The document discusses classical lamination theory (CLT) for analyzing laminated composite materials. It defines the key assumptions of CLT, including each lamina being orthotropic and elastic. It also describes how the loads, forces and bending moments applied to a laminate can be related to the midplane strains and curvatures using the laminate stacking sequence, thickness of each lamina, and the material properties. The stresses and strains in each lamina are defined as functions of the midplane strains/curvatures using the laminate constitutive equations from CLT.
Autoclave is a closed vessel (Round or Cylindrical) in which processes occur under simultaneous application of high temperature and pressure. Autoclave molding technique is similar to vacuum bag and pressure bag molding method with some modifications. This method employs an autoclave to provide heat and pressure to the composite product during curing.
RTM is a low-pressure molding process, where a mixed resin and catalyst are injected into a closed mold containing a fiber pack or preform . when the resin has cured the mold can be opened and finished component removed.
Autoclave is a closed vessel (Round or Cylindrical) in which processes occur under simultaneous application of high temperature and pressure. Autoclave molding technique is similar to vacuum bag and pressure bag molding method with some modifications. This method employs an autoclave to provide heat and pressure to the composite product during curing.
RTM is a low-pressure molding process, where a mixed resin and catalyst are injected into a closed mold containing a fiber pack or preform . when the resin has cured the mold can be opened and finished component removed.
Series of powerpoint slides showing 6 different composite forming techniques: Hand lay-up, vacuum bagging, compression moulding, filament winding, pultrusion and resin transfer moulding. The slides are adapted from the University of Liverpool "Composite Materials" lectures [MATS311] by Prof. W. Cantwell.
The fabrication methodology of a composite part depends mainly on three factors:
(i) the characteristics of matrices and reinforcements,
(ii) the shapes, sizes and engineering details of products, and
(iii) end uses.
The composite products are too many and cover a very wide domain of applications ranging from an engine valve to an aircraft wing.
The fabrication technique varies from one product to the other.
Series of powerpoint slides showing 6 different composite forming techniques: Hand lay-up, vacuum bagging, compression moulding, filament winding, pultrusion and resin transfer moulding. The slides are adapted from the University of Liverpool "Composite Materials" lectures [MATS311] by Prof. W. Cantwell.
The fabrication methodology of a composite part depends mainly on three factors:
(i) the characteristics of matrices and reinforcements,
(ii) the shapes, sizes and engineering details of products, and
(iii) end uses.
The composite products are too many and cover a very wide domain of applications ranging from an engine valve to an aircraft wing.
The fabrication technique varies from one product to the other.
First order shear deformation (FSDT) theory for laminated composite beams is used to study free vibration of
laminated composite beams, and finite element method (FEM) is employed to obtain numerical solution of the
governing differential equations. Free vibration analysis of laminated beams with rectangular cross – section for
various combinations of end conditions is studied. To verify the accuracy of the present method, the frequency
parameters are evaluated and compared with previous work available in the literature. The good agreement with
other available data demonstrates the capability and reliability of the finite element method and the adopted beam
model used.
TRANSIENT ANALYSIS OF PIEZOLAMINATED COMPOSITE PLATES USING HSDTP singh
Piezoelectric materials have excellent sensing and actuating capabilities have made them the most practical smart materials to integrate with laminated structures. Integrated structure system can be called a smart structure because of its ability to perform self-diagnosis and quick adaption to environment changes. An analytical procedure has been developed in the work based on higher order shear deformation theory subjected to electromechanical loading for investigating transient characteristics of smart material plates. For analysis two displacement models are to be considered i.e., model-1 accounts for strain in thickness direction is zero whereas in model-2 in-plane displacements are expanded as cubic functions of the thickness coordinate. Navier’s technique has been adopted for obtaining solutions of anti-symmetric cross–ply and angle-ply laminates of both model-1 and model-2 with simply supported boundary conditions. For obtaining transient response of a laminated composite plate attached with piezoelectric layer Newmark’s method has been used. Effect of thickness coordinate of composite laminated plates attached with piezoelectric layer subjected to electromechanical loadings is studied.
