BUCKLING BEHAVIOUR OF CFRP SANDWICH STRUCTURE

BUCKLING BEHAVIOUR
OF CFRP SANDWICH
STRUCTURE

Department of Mechanical Engineering, VIT Page 2
List of Contents
LIST OF CONTENTS.................................................................................................................................................2
LIST OF FIGURES.....................................................................................................................................................3
LIST OF TABLES ......................................................................................................................................................4
CHAPTER 1.............................................................................................................................................................5
1. INTRODUCTION ................................................................................................................................................5
1.1 UAV’s........................................................................................................................................................6
1.2 Aircraft Structure...........................................................................................................................................7
1.3 Composite ................................................................................................................................................8
1.4 Sandwich Composite..............................................................................................................................10
1.5 Introduction to Panel Buckling...............................................................................................................11
1.6 Rohacell Foam........................................................................................................................................12
1.7 Literature survey on Buckling of composite panels.......................................................................................12
1.8 Problem Definition .................................................................................................................................15
CHAPTER 2...........................................................................................................................................................17
2. THEORETICAL PREDICTION OF BUCKLING LOAD..........................................................................................................17
2.1 Stress- Strain Relation............................................................................................................................17
2.2 Computation of [A][B][D] matrices ........................................................................................................20
2.3 Buckling analysis of sandwich panel by analytical method. ..................................................................24
2.4 Estimation of Critical Buckling by Engineering Standard Data Unit ......................................................27
2.5 Calculation of Critical Buckling load by ESDU sheet......................................................................................28
2.6 FEA.........................................................................................................................................................29
CHAPTER 3...........................................................................................................................................................33
3. FABRICATION AND TESTING ...........................................................................................................................33
3.1 Fabrication of CFRP Laminates ..............................................................................................................34
3.2 Cutting ...................................................................................................................................................38
3.3 Fabrication Procedure............................................................................................................................38
3.4 Vacuum Bagging process.......................................................................................................................40
3.5 Post curing .............................................................................................................................................40
3.6 Testing ...................................................................................................................................................41
CHAPTER 4...........................................................................................................................................................44
4. RESULTS AND DISCUSSION...............................................................................................................................44
4.1 LOAD vs. DISPLACEMENT PLOTS............................................................................................................45
4.2 FEA RESULTS..................................................................................................................................................54
CHAPTER 5...........................................................................................................................................................57
5. CONCLUSION ...........................................................................................................................................................57
REFERENCES................................................................................................................................................................58

List of Figures
FIGURE.1.1 STRUCTURE OF SANDWICH PANEL .........................................................................................................................6
FIGURE 2.1FORCES AND MOMENTS IN A FLAT LAMINATES .......................................................................................................18
FIGURE 2.2GEOMETRY OF N-LAYERED LAMINATE ...................................................................................................................19
FIGURE 2.3 ORIENTATION 1 FIGURE 2.4 ORIENTATION 2 FIGURE 2.5 ORIENTATION 3 ........................................................20
FIGURE 2.6 BUCKLING OF THIN PLATES .................................................................................................................................25
FIGURE 2.7ESDU DATA SHEET (80023) FOR UNIAXIAL LOAD....................................................................................................27
FIGURE 2.8GEOMETRY AS PER DIMENSIONS...........................................................................................................................31
FIGURE 2.9 LOADING CONDITION........................................................................................................................................31
FIGURE 2.10 CONSTRAINING THE TOP AND BOTTOM EDGES......................................................................................................32
FIGURE 3.1HAND-LAYUP PROCESS.......................................................................................................................................33
FIGURE 3.2VACUUM BAG PROCESS ......................................................................................................................................34
FIGURE 3.3PEEL PLY USED IN INITIAL STAGE OF FABRICATION. ...................................................................................................35
FIGURE 3.4 PERFORATED RELEASE FILMS ..............................................................................................................................35
FIGURE 3.5VACUUM BAGGING FILMS ...................................................................................................................................36
FIGURE 3.6SEALANT TAPES.................................................................................................................................................37
FIGURE 3.7BREATHER/BLEEDER CLOTH ................................................................................................................................37
FIGURE 3.8VACUUM FITTINGS ............................................................................................................................................38
FIGURE 3.9CUTTING OF CONSUMABLES AND CUTTING MACHINE................................................................................................38
FIGURE 3.10 SPECIMENS PREPARED FOR VACUUM BAGGING PROCESS.........................................................................................39
FIGURE 3.11 VACUUM BAGGING TECHNIQUE........................................................................................................................40
FIGURE 3.12 POST CURING OF CFRP LAMINATES ...................................................................................................................41
FIGURE 3.13 UNIVERSAL TESTING MACHINE ..........................................................................................................................41
FIGURE 3.14 TEST FIXTURES USED FOR CLAMPING ..................................................................................................................42
FIGURE 3.15PANEL BEFORE FAILURE ....................................................................................................................................43
FIGURE 3.16PANEL AFTER FAILURE ......................................................................................................................................43
FIGURE 3.1 PLOT OF COMPRESSIVE LOAD VS. DISPLACEMENT FOR ORIENTATION 1 .......................................................................45
FIGURE 3.2PLOT OF COMPRESSIVE LOAD VS DISPLACEMENT FOR ORIENTATION 2 .........................................................................46
FIGURE 3.3PLOT OF COMPRESSIVE LOAD VS. DISPLACEMENT FOR ORIENTATION 3 ........................................................................47
FIGURE 3.4PANEL 1C PLOT IN TRANSVERSE DIRECTION............................................................................................................49
FIGURE 3.5PANEL 2G PLOT IN TRANSVERSE DIRECTION ............................................................................................................51
FIGURE 3.6PANEL 3K PLOT IN TRANSVERSE DIRECTION.............................................................................................................53
FIGURE 3.7 PANEL 1 FEA RESULT........................................................................................................................................54
FIGURE 3.8PANEL 2 FEA RESULT.........................................................................................................................................55
FIGURE 3.9PANEL 3 FEA RESULT.........................................................................................................................................56

List of Tables
TABLE 2.1PROPERIES OF CFRP LAMINA................................................................................................................................20
TABLE 2.2PROPERIES OF ROHACELL FOAM ............................................................................................................................21
TABLE 3.1COMPARISON OF THE CRITICAL LOAD FOR BUCKLING ANALYSIS FOR VARIOUS METHODS.....................................................44
TABLE 3.2 CRITICAL BUCKLING LOADS FOR DIFFERENT ORIENTATIONS..........................................................................................56

CHAPTER 1
1. INTRODUCTION
Composite materials are made from two or more constituent materials with significantly
different physical or chemical properties, that when combined, produce a material with
characteristics different from the individual components. The individual components remain
separate and distinct within the finished structure. The new material may be preferred for many
reasons: common examples include materials which are stronger, lighter or less expensive when
compared to traditional materials. Typical engineered composite materials include: Composite
building materials such as cements, concrete.
Composite materials are ideal for structural applications where high strength to weight and
stiffness to weight ratio are required. Aircraft and spacecraft are typical and are cost effective.
Hence the advantages of composite materials should be utilized both in aircraft and spacecraft. It
has to be designed in a manner which is different from the present one.
Composites are made up of individual materials referred to as constituent materials. There are
two main categories of constituent materials: matrix and reinforcement. At least one portion of
each type is required. The matrix material surrounds and supports the reinforcement materials by
maintaining their relative positions. The reinforcements impart their special mechanical and
physical properties to enhance the matrix properties. A synergism produces material properties
unavailable from the individual constituent materials, while the wide variety of matrix and
strengthening materials allows the designer of the product or structure to choose an optimum
combination.
Composite materials are also used for buildings, bridges and structures such as boat hulls,
swimming pool panels, race car bodies, shower stalls, bathtubs, storage tanks, imitation granite
and cultured marble sinks and counter tops. The most advanced examples perform routinely on
spacecraft in demanding environments.

