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IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 03 Special Issue: 03 | May-2014 | NCRIET-2014, Available @ http://www.ijret.org 638
A SURVEY ON FEM MODELLING FOR COMPOSITES
Subhash S1
, A.N. Hari Rao2
1
PhD Student, Department of Mechanical Engineering S J C E, Mysore, Karnataka, India
2
Professor, Department of Mechanical Engineering S J C E, Mysore, Karnataka, India
Abstract
FEM modelling methods are increasingly used to simulate and predict the behavior in design, service condition and subsequent
damage of composite materials. This paper is intended to capture the recent advancements in the area of modeling and simulation in
composite materials. The work provides an extremely useful insight into how modern computational methods can be used to predict
damage inflicted upon composite components during events encountered during service. The rapid growth in the usage of composite
materials has made it necessary to summarize the progress made in the modeling and simulation fields and thus determine future
perspectives.
Keywords: Composites, FEM, Modelling
-----------------------------------------------------------------------***-----------------------------------------------------------------------
1. INTRODUCTION
Composite materials are multi-phase materials comprising a
matrix reinforced with one or more types of fibers and
particles. Their properties are defined by the properties of
constituents, reinforcement distribution, and characteristics of
the reinforcement-matrix interface. Recent times it has been
observed that many composites are developed and in use in
various areas like Aircraft, Automotive, civil infrastructure,
Electrical and Marine fields. Figure 1 presents an overview of
usage of composite materials in civilian aircraft structures for
several major aircraft models [1].
Fig -1: Usage of composite materials aircraft industry.
After the initial surge in the applications of composites in this
sector in 1980’s, the field saturated in 1990. In recent years, a
steep increase in the usage of composites in this sector is
observed as the Boeing Dreamliner and Airbus 380 and 350
heavily incorporate composites in their structure. Research
and development in a diverse range of fields have contributed
to this recent steep increase in the usage of composites.
Understanding of fatigue failure, long term environmental
damage, combined effects of temperature and mechanical
loads, and effect of processing parameters on the quality of the
fabricated components are among the factors that have helped
composites. In addition, availability of predictive models and
improved simulation methods has helped in designing
composites as per the requirements of the applications.
The complexity in modeling the behavior of composite
materials makes it challenging to develop approaches that can
lead to “Materials by Design”. In addition, a number of
advanced composites have hierarchical microstructures that
span from nano to macro-scale, which require considerable
advancement of the present modeling and simulation methods.
An example is shown in Figure 2,
Fig-2 An example of multiscale composite material that has
features spanning from a few nanometers to several meters
Where carbon nanofiber toughened resin is filled with glass
hollow particles to make a syntactic foam that is used as the
core material in sandwich structures. The skins are made of
glass fibers. The scale bar included in this figure shows the
spread in the dimensions of various materials. Extensive use
IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 03 Special Issue: 03 | May-2014 | NCRIET-2014, Available @ http://www.ijret.org 639
of carbon nanotubes, carbon nanofibers, and nanoclay requires
development of nanomechanics and multiscale modeling
techniques.
These challenges are not unique to polymer matrix
composites. Metal matrix composites are also striving for
similar advancements because their structures may contain
grains, precipitates, interfacial phases, and reinforcements
across various length scales. Recent developments in
simulation methods have been very useful in studying
composite materials. Finite element analysis (FEA) methods
have been used for the past several decades. Recently,
techniques have been developed to incorporate microstructural
details in solid models that are used for FEA.
Utility of FEA at the nanoscale is debatable because of
increased contribution of molecular level interactions.
Methods that can work across length scales, computationally
efficient algorithms, and availability of powerful computer
hardware are key components in the future development in the
area of simulation methods. Experimental studies on
composite materials under extreme environments, such as high
speed automobile crashes, bomb blasts, radiation, and long
term environmental damage can be very expensive and
technically challenging. Such fields can especially benefit
from the development in modeling and simulation methods.