A COMPARATIVE STUDY OF VARIOUS METHODS TO EVALUATE IMPEDANCE FUNCTION FOR SHA...Samirsinh Parmar
Impedance function, Foundation Vibration, dynamic soil-structure interaction, Barkan, Dominguez, Dobry and Gazetas for evaluation of impedance functions for various modes of vibration of shallow foundation
Effect of Piezoelectric Layer on Beam Parameters using Zigzag TheoryIDES Editor
An efficient higher order theory is presented for
static analysis of multilayered composite beams with
piezoelectric layers embedded or bonded to the surface, under
static electromechanical load. In this theory, the in-plane
displacement field is taken as a combination of a layer-wise
linear variation and a cubic variation across the thickness.
Transverse normal strains are neglected. The electric field is
also approximated as piecewise linear across the sub layers.
The displacement field is expressed in terms of only three
primary displacement variables excluding electric potential
variables by enforcing the conditions of zero transverse shear
stress at top and bottom of the beam and its continuity at layer
interfaces under general electromechanical loading. The effect
of thickness of the piezo-layer is observed for various loading
conditions. Also, the effect of beam lay-up on various
parameters is studied.
Torsional-Distortional Performance of Multi-Cell Trapezoidal Box Girder with ...IJERA Editor
In this study, the torsional and distortional performance of a three triangular cell trapezoidal box girder section was studied using Vlasov’s theory of thin walled structures. The potential energy of a system under equilibrium was used to obtain the governing differential equations of equilibrium for torsionl-distortional analysis of the box structure. The strain modes diagrams representing torsional and distortional interactions of the box girder structure were obtained as well as the distortional bending moment diagram for the box girder structure. These were used to compute Vlasov’s coefficients contained in the differential equations of equilibrium. The fourth order differential equations obtained were solved using method of trigonometric series with accelerated convergence to obtain the distortional and torsional deformations which were compared with torsional and distortional deformations of a single cell mono symmetric box girder section of similar overall dimensions and plates thicknesses. The maximum distortional deformation was found to be 168% lower than that of a single cell mono-symmetric box girder section of the same size and dimensions. The inclined internal web members, which also act as diaphragms, brought about increase in the pure torsional and distortional components of the applied torsional load, resulting to marginal increase in the torsional deformation but major decrease in the distortional deformation.
Non-Linear Analysis of Steel Frames Subjected To Seismic ForceIJERA Editor
In this paper; non-linear analysis of steel frames subjected to seismic forces is presented. The analysis adopts the beam-column approach. The formulation of beam-column element is is based on Eulerian approach. Changes in member chord length due to axial strain and flexural bowing are taken into account. A modified tangent stiffness matrix which takes into consideration the geometrical non-linearity is used. A special form to formulate the seismic forces and the monotonic load-deflection response of frames is traced using the incremental load control Newton-Raphson iterative technique. It was concluded that considering large displacements tend to reduce the collapse loads of steel frame in the order of (4-40%) depending upon the number of stories of the frame.
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Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
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TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
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Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
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When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
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Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
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Immunizing Image Classifiers Against Localized Adversary Attacks
Classical Lamination Theory
1. Pendahuluan Material Komposit
BAB 4 Macromechanical Analysis of a Laminate
Classical Lamination Theory
Qomarul Hadi, ST,MT
Teknik Mesin
Universitas Sriwijaya
Sumber Bacaan
Mechanics of Composite Materials by Kaw
3. Laminate Behavior
• Modulus Elastis
• The Stacking Position
• Thickness
• Angles of Orientation
• Coefficients of Thermal Expansion
• Coefficients of Moisture Expansion
4. x
P
P
P
P
z
x
(a)
z
(c)
x
z
M M
(b)
x
M
M
A
P
=
xx
(4.1)
Strains in a
Gambar 4.2
A beam under (a) axial load, (b) bending moment,
and (c) combined axial and bending moment.
AE
P
=
xx
I
Mz
=
xx
z
=
xx
M
EI
z
+
P
AE
1
=
xx
1
z
+
= 0
z
+
= 0
5. Types of loads allowed in CLT analysis
x
y
z
Ny
Nx
Nxy
Nyx
(a)
y
x
z
My
Myx
Mxy
Mx
(b)
Nx = normal force resultant in the x direction (per unit length)
Ny = normal force resultant in the y direction (per unit length)
Nxy = shear force resultant (per unit length)
Gambar 4.3
Resultant forces and moments on a
laminate.
7. Classical Lamination Theory
Each lamina is orthotropic.
