Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations for Conical Shells
Thermoplastic composite automated fiber placement technology, as one of the extreme manufacturing technologies for large or extra large composite components with complex surface shapes, has been widely used in the field of aerospace vehicles. This paper takes 8 lamination groups with different...
Збережено в:
| Опубліковано в: : | Проблемы прочности |
|---|---|
| Дата: | 2014 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут проблем міцності ім. Г.С. Писаренко НАН України
2014
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/112708 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations for Conical Shells / Z.Y. Han, Y.H. Li, H.Y. Fu // Проблемы прочности. — 2014. — № 2. — С. 147-155. — Бібліогр.: 11 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859643520692781056 |
|---|---|
| author | Han, Z.Y. Li, Y.H. Fu, H.Y. |
| author_facet | Han, Z.Y. Li, Y.H. Fu, H.Y. |
| citation_txt | Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations for Conical Shells / Z.Y. Han, Y.H. Li, H.Y. Fu // Проблемы прочности. — 2014. — № 2. — С. 147-155. — Бібліогр.: 11 назв. — англ. |
| collection | DSpace DC |
| container_title | Проблемы прочности |
| description | Thermoplastic composite automated fiber placement
technology, as one of the extreme manufacturing
technologies for large or extra large
composite components with complex surface
shapes, has been widely used in the field of
aerospace vehicles. This paper takes 8 lamination
groups with different initial placement angles
generated by the conical shell variable
angle placement algorithm as research objects.
Variable angle placement algorithm for conical
shell and finite element model establishment
method for thermoplastic composite laminations
of variable angle with different initial
placement angles are presented. Static, modal
and buckling analyses are conducted for each
group. The results show that stress-strain relation,
modal and buckling strength of
variable-angle laminations vary regularly with
the initial placement angle.
Технология автоматической укладки термопластичного композитного волокна, являющаяся
одной из радикальных технологий получения больших или очень больших компонентов композитов с комплексными формами поверхности, широко используется в авиационно-космической промышленности. В качестве объектов исследования использовали восемь групп слоистых материалов с различными углами конструктивного размещения, которые были созданы с
помощью алгоритма размещения переменного угла конической оболочки. Представлены алгоритм размещения переменного угла для конической оболочки и модель на основе метода
конечных элементов для термопластичных слоистых композитов с переменным углом. Для
каждой группы материалов проведены статистический анализ, исследование методом разложения по собственным формам и расчет устойчивости. Установлено, что зависимость
напряжение–деформация, модальная прочность и прочность при продольном изгибе слоистых
материалов с переменным углом периодически изменяются в зависимости от угла конструктивного размещения.
Технологія автоматичного укладання термопластичного композитного волокна, що є
однією з радикальних технологій отримання великих або дуже великих компонентів
композитів із комплексними формами поверхні, широко використовується в авіаційно-космічній промисловості. Об’єктом дослідження слугували вісім груп шаруватих
матеріалів із різними кутами конструктивного розміщення, які отримано за допомогою алгоритма розміщення змінного кута конічної оболонки. Представлено алгоритм
розміщення змінного кута для конічної оболонки і модель на основі методу скінченних елементів для термопластичних шаруватих композитів зі змінним кутом. Для
кожної групи матеріалів проведено статистичний аналіз, дослідження методом розкладання за власними формами і розрахунок стійкості. Установлено, що залежність
напруження–деформація, модальна міцність і міцність при поздовжньому згині шаруватих матеріалів зі змінним кутом періодично змінюються в залежності від кута конструктивного розміщення.