2. MODELLING APPROACH
2.1 Basics
The basic design characteristics of modern aircraft are the use
of complex software packages, in both design and service.
Most of these software’s are based on the Finite Element
Method (FEM). With the help of these programs, it is possible
to determine the accurate number of measurable places on the
structure, with increasing stress values. This enables
optimization of necessary measure equipment, which is
integrated on aircraft and directly contributes to shorten the
time of testing and project price reduction. The same kind of
procedure provides an opportunity for tracking defects in
structures during their service life within maintenance
procedures. Structural analysis is the process by which the
relevant data for the structure are obtained. These data can be
the following: stresses, deformations, displacements,
oscillations, etc [7]. It can be said for structural analysis that it
presents an integral and important part of the design.
Methods for structural analysis are divided into: analytical,
numerical and experimental. In modern design a wide range of
software packages are used, such as CATIA, PRO/Engineer,
Solid Works, Inventor, and others that enable fast work on
different projects.
Finite Element Method (FEM) is a numerical method of
structural analysis [8]. The basic idea of this method is a
physical discretization of a continuum. This implies a dividing
accounted domain (some structures) on the finite number of
small dimensions and simple shapes, which represent the basis
for all considerations. This makes a mesh of so-called “'finite
elements”'. Over discretization of a continuum, one type of
finite elements or combination of several types may be used.
The finite elements are connected by common nodes, so that
they make the original structure. Mesh generation is the
division of a certain area on nodes and finite elements.
Commercial software packages have a built automatic division
of the areas for the purpose of obtaining one faster as well as
qualitative solutions. This is of big importance in large or very
complex engineering tasks [10].
2.2 Approach
The main task of stress analysis on composite structure
consists of three parts [2]:
• Finite element modeling
• Finite element analysis
• Computer aided detail stress analysis
The FEM is used to find out: stresses and deformations in the
complex and unusually shaped components; conditions of
fluid flow around buildings; heat transfer through gases and in
other applications. A complete model takes into account
geometry components, used materials, load conditions,
boundary conditions and other significant factors. Appropriate
use of FEM permits that component is tested before it is made.
Consecutive iterations of that part would be modified, in order
to attain the minimum weight with supply of an adequate
strength. To view the basic equations in the FEM, various
methods are used [9]. Commercially available FEA software is
as below (Miracle & Donaldson, 2001)
Table 1: Commercially available FEA software (Miracle &
Donaldson, 2001)
IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 03 Special Issue: 03 | May-2014 | NCRIET-2014, Available @ http://www.ijret.org 640
It can be said that the FEM solution process consists of the
following steps:
• Divide structure into piece elements with nodes
(discretization/meshing);
• Connect (assemble) the elements at the nodes to form an
approximate system of equations for the whole structure
(forming element matrices);
• Solve the system of equations involving unknown quantities
at the nodes;
• Calculate desired quantities (e.g., strains and stresses) at
selected elements.
The FEM is used in deformable bodies’ mechanics to solve
various static and dynamic problems. There are linear and
nonlinear FEM analyses. Linear FEM analysis is based on a
few basic assumptions: theory of small deformation, material
is linear elastic. Nonlinear analysis takes into account the
material nonlinearity and geometrical nonlinearity (large
deformations) of a considered system.
3. RESEARCH ON COMPOSITE MODELLING
Considerable progress has been made in recent times in
modeling and simulation of composite materials. The present
thematic topic is an attempt to capture the present state of the
art in these areas through research and review articles related
to a wide variety of composite materials, loading conditions,
and problem solution methods. The topic is sponsored by the
Composite Materials Committee of Structural Materials
Division of TMS [1]. A brief overview papers that appear
under this topic is presented below
3.1 Molecular Dynamic (MD) Methods
Variety of problem sets including mechanical and thermal
analysis in polymer and metal based systems. The MD
simulation methods have enabled both quantitative and visual
understanding in the behavior of individual atoms and
interatomic bonds present in the system.
3.2 Composite Dynamic Behavior under High Strain
Rate Deformation.