Each lamina is homogeneous.
A line straight and perpendicular to the middle surface remains
straight and perpendicular to the middle surface during
deformation. )
0
=
γ
=
γ
( yz
xz .
The laminate is thin and is loaded only in its plane (plane stress)
)
0
=
τ
=
τ
=
σ
( yz
xz
z .
Displacements are continuous and small throughout the laminate
|)
h
|
|
w
|
|,
v
|
|,
u
(| , where h is the laminate thickness.
Each lamina is elastic.
No slip occurs between the lamina interfaces.
12. Pendahuluan Material Komposit
BAB 4 Macromechanical Analysis of a Laminate
Relating Loads to Midplane
Strains/Curvatures
Qomarul Hadi, ST,MT
Teknik Mesin
Universitas Sriwijaya
Sumber Bacaan
Mechanics of Composite Materials by Kaw
14. Types of loads allowed in CLT
analysis
x
y
z
Ny
Nx
Nxy
Nyx
(a)
y
x
z
My
Myx
Mxy
Mx
(b)
Nx = normal force resultant in the x direction (per unit length)
Ny = normal force resultant in the y direction (per unit length)
Nxy = shear force resultant (per unit length)
Gambar 4.3
Resultant forces and moments on a
laminate.
15. x
y
z
Ny
Nx
Nxy
Nyx
(a)
y
x
z
My
Myx
Mxy
Mx
(b)
Mx = bending moment resultant in the yz plane (per unit length)
My = bending moment resultant in the xz plane (per unit length)
Mxy = twisting moment resultant (per unit length)
Types of loads allowed in CLT
analysis
23. Stiffness Matrices
[A] – Extensional stiffness matrix relating the resultant in-
plane forces to the in-plane strains.
[B] – Coupling stiffness matrix coupling the force and
moment terms to the midplane strains and midplane
curvatures.
29. Stiffness Matrices
[A] – Extensional stiffness matrix relating the resultant in-
plane forces to the in-plane strains.
[B] – Coupling stiffness matrix coupling the force and
moment terms to the midplane strains and midplane
curvatures.
[D] – Bending stiffness matrix relating the resultant
bending moments to the plate curvatures.
30. Forces, Moments, Midplane Strains,
Midplane Curvatures
κ
κ
κ
γ
ε
ε
D
D
D
B
B
B
D
D
D
B
B
B
D
D
D
B
B
B
B
B
B
A
A
A
B
B
B
A
A
A
B
B
B
A
A
A
=
M
M
M
N
N
N
xy
y
x
xy
y
x
xy
y
x
xy
y
x
0
0
0
66
26
16
66
26
16
26
22
12
26
22
12
16
12
11
16
12
11
66
26
16
66
26
16
26
22
12
26
22
12
16
12
11
16
12
11
32. Pendahuluan Material Komposit
BAB 4 Macromechanical Analysis of a Laminate
Laminate Analysis Steps
Qomarul Hadi, ST,MT
Teknik Mesin
Universitas Sriwijaya
Sumber Bacaan
Mechanics of Composite Materials by Kaw
35. Steps
1. Find the value of the reduced stiffness matrix [Q] for each ply using its four
elastic moduli, E1, E2, v12, G12 in Equation (2.93).
2. Find the value of the transformed reduced stiffness matrix ]
Q
[ for each ply
using the [Q] matrix calculated in Step 1 and the angle of the ply in Equation
(2.104) or Equations (2.137) and (2.138).
3. Knowing the thickness, tk of each ply, find the coordinate of the top and
bottom surface, hi, i = 1, . . . . . . . , n of each ply using Equation (4.20).
4. Use the ]
Q
[ matrices from Step 2 and the location of each ply from Step 3 to
find the three stiffness matrices [A], [B] and [D] from Equation (4.28).
5. Substitute the stiffness matrix values found in Step 4 and the applied forces
and moments in Equation (4.29).
36. Steps
6. Solve the six simultaneous Equations (4.29) to find the mid-plane strains and
curvatures.
7. Knowing the location of each ply, find the global strains in each ply using
Equation (4.16).