Engineering composite materials must be formed to shape. The matrix material can be
introduced to the reinforcement before or after the reinforcement material is placed into the mold
cavity or onto the mold surface. The laminate is a material that can be constructed by uniting two
or more layers of material together [1], (R.M JONES, Mechanics of Composite Materials,
2ndedition, McGraw Hill 1999).
Figure.1.1 Structure of Sandwich Panel
1.1 UAV’s
A growing area in aerospace engineering is the use and development of Unmanned
Aerial Vehicles for military and civilian applications. Currently there has been a huge demand
for UAVs and services for real time and remote sensing .Unmanned aerial vehicles can be
deployed to solve a number of civilian tasks ,it can be used as an effective means of search,
detection and identifying of objects or subjects of interest as well as their precise coordinates.
UAVs are also very useful in disaster management, in the occurrence of a forest fire for instance,
it is very difficult to have a precise data on the development of the situation, but with the
deployment of a UAV which is capable of flying at low altitudes and able to navigate with GPS
waypoints and machine vision, the situation can be controlled very efficiently. The most
significant advantage of piloted vehicles is their ability to use humans to sense events within and
outside the vehicle, which is known in military jargon as situational awareness. A related
advantage of the reliance of humans is that no two pilots react the same in every situation, which
in military operations involves how humans identify threats and targets, make decisions in
unfamiliar and ambiguous situations, and function in an analytic and creative fashion.
UAVs fall into two distinct groups of remotely piloted and autonomous vehicles. A useful
concept for distinguishing between these types of vehicles is to remember that remotely operated
vehicles remove the operator from the vehicle, while autonomous vehicles remove the operation
of the vehicle from the control of the human operator.

Figure 1.2 Unmanned Aerial Vehicles.
1.1.1 Applications of UAV
1. Fire-fighting.
2. Disaster assessment and management.
3. Life search and rescue.
4. Border surveillance.
5. Counter terrorism operations.
6. Large scale public outdoor events surveillance.
7. Police surveillance.
8. Important objects and VIP guard.
9. Ground and sea traffic surveillance.
10. Environmental control and monitoring.
11. Telecommunications.
12. Crop monitoring.
13. Animal surveillance.
14. Fisheries protection.
15. Mineral exploration.
16. Ground mapping and photography.
17.Meteorological observations.
1.2 Aircraft Structure
In an aircraft, the combination of outside fairing panels that provide the basic
aerodynamic lifting surfaces and the inside supporting members that transmit the lifting force to
the fuselage; the primary load-carrying portion of a wing is a box beam made up of two or more
vertical webs, plus a major portion of the upper and lower skins of the wing, which serve as
chords of the beam.

On the underside of the wing, a high pressure region forms accelerating the air
downwards, out of the path of the oncoming wing. The pressure difference between these two
regions produces an upward force on the wing, called "lift".
The pressure differences, the acceleration of the air and the lift on the wing are
intrinsically one mechanism. It is therefore possible to derive the value of one by calculating
another. For example, lift can be calculated by reference to the pressure differences or by
calculating the energy used to accelerate the air. [2], (T.H.G MEGSON, Aircraft structures for
engineering students, 3rd
edition, ISBN 0 340 70588 4).
Figure1.3. Structure of an Aircraft
1.3 Composite
1.3.1 Types of Composites
1. Flake composites
2. Particulate composites
3. Fiber composites

4. Nano composites
1.3.2 Characteristics of Composite Materials
1. High specific strength and modulus, as well as high fatigue strength and fatigue damage
tolerance.
2. Anisotropic.
3. Designable or tailor able materials for both microstructure and properties.
4. Production of both material and structure or component in a single operation
manufacturing flexible, net-shape, complex geometry.
5. Corrosion resistance and durable.
6. Other unique functional properties - damping, low CTE (coefficient of thermal
Expansion).
1.3.3 Advantages of Composite
1. They are more efficient and high performance materials in competitive fields of
Engineering like Aerospace, Automotive and Aircraft industry.
2. Complex sections can be easily made.
3. High resistance to corrosion.
4. Light weight with high stiffness and strength.
5. Reduced machining methods and cost.
1.3.4 Disadvantages of Composites
1. High cost of fabrication of composites.
2. Mechanical characterization of a composite structure is more complex than a metal
structure.
3. Repair of composites is not a simple process compared to that for metals.
4. Composites do not have a high combination of strength and fracture toughness
compared to metals.
5. Composites do not necessarily give higher performance in all the properties.
1.3.5 Applications of Composite Materials
1. Aircraft, spacecraft, satellites, space telescopes, space shuttle, space station, missiles,
rocket boosters, helicopters (due to high specific strength and stiffness) fatigue life,
dimensional stability.

2. All composite voyager aircraft flew nonstop around the world with refueling.
3. Carbon/carbon composite is used on the leading edges nose cone of the shuttle.
4. B2 bomber - both fiber glass and graphite fibers are used with epoxy matrix and
polyimide matrix.
5. The indigenous Light Combat Aircraft (LCA - Tejas) has Kevlar composite in nose
cone, Glass composites in tail fin and carbon composites form almost all part of the
fuselage and wings, except the control surfaces of the wing.
Further, the indigenous Light Combat Helicopter (LCH – Dhruvh) has carbon composites
for its main rotor blades. The other composites are used in tail rotor, vertical fin,
stabilizer, cowling, radome, doors, cockpit, side shells, etc. [3], (AUTHAR K. KAW, 2nd
edition Published in 2006 by CRC Press Taylor & Francis Group).
1.4 Sandwich Composite
Today, the exploitation of the economic advantages of weight reduction has
become essential for many industries. It is well known that the task distribution in sandwich
construction enables high stiffness and strength for light weight panels and parts. Sandwich
construction with low cost core materials can not only be more lightweight but also more cost
effective, especially because the advancement and automation of production processes results in
a reduction of the production cost for lightweight sandwich panels.
The combination of materials to utilize their favorable properties is the basic idea of composites
engineering. With a monolithic material, a thickness increase leads to an increase of both weight
and material cost of a panel.
Sandwich constructions use the fact that the core of a panel that is loaded in bending does
not carry much in-plane stresses and does not represent the surface of the panel. The core can
thus be made from a different, more lightweight and/or less expensive material.
Sandwich construction takes the different demands on the central layer (core) and surface layers
(skins) into account.
The selection and optimization of the different material layers according to their demands
enables to improve their weight and/or cost specific properties of their construction. The
potential economic advantage of low cost materials is a big advantage as the potential weight

savings due to low density core materials.[4], (VINSON, JACK R . The Behavior of Sandwich
Structures of Isotropic and Composite Materials, published by Taylor & Francis Routledge , in
the year 1999)
Figure 1.4Structure of sandwich composite
1.5 Introduction to Panel Buckling
The buckling strength of stiffened composite panels is usually sensitive to the variation of
boundary conditions, stacking sequences and lamina thickness. In order to permit stiffened
composite panels to be designed efficiently with high reliability and safety against buckling, a
parametric study to investigate the effects of boundary conditions, stacking sequences and
lamina thickness on buckling strength of stiffened composite panels with various types of
stiffeners has been studied. Steel plates are widely used in buildings, bridges, automobiles and
ships. Unlike beams and columns, which have lengths longer than the other two dimensions and
so are modeled as linear members, steel plates have widths comparable to their lengths and so
are modeled as two-dimensional plane members.
Just as long slender columns undergo instability in the form of buckling, steel plates under
membrane compression also tend to buckle out of their plane. The buckled shape depends on the
loading and support conditions in both length and width directions.
However, unlike columns, plates continue to carry loads even after buckling in a stable manner.
Their post-buckling strengths, especially in the case of slender plates, can thus be substantially
greater than the corresponding buckling strengths. This property is of great interest to structural
engineers as it can be utilized to their advantage. [5], (HOWARD G ALLEN, © 1969
PERGAMON PRESS)

