos
 (2.63) 
b. Thickness of hoop wound layer on the cylinder 
 
 c
eqeqcb
c
hp
h

 2sin.. 
 (2.67) 
2.4. Conclusion of chapter 2 
On the basis of the netting theory, the dissertation has synthesized and 
systematized the general theory of the design of two-dome cylindrical 
composite shells, in which: 
1. Gave out the general mathematical model for designing the dome 
profile and investigated for specific cases of the geodetic and non-geodesic 
winding with the slippage coefficient distributed as the desired law. 
Simultainously, it also proposed the solution of fitting the dome profile due 
to the inflection of the basic dome profile curve. 
2. Established the equations to determine the thickness of composite 
layers (helical, hoop winding) on the cylindrical part and the dome 
depending on the winding angle, burst pressure and strength of composite 
materials. 
3. Gave out the method for determining the geometric dimensions of two-
dome cylindrical composite shells that is enough to build the geometry of the 
cylindrical shell according to given volumetric conditions. 
CHAPTER 3. BUILD MATHEMMATICAL MODEL FOR 
DESIGNING THE PLANAR WOUND TWO-DOME CLYNDRICAL 
COMPOSITE SHELL 
3.1. Mathematical model of the dome of the cylindrical shell according 
to the planar winding scheme 
13 
Figure 3.11. Geometric parameters of the planar wound cylindrical composite shell. 
 Relationship between the winding angle  and geometric parameters of 
the planar wound dome (in non-dimensional coordinate): 
 222 tan..'1
tan.'.tan.
tan
ezrr
ezrr


 (3.9) 
 Substituting (3.9) into the first equation of (2.35), we will get the equation 
describing the dome profile in the general case. In the case of cylindrical 
shells with closed polar holes, we have the dome profile equation of the dome 
profile as follows: 
 r
r
etgzrr
etgzrtgr
r
2
2
222
'1
2
..'1
.'..
''


 (3.11) 
To solve equation (3.11), the initial parameters, e and , need to be given 
with the boundary condition being: 0)0( z , 1)0( r , 0)0(' r . 
For planar winding, the polar radius, 
pr , cannot be given since it is 
necessary to satisfy the following relationship: 
ezr pp tan. (3.13) 
3.2. Constraint of geometric parameters 
a. The constraint of the parameters e and : 
Since the dome meridian obtained from equation (3.11) and the winding 
angle  determined via equation (3.9) only depend on the couple of the 
parameters e and , so from equation (2.27), we see that the slippage 
14 
coefficient, will be only depend on e and . But because of the non-
slippage constraint of the fiber as in equation (2.30), there will be justly a 
limited range of e and  to be satisfied. 
b. Các ràng buộc của bán kính cực, pr 
The polar radius, pr , must to satisfy the fitting equation (2.52) and the 
geometric relation (3.13), thus, it will be the root of the following equation: 
fzz
f
ffffpfff
p
r
RrRrzR
er
2/12
2
1
2
1
2
1
)1(arccos
cos.sin.
tan
 (3.14) 
c. The limit of the cylinder length, L 
The relation between L and (e and ): 
tan
.2
.
.2 e
R
e
R
L
L (3.15) 
d. The limit of the cylinder radius, R 
 The cylinder radius is determined as follows: 
3
2 dc VV
V
R
 (3.17) 
where 
cV and dV are the non-dimensional volume of the cylinder and the dome 
3.3. Results and discussion 
3.3.1. Dome shape and distribution of slippage coefficient 
Figure 3.2. Meridian of the dome with �̅� =
0 and different values of . 
Figure 3.3. Meridian of the dome with �̅� =
0.1 and different values of . 
15 
Figure 3.4. Meridian of the dome with �̅� =
0.2 and different values of . 
Figure 3.5. Meridian of the dome with �̅� =
0.3 and different values of . 
Figure 3.6. Meridian of the dome with �̅� =
0.4 and different values of . 
Figure 3.7. Meridian of the dome with �̅� =
0.5 and different values of . 
Figure 3.8. Dependence of the slippage 
coefficient on 𝑧̅ with e̅ = 0. 
Figure 3.9. Dependence of the slippage 
coefficient on 𝑧̅ with e̅ = 0.1. 
16 
Figure 3.10. Dependence of the slippage 
coefficient on 𝑧̅ with e̅ = 0.2. 
Figure 3.11. Dependence of the slippage 
coefficient on 𝑧̅ with e̅ = 0.3. 
Figure 3.12. Dependence of the slippage 
coefficient on 𝑧̅ with e̅ = 0.4. 
Figure 3.13. Dependence of the slippage 
coefficient on 𝑧̅ with e̅ = 0.5. 
 Comment: When the bigger the couple (�̅�, ) is, the higher the slippage 
tendency of the fiber will be. When  is small, the slippage trend of the fiber 
at points close to the equator will be higher, whereas, if  is big, the slippage 
trend of the fiber at points close to the polar hole will be bigger. 