|
| first_indexed | 2025-12-07T13:24:28Z |
| format | Article |
| fulltext |
UDC 539.4
Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations
for Conical Shells
Z. Y. Han,
a
Y. H. Li,
b
and H. Y. Fu
a,1
a School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, China
b College of Mechanical Engineering, Hebei University of Science and Technology, Shijiazhuang,
China
1 hongyafu@hit.edu.cn
ÓÄÊ 539.4
Ìåõàíè÷åñêèå ñâîéñòâà òåðìîïëàñòè÷íûõ ñëîèñòûõ êîìïîçèòîâ
ñ ïåðåìåííûì óãëîì äëÿ êîíè÷åñêèõ îáîëî÷åê
Ç. ß. Õàí
à
, ß. Õ. Ëè
á
, Õ. ß. Ôó
à,1
à Ôàêóëüòåò ìåõàòðîííîé òåõíèêè, Õàðáèíñêèé òåõíîëîãè÷åñêèé èíñòèòóò, Õàðáèí, Êèòàé
á Ôàêóëüòåò ìàøèíîñòðîåíèÿ, Õýáýéñêèé íàó÷íî-òåõíîëîãè÷åñêèé óíèâåðñèòåò, Øèäæèàæóàíã,
Êèòàé
Òåõíîëîãèÿ àâòîìàòè÷åñêîé óêëàäêè òåðìîïëàñòè÷íîãî êîìïîçèòíîãî âîëîêíà, ÿâëÿþùàÿñÿ
îäíîé èç ðàäèêàëüíûõ òåõíîëîãèé ïîëó÷åíèÿ áîëüøèõ èëè î÷åíü áîëüøèõ êîìïîíåíòîâ êîìïî-
çèòîâ ñ êîìïëåêñíûìè ôîðìàìè ïîâåðõíîñòè, øèðîêî èñïîëüçóåòñÿ â àâèàöèîííî-êîñìè-
÷åñêîé ïðîìûøëåííîñòè.  êà÷åñòâå îáúåêòîâ èññëåäîâàíèÿ èñïîëüçîâàëè âîñåìü ãðóïï ñëîèñ-
òûõ ìàòåðèàëîâ ñ ðàçëè÷íûìè óãëàìè êîíñòðóêòèâíîãî ðàçìåùåíèÿ, êîòîðûå áûëè ñîçäàíû ñ
ïîìîùüþ àëãîðèòìà ðàçìåùåíèÿ ïåðåìåííîãî óãëà êîíè÷åñêîé îáîëî÷êè. Ïðåäñòàâëåíû àëãî-
ðèòì ðàçìåùåíèÿ ïåðåìåííîãî óãëà äëÿ êîíè÷åñêîé îáîëî÷êè è ìîäåëü íà îñíîâå ìåòîäà
êîíå÷íûõ ýëåìåíòîâ äëÿ òåðìîïëàñòè÷íûõ ñëîèñòûõ êîìïîçèòîâ ñ ïåðåìåííûì óãëîì. Äëÿ
êàæäîé ãðóïïû ìàòåðèàëîâ ïðîâåäåíû ñòàòèñòè÷åñêèé àíàëèç, èññëåäîâàíèå ìåòîäîì ðàçëî-
æåíèÿ ïî ñîáñòâåííûì ôîðìàì è ðàñ÷åò óñòîé÷èâîñòè. Óñòàíîâëåíî, ÷òî çàâèñèìîñòü
íàïðÿæåíèå–äåôîðìàöèÿ, ìîäàëüíàÿ ïðî÷íîñòü è ïðî÷íîñòü ïðè ïðîäîëüíîì èçãèáå ñëîèñòûõ
ìàòåðèàëîâ ñ ïåðåìåííûì óãëîì ïåðèîäè÷åñêè èçìåíÿþòñÿ â çàâèñèìîñòè îò óãëà êîíñòðóê-
òèâíîãî ðàçìåùåíèÿ.
Êëþ÷åâûå ñëîâà: òåðìîïëàñòè÷íûé êîìïîçèò, òåõíîëîãèÿ àâòîìàòè÷åñêîé óêëàäêè
âîëîêíà, ñëîèñòûå ìàòåðèàëû ñ ïåðåìåííûì óãëîì, çàâèñèìîñòü íàïðÿæåíèå–äåôîð-
ìàöèÿ, ìîäàëüíàÿ ïðî÷íîñòü, ïðî÷íîñòü ïðè ïðîäîëüíîì èçãèáå.
Introduction. With the continuous development of science and technology, composite
materials have demonstrated their superior performance and are widely studied and used in
production of almost all areas of life, such as damping structure design [1, 2], biomimetic
prostheses [3], commercial aircraft [4], carbon nanotube reinforcing [5], etc. This paper
focuses on the mechanical properties of thermoplastic composite variable-angle laminations
for conical shells. These laminations are produced by automated fiber placement technology.