1.6 Rohacell Foam
The principle of increasing stiffness of a composite structure by means of a sandwich
construction is now well established. Sandwich structures realize their full potential when their
super-light cores prove extremely shear and pressure-resistant, even at high temperatures as is
the case with rohacell structural foam.
Its low density, outstanding material properties, temperature resistance of up to 220°C,
and 100% closed cell structure, make ROHACELL foam ideal for high performance sandwich
structures which offer unmatched strength to weight ratios.
Reduce cycle time, or bond both facings to the structural core in just one work step. rohacell
makes it possible. Take full advantage of these potential savings in your fabrication process..
1.6.1 Properties of rohacell
1. Excellent mechanical properties over a wide temperature range, even at low densities
2. High temperature resistance up to 220°C
3. Unique compressive creep behavior for processing up to 180°C and 0.7 MPa
4. Excellent dynamic strength
5. Cell sizes that can be tailored for each processing method
The 100 percent-closed-cell foam uptakes resin only in the exposed cut cells at the surface. This
prevents excess resin from infiltrating further into the foam, which would add unnecessary
weight, and also provides an adequate means of restraining the ROHACELL by way of vacuum
fixation during mechanical processing. ROHACELL can be processed by common machining
methods which include milling, drilling, turning, and sanding.
1.7 Literature survey on Buckling of composite panels
Wrinkling Analysis of Rectangular Soft-Core Composite Sandwich Plates [6] In the present
chapter, a new improved higher-order theory is presented for wrinkling analysis of sandwich
plates with soft orthotropic core. Third-order plate theory is used for face sheets and quadratic
and cubic functions are assumed for transverse and in-plane displacements of the core,
respectively. Continuity conditions for transverse shear stresses at the interfaces as well as the
conditions of zero transverse shear stresses on the upper and lower surfaces of plate are satisfied.

The nonlinear von Kármán type relations are used to obtain strains. Also, transverse flexibility
and transverse normal strain and stress of the orthotropic core are considered. An analytical
solution for static analysis of simply supported sandwich plates under uniaxial in-plane
compressive load is presented using Navier‟s solution. The effect of geometrical parameters and
material properties of face sheets and core are studied on the face wrinkling of sandwich plates.
Comparison of the present results with those of plate theories confirms the accuracy of the
proposed theory.
Manufacturing And Applications of Structural Sandwich Components [7], techniques to
manufacture sandwich components for structural applications are summarized and discussed in
terms of processing steps, components, and application examples. The structural sandwich
concept involves combining two thin and stiff faces with a thick and relatively weak core. By
sandwiching the core between the two faces and integrally bonding them together, a structure of
superior bending stiffness and low weight is obtained. Since the core often has exceptional
insulative properties, the entire sandwich structure may further be characterized by excellent
thermal insulation and also acoustic damping at certain frequencies.
Sandwich structures are used in a wide variety of applications, such as Automobiles,
Refrigerated transportation containers, pleasure boats and commercial vessels, aircraft, building
panels, etc. The face materials in common use include sheet metal and fiber-reinforced polymers,
while common core materials are balsa wood, honeycomb and expanded polymer foam. These
materials and material combinations all have their own market share and one or more of
advantages such as low cost, high mechanical and thermal properties, thermal and acoustic
insulation, fire retardancy, low smoke emission, compliance, ease of machining, ease of forming,
etc.
Buckling analyses of composite laminated panels with delamination [8] , Buckling response of
composite laminated panels with an artificial delamination was numerically investigated.
Implementation of the Finite-element models required a previous study on the simulation of
fracture mechanisms under general mixed-mode loading conditions with the use of cohesive
elements. To pursue this aim, a methodology based on numerical analyses and parametric studies
of the DCB (Double Cantilever Beam) and ENF (End Notched Flexure) tests on AS4/PEEK
laminates was developed. Comparison to available experimental data enabled to determine a

reduced set of parameters which, controlling the response of cohesive elements and the variable
discretization pattern over the model, provided a good compromise between accuracy and
computational cost in both single-mode delamination cases. Validation of the obtained set of
parameters took place through the simulation of the MMB (Mixed-Mode Bending) test at three
different mode ratios. Good agreement with experimental measurements found in literature
suggested extending the usage of the found set in more complex problems, such as delamination
buckling of a damaged HTA/6376C plate, whose fracture-related properties are comparable to
those of AS4/PEEK. Through a careful definition of the geometric imperfection, the adopted
Non-linear static approach showed to yield predictions of the failure load in good agreement with
experimental results reported in literature. Finally, a qualitative study was conducted about the
reduction of compressive strength caused by delaminations of different sizes, shapes and
through-the-thickness locations within an AS4/PEEK panel. Conclusions showed to be
consistent with similar previous works conducted by other authors, evidencing a reduction of the
compressive strength with the delamination size and depth. On the contrary, no significant
influence of the delamination shape (circular or square) was observed.
A Comparison of Bending Properties for Cellular Core Sandwich Panels [9], In this study,
various sandwich panel structures with different reticulate lattice core geometries were designed
and then fabricated in titanium via the electron beam melting (EBM) process. Bending tests were
performed on the titanium samples, and mechanical properties such as modulus, bending
strength, and energy absorption were evaluated. Different failure mechanisms were observed,
and it was found that sandwich structures with auxetic cores exhibited more homogeneous
deflection and bending compliance compared with other structures. It was also demonstrated that
properties of auxetic sandwich structures can be tailored using different cell structure geometries
to suit the needs of a given design application. Furthermore, it was found that other 3D cellular
sandwich structures can also exhibit high stiffness and strength, which is desirable in potential
applications.
Buckling and Post-buckling Analysis of Composite Plates [10], Thin walled stiffened composite
panels are among the most utilized structural elements in ship structures. The composite layered
panels with fibers are the most usually used in shipbuilding, aerospace industry and in
engineering constructions as well. These structures possess the unfortunate property of being
highly sensitive to geometrical and mechanical imperfections. These panels, unfortunately, have