8. For finding the global stresses, use the stress-strain Equation (2.103).
9. For finding the local strains, use the transformation Equation (2.99).
10. For finding the local stresses, use the transformation Equation (2.94).
37. Step 1: Analysis Procedures for Laminate
Step 1: Find the reduced stiffness matrix [Q] for each ply
ν
ν
-
E
=
Q
12
21
1
11
1 ν
ν
E
ν
=
Q
12
21
2
12
12
1
ν
ν
E
=
Q
12
21
2
22
1 G
=
Q 12
66
38. Step 2: Analysis Procedures for Laminate
c
s
Q
+
Q
+
s
Q
+
c
Q
=
Q
2
2
66
12
4
22
4
11
11
)
2
(
2
)
(
)
4
( 4
4
12
2
2
66
22
11
12 s
+
c
Q
+
c
s
Q
Q
+
Q
=
Q
c
s
Q
Q
Q
s
c
Q
Q
Q
=
Q
3
66
12
22
3
66
12
11
16
)
2
(
)
2
(
c
s
Q
+
Q
+
c
Q
+
s
Q
=
Q
2
2
66
12
4
22
4
11
22
)
2
(
2
s
c
Q
Q
Q
cs
Q
Q
Q
=
Q
3
66
12
22
3
66
12
11
26
)
2
(
)
2
(
)
(
)
2
2
( 4
4
66
2
2
66
12
22
11
66 c
+
s
Q
+
c
s
Q
Q
Q
+
Q
=
Q
Step 2: Find the transformed stiffness matrix [Q] using the
reduced stiffness matrix [Q] and the angle of the ply.
39. Step 3: Analysis Procedures for Laminates
Step 3: Find the coordinate of the top and bottom surface of
each ply.
hk-1
hk
hn
h2
h1
h0
Mid-Plane
1
2
3
n
k-1
k
k+1
h3
z
h/2
tk
hn-1
h/2
Gambar 4.6
Coordinate locations of plies in the laminate.
40. Step 4: Analysis Procedures for Laminates
Step 4: Find three stiffness matrices [A], [B], and [D]
6
2
1
6
2
1
)
(
)]
[( 1
1
,
,
; j =
,
,
, i =
h
-
h
Q
=
A k -
k
k
ij
n
k =
ij
6
2
1
6
2
1
)
(
)]
[(
2
1 2
1
2
1
,
,
; j =
,
,
, i =
h
-
h
Q
=
B k -
k
k
ij
n
k =
ij
6
2
1
6
2
1
),
(
)]
[(
3
1 3
1
3
1
,
,
; j =
,
,
i =
h
-
h
Q
=
D k -
k
k
ij
n
k =
ij
41. Step 5: Analysis Procedure for Laminates
Step 5: Substitute the three stiffness matrices [A], [B], and [D]
and the applied forces and moments.
κ
κ
κ
γ
ε
ε
D
D
D
B
B
B
D
D
D
B
B
B
D
D
D
B
B
B
B
B
B
A
A
A
B
B
B
A
A
A
B
B
B
A
A
A
=
M
M
M
N
N
N
xy
y
x
xy
y
x
xy
y
x
xy
y
x
0
0
0
66
26
16
66
26
16
26
22
12
26
22
12
16
12
11
16
12
11
66
26
16
66
26
16
26
22
12
26
22
12
16
12
11
16
12
11
42. Step 6: Analysis Procedures for Laminates
Step 6: Solve the six simultaneous equations to find the
midplane strains and curvatures.
κ
κ
κ
γ
ε
ε
D
D
D
B
B
B
D
D
D
B
B
B
D
D
D
B
B
B
B
B
B
A
A
A
B
B
B
A
A
A
B
B
B
A
A
A
=
M
M
M
N
N
N
xy
y
x
xy
y
x
xy
y
x
xy
y
x
0
0
0
66
26
16
66
26
16
26
22
12
26
22
12
16
12
11
16
12
11
66
26
16
66
26
16
26
22
12
26
22
12
16
12
11
16
12
11
43. Step 7: Analysis Procedures for Laminates
Step 7: Find the global strains in each ply.
xy
y
x
0
xy
0
y
0
x
xy
y
x
z
+
=
44. Step 8: Analysis Procedure for Laminates
Step 8: Find the global stresses using the stress-strain
equation.
xy
y
x
66
26
16
26
22
12
16
12
11
xy
y
x
Q
Q
Q
Q
Q
Q
Q
Q
Q
=
45. Analysis Procedures for Laminated Composites
Step 9: Find the local strains using the transformation equation.