Automated fiber placement technology, as one of the extreme manufacturing technologies
for large or extra large composite components with complex surface shapes, has been
widely used in the field of aerospace vehicles. In the practical engineering application,
taking into consideration the manufacturing complexity of the composite laminations and
such influencing factors as tension, compression and shear, laminated composite structure
© Z. Y. HAN, Y. H. LI, H. Y. FU, 2014
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 147
is mainly manufactured by overlaying laminations of 0, �45, and 90� in a certain order. The
unicity of the fiber direction makes the composite material unable to properly demonstrate
its directional characteristics, which greatly limits the design flexibility of the composite
laminations. In recent years, with the development of automated fiber placement technology,
the constant change of fiber placement angle in the same lamination becomes possible.
Thus, many scholars start to investigate the phenomenon of change in overall mechanical
properties of the laminations caused by fiber placement angle variation. The laboratory of
Prof. Gürdal in Delft University Technology of Netherland has conducted research in the
variable-angle lamination characteristics of the composite components of various shapes.
Hyer studied the laminated composite plate with holes using wavy fibers instead of straight
ones. Based on the above study, Gürdal proposed the concept of variable-angle fiber
placement and applied it into practice. Lopes, one of the laboratory members, has
constructed a finite element model of the variable angle laminated plate, and carried out
buckling load and first layer failure analyses [6]. Blom studied the variable-angle trajectory
planning algorithms for cylindrical and conical shells, the static and dynamic characteristics
of the variable-angle laminations made by the above algorithms [7, 8]. In addition, Wu et
al, from Queen’s University of Belfast in England, provided a new kind of mathematic
definition to describe the fiber direction angle, and conducted buckling analysis and
optimization of the variable-angle laminated composite plate [9]. In that research,
Rayleigh–Ritz method was adopted to determine the distribution of the pre-buckling and
critical buckling loads, while the fiber direction angle was optimized based on the
optimization objective of maximizing the buckling load. Akhavan from the University of
Porto in Portugal investigated the natural frequency and vibration mode of the rectangle
laminated composite plate where the fiber placement angle varied linearly along the
coordinate axis [10].
However, the above studies did not consider the overlap and the gap of adjacent
towpregs, which affect the shape accuracy of composite components, increase operation
times of cut and re-send, and have a great impact on the overall mechanical properties. So
in this paper, a new variable-angle trajectory planning algorithm for a conical shell, which
can avoid the overlap and the gap, is proposed. Based on this algorithm for conical shell
proposed by author [11], this paper performs finite element modeling from three aspects,
which are stress-strain, modal and linear buckling, aiming to find the rules of the change
between the mechanical properties of the laminations and the initial placement angle.
Variable-Angle Trajectory Planning Algorithm for a Conical Shell. Overlap and
gap of adjacent towpregs would, on one hand, affect the shape accuracy of composite
components, and increase operation times of cut and re-send. On the other hand, they have
a strong impact on the overall mechanical properties. Therefore, the main purpose of the
trajectory planning algorithm for the automatic fiber placement is to design reasonable
placement paths in order to reduce or eliminate the gap or the overlap of adjacent towpregs.
A variable-angle trajectory planning algorithm has been proposed by Han et al. [11].
Equations (1) and (2) are used for calculation of placement angle and trajectory point,
respectively [6]:
cos ,�
�
�
dl
d
(1)
�
�
( ) tan arccos
( )cos
s
Nbc
r l
ds
s
s
s
�
�
��
�
��
�
�
�
�
�
��
2
0
sin
,
� (2)
where � is the placement angle, l is the distance from the arbitrary point along generatrix
to the small end, � is the arc length of the trajectory line, N is the number of trajectory
lines, b is the theoretical width of a single towpreg, c is the number of towpregs for single
Z. Y. Han, Y. H. Li, and H. Y. Fu
148 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
trajectory lines, r l( ) is the radius of arbitrary cross section along axis, � is the cone
opening semi-angle, is the set placement angle for the initial point, s is the distance
from the arbitrary point to the center of the developed conical shell, and �( )s is the angle
between the horizontal axis and section s on the developed conical shell. The formulas for
calculation of the above parameters can be obtained from [11].
Finite Element Model of Variable-Angle Laminations. In this paper, APC-2
(AS4/PEEK) is chosen as the lamination material for the finite element modeling and
analysis. The material parameters of APC-2 towpreg are summarized below: elastic moduli
E1 131� GPa and E2 8 7� . GPa, shear moduli G12 5 0� . GPa, G13 5 0� . GPa, and
G23 1 79� . GPa, and Poisson’s ratio �12 0 28� . .