one important characteristic connected to big sensitivity on geometrical imperfections (different
dimensions comparative with the design ones). The defects are of following types: different
directions of fibers design, variations in thickness, inclusions, delaminations or initial transversal
deformations. Ship structure plates are subjected to any combination of in plane, out of plane and
shear loads during application. Due to the geometry and general load of the ship hull, buckling is
one of the most important failure criteria of these structures. This is why it is necessary to
develop the appropriate methodologies able to correctly predict the behavior of a laminated
composite plate in the deep post buckling region, at the collapse load, which is characterized by
separation between the skin and the stiffeners, delaminations, crack propagations and matrix
failure, as well as to understand its behavior under repeated buckling.
Finite Element Modeling of Delamination Buckling of Composite Panel Using ANSYS [11],
Delamination buckling analysis of composite panels is of considerable interest to aerospace
industries. In this paper, finite element modeling of delamination buckling of composite panels is
discussed. ANSYS 5.4 has been used for modeling the delamination buckling. A 3-D model with
8-node composite shell element is used. The panel is hypothetically divided into two sub-
laminates by a plane containing the delamination. The two sub-laminates are modeled separately
using 8-node composite shell element. Appropriate constraint conditions are added for the nodes
in the non-delaminated region using Coupled Nodes facility of ANSYS. The nodes in the
delaminated region, whether in the top or bottom laminate, are left free. Using this modeling
approach, a few typical test problems have been solved. The computed buckling loads and strain
energy release rate values for the test problems tally closely with that of theory and other
researchers. In addition to the test problems, some results on delamination buckling of a woven-
fabric carbon-epoxy composite panel are also presented. The two sub-laminate model discussed
here provides a convenient approach to delamination buckling analysis.
1.8 Problem Definition
Sandwich composite panels have high specific strength and stiffness when compared to
other metallic materials. These composite panels are used in the aircraft panels to cover as skin.
Sandwich panels have high capability to carry more load before buckling. Hence sandwich
panels are preferred in aircraft construction. In the current work CFRP panels have been studied
for their adequate buckling strength. Initial studies have been carried out through analytical and

ESDU methods followed by numerical method using commercial code Nastran. The theoretical
study is followed by fabrication of the CFRP panels and testing. In the present study three layup
sequences are considered as used in an aircraft panel and the buckling behavior is studied and
compared for all the three sequence. This study gives a good understanding of the CFRP panel
buckling behavior with a particular end fixity condition.

CHAPTER 2
This chapter elucidates the theoretical prediction of panel buckling. Initially the axial and
bending stiffness of the composite panel has to be established through classical lamination plate
theory. The estimated stiffness values of the panel are used in the prediction of the critical
buckling load of the panel. In the current chapter theoretical prediction both through the
analytical method as well as ESDU is presented.
2. Theoretical Prediction of Buckling Load
2.1 Stress- Strain Relation
The stress-strain relations in principal material coordinates for a lamina of an orthotropic
material under in-plane stress are given in equation (2.1) ,
[
𝜎
𝜎
𝜏
] = ⌈
𝑄 𝑄 0
𝑄 𝑄 0
0 0 𝑄
⌉ ⌈
𝜀
𝜀
𝛾
⌉ … … (2.1)
The reduced stiffness matrix the value of 𝑄 are defined in terms of the engineering constants
(𝑄 𝑄 𝑄 𝑄 𝑄 ) shown in equation (2.2).
𝑄 =
( )
, 𝑄 =
( )
, 𝑄 = 𝐺 ,
𝑄 =
𝜗 𝐸
1 − (𝜗 𝜗 )
, 𝑄 =
𝐸
1 − (𝜗 𝜗 )
… … … (2.2)
The stress-strain relations for a lamina of an arbitrary orientation is given as follows,
[
𝜎
𝜎
𝜏
] = [
𝑄̅ 𝑄̅ 𝑄̅
𝑄̅ 𝑄̅ 𝑄̅
𝑄̅ 𝑄̅ 𝑄̅
] ⌈
𝜀
𝜀
𝛾
⌉ … … … (2.3)

Where the transformed reduced stiffness, 𝑄̅ are given in terms of the reduced stiffness𝑄 , in
equation (2.4).
𝑄̅ = 𝑄 2(𝑄 2𝑄 ) 𝑄
𝑄̅ = 𝑄 2(𝑄 2𝑄 ) 𝑄
𝑄̅ = (𝑄 𝑄 − 2𝑄 − 2𝑄 ) 𝑄 ( ) ... … (2.4)
𝑄̅ = (𝑄 − 𝑄 − 2𝑄 ) (𝑄 − 𝑄 − 2𝑄 )
𝑄̅ = (𝑄 − 𝑄 − 2𝑄 ) (𝑄 − 𝑄 − 2𝑄 )
𝑄̅ = (𝑄 𝑄 − 4𝑄 ) 𝑄 ( )
Where, m= cos , n= sin .
Figure 2.1 Forces and Moments in a Flat Laminates
[ ] = ∫ [
𝜎
𝜎
𝜏
] [ ] = ∫ [
𝜎
𝜎
𝜏
] ….. (2.5)

Figure 2.2 Geometry of N-layered Laminate
[ ] = [ ] [ ] [ ] [ ]
[ ] = [ ] [ ] [ ] [ ] …... (2.6)
Where (Nx, Ny, Nxy) and (Mx, My, Mxy) represent the in-plane loading and bending moments,
(as shown in figure 2.1and 2.2 ) respectively, which are almost contributed by the faces;(Qx, Qy)
are the transverse shear forces, which are undertaken by the core; (εx, εy, γxy) and ( x, ky, xy) are
the mid-plane strain and curvature of the sandwich plates; γxz and γyz are the transverse shear
strain of the x-z and y-z planes. Aij, Bij, and Dij are the extensional, coupling, and the bending
stiffness, respectively, which are related to the location zk and the transformed reduced stiffness
𝑄̅ of each lamina is shown in equation (2.7)
𝐴 = = 1 [𝑄̅ ] ( − )
𝐵 = ∑ [𝑄̅ ] ( − ) ... ... (2.7)
𝐷 =
1
3
∑[𝑄̅ ] ( − )
Unlike the classical laminate theory in which Aij, Bij, and Dij are calculated based on the
coordinate where z=0 is the middle surface of the laminate, here the plane z=0 is located on the
mid-surface of the core.

2.2 Computation of [A][B][D] matrices
[A] is referred to as the in-plane stiffness matrix. The Aij terms are the in plane stiffness
terms which relate the in-plane forces to in-plane strains .Aij is termed as the in-plane stiffness
coefficient of the laminate they are independent of the stacking sequence of the laminate. The
weighting factor is the thickness of the lamina Zk-Zk-1.
[B] is the coupling stiffness matrix. The Bij terms are the coupling terms which relate the
in-plane forces to radius of curvatures and moments to in-plane strains the elements Bij are called
the coupling stiffness coefficients of the laminate. Physically, this means that if Bij ≠0, in-plane
forces produces flexural and twisting deformation in addition to in-plane deformation. Similarly
for Bij ≠0, moments produce in-plane deformation in addition to flexural and twisting
deformations. The elements Bij are dependent on the stacking sequence.
[D] is the bending stiffness matrix .The Dij terms are bending stiffness which relate
moments to curvature the elements Dij are the bending stiffness coefficient of the laminate. They
are strongly dependent on the stacking sequence of the laminate.
The different orientations are shown in respective figures (2.3, 2.4 and 2.5)
Figure 2.3 orientation 1 Figure 2.4 orientation 2 Figure 2.5 orientation 3
Table 2.1 Properties of CFRP lamina
S.I NO MATERIAL PRORPERTIES VALUES
1 E11=E22 65 GPa
2 𝛾 0.2
3 G12 2.5 Gpa
4 Thickness 0.2mm
X
+
+
X
FOAM
X
+
+
X
+
X
X
+
FOAM
+
X
X
+
X
X
+
+
FOAM
+
+
X
X