Solve a complex problem of fluid-structure interaction when
shock waves interact with a composite plate and to
microstructure effects on the properties of composites.
3.3 Multiscale Models
Multiscale models are very useful in constructing approaches
that can predict the materials properties across length scales.
Such methodologies are gaining more importance due to the
recent surge in the use of composites in structural applications.
3.4 Mechanics Based Modeling Approaches
These models are theoretically grounded and can provide
predictions of mechanical, thermal, and electrical properties of
composite materials. A review paper presents available
theoretical models that can predict thermal conductivity of
hollow particle filled polymer matrix composites called
syntactic foams.
3.5 Finite Element Analysis (FEA)
Finite element analysis (FEA) is a widely used simulation
method. The capabilities of this method in understanding
structural, thermal, magnetic, and other properties ex: wear of
composites have been well utilized in the published literature.
4. CONCLUSIONS
In current scenario there is a tendency to develop software
packages, which could predict conditions on the constructions
& structural health monitoring. These programs for structural
analysis are mainly based on the finite element method
(FEM). With these program packages on a formed model
realistic conditions that construction was subjected to during
service life can be simulated. Rapid growth of Modeling and
simulation in composite materials field has been encouraging
and is expected to continue in the near future, particularly with
regards to the microstructure based simulation technique and
multiscale modeling methods to study structural health
monitoring of composites.
One composite material is chosen and appropriate models are
formed, which are composed of only a single layer or
Multilayer or Hybrid composites. Simulation testing of the
models on tension, shear, pressure and other parameters like
wear etc are done. By using appropriate program, stress
distributions on the model were achieved.
The results of simulations offer the possibility of tracking and
analysis of critical positions in construction during the design
process, but also during its exploitation. In order to determine
material properties Ex: stresses, wears in the composite
materials, software packages (any of the suitable software
listed in table 1) are used. On the basis of the results from the
tests of these programs, potentially critical locations in model
structures are determined, due to the existence of maximum
stress/wear, and accordingly possible occurrence of damage
and fracture. Obtained data can be used for further testing and
analysis of damage present in these locations on the real
constructions. With a particular probability, the model behaves
almost the same as the actual construction. However, these
facts have to be proved and confirmed by experiments. In that
way, we can get accurate insight into the structure state
because of damage, with the maximum optimization in terms
of time and cost of testing the same.
IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 03 Special Issue: 03 | May-2014 | NCRIET-2014, Available @ http://www.ijret.org 641
It has been found after analyzing various papers on simulation
modeling of composites that very few works has been done
correlation between the computational model and the
experimental analysis of composite materials. Similarly
correlation can also be extended to many software packages
available in the market and can be compared with
experimental results.
REFERENCES
[1]. Nikhil Gupta Modeling and simulation in composite
materials – integration from nanostructure to component level
Design JOM, 2013, Vol. 65, No. 2, pp. Composite Materials
and Mechanics Laboratory, Polytechnic Institute of New York
University, Brooklyn, NY 11201 USA
[2]. Dragan D. Kreculj Faculty of Mechanical Engineering,
Kraljice Marije 16, 11120 Belgrade 35, Serbia BelgradeStress
Analysis in an Unidirectional Carbon/Epoxy Composite
Material 128 ▪ VOL. 36, No 3, 2008.
[3]. Baker, A., Dutton, S. and Kelly, D.: Composite Materials
for Aircraft Structures, American Institute of Aeronautics and
Astronautics, Reston,2004.
[4]. Henkhaus, K.: Overview of research on composite
material impact behavior, in: Electronic Proceedings of the
16th ASCE Engineering Mechanics Conference, 16-
18.07.2003, Seattle, Paper 86.
[5]. Rasuo, B.: Aircraft Production Technology, Faculty of
mechanical engineering, Belgrade, 1995, (in Serbian).