The steps of finite element modeling for variable angle laminations in the ABAQUS
are as follows. Firstly, the element type is chosen, and the laminations are discretized;
secondly, the nodes and elements are numbered; then, the material properties for each
element are set; finally, the stacking sequences of laminations are set. An S4 shell element
with four integration points is chosen as the element type for finite element modeling and
analysis, whereas Fig. 1 shows the laminations’ discretization, nodal and element labels. In
the ABAQUS, the local coordinate system is used for shell element. The conical shell is a
kind of revolved body, so the cylindrical coordinate system is chosen as the local
coordinate system. The APC-2 towpreg has an orthogonal anisotropy, so that the material
properties of each element are related to placement angle at the center point of each
element. Therefore, the local material properties can be set by rotation of the local
coordinate system.
Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 149
a b
c
Fig. 1. Finite element model of variable-angle laminations: discretization (a), nodal (b) and element (c)
data.
Eight groups of variable-angle laminations are analyzed by the finite element method.
The relative information of each lamination group is illustrated in Table 1. Each group
consists of 40 symmetrically arranged laminations with 0.2 mm thickness each. In the last
column of Table 1, the stacking sequence of laminations is listed as follows: “�(placement
angle at the small end, placement angle at the large end) | (s placement angle at the small
end, placement angle at the large end)s s� .” Here sign “|” stands for the separator of
laminations, while the particular value of s sindicates the number of laminations.
Stress and Strain Analysis for Variable-Angle Laminations. In this section, the
static analysis is conducted for eight variable-angle lamination groups tabulated in Table 1.
Both ends of the conical shell are fully constrained, and pressure of 106 Pa directed
towards the outer surface is applied to the inner surface of the conical shell. Figure 2a
shows the maximum strain of eight variable-angle laminations groups, while Figs. 2b and
2c show the strain distribution of the 1st and 6th lamination groups in the axial direction,
respectively.
From Fig. 2a it can be seen that the maximum strain value exhibits the initial decrease
followed by a further increase: the initial placement angle at the small end monotonously
increases with the serial number of the group, whereas the difference between the
maximum strain values of the 1st and the 6th lamination groups is about 2%. For large or
extra large components, a possibility of reducing deformation by 2% via changing the
placement angle is of practical importance. Taking the 1st lamination group (with the
highest maximum strain value) and the 6th one (with the lowest respective value) as
examples, strain variations of these two lamination groups along the axial line are shown in
Figs. 2b and 2c. The small end of each group is located at the starting point of the axial
line, while the large end is located at the finishing point of the axial line. Since the value of
150 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
Z. Y. Han, Y. H. Li, and H. Y. Fu
T a b l e 1
Parameters of Laminations for a Conical Shell
Group Placement
angle
(small end)
Placement
angle
(large end)
Number
of tow
(single
lamination)
Stacking sequence
1 1106. �
� �1106.
50 80. �
� �50 80.
185 � � � �( . , . ) |( . , . )1106 50 80 1106 50 805 5 4
2 2012. �
� �2012.
52 79. �
� �52 79.
177 � � � �( . , . ) |( . , . )2012 52 79 2012 52 795 5 4
3 3016. �
� �3016.
5617. �
� �5617.
163 � � � �( . , . ) |( . , . )3016 5617 3016 56175 5 4
4 40 21. �
� �40 21.
60 54. �
� �60 54.
144 � � � �( . , . ) |( . , . )40 21 60 54 40 21 60 545 5 4
5 50 09. �
� �50 09.
65 60. �
� �65 60.
121 � � � �( . , . ) |( . , . )50 09 65 60 50 09 65 605 5 4
6 6012. �
� �6012.
7129. �
� �7129.
94 � � � �( . , . ) |( . , . )6012 7129 6012 71295 5 4
7 7019. �
� �7019.
77 40. �
� �77 40.
64 � � � �( . , . ) |( . , . )7019 77 40 7019 77 405 5 4
8 79 96. �
� �79 96.
83 57. �
� �83 57.
33 � � � �( . , . ) |( . , . )79 96 83 57 79 96 83 575 5 4
pressure exerted on the internal face of each group is the same, and the laminations are
bodies of revolution, the strain of the laminations is distributed in a ring-like pattern; the
maximum strain of the laminations is located in the middle of the conical shell, thereby the
strain value decreases from the location of the maximum strain to both ends.