γ
ε
ε
R
T
R
=
γ
ε
ε
xy
y
x
1
12
2
1
]
[
]
[
]
[
2
0
0
0
1
0
0
0
1
]
[ =
R
s
-
c
sc
-sc
sc
-
c
s
sc
s
c
=
T
2
2
2
2
2
2
2
2
]
[
)
cos(
=
c
)
sin(
=
s
46. Step 10: Analysis Procedures for Laminates
Step 10: Find the local stresses using the transformation
equation.
τ
σ
σ
T
=
xy
y
x
12
2
1
1
]
[
s
c
sc
sc
sc
c
s
sc
s
c
=
T
2
2
2
2
2
2
1
2
2
]
[
)
cos(
=
c
)
sin(
s
48. Pendahuluan Material Komposit
BAB 4 Macromechanical Analysis of a Laminate
Laminate Analysis: Example
Qomarul Hadi, ST,MT
Teknik Mesin
Universitas Sriwijaya
Sumber Bacaan
Mechanics of Composite Materials by Kaw
50. Problem
A [0/30/-45] Graphite/Epoxy
laminate is subjected to a load of
Nx = Ny = 1000 N/m. Use the
unidirectional properties from
Table 2.1 of Graphite/Epoxy.
Assume each lamina has a
thickness of 5 mm. Find
a) the three stiffness matrices [A],
[B] and [D] for a three ply [0/30/-
45] Graphite/Epoxy laminate.
b) mid-plane strains and
curvatures.
c) global and local stresses on top
surface of 300 ply.
d) percentage of load Nx taken by
each ply.
0o
30o
-45o
5mm
5mm
5mm
z = -2.5mm
z = 2.5mm
z = 7.5mm
z
z = -7.5mm
Gambar 4.7
Thickness and coordinate locations
of the three-ply laminate.
51. Solution
A) The reduced stiffness matrix for the Oo Graphite/Epoxy ply
is
0
Pa
)
10
(
7.17
0
0
0
10.35
2.897
0
2.897
181.8
=
[Q] 9
53. The total thickness of the laminate is
h = (0.005)(3) = 0.015 m.
h0=-0.0075 m
h1=-0.0025 m
h2=0.0025 m
h3=0.0075 m
0o
30o
-45o
5mm
5mm
5mm
z = -2.5mm
z = 2.5mm
z = 7.5mm
z
z = -7.5mm
Coordinates of top & bottom of
plies
Gambar 4.7
Thickness and coordinate locations
of the three-ply laminate.
54. Calculating [A] matrix
(-0.0075)]
-
[(-0.0025)
)
10
(
7.17
0
0
0
10.35
2.897
0
2.897
181.8
=
[A] 9
(-0.0025)]
-
[0.0025
)
10
(
36.74
20.05
54.19
20.05
23.65
32.46
54.19
32.46
109.4
+ 9
0.0025]
-
[0.0075
)
10
(
46.59
42.87
-
42.87
-
42.87
-
56.66
42.32
42.87
-
42.32
56.66
+ 9
)
h
-
h
(
]
Q
[
=
A 1
-
k
k
k
ij
3
1
=
k
ij
)
(
]
[ 1
3
1
h
-
h
Q
=
A k -
k
k
ij
k =
ij
70. D) Portion of load taken by each ply
Portion of load Nx taken by 00 ply = 4.464(104)(5)(10-3) = 223.2 N/m
Portion of load Nx taken by 300 ply = 1.063(105)(5)(10-3) = 531.5 N/m
Portion of load Nx taken by -450 ply = 4.903(104)(5)(10-3) = 245.2 N/m
The sum total of the loads shared by each ply is 1000 N/m, (223.2 +
531.5 + 245.2) which is the applied load in the x-direction, Nx.
0o
30o
-45o
5mm
5mm
5mm
z = -2.5mm
z = 2.5mm
z = 7.5mm
z
z = -7.5mm
Gambar 4.7
Thickness and coordinate locations of the three-ply laminate.
71. Percentage of load Nx taken by 00 ply
Percentage of load Nx taken by 300 ply
Percentage of load Nx taken by -450 ply
%
22.32
=
100
1000
223.2
%
53.15
=
100
1000
531.5
%
24.52
=
100
1000
245.2