[6]. Zhao, H: Stress Analysis of Tapered Sandwich Panels
with Isotropic or Laminated Composite Facings, MSc thesis,
The Graduate School, University of Maine, Maine, 2002.
[7]. Niu, M.C.Y.: Airframe Structural Design, Conmilit Press
Ltd, Hong Kong, 1988.
[8] Jovanovic, M. and Filipovic, Z.: Applying of Software
Packages CATIA in Prediction of Possible Damages to Real
Aircraft Construction, Flight test center, Belgrade, 2005 (in
Serbian).
[9] Bathe, K.-J.: Finite Element Procedures in Engineering
Analysis, Prentice-Hall, Englewood Cliffs, 1982.
[10]. Montemurro, M.P., Houde, M.J.L. and Hansen, J.S.:
Finite Element Analysis of the Impact Response of Composite
Structures, Institute for 132 ▪ VOL. 36, No 3, 2008 FME
Transactions aerospace studies, University of Toronto,
Toronto, 1993.
[11]. Ritter, W.J.: Application of Energy Methods to Modeling
Failures in Composite Materials and Structures, MSc thesis,
Montana State University,Montana, 2004.
[12]. Dash, P.K. and Chatterjee, A.K.: Effects of environment
on fracture toughness of woven carbon/epoxy composite,
Journal of the Institution of Engineers (India), Vol. 85, No. 5,
pp. 1-9, 2004
[13]. Rohwer, K., Friedrichs, S. and Wehmeyer, C.: Analyzing
laminated structures from fiberreinforced composite material –
an assessment, Technische Mechanik, Vol. 25, No. 1, pp. 59-
79, 2005.
[14]. Smojver, I.: Mechanics of composite materials, Faculty
of Mechanical and Naval Engineering, Zagreb, 2007, (in
Croatian).
[15]. Jones, R.M.: Mechanics of Composite Material, Taylor
& Francis, Philadelphia, 1999.
[16]. Ming, C., Wu, T.-S., Lee, C.-H. and Lee, N.-H.:
Integrating MSC Software and CADSA Program for the
Aircraft Detail Stress Analysis, Aerospace
[17]. Emery, T.R.: Identification of Damage in Composite
Materials using Thermoelastic Stress Analysis, PhD thesis,
School of Engineering Sciences, University of Southampton,
Southampton, 2007

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A survey on fem modelling for composites

  • 1. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 __________________________________________________________________________________________ Volume: 03 Special Issue: 03 | May-2014 | NCRIET-2014, Available @ http://www.ijret.org 638 A SURVEY ON FEM MODELLING FOR COMPOSITES Subhash S1 , A.N. Hari Rao2 1 PhD Student, Department of Mechanical Engineering S J C E, Mysore, Karnataka, India 2 Professor, Department of Mechanical Engineering S J C E, Mysore, Karnataka, India Abstract FEM modelling methods are increasingly used to simulate and predict the behavior in design, service condition and subsequent damage of composite materials. This paper is intended to capture the recent advancements in the area of modeling and simulation in composite materials. The work provides an extremely useful insight into how modern computational methods can be used to predict damage inflicted upon composite components during events encountered during service. The rapid growth in the usage of composite materials has made it necessary to summarize the progress made in the modeling and simulation fields and thus determine future perspectives. Keywords: Composites, FEM, Modelling -----------------------------------------------------------------------***----------------------------------------------------------------------- 1. INTRODUCTION Composite materials are multi-phase materials comprising a matrix reinforced with one or more types of fibers and particles. Their properties are defined by the properties of constituents, reinforcement distribution, and characteristics of the reinforcement-matrix interface. Recent times it has been observed that many composites are developed and in use in various areas like Aircraft, Automotive, civil infrastructure, Electrical and Marine fields. Figure 1 presents an overview of usage of composite materials in civilian aircraft structures for several major aircraft models [1]. Fig -1: Usage of composite materials aircraft industry. After the initial surge in the applications of composites in this sector in 1980’s, the field saturated in 1990. In recent years, a steep increase in the usage of composites in this sector is observed as the Boeing Dreamliner and Airbus 380 and 350 heavily incorporate composites in their structure. Research and development in a diverse range of fields have contributed to this recent steep increase in the usage of composites. Understanding of fatigue failure, long term environmental damage, combined effects of temperature and mechanical loads, and effect of processing parameters on the quality of the fabricated components are among the factors that have helped composites. In addition, availability of predictive models and improved simulation methods has helped in designing composites as per the requirements of the applications. The complexity in modeling the behavior of composite materials makes it challenging to develop approaches that can lead to “Materials by Design”. In addition, a number of advanced composites have hierarchical microstructures that span from nano to macro-scale, which require considerable advancement of the present modeling and simulation methods. An example is shown in Figure 2, Fig-2 An example of multiscale composite material that has features spanning from a few nanometers to several meters Where carbon nanofiber toughened resin is filled with glass hollow particles to make a syntactic foam that is used as the core material in sandwich structures. The skins are made of glass fibers. The scale bar included in this figure shows the spread in the dimensions of various materials. Extensive use