Figures 3a and 3b depict the maximum and minimum equivalent stress of these 8
variable angle-lamination groups, respectively, while Figs. 3c and 3d show the equivalent
stress distribution of the 1st and 8th lamination groups in the axial direction. From Fig. 3a it
can be seen that the maximum equivalent stress value is in the trend of monotonous
decrease along with the serial number of the group; whereas, the maximum equivalent
stress values of the 1st and the 8th lamination groups differ by about 2.4%. From Fig. 3b
one can see that the minimum equivalent stress value manifests a monotonous increase with
the serial number of the group; while, the minimum equivalent stress values of the 1st and
the 8th lamination groups differ by about 10%. The maximum equivalent stress value is one
order of magnitude larger than the minimum one. Therefore, if the laminations performance
is estimated by the maximum equivalent stress value, the 8th lamination group would be the
one with the optimal performance. Since the maximum equivalent stress value is one order
of magnitude higher than the minimum one, the former value is worthy to be especially
analyzed. Taking the 1st lamination group (with the highest maximum equivalent stress
value) and the 8th one group (with the lowest respective value) as examples, variations of
the equivalent stresses in these two lamination groups along the axial line are plotted in Figs.
3c and 3d. The small end of a cone for each group is located at the starting point of the
axial line, and the large end is located at the finishing point of the axial line. It could be
deduced from these plots that the maximum equivalent stresses for these two lamination
groups are located near the side of the large end; by comparing the curves in Figs. 3c and
3d, it could be observed that variation of the equivalent stress along the axial line in the 8th
lamination group is smoother than that of the 1st group. Therefore, as for the lamination
equivalent stresses, the 8th lamination group is the one with the optimal performance. In
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 151
Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations ...
a
b
Fig. 2. Strain values for 8 variable-angle lamination groups: the maximum strain of 8 variable-angle
lamination groups (a), strain distribution of the 1st (b) and 6th (c) lamination groups in the axial
direction.
c
Figs. 3c and 3d, there are some terraced steps of increase or decrease in the curves. After
measurement, the width of each step is found to be 2 mm, which coincides with the unit
length used in the lamination modeling. The discrete phenomenon of the above equivalent
stress is caused by different material attributes in the adjacent units, i.e., the material
attribute is discrete because of different placing angles for the adjacent units. The change in
the placement angle at the small end of the 1st lamination group is larger than that of the
8th one, which makes the material attribute discreteness for adjacent units at the small end
of the 1st lamination group larger than that of the 8th one. Therefore, the discrete and
fluctuating phenomena of the equivalent stress at the small end of the 1st lamination group
are more obvious than those of the 8th one.
Modal Analysis for Variable-Angle Laminations. The main goal of the modal
analysis is to determine the vibration performance of the variable-angle laminations,
including frequency of each lamination group and its corresponding vibration mode, to
provide guidance for lamination design; on the other hand, the modal frequency is the
foundation of dynamic analysis on the variable angle lamination (such as the transient state,
harmonic response, spectral analysis, etc.). A successful acquisition of the inherent
frequency and vibration mode of the variable-angle laminations makes it possible to avoid
resonance or vibration at a specific frequency. The ends of the variable-angle laminations
for a conical shell are fully constrained. The finite-element software ABAQUS and the
Lanczos method are applied to conduct the model analysis on the 8 variable-angle
lamination groups depicted in Table 1. Figure 4a shows the frequency curves of the top ten
orders for these 8 variable-angle lamination groups.
The eigenvalues and frequencies for each order pair (such as 1-2, 3-4, 5-6, 7-8, and
9-10) have basically the same values, which fact is related to the symmetrical structure of
the laminations for a conical shell and the symmetrical constraints. Under the above
conditions, the eigenvalues and frequencies of two orders will be equal to each other. The
eigenvalue and frequency of the variable-angle lamination structure are related to the fiber
placement angle. It can be seen from Fig. 4a that the eigenvalues and frequencies of these
Z. Y. Han, Y. H. Li, and H. Y. Fu
152 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
ba
c d
Fig. 3. Distibutions of the equivalent stresses in 8 variable angle lamination groups: the maximum (a),
the minimum (b), of the 1st (c) and 8th (d) lamination groups in the axial direction.
eight lamination groups manifest a monotonous decrease with the increase of the serial
number for groups, whereas the initial placement angle increases with the serial number. By
analyzing the frequencies of these 8 lamination groups, it can be observed that the
frequency value varies between 10 and 190 Hz for various initial placement angles. From
the above analysis, we can draw a conclusion that by changing the fiber placement angle,
the eigenvalue and frequency of the laminations can also be changed. When designing the
variable-angle laminations, this feature can be used to design laminations that can meet the
overall requirements. In addition, this feature will make it possible to avoid the resonance
frequency for structures or systems that are relatively sensitive to vibration.