Table 2.2 Properies of Rohacell foam
S.I NO MATERIAL PRORPERTIES VALUES
1 E11=E22 70MPa
2 𝛾 0.2
3 G12 21Mpa
4 Thickness 5mm
From tables (2.1 and 2.2 respectively), the coefficient of [A][B] [D] matrices are computed by
referring the equation (2.2,2.4 and 2.7 respectively) as shown below for orientation 3(figure 2.5).
𝛾 = =
.
= 0.2
Q11= =
( . . )
=67.7*103
MPa
Q12= =
.
( . . )
= 13.54*103
MPa.
Q66 = G12=2.5*103
MPa
Therefore, for 00
ply Qij (0) =[
67.7 13.54 0
13.54 67.7 0
0 0 2.5
]*103
MPa
For =450
ply,(refer equation 2.4)
Therefore for 450
ply
𝑄 (45)=[
43.094 38.09 0
38.09 43.094 0
0 0 27.08
]*103
MPa
Now considering the foam,
Q11 (foam)= =
( . . )
=72.916MPa
Q22 (foam) = =
( . . )
=72.916MPa
Q12 (foam) = =
.
( . . )
=14.583MPa

For foam,
Qij(foam) =[
72.916 14.583 0
14.583 72.916 0
0 0 27.08
]MPa
X Y
Orientation 3
Let, XY be the reference line i-e, at the Centre of the foam (panel).
Now,
Ply number Zk (mm) Zk-1 (mm)
1 3.3 3.1
2 3.1 2.9
3 2.9 2.7
4 2.7 2.5
FOAM
5 -2.5 -2.7
6 -2.7 -2.9
7 -2.9 -3.1
8 -3.1 -3.3
Now
𝐴 = ∑[𝑄̅ ] ( − )
𝐴 = [
88.999 41.344 0
41.334 37.86 0
0 0 23.769
] ... ....(a3)
X
X
+
+
FOAM
+
+
X
X

𝐵 =
1
2
∑[𝑄̅ ] ( − )
𝐵 = [
0 0 0
0 0 0
0 0 0
] ... ... (b3)
𝐷 =
1
3
∑[𝑄̅ ] ( − )
𝐷 = [
733.337 372.0739 0
372.0739 733.337 0
0 0 224.0539
] . ... ....(c3)
Now for the Orientation 2 (figure 2.4), the [A][B] [D] matrices are computed using equation (2.7).
𝐴 = ∑[𝑄̅ ] ( − )
𝐴 = [
88.999 41.344 0
41.334 37.86 0
0 0 23.769
] ... ...(a2)
𝐵 =
1
2
∑[𝑄̅ ] ( − )
𝐵 = [
0 0 0
0 0 0
0 0 0
] ... ...(b2)
𝐷 =
1
3
∑[𝑄̅ ] ( − )
𝐷 = [
757.0497 351.182 0
351.182 757.0497 0
0 0 201.273
] . ... ...(c2)

Similarly for the Orientation 3 (figure 2.3), the [A][B] [D] matrices are computed using equation
(2.7).
𝐴 = ∑[𝑄̅ ] ( − )
𝐴 = [
88.999 41.344 0
41.334 37.86 0
0 0 23.769
] ... ... (a1)
𝐵 =
1
2
∑[𝑄̅ ] ( − )
𝐵 = [
0 0 0
0 0 0
0 0 0
] ... ... (b1)
𝐷 =
1
3
∑[𝑄̅ ] ( − )
𝐷 = [
755.475 351.182 0
351.182 755.475 0
0 0 202.843
] . ... ... (c1)
2.3 Buckling analysis of sandwich panel by analytical method.
The first significant contribution to the theory of the buckling of columns was made by
Euler. His classical approach is still valid, and likely to remain so, for slender columns
possessing a variety of end restraints. Our initial discussion is therefore a presentation of the
Euler theory for the small elastic deflection of perfect columns. However, we investigate first the
nature of buckling and the difference between theory and practice. On similar basis buckling of
thin plates can also be studied in a similar manner. A thin plate may buckle in a variety of modes
depending upon its dimensions, the loading and the method of support. Usually, however,
buckling loads are much lower than those likely to cause failure in the material of the plate. The
simplest form of buckling arises when compressive loads are applied to simply supported

opposite edges and the unloaded edges are free, as shown in Figure (2.6). A thin plate in this
configuration behaves in exactly the same way as a pin-ended column so that the critical load is
that predicted by the Euler theory. Once this critical load is reached the plate is incapable of
supporting any further load. Buckling of plates, takes the form of a bulging displacement of the
central region of the plate while the parts adjacent to the supported edges remain straight. These
parts enable the plate to resist higher loads; an important factor in aircraft design.
Figure 2.6 Buckling of thin plates
𝐏 = (𝐃 ( ) (𝐃 𝐃 ) ( ) 𝐃 ( ) ) ….… (2.8)
Where,
= Critical buckling per unit width (N/mm)
a= length of the plate (mm) = 300 mm
b= width of the plate (mm) = 300 mm
m, n = buckling mode (here m=1 and n=1, for lowest buckling load)
D11 D12 D33 are the coefficients of [D] matrix.
2.3.1 Computation of critical buckling load using analytical method.
For figure 2.5,the critical buckling load is calculated using equation (2.8) and the coefficients
[D] matrix from equation (c3) respectively

=
π (300)
1
(733.337 (
1
300
) 2(373.289) 2(224.8039)) (
1 1
300 300
)
733.337 (
1
300
) )
𝑷 = . 𝟎 𝑵 𝒎𝒎
Now, for figure 2.4, the critical buckling load is calculated using equation (2.8) and the
coefficients [D] matrix from equation (c2) respectively
=
π (300)
1
(757.0497 (
1
300
) 2(351.182) 2(201.273)) (
1 1
300 300
)
757.0497 (
1
300
) )
𝑷 = 𝟎. 𝟗𝟖 𝑵 𝒎𝒎
Similarly for figure 2.3, the critical buckling load is calculated using equation (2.8) and the
coefficients [D] matrix from equation (c1) respectively
=
π (300)
1
(755.475 (
1
300
) 2(351.182) 2(202.843)) (
1 1
300 300
)
755.475 (
1
300
) )
𝑷 = . 𝟔𝟗 𝑵 𝒎𝒎

2.4 Estimation of Critical Buckling by Engineering Standard Data Unit
The buckling of specially orthotropic rectangular plate is referred from ESDU (80023).
Figure 2.7 ESDU data sheet (80023) for uniaxial load