  • 2. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 __________________________________________________________________________________________ Volume: 03 Special Issue: 03 | May-2014 | NCRIET-2014, Available @ http://www.ijret.org 639 of carbon nanotubes, carbon nanofibers, and nanoclay requires development of nanomechanics and multiscale modeling techniques. These challenges are not unique to polymer matrix composites. Metal matrix composites are also striving for similar advancements because their structures may contain grains, precipitates, interfacial phases, and reinforcements across various length scales. Recent developments in simulation methods have been very useful in studying composite materials. Finite element analysis (FEA) methods have been used for the past several decades. Recently, techniques have been developed to incorporate microstructural details in solid models that are used for FEA. Utility of FEA at the nanoscale is debatable because of increased contribution of molecular level interactions. Methods that can work across length scales, computationally efficient algorithms, and availability of powerful computer hardware are key components in the future development in the area of simulation methods. Experimental studies on composite materials under extreme environments, such as high speed automobile crashes, bomb blasts, radiation, and long term environmental damage can be very expensive and technically challenging. Such fields can especially benefit from the development in modeling and simulation methods. 2. MODELLING APPROACH 2.1 Basics The basic design characteristics of modern aircraft are the use of complex software packages, in both design and service. Most of these software’s are based on the Finite Element Method (FEM). With the help of these programs, it is possible to determine the accurate number of measurable places on the structure, with increasing stress values. This enables optimization of necessary measure equipment, which is integrated on aircraft and directly contributes to shorten the time of testing and project price reduction. The same kind of procedure provides an opportunity for tracking defects in structures during their service life within maintenance procedures. Structural analysis is the process by which the relevant data for the structure are obtained. These data can be the following: stresses, deformations, displacements, oscillations, etc [7]. It can be said for structural analysis that it presents an integral and important part of the design. Methods for structural analysis are divided into: analytical, numerical and experimental. In modern design a wide range of software packages are used, such as CATIA, PRO/Engineer, Solid Works, Inventor, and others that enable fast work on different projects. Finite Element Method (FEM) is a numerical method of structural analysis [8]. The basic idea of this method is a physical discretization of a continuum. This implies a dividing accounted domain (some structures) on the finite number of small dimensions and simple shapes, which represent the basis for all considerations. This makes a mesh of so-called “'finite elements”'. Over discretization of a continuum, one type of finite elements or combination of several types may be used. The finite elements are connected by common nodes, so that they make the original structure. Mesh generation is the division of a certain area on nodes and finite elements. Commercial software packages have a built automatic division of the areas for the purpose of obtaining one faster as well as qualitative solutions. This is of big importance in large or very complex engineering tasks [10]. 2.2 Approach The main task of stress analysis on composite structure consists of three parts [2]: • Finite element modeling • Finite element analysis • Computer aided detail stress analysis The FEM is used to find out: stresses and deformations in the complex and unusually shaped components; conditions of fluid flow around buildings; heat transfer through gases and in other applications. A complete model takes into account geometry components, used materials, load conditions, boundary conditions and other significant factors. Appropriate use of FEM permits that component is tested before it is made. Consecutive iterations of that part would be modified, in order to attain the minimum weight with supply of an adequate strength. To view the basic equations in the FEM, various methods are used [9]. Commercially available FEA software is as below (Miracle & Donaldson, 2001) Table 1: Commercially available FEA software (Miracle & Donaldson, 2001)