Buckling Strength Analysis for Variable-Angle Laminations. The aim of the linear
buckling analysis, which is also called eigenvalue buckling analysis, is to study the critical
pressure and the corresponding after-buckling shape of the variable-angle laminations
under a specific load. When using the linear buckling analysis to forecast the theoretical
buckling strength of the variable-angle laminations, the solution obtained will be non-
conservative since the non-linear or initial defects are disregarded. In this section, the
Lanczos method is used to conduct the linear buckling analysis for eight variable-angle
lamination groups given in Table 1. Both ends of the conical shell are fully constrained, and
pressure of 106 Pa directed towards the inner surface is applied to the outer surface of the
conical shell. Figure 4b depicts the critical pressure curves of the top ten orders of these
eight variable-angle lamination groups.
The critical pressures in each order pair (i.e., 1-2, 3-4, 5-6, 7-8, and 9-10) are nearly
the same, similar to the case described in the previous section, due to the symmetry of
structure and constraints. Under the above conditions, the critical pressure of two orders
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 153
Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations ...
a
b
Fig. 4. Frequency (a) and the critical pressure (b) curves of the top ten orders for 8 variable-angle
lamination groups.
will be equal to each other. The critical pressure of the variable-angle lamination structure
is related to the fiber placement angle. It can be seen from Fig. 4b that with the increase in
the serial number for groups the critical pressure of order pair 1-2 manifests a monotonous
decrease, while that of order pair 3-4 exhibits a monotonous increase. However, for order
pairs of 5-6, 7-8, and 9-10, no manifested trends of the critical pressure.variation are
observed. In practical applications, the critical pressure of order 1 is often treated as the
most critical. Comparison of the critical pressures of order 1 of eight variable-angle
lamination groups, the difference between the 1st and the 8th group could reach about 1%.
Conclusions. In this study, the static, modal, and buckling analyses of eight lamination
groups with different initial placement angles formed by the conical shell variable-angle
placement algorithm have been conducted. This study demonstrates a regular variation of
strain, the equivalent stress, frequency and the critical pressure with the initial placement
angle values. The main results of this study are as follows:
1. The maximum strain value decreases first and then increases with the increase in
the initial placement angle at the small end.
2. The maximum equivalent stress value decreases with the increase in the initial
placement angle at the small end. The minimum equivalent stress value increases with the
increase in the initial placement angle at the small end.
3. The eigenvalues and frequencies of the studied eight lamination groups decrease
with the increase in the initial placement angle at the small end.
4. The critical pressure of orders 1 and 2 of eight variable-angle lamination groups
decrease with the increase in the initial placement angle at the small end.
Acknowledgments. This material is based upon work supported by the National
Science Foundation of China (Grant No. 51005060) and the Key State Science and
Technology Projects of China (Grant No. 2009ZX04004-111).