Table 2.3 Conditions for computation of ESDU
Table 2.3 lists all the load and edge support conditions for which curves are provided in
this Item. The data for plates loaded either uniaxial or biaxial are presented in terms of the
buckling coefficient K0 and a coefficient C, the latter being only dependent upon plate edge
conditions. To obtain the buckling load the following equation must be evaluated.
=
𝐾 ( 𝐷 𝐷 ) ⁄
𝑏
𝐶𝜋 (𝐷 2𝐷 )
𝑏
… … … (2.10)
The exact value of C for plates with all edges simply-supported is 2.0
2.5 Calculation of Critical Buckling load by ESDU sheet
For figure 2.5, the critical buckling load is calculated using equation (2.10) and the
coefficients [D] matrix from equation (c3) respectively.
From graph (figure2.7) by considering approximate boundary condition;
we get the value of Ko= 20 ; C=2
𝑃 =
20(733.337 733.337) ⁄
300
2π (373.289 2(224.8039))
300
𝐏 = . 𝟓 𝐍
Plate Loading Conditions at Plate edges Figure No.
Uniaxial
All sides simply-supported
All sides clamped
One pair of opposite sides simply-supported, the
other pair clamped against rotation
1
1
1
Biaxial
All sides simply-supported
One pair of opposite sides simply-supported, the other pair
clamped
Long plates with the long sides simply-supported
2
3
4a &4b

Now for figure 2.4, the critical buckling load is calculated using equation (2.10) and the
From graph (figure2.7) the value of Ko= 20 ; C=2
𝑃 =
20(757.04957 757.04957) ⁄
300
2π (351.182 2(201.273))
300
𝐏 = . 𝟓 𝟕 𝐍
Similarly for figure 2.3, the critical buckling load is calculated using equation (2.10) and the
From graph (figure2.7) , the value of Ko= 20; C=2
𝑃 =
20(755.475 755.475) ⁄
300
2π (351.182 2(202.843))
300
𝐏 = . 𝟖𝟖 𝐍
2.6 FEA
The finite element method(FEM), or finite element analysis(FEA), is based on the
idea of building a complicated object with simple blocks, or, dividing a complicated object into
small and manageable pieces. Application of this simple idea can be found everywhere in
everyday life as well as in engineering.
Many practical problems in engineering are either extremely difficult or impossible to
solve by conventional analytical methods. Such methods involve finding mathematical equations
which define the required variables.
2.6.1 Applications of FEA
1. Stress and thermal analyses of industrial parts such as electronic chips, electric devices,
valves, pipes, pressure vessels, automotive engines and aircraft.
2. Seismic analysis of dams, power plants, cities and high-rise buildings.
3. Crash analysis of cars, trains and aircraft.
4. Fluid flow analysis of coolant ponds, pollutants and contaminants, and air in ventilation
systems.

5. Electromagnetic analysis of antennas, transistors and aircraft signatures.
6. Analysis of surgical procedures such as plastic surgery, jaw reconstruction, correction of
scoliosis and many others.
The software used in FEA for buckling is MSC Patran 2012 as pre-processor and
post-processor, MSC Nastran 2012 as solver.
2.6.2 Steps involved in FEA
1. Create the required geometry as per the dimensions as shown is figure (2.8).
2. Mesh the geometry of optimum elemental size of 15 by using QUAD-elements as
shown is figure (2.8).
3. Specify the required material properties to the geometry.
4. Creating 2D-orthotropy components i.e. CFRP, foam and composite using 2D-
orthotropy material.
5. Select the 2D-shell which it carries all types of loads as shown is figure (2.9).
6. Applying 1N using RB2 (rigid body) element as shown is figure (2.9).
7. Applying boundary conditions by constraining the top and bottom edges of the
plate as shown is figure (2.10).
8. Buckling analysis is carried out by providing the code 105 for buckling.
9. The output file is created in BDF (bulk data format) file.
10. The BDF file is imported to Nastran and RUN option is given.
11. From the analysis the buckling factor and displacement plots are obtained.

Figure 2.8 Geometry as per dimensions
Figure 2.9 Loading Condition

Figure 2.10 Constraining the top and bottom edges

CHAPTER 3
3. FABRICATION AND TESTING
There are numerous methods for fabricating composite components. Some methods have
been borrowed (injection molding, for example), but many were developed to meet specific
design or manufacturing challenges. Selection of a method for a particular part, therefore, will
depend on the materials, the part design and end-use or application.
Composite fabrication processes involve some form of molding, to shape the resin and
reinforcement. A mold tool is required to give the unformed resin /fiber combination its shape
prior to and during cure. For an overview of mold types and materials and methods used to make
mold tools.
The most basic fabrication method for thermoset composites is hand layup. The figure
(3.2) shows, which typically consists of laying dry fabric layers, or “plies,” or prepreg plies, by
hand onto a tool to form a laminate stack. Resin is applied to the dry plies after layup is complete
(e.g., by means of resin infusion). In a variation known as wet layup, each ply is coated with
resin and “debulked” or compacted after it is placed.
Testing is a method of evaluating the results by physically performing various
mechanical tests there by obtaining the desired results. Usually buckling test is carried out on
UTM (Universal Testing Machine) with the help of fixtures, which are used to hold the panels in
place and quasi-static load is applied gradually. By testing we arrive at various results which are
checked for the correctness with the analytical results and the ESDU results.
Figure 3.1 Hand-Layup process

3.1 Fabrication of CFRP Laminates
Fabrication is stage wherein the necessary things i.e. CFRP's, consumables required are
cut and made ready for the fabrication process.
The figure (3.2) shows a simple vacuum stack indicating the products that are typically used for
vacuum bag curing of composite components in low temperature.
Figure 3.2 Vacuum bag process
The following are the consumables required for fabrication of CFRP plates:-
3.1.1 Peel Plies
Peel Plies are woven fabrics that are generally applied as the last material in the
composite laminate sequence. They are designed to be peeled from the surface following cure to
leave a textured surface, which is clean and contaminant free. The textured surface left on the
laminate is an imprint of the weave of the peel ply and therefore fine weaves will impart a finely
textured surface.
Peel plies as shown in figure (3.3), are usually made from polyamide (nylon) or polyester fibers.
Polyamide fabrics are more commonly used; though polyester fabrics must be used with phenol-
based resin systems.
Resin content materials such as prepregs, in the manufacture of thin laminates, since excessive
resin may otherwise be extracted. Prepregged peel plies are available to overcome this issue, or
the use of a finely woven peel ply, which will absorb less resin, may also help in these instances.

Figure 3.3 Peel Ply used in initial stage of fabrication.
3.1.2 Release Films
Release Films are used to separate and release the laminate from the vacuum
stack following the cure of the composite component films are supplied both as
perforated and imperforated to allow resin and volatiles to bleed out of the laminate. The
latter are manufactured using hot needle perforating which ensures that the holes do not
close up during consolidation and ensure a high quality perforation pattern. For a fixed
cure cycle, the amount of resin that will bleed out of the laminate is determined by the
flow characteristics of the resin system, the cure pressure and temperature, and by the
spacing and size of the perforations. The selection of a release film should be based on
the resin system being used, the temperature and pressure of the cure cycle, the shape of
the component to be cured and the amount of resin bleed that is required. The release
film is as shown in figure (3.4).
Figure 3.4 Perforated Release films

3.1.3 Vacuum Bagging Films
Vacuum Bagging Films are used to seal the whole of the composite laminate,
including the other vacuum consumables, to the tooling surface. A vacuum is then applied in
order to apply atmospheric pressure to the component. This pressure can be increased, or
maintained for a standard, one-atmosphere cure cycle at the chosen cure temperature. Many
films can be used for this purpose, but nylon films are commonly used, due to their good
temperature resistance, cost effectiveness, ease of use and low air permeability (necessary to
achieve a good quality laminate and vacuum integrity). Nylon films are susceptible to
variations in humidity, since moisture is used as a natural plasticizer; vacuum bag process is
used as shown in figure (3.5).
Figure 3.5 Vacuum bagging films
3.1.4 Sealant Tape
Sealant tapes as shown in figure (3.6) are used to provide an integral seal between the
tool surface and the vacuum bag. The range of sealant tapes are manufactured from a blend of
synthetic rubbers combined with inert fillers, plasticizers and stackifiers. These provide the
optimum combination of properties required for sealing against a variety of tool surfaces, such
as composite, metal or glass and for the subsequent curing of the composite.