  • 3. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 __________________________________________________________________________________________ Volume: 03 Special Issue: 03 | May-2014 | NCRIET-2014, Available @ http://www.ijret.org 640 It can be said that the FEM solution process consists of the following steps: • Divide structure into piece elements with nodes (discretization/meshing); • Connect (assemble) the elements at the nodes to form an approximate system of equations for the whole structure (forming element matrices); • Solve the system of equations involving unknown quantities at the nodes; • Calculate desired quantities (e.g., strains and stresses) at selected elements. The FEM is used in deformable bodies’ mechanics to solve various static and dynamic problems. There are linear and nonlinear FEM analyses. Linear FEM analysis is based on a few basic assumptions: theory of small deformation, material is linear elastic. Nonlinear analysis takes into account the material nonlinearity and geometrical nonlinearity (large deformations) of a considered system. 3. RESEARCH ON COMPOSITE MODELLING Considerable progress has been made in recent times in modeling and simulation of composite materials. The present thematic topic is an attempt to capture the present state of the art in these areas through research and review articles related to a wide variety of composite materials, loading conditions, and problem solution methods. The topic is sponsored by the Composite Materials Committee of Structural Materials Division of TMS [1]. A brief overview papers that appear under this topic is presented below 3.1 Molecular Dynamic (MD) Methods Variety of problem sets including mechanical and thermal analysis in polymer and metal based systems. The MD simulation methods have enabled both quantitative and visual understanding in the behavior of individual atoms and interatomic bonds present in the system. 3.2 Composite Dynamic Behavior under High Strain Rate Deformation. Solve a complex problem of fluid-structure interaction when shock waves interact with a composite plate and to microstructure effects on the properties of composites. 3.3 Multiscale Models Multiscale models are very useful in constructing approaches that can predict the materials properties across length scales. Such methodologies are gaining more importance due to the recent surge in the use of composites in structural applications. 3.4 Mechanics Based Modeling Approaches These models are theoretically grounded and can provide predictions of mechanical, thermal, and electrical properties of composite materials. A review paper presents available theoretical models that can predict thermal conductivity of hollow particle filled polymer matrix composites called syntactic foams. 3.5 Finite Element Analysis (FEA) Finite element analysis (FEA) is a widely used simulation method. The capabilities of this method in understanding structural, thermal, magnetic, and other properties ex: wear of composites have been well utilized in the published literature. 4. CONCLUSIONS In current scenario there is a tendency to develop software packages, which could predict conditions on the constructions & structural health monitoring. These programs for structural analysis are mainly based on the finite element method (FEM). With these program packages on a formed model realistic conditions that construction was subjected to during service life can be simulated. Rapid growth of Modeling and simulation in composite materials field has been encouraging and is expected to continue in the near future, particularly with regards to the microstructure based simulation technique and multiscale modeling methods to study structural health monitoring of composites. One composite material is chosen and appropriate models are formed, which are composed of only a single layer or Multilayer or Hybrid composites. Simulation testing of the models on tension, shear, pressure and other parameters like wear etc are done. By using appropriate program, stress distributions on the model were achieved. The results of simulations offer the possibility of tracking and analysis of critical positions in construction during the design process, but also during its exploitation. In order to determine material properties Ex: stresses, wears in the composite materials, software packages (any of the suitable software listed in table 1) are used. On the basis of the results from the tests of these programs, potentially critical locations in model structures are determined, due to the existence of maximum stress/wear, and accordingly possible occurrence of damage and fracture. Obtained data can be used for further testing and analysis of damage present in these locations on the real constructions. With a particular probability, the model behaves almost the same as the actual construction. However, these facts have to be proved and confirmed by experiments. In that way, we can get accurate insight into the structure state because of damage, with the maximum optimization in terms of time and cost of testing the same.