Ð å ç þ ì å
Òåõíîëîã³ÿ àâòîìàòè÷íîãî óêëàäàííÿ òåðìîïëàñòè÷íîãî êîìïîçèòíîãî âîëîêíà, ùî º
îäí³ºþ ç ðàäèêàëüíèõ òåõíîëîã³é îòðèìàííÿ âåëèêèõ àáî äóæå âåëèêèõ êîìïîíåíò³â
êîìïîçèò³â ³ç êîìïëåêñíèìè ôîðìàìè ïîâåðõí³, øèðîêî âèêîðèñòîâóºòüñÿ â àâ³àö³é-
íî-êîñì³÷í³é ïðîìèñëîâîñò³. Îá’ºêòîì äîñë³äæåííÿ ñëóãóâàëè â³ñ³ì ãðóï øàðóâàòèõ
ìàòåð³àë³â ³ç ð³çíèìè êóòàìè êîíñòðóêòèâíîãî ðîçì³ùåííÿ, ÿê³ îòðèìàíî çà äîïîìî-
ãîþ àëãîðèòìà ðîçì³ùåííÿ çì³ííîãî êóòà êîí³÷íî¿ îáîëîíêè. Ïðåäñòàâëåíî àëãîðèòì
ðîçì³ùåííÿ çì³ííîãî êóòà äëÿ êîí³÷íî¿ îáîëîíêè ³ ìîäåëü íà îñíîâ³ ìåòîäó ñê³í-
÷åííèõ åëåìåíò³â äëÿ òåðìîïëàñòè÷íèõ øàðóâàòèõ êîìïîçèò³â ç³ çì³ííèì êóòîì. Äëÿ
êîæíî¿ ãðóïè ìàòåð³àë³â ïðîâåäåíî ñòàòèñòè÷íèé àíàë³ç, äîñë³äæåííÿ ìåòîäîì ðîç-
êëàäàííÿ çà âëàñíèìè ôîðìàìè ³ ðîçðàõóíîê ñò³éêîñò³. Óñòàíîâëåíî, ùî çàëåæí³ñòü
íàïðóæåííÿ–äåôîðìàö³ÿ, ìîäàëüíà ì³öí³ñòü ³ ì³öí³ñòü ïðè ïîçäîâæíüîìó çãèí³ øàðó-
âàòèõ ìàòåð³àë³â ç³ çì³ííèì êóòîì ïåð³îäè÷íî çì³íþþòüñÿ â çàëåæíîñò³ â³ä êóòà
êîíñòðóêòèâíîãî ðîçì³ùåííÿ.
1. A. Hazrati Niyari, “Nonlinear finite element modelling investigation of flexural
damping behaviour of triple core composite sandwich panels,” Mater. Design, 46,
842–848 (2013).
2. A. Fereidoon and A. Hazrati Niyari, “Investigation of the nonlinear behaviour of
damping of aluminum foam core sandwich composite beams,” J. Reinf. Plast. Compos.,
31, No. 9, 639–653 (2012).
3. A. Gloria, D. Ronca, T. Russo, et al.,”Technical features and criteria in designing
fiber-reinforced composite materials: from the aerospace and aeronautical field to
biomedical applications,” J. Appl. Biomater. Biomech., 9, No. 2, 151–163 (2011).
154 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
Z. Y. Han, Y. H. Li, and H. Y. Fu
4. J. C. Seferis and L. Nicolais, “The role of the polymeric matrix in the processing and
structural properties of composite materials,” in: Proc. Joint U.S.–Italy Symp. on
Composite Materials, Capri, Italy (1981).
5. H. K. Wei, Y. J. Zhang, and H. Y. Gong, “Preparation and characteristics of
multiwalled carbon nanotubes reinforced boron carbide composites,” Mater. Res.
Innov., 13, No. 1, 70–73 (2009).
6. C. S. Lopes, Z. Gürdal, and P. P. Camanho, “Variable-stiffness composite panels:
buckling and first-ply failure improvements over straight-fibre laminates,” Comput.
Struct., 86, No. 9, 897–970 (2008).
7. A. W. Blom, Structural Performance of Fiber-Placed Variable-Stiffness Composite
Conical and Cylindrical Shells, Doctoral Dissertation, Netherlands, Delft University
of Technology (2010).
8. A. W. Blom, S. Setoodeh, J. M. A. M. Hol, and Z. Gürdal, “Design of variable-
stiffness conical shells for maximum fundamental eigenfrequency,” Comput. Struct.,
86, No. 9, 870–878 (2008).
9. Z. M. Wu, P. M. Weaver, G. Raju, and B. C. Kim, “Buckling analysis and
optimization of variable angle tow composite plates,” Thin-Walled Struct., 60, 163–
172 (2012).
10. H. Akhavan and P. Ribeiro, “Natural modes of vibration of variable stiffness
composite laminates with curvilinear fibers,” Comp. Struct., 93, No. 11, 3040–3047
(2011).
11. Z. Y. Han, Y. H. Li, H. Y. Fu, and Z. X. Shao, “Variable angles trajectory planning
algorithm of automated fiber placement for conical shell,” J. Comp. Design Comp.
Graph., 24, No. 3, 400–405 (2012).