Figure 3.6 Sealant tapes
3.1.5 Breather / Bleeder Fabrics & Infusion Meshes
The breather shown below in figure (3.7), the fabric performs two functions during the
cure cycle. The first, as the name suggests, is to allow the vacuum stack to „breathe‟. This
breathing function ensures that the air sealed under the vacuum bag can be easily extracted. It
also provides a path for the flow of any entrapped air, or volatiles, from within the laminate
during the cure cycle.
The second function, in combination with the perforated release film, is to absorb any excess
resin that is bled from the laminate. Where a separate layer of breather fabric is used for this
secondary function, it is often known as a „bleeder‟. In most simple vacuum bag processes, one
layer of fabric acts as both a bleeder and a breather.
Figure 3.7 Breather/Bleeder cloth

3.1.6 Vacuum Fittings
Vacuum fittings shown below in figure (3.8) are used to plumb the whole of the „bagged‟
composite component to the vacuum pump. This therefore allows a vacuum to be applied and
maintained to the material for either a debulk operation or for a final cure.
Figure 3.8 Vacuum fittings
3.2 Cutting
The CFRP cloth is cut in to 340x350mmsize. After fabrication and post-curing process,
the panels are cut to exact dimensions of 300x300mm with the help of cutting machine.
The CFRP cloth is cut into different orientations and sizes as per the requirements. The
CFRP cloths are cut manually and stacked in proper sequence as shown in figure 3.9.
Figure 3.9 Cutting of consumables and cutting machine
3.3 Fabrication Procedure
1. Initially the cut and stacked fabric along with foam is weighed on digital weighing
machine, to estimate the proportion of resin and hardener mixture.

2. Mix the resin and hardener thoroughly in the ratio 100:38 by weight at room
temperature.
3. Make the necessary arrangements (cleaning the surface table by using acetone) for
the fabrication and apply wax on to the surface before starting fabrication for ease
for removal of laminates.
4. The consumable (peel ply) is placed on to the surface table before stacking the first
layer of laminates and place the lower sequence of laminates as per the given
orientation.
5. Rochcell foam is placed and stack the remaining layers of laminates.
6. Red film and breather cloth is placed and packed with the vacuum bag along with
the sealant.
7. Provision is made to suck the air from the vacuum bag using a vacuum pump
operating at 690-700mm of Hg for 6 hours.
8. Post-Curing is carried out.
9. The laminates are cut as per the given dimensions with the aid of cutting machine.
10. The laminates are inspected for any defects.
Figure 3.10 Specimens prepared for vacuum bagging process.

3.4 Vacuum Bagging process
Vacuum bagging (or vacuum bag laminating) shown below in figure (3.11) is a clamping
method that uses atmospheric pressure to hold the adhesive or resin-coated components of a
lamination in place until the adhesive cures. Moderate room-temperature-cure adhesives have
helped to make vacuum bag laminating techniques available to the average builder by
eliminating the need for much of the sophisticated and expensive equipment required for
laminating in the past. The effectiveness of vacuum bagging permits the laminating of a wide
range of materials from traditional wood veneers to synthetic fibers and core materials.
The vacuum pressure developed in the fabrication of CFRP laminates is 690 mm of Hg
for 6-8 hours.
Figure 3.11 Vacuum Bagging Technique
3.5 Post curing
Post curing carried out to improve the mechanical properties. In general curing
refers to process of solidification of polymer matrix material. It was carried out for 8 hours
80°C.

Figure 3.12 Post curing of CFRP laminates
3.6 Testing
It is a process of determining the required mechanical properties by performing
tests. The sandwich panels after fabrication is ready for testing. The testing used is MTS
(Material Test System) Universal testing machine. The experiments are conducted in UTM
as shown in figure (3.13) ,and critical buckling load is determined.
Figure 3.13 Universal testing machine
3.6.1 Specification of UTM
1. MTS (Material Test System).
2. Frame Number 810.
3. Maximum capacity: 100KN

4. Maximum Pressure: 21MPa / 3000 Psi.
5. MTS 647 Hydraulic wedge grip.
6. Oil working temperature range: -18°C to 65°C.
3.6.2 Test Fixture
Figure 3.14 Test Fixtures used for clamping
Fixtures as shown in figure (3.14) , are the devices which hold the specimen during
testing. This provides an end support .In this; the jaws are adjustable which help in proper
clamping and alignment.
3.6.3 Test Methodology
1. The functioning of UTM is checked i.e. hydraulic system.
2. The actual dimensions of the panels are measured using vernier calipers and noted
down.
3. The jaws of the fixtures are aligned in accordance to the thickness of the panels.
4. The fixtures are mounted on the UTM and checked for alignment before loading.
5. The test is carried out with the aid of DAS (Data Acquisition system) and other
necessary arrangements like LVDT (Linear variable differential transformer) setup
etc. Before loading.
6. The panels are mounted on to the test fixture and load is given at the rate of 0.5
mm/min.
7. Finally, after the specimen buckles the critical buckling load is calculated and the
graphs are plotted.

Figure 3.15 Panel before failure
Figure 3.16 Panel after failure

CHAPTER 4
4. RESULTS AND DISCUSSION
The experiments were conducted on CFRP panels of three different orientations. The following
observations were made.
1. Panel 1 has a critical buckling load of 29979.522N; on FE Analysis the result was found to
be 29997N.
2. Now, panel 2 has a critical buckling load of 27891.405N; on FE Analysis the result was
found to be 30112N.
3. And for panel 3 has a critical buckling load of 28998.363; on FE Analysis the result was
found to be 29058N.
Table 3.1 Comparison of the critical load for buckling analysis for various methods
The variations in the experimental and FE Analysis were due to few inevitable causes
like temperature change during fabrication, human error etc. Even after considering the
variations the percentage of variation was found to be
Panel 1=0.058%
SL
No
Analytical
Result(N)
ESDU
Result(N)
Numerical
Result(N)
Test
Result(N)
Test Result
Average(N)
Case
1
1
102396 103035 29997
29958. 012
29979.522
2 30261.029
3 30366.398
4 29332.648
Case
2
5
99288 100064.1 30112
27844.095
27891.405
6 27644.534
7 28051.574
8 28025.416
Case
3
9
99507.9 100164 29058
28919.523
28998.363
10 29131.578
11 28878.362
12 29063.992