3.3.2. Limited range of geometric parameters based on non-slippage 
condition 
The relation between 
max
 and (�̅� and ) is as Figure 3.15. 
17 
Figure 3.15. The contour 
diagram expresses the 
relation of 
max
 and the 
parameters, e and . 
Figures 3.16 to 3.19 allow to select suitable pairs (�̅�, ) satisfying the non-
slippage condition of the fiber. The relation between the cylinder length L
and 
max
 as in Figure 3.20, it can be found that: 
- If 
max
 = 0.1, L must be less than 2, for all,  45o; 
- If 
max
 = 0.2, L must be less than 3.8, for all,  30o; 
- If 
max
 = 0.4, L must be less than 7.5, for all,  18o; 
Figure 3.16. The limited range of e
and  with  = 0.1. 
Hình 3.17. Phạm vi giới hạn của e và  
với   = 0,2. 
18 
Hình 3.18. Phạm vi giới hạn của e và  
với   = 0,3. 
Hình 3.19. Phạm vi giới hạn của e và  
với   = 0,4. 
Figure 3.20. The relation of the cylinder length and the maximum slippage 
coefficient
max
 . 
3.4. Conclusion of chapter 3 
Gave out the mathematical model for designing the planar wound 
filamentary composite cylindrical shell, and the limited ranges of the geometric 
parameters based on the non-slippage condition of the fiber. The core results are 
as follows: 
- The planar winding is justly proper for cases where the eccentricity distance 
�̅�, the cylinder length �̅� and the initial angle  are small; 
- When the eccentricity distance �̅�, and the initial angle  are big, the slippage 
trend of the fiber is higher at both the equator and near the polar hole; 
- For the case of wet winding ([] 0.2), the values of �̅�, �̅� and  can 
respectively reach 0.21, 3.8 and 380; 
- For the case of dry winding ([] 0.4), the values of �̅�, �̅� and  can 
respectively reach 0.38, 7.5 and 450. 
19 
CHAPTER 4. EXPERIMENT ON FABRICATING A TWO-DOME 
COMPOSITE PRESSURE VESSEL USING WINDING METHOD 
4.1. General requirements on structure and materials for fabricating 
cylindrical composite shell 
a. Design Tasks 
- Internal volume: V = 1.0 liter; 
- Strength pressure: 10 MPa. 
b. Design parameters 
Figure 4.1. Structure of the internally-presurized cylindrical composite shell. 
- Initial geometric parameters: e, . 
- Used technology: Wet winding ( = 0,2). 
- Parameters to be calculated: Dome profile; polar radius and bosses: rp, rb 
(rf); cylinder length and radius: L, R; Thickness of composite layers: heq ,hp, hc. 
c. Selected materials 
- Composite material: E-glass fiber (width: 5 mm, thickness: 0.3 mm); modified 
epoxy resin ED-20/EDG-1/P-9-14/MPDA. 
- Liner: HDPE plastic, its strength of 34 MPa, elongation of 35%. 
- Bosses: Aluminum alloy 6061-T4; 
Mechanical properties of the used composite material determined by 
using using the ring test method as in Table 4.3. 
Table 4.3. Mechanical properties of the used composite material. 
Mechanical 
properties 
Units 
Samples Average 
values M1 M2 M3 
Tensile strength, [c] MPa 680 682 684 682 
Elastic modulus, Ec GPa 45.6 45.9 46.0 45.8 
Elongation % 2.6 2.6 2.8 2.7 
4.2. Calculation of structural-processing parameters 
20 
4.2.1. Courses of calculating structural-processing parameters 
Figure 4.8. The second flow chart of calculatig structural-processing parameters 
of the planar wound cylindrical composite shell. 
 Results of calculating structural-processing parameters of the planar 
wound cylindrical composite shell is as in Table 4.4. 
Table 4.4. Calculated structural-processing parameters. 
21 
No Parameters Symbols Units Value 
1 Initial winding angle on the cylinder 𝛾 - /20 
2 Non-dimensional eccentricity distance �̅� - 0.2 
3 Non-dimensional length of the cylinder �̅� - 2.51 
4 Non-dimensional radial radius of bosses �̅�𝑏 - 0.42 
5 Non-dimensional polar radius �̅�𝑝 - 0.3 
6 True radius of the cylinder 𝑅 mm 45 
7 True length of the cylinder 𝐿 mm 113 
8 Thickness of the planar layer on the equator ℎ𝑝 mm 0.51 
9 Thickness of the hoop layer ℎ𝑐 mm 0.90 
10 Number of the planar layer 𝑛𝑝 2 
11 Number of the hoop layer 𝑛𝑐 3 
12 Number of planar wound revolutions 𝑖𝑝 57 
13 Number of hoop wound revolutions 𝑖𝑐 20 
Figure 4.9. Meridional profile of 
the planar wound dome with 
�̅� = 0.2 and  = /20. 
Figure 4.10. Dependence of the 
slippage coefficient, , on the axis 
coordinate, 𝑧̅. 
a) b) 
Figure 4.11. Thickness distribution on the dome with respect to 𝑧̅ (a) and 
the dome meridian (b). 