  • 4. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 __________________________________________________________________________________________ Volume: 03 Special Issue: 03 | May-2014 | NCRIET-2014, Available @ http://www.ijret.org 641 It has been found after analyzing various papers on simulation modeling of composites that very few works has been done correlation between the computational model and the experimental analysis of composite materials. Similarly correlation can also be extended to many software packages available in the market and can be compared with experimental results. REFERENCES [1]. Nikhil Gupta Modeling and simulation in composite materials – integration from nanostructure to component level Design JOM, 2013, Vol. 65, No. 2, pp. Composite Materials and Mechanics Laboratory, Polytechnic Institute of New York University, Brooklyn, NY 11201 USA [2]. Dragan D. Kreculj Faculty of Mechanical Engineering, Kraljice Marije 16, 11120 Belgrade 35, Serbia BelgradeStress Analysis in an Unidirectional Carbon/Epoxy Composite Material 128 ▪ VOL. 36, No 3, 2008. [3]. Baker, A., Dutton, S. and Kelly, D.: Composite Materials for Aircraft Structures, American Institute of Aeronautics and Astronautics, Reston,2004. [4]. Henkhaus, K.: Overview of research on composite material impact behavior, in: Electronic Proceedings of the 16th ASCE Engineering Mechanics Conference, 16- 18.07.2003, Seattle, Paper 86. [5]. Rasuo, B.: Aircraft Production Technology, Faculty of mechanical engineering, Belgrade, 1995, (in Serbian). [6]. Zhao, H: Stress Analysis of Tapered Sandwich Panels with Isotropic or Laminated Composite Facings, MSc thesis, The Graduate School, University of Maine, Maine, 2002. [7]. Niu, M.C.Y.: Airframe Structural Design, Conmilit Press Ltd, Hong Kong, 1988. [8] Jovanovic, M. and Filipovic, Z.: Applying of Software Packages CATIA in Prediction of Possible Damages to Real Aircraft Construction, Flight test center, Belgrade, 2005 (in Serbian). [9] Bathe, K.-J.: Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, 1982. [10]. Montemurro, M.P., Houde, M.J.L. and Hansen, J.S.: Finite Element Analysis of the Impact Response of Composite Structures, Institute for 132 ▪ VOL. 36, No 3, 2008 FME Transactions aerospace studies, University of Toronto, Toronto, 1993. [11]. Ritter, W.J.: Application of Energy Methods to Modeling Failures in Composite Materials and Structures, MSc thesis, Montana State University,Montana, 2004. [12]. Dash, P.K. and Chatterjee, A.K.: Effects of environment on fracture toughness of woven carbon/epoxy composite, Journal of the Institution of Engineers (India), Vol. 85, No. 5, pp. 1-9, 2004 [13]. Rohwer, K., Friedrichs, S. and Wehmeyer, C.: Analyzing laminated structures from fiberreinforced composite material – an assessment, Technische Mechanik, Vol. 25, No. 1, pp. 59- 79, 2005. [14]. Smojver, I.: Mechanics of composite materials, Faculty of Mechanical and Naval Engineering, Zagreb, 2007, (in Croatian). [15]. Jones, R.M.: Mechanics of Composite Material, Taylor & Francis, Philadelphia, 1999. [16]. Ming, C., Wu, T.-S., Lee, C.-H. and Lee, N.-H.: Integrating MSC Software and CADSA Program for the Aircraft Detail Stress Analysis, Aerospace [17]. Emery, T.R.: Identification of Damage in Composite Materials using Thermoelastic Stress Analysis, PhD thesis, School of Engineering Sciences, University of Southampton, Southampton, 2007