Panel 2=7.37%
Panel 3=0.205%
The analytical and ESDU results shows very high buckling load due to unsatisfied
boundary conditions, i.e. the required boundary condition was both ends clamped which was not
available. Hence the results obtained from analytical and ESDU calculations cannot be correlated
with FEA and test results due to insufficient boundary conditions.
4.1 LOAD vs. DISPLACEMENT PLOTS
The figure (4.1) shows the plot of compressive load vs. displacement of orientation 1.
This graph is obtained by using MATLAB R2011b. According to this graph when the
compressive load is applied, the displacement of the panel takes place along the axis direction
and the curve will be linear up to certain load. When the compressive load reaches the maximum
of about 3.0 tons, the displacement of the panel will be maximum of 1.1mm along the axial
direction. When the load reaches beyond 3.0 tons, the panel fails due to buckling.
Figure 3.1 Plot of Compressive Load vs. Displacement for orientation 1

of about 2.8 tons, the displacement of the panel will be maximum of 1mm along the axial
Figure 3.2 Plot of Compressive Load vs Displacement for orientation 2
of about 2.95 tons, the displacement of the panel will be maximum of 0.9mm along the axial

Figure 3.3 Plot of Compressive Load vs. Displacement for orientation 3
Therefore from the three orientations, orientation 1 is found to take a maximum compressive
load of 3 tons and other two orientations are comparatively less and nearing up to 3 tons. So
orientation 1 is found to withstand maximum compressive load.
The plots shown with different colors represent different panels of the same orientation.
4.1.1 Test results of LVDT
The figure (4.4) shows the plots of load and displacement Vs. time which is obtained by
LVDT (Linear Variable Differential Transformer). This is mainly used to find out the
displacement of the testing sample along the transverse direction.
According to the plot, the graph of load and displacement Vs. Time, is a straight line up to
630secondsdue to cover the clearance present between the fixture and the panel, gradually the
panel starts to take the load and the time varies as the load varies and the maximum transverse

displacement of 4.5 mm is observed. After 830 seconds the panel is found to buckle under
compression. When the load reaches maximum limit i.e. nearly 3tons, panel failing due to
buckling. The LVDT records this transverse displacement of the buckled plate and the values are
recorded using sensors and these values are transformed in to plots as shown in figure (4.4).
Red and blue lines represents the displacement of LVDT 1 and LVDT 2 respectively. The
purple line represents the compressive load applied to the panel.

Figure 3.4 Panel 1c plot in transverse direction

According to the plot, the graph of load and displacement Vs. time, is a straight line up to
80seconds due to cover the clearance present between the fixture and the panel, gradually the
panel starts to take the load and the time varies as the load varies and the maximum transverse
displacement of 5 mm is observed. After 220 seconds the panel is found to buckle under
compression. When the load reaches maximum limit i.e. nearly 3tons, panel failing due to
recorded using sensors and these values are transformed in to plots as shown in below figure 4.5.

Figure 3.5 Panel 2g plot in transverse direction

According to the plot, the graph of load and displacement Vs. time, is a straight line up to 105
seconds due to cover the clearance present between the fixture and the panel, gradually the panel
starts to take the load and the time varies as the load varies and the maximum transverse
displacement of 5 mm is observed. After 235 seconds the panel is found to buckle under
compression. When the load reaches maximum limit i.e. nearly 2.8 tons, panel failing due to
recorded using sensors and these values are transformed in to plots as shown in below figure 4.6.

Figure 3.6 Panel 3k plot in transverse direction

4.2 FEA RESULTS
The figure given below refers to panel 1, which is carried out using MSC Nastran‟s
Solver and Patran as Post Processor. The panel is generated in MSC Patran. QUAD
elements are used for meshing, of element size 20.
Figure 3.7 Panel 1 FEA result
From the figure 4.7 shows that, when the compressive load reaches a maximum of
29997N, the panel gets buckled and the maximum axial displacement of 1mm is obtained
from FEA analysis. From the above figure 4.7, the region with red color shows the areas
of the panel which are susceptible to buckling with high stresses.

Similarly, from the figure 4.8 shows that, when the compressive load reaches a
maximum of 30112N, the panel gets buckled and the maximum axial displacement of
1mm is obtained from FEA analysis. From the above figure 4.8, the region with red color
shows the areas of the panel which are susceptible to buckling with high stresses.

Similarly, from the figure 4.9 shows that, when the compressive load reaches a maximum
of 29058N, the panel gets buckled and the maximum axial displacement of 1mm is obtained
from FEA analysis. From the above figure 4.9, the region with red color shows the areas of the
panel which are susceptible to buckling with high stresses.
Table 3.2 Critical buckling loads for different orientations
Orientations Critical Buckling load in N
1 29997
2 30112
3 29058
In the table 4.2, the critical buckling loads are computed by numerical methods for
different orientations. It is found that orientation 2 is said to withstand maximum compressive
load of 30112 N when compared to other orientations, which are comparatively lower to
orientation 2.

CHAPTER 5
5. Conclusion
An analysis of the buckling of CFRP Sandwich panels has been done in this study. A
rectangular sandwich laminate of the orientations has been chosen for the analysis. It consists of
8 layers of CFRP; 4 at the top and in the bottom with a layer of ROHECELL foam in between
them. Experiments were conducted for the boundary conditions of top and bottom sides clamped.
The experimented setup was so fabricated to facilitate the above boundary conditions. The
buckling behavior of these sandwich panels with different orientations was achieved.
The CFRP panels could withstand a very high load ranging from 2.7 to 3 tons which can be used
in the aircraft wing structure.

References
1. R.M JONES, Mechanics of Composite Materials, 2nd
edition, McGraw Hill 1999.
2. T.H.G MEGSON, Aircraft structures for engineering students, 3rd
edition, ISBN 0 340
70588 4.
3. AUTHAR K. KAW, 2nd
edition Published in 2006 by CRC Press Taylor & Francis
Group.
4. VINSON, JACK R . The Behavior of Sandwich Structures of Isotropic and Composite
Materials , published by Taylor & Francis Routledge , in the year 1999.
5. HOWARD G ALLEN, Analysis and design of structural sandwich panels ,© 1st
Edition,
1969 PERGAMON PRESS.
6. Mohammad Mahdi Kheirikhah and Mohammad Reza Khalili, Wrinkling Analysis of
Rectangular Soft-Core Composite Sandwich Plates .A. Öchsner et al. (eds.), Mechanics
and Properties of Composed Materials and Structures, Advanced Structured Materials 31,
DOI: 10.1007/978-3-642-31497-1_2, _ Springer-Verlag Berlin Heidelberg 2012.
7. Kicki ,Detartment of Aeronautics structures , Royal Institute of Techonology ,
Manufacturing And Applications of Structural Sandwich Components,Vol 28,1997.
8. Prof. Chiara BISAGNI, Buckling analyses of composite laminated panels with
delamination, Tesi di Laurea di: David ALBIOL Matr. 706811..
9. Li Yang1, Ola Harrysson2, Harvey West2, Denis Cormier3, A Comparison of Bending
Properties for Cellular Core Sandwich Panels, 1Department of Industrial Engineering,
University of Louisville, Louisville, USA; 2Department of Industrial & Systems
Engineering, North Carolina State University, Raleigh, USA; 3Department of Industrial
& Systems Engineering, Rochester Institute of Technology, Rochester, USA. Received
May 15th, 2013; revised June 21st, 2013; accepted July 2nd, 2013.
10. Elena-Felicia Beznea and Ionel Chirica University Dunarea de Jos of Galati Romania,
Buckling and Post-buckling Analysis of Composite Plates.
11. Finite Element Modelling of Delamination Buckling of Composite Panel Using ANSYS,
S.Rajendran and D.Q.Song, Materials Technology Application Centre Singapore
Productivity and Standards Board Science Park Drive Singapore 118221.

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