4.3. Process for fabricating the planar wound two-dome cylindrical shell 
22 
4.3.1. Planar winding machine 
Figure 4.12. Combined 
filament winding machine: 1- 
Planar filament winding 
block; 2- Lead screw; 3, 4- 
legs (platforms) of machine; 
5- mandrel; 6- fiber rack. 
4.3.3. Fabricating product 
Figure 4.20. A sample of the planar 
wound two-dome cylindrical 
composite shell. 
 Results: No slippage was observed; the wound layers are distributed 
evenly; the composite thickness of the cylinder is guaranteed according to 
the design. 
4.4. Testing and evaluating performance of fabricated products 
Table 4.6. Testing results of the planar wound shells. 
No Signs 
Calculated 
thickness of 
composite 
layer 
Tested 
thickness of 
composite 
layer 
Required 
burst 
pressure, 
MPa 
Theoretical 
burst 
pressure, 
MPa 
Tested 
burst 
pressure
, MPa 
Error 
% 
1 VTCP-N1 1.5 1.65 15 17.6 16.3 8,7 
2 VTCP-N2 1.5 1.67 15 17.6 15.9 6,0 
Result: It is suitable to the calculated results, the error of < 10%. 
4.5. Conclusion of chapter 4 
1. Practiced the design and fabrication of a composite cylindrical shell 
23 
using planar winding technology with the shell’s volume of 1.0 liter, burst 
pressure up to 15 MPa with E glass fiber reinforced material/epoxy resin; 
2. Designed and fabricated simple planar winding machine, qualified for 
planar-winding experiments; 
3. Practiced winding and confirmed that the design was suitable, the 
slippage of the fiber did not occur; 
4. Performed the pressure tests to measure burst pressure and found that the 
calculated results were consistent with reality, the error did not exceed 10%. 
GENERAL CONCLUSIONS 
I. Main results of the dissertation 
1. The internally-pressurized composite shell structure of revolution has 
been widely researched, produced and applied in civil and defense. From the 
literature review, the dissertation has oriented to build a mathematical model 
for designing the two-dome composite cylindrical shell, in which, focused 
on designing the planar wound dome profile and determined limited range 
of geometric parameters according to the non-slippage condition of the fiber. 
 2. On the basis of the netting theory with the assumption that the 
composite is monotropic materials (a hypothesis accepted by scientists) and 
inherit related science and technology achievements, the dissertation has 
synthesized and systematized the general theory of the design of two-dome 
cylindrical composite shells, namely: 
- Established a equation system of describing the basic dome profile, then, 
calculated for specific cases of the geodetic and non-geodetic winding with 
slip coefficient distributed as a certain law; 
- Proposed a solution to fit the dome profile due to the inflection of the 
basic dome profile; 
Established equations for determining composite layer thicknesses 
(helical, hoop winding) on the cylinder and dome depending on the winding 
angle, burst pressure and strength of composite materials. 
3. From the general theory, based on geometric relations of the planar 
trajectory of the fiber, the dissertation has built up a mathematical equation 
describing the planar wound composite dome profile. From that, the 
influence of the initial parameters consisting of the eccentricity distance, e, 
and initial wound angle, , on the dome profile has been investigated, 
especially on the slippage coefficient distribution, thereby serving as a basis 
for determining the limited range of initial geometric parameters under the 
24 
non-slippage condition. The results showed, for the planar winding, the 
following parameters: eccentricity distance e, cylinder length L and initial 
winding angle  should be small to ensure that the fiber does not slip during 
winding, in particular: 
- For wet winding ([] 0.2), e 0.21R, L 3.8R and  380. 
- For dry winding ([] 0.4), e 0.38R, L 7.5R and  450. 
4. From the mathematical model of the planar wound cylindrical 
composite shell, the dissertation gave out a course of calculation and 
concretized for a two-dome composite cylindrical shell having the volume 
of 1.0 liter, burst pressure of 10 MPa, which is fabricated from 
fiberglass/epoxy based composite. Designed and fabricated a planar winding 
device matching the existing device and practiced the technology to 
demonstrate. The results confirm, the mathematical model is reliable. 
II. New contributions of the dissertation 
- Researched to systematize the theoretical model for designing the 
internally-pressurized two-dome composite cylinders received by filament 
winding method. Since then, contributing to clarify and supplement the 
scientific basis for designing two-dome cylindrical composite pressure 
vessels which are currently incomplete in Vietnam. 
- Built a mathematical model of the planar wound two-dome composite 
pressure cylinder, in which the initial geometric parameter ranges were 
defined as eccetricity distance e, cylinder length L and angle  according to 
the non-slippage conditions of the fiber to serve the design. 
- Proposed the design-calculating course, technology, designed and 
fabricated a winding device and test products satisfying the given 
requirements. 
III. Problems that need to be investigated in the future 
From research results, the mathematical model in the case of the effects 
of temperature, pulse pressure and different polar radius will be developed.