Received 22. 11. 2013
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 155
Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations ...
|
| id | nasplib_isofts_kiev_ua-123456789-112708 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-07T13:24:28Z |
| publishDate | 2014 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Han, Z.Y. Li, Y.H. Fu, H.Y. 2017-01-26T18:44:12Z 2017-01-26T18:44:12Z 2014 Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations for Conical Shells / Z.Y. Han, Y.H. Li, H.Y. Fu // Проблемы прочности. — 2014. — № 2. — С. 147-155. — Бібліогр.: 11 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/112708 539.4 Thermoplastic composite automated fiber placement technology, as one of the extreme manufacturing technologies for large or extra large composite components with complex surface shapes, has been widely used in the field of aerospace vehicles. This paper takes 8 lamination groups with different initial placement angles generated by the conical shell variable angle placement algorithm as research objects. Variable angle placement algorithm for conical shell and finite element model establishment method for thermoplastic composite laminations of variable angle with different initial placement angles are presented. Static, modal and buckling analyses are conducted for each group. The results show that stress-strain relation, modal and buckling strength of variable-angle laminations vary regularly with the initial placement angle. Технология автоматической укладки термопластичного композитного волокна, являющаяся одной из радикальных технологий получения больших или очень больших компонентов композитов с комплексными формами поверхности, широко используется в авиационно-космической промышленности. В качестве объектов исследования использовали восемь групп слоистых материалов с различными углами конструктивного размещения, которые были созданы с помощью алгоритма размещения переменного угла конической оболочки. Представлены алгоритм размещения переменного угла для конической оболочки и модель на основе метода конечных элементов для термопластичных слоистых композитов с переменным углом. Для каждой группы материалов проведены статистический анализ, исследование методом разложения по собственным формам и расчет устойчивости. Установлено, что зависимость напряжение–деформация, модальная прочность и прочность при продольном изгибе слоистых материалов с переменным углом периодически изменяются в зависимости от угла конструктивного размещения. Технологія автоматичного укладання термопластичного композитного волокна, що є однією з радикальних технологій отримання великих або дуже великих компонентів композитів із комплексними формами поверхні, широко використовується в авіаційно-космічній промисловості. Об’єктом дослідження слугували вісім груп шаруватих матеріалів із різними кутами конструктивного розміщення, які отримано за допомогою алгоритма розміщення змінного кута конічної оболонки. Представлено алгоритм розміщення змінного кута для конічної оболонки і модель на основі методу скінченних елементів для термопластичних шаруватих композитів зі змінним кутом. Для кожної групи матеріалів проведено статистичний аналіз, дослідження методом розкладання за власними формами і розрахунок стійкості. Установлено, що залежність напруження–деформація, модальна міцність і міцність при поздовжньому згині шаруватих матеріалів зі змінним кутом періодично змінюються в залежності від кута конструктивного розміщення. This material is based upon work supported by the National Science Foundation of China (Grant No. 51005060) and the Key State Science and Technology Projects of China (Grant No. 2009ZX04004-111). en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations for Conical Shells Механические свойства термопластичных слоистых композитов с переменным углом для конических оболочек Article published earlier |
| spellingShingle | Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations for Conical Shells Han, Z.Y. Li, Y.H. Fu, H.Y. Научно-технический раздел |
| title | Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations for Conical Shells |
| title_alt | Механические свойства термопластичных слоистых композитов с переменным углом для конических оболочек |
| title_full | Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations for Conical Shells |
| title_fullStr | Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations for Conical Shells |
| title_full_unstemmed | Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations for Conical Shells |
| title_short | Mechanical Properties of Thermoplastic Variable-Angle Composite Laminations for Conical Shells |
| title_sort | mechanical properties of thermoplastic variable-angle composite laminations for conical shells |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/112708 |
| work_keys_str_mv | AT hanzy mechanicalpropertiesofthermoplasticvariableanglecompositelaminationsforconicalshells AT liyh mechanicalpropertiesofthermoplasticvariableanglecompositelaminationsforconicalshells AT fuhy mechanicalpropertiesofthermoplasticvariableanglecompositelaminationsforconicalshells AT hanzy mehaničeskiesvoistvatermoplastičnyhsloistyhkompozitovsperemennymuglomdlâkoničeskihoboloček AT liyh mehaničeskiesvoistvatermoplastičnyhsloistyhkompozitovsperemennymuglomdlâkoničeskihoboloček AT fuhy mehaničeskiesvoistvatermoplastičnyhsloistyhkompozitovsperemennymuglomdlâkoničeskihoboloček |