*Corresponding author:Prasanna Kumar T J, ISSN: 0976-3031
Research Article
COMPUTATIONAL INVESTIGATION ON STATIC AND DYNAMIC ANALYSIS OF
COMPOSITE LAMINATE USING FINITE ELEMENT TECHNIQUE
Prasanna Kumar T J, K Venkata Ra, Mastan Rao P and Venkatesh B
Department of Mechanical Engineering PVP Siddhartha Institute of Technology Vijayawada, India
DOI: http://dx.doi.org/10.24327/ijrsr.2019.1009.4010ARTICLE INFO ABSTRACT
Composite laminate are assemblies of layers of fibrous composite materials which can be joined to provide required engineering properties, including in-plane stiffness, bending stiffness, strength and coefficient of thermal expansion. The individual layers consist of high-modulus, high-strength fibers in a polymeric, metallic, or ceramic matrix material. Typical fibres used include graphite, glass, boron, and silicon carbide, and some matrix materials are epoxies, polyimide, aluminium, titanium and alumina. Layers of different materials are used, resulting in a laminate. The individual layers generally are transversely isotropic (with isotropic properties in the transverse plane) with the laminate then exhibiting anisotropic (with variable direction of principal properties), orthotropic or quasi-isotropic properties. Quasi-isotropic laminates exhibit isotropic (that is, independent of direction) in plane response but are not restricted to isotropic out-of-plane (bending) response. Depending upon the stacking sequence of the individual layers, the laminate may exhibit coupling between in plane and out-of-plane response. An example of bending-stretching coupling is the presence of curvature developing as a result of in plane loading.
The strength and lightness of composites has made them particularly attractive for transportation. It have made airplanes lighter and more economical and more affordable and solved problems such as cracking and metal fatigue. High-temperature ceramic-matrix composites are also making possible cleaner-burning, more fuel-efficient engines for plane. By using these composites the aircraft is designed to withstand the severe loads associated with operations from informal landing strips like deserts and fields and it benefits from the superior fatigue resistance of carbon composites.
The present problem is used to identify best composite static sequence among the considered layup of composite plate subjected to static and dynamic analysis.
Stages in the problem modeling includes:
1. Identify the composite plate dimensions and materials.
2. Study of effect of fibre orientation number of layers on composite plate subjected to airplane.
3. Stimulation of composite plate by considering different boundary conditions. 4. Finally obtaining solution using ANSYS.
In addition to providing static and dynamic loads to an aircraft so that we observe that how stresses and strains are affected the aircraft and also its behaviour. So that aircraft must be affected as issues of damage and safe-life, life extension and extensive fatigue. Now this can be done in ansys with composite materials which are used in structure.
INTRODUCTION
Composite laminate
A composite materials a material 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 for examples include materials which are stronger, lighter, or less expensive when compared to traditional materials.
In materials science, composite laminates are assemblies of layers of fibrous composite materials which can be joined to provide required engineering properties, including in-plane stiffness, bending stiffness, strength and coefficient of thermal expansion. The individual layers consist of high-modulus, high-strength fibers in a polymeric, metallic, or ceramic matrix
International Journal of
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Research
International Journal of Recent Scientific Research
Vol. 10, Issue, 09(G), pp. 34978-34985, September, 2019
Copyright © Prasanna Kumar T J, K Venkata Rao, Mastan Rao P and Venkatesh B, 2019, this is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited.
DOI: 10.24327/IJRSR CODEN: IJRSFP (USA)
Article History: Received 15th June, 2019
Received in revised form 7th July, 2019 Accepted 13th August, 2019
Published online 28th September, 2019
Key Words:
International Journal of Recent Scientific Research Vol. 10, Issue, 09(G), pp. 34978-34985, September, 2019
material. Typical fibers used include graphite, glass, boron and silicon carbide and matrix materials are epoxies, polyamides, aluminium, titanium, and alumina.
Layers of different materials are used, resulting in a hybrid laminate. The individual layers generally are orthotropic with the laminate then exhibiting anisotropic, orthotropic, or quasi-isotropic properties. Quasi-quasi-isotropic laminates exhibit quasi-isotropic (that is, independent of direction) in plane response but are not restricted to isotropic out-of-plane (bending) response. Depending upon the stacking sequence of the individual layers, the laminate may exhibit coupling between in plane and out-of-plane response. An example of bending-stretching coupling is the presence of curvature developing as a result of in plane loading.
Properties of composite materials
High strength to weight ratio.
Light weights.
Fire resistance.
Chemical & weathering resistance.
Low thermal conductivity. Advantages
Weight reduction - savings in the range 20%-50% are often quoted.
It is easy to assemble complex components using automated layup machinery a rotational molding processes.
It is easy to assemble complex components using automated layup machinery and rotational molding processes.
Mechanical properties can be tailored by 'lay-up' design, with tapering thicknesses of reinforcing cloth and cloth orientation.
Thermal stability of composites means they don't expand/contract excessively with change in temperature.
Applications
Applications of composites on aircraft include:
Fairings
Flight control surface
Landing gear doors
Leading and trailing edge panels on the wing and stabilizer
Interior components
Floor beams and floor boards
Vertical and horizontal stabilizer primary structure on large aircraft
Primary wing and fuselage structure on new generation large aircraft
Turbine engine fan blades
Propellers Major Components of a Laminate
LITERATURESUEVEY
The composite materials are widely used in the aviation, space industries and mechanical engineering because of their good command of mechanical property. The laminated composite plate is made up of multilayer lamination. Their inter-laminar
stresses can significantly con-tribute to delamination even when they are much lower than the failure strength of the classical lamination theory. They may make the potential of laminated composite plate cannot be worked out for its carrying capacity deteriorated because of the delamination. In the vicinity of the free edge, the inter-laminar stresses are varied fast, which is the main reason of delamination. And the delamination of the laminated composite plates is the most common destruction form of laminated composite plates. Therefore, the research of inter-laminar stresses is of great significance to practical applications. Many researchers have done a lot of work about it. The stresses in the vicinity of free edge are expressed as a two-dimensional state by the classical lamination theory.
The first shear theory is combined with the Layer wise theory to analyze the inter-laminar stresses of the laminated composite plates in this paper. The first shear theory assumed the plate as an equi-single layer as to build the displacement field whose component is continuity. The Layer wise theory builds the displacement field by dispersing the plate to many numerical layers. In this paper, the inter-laminar stresses are analyzed by superimposed the first shear theory on the Layer wise theory. Then, the displacement field is simplified for the symmetric ply composite plate which subjected to a uniform axial strain. The finite element equation is derived by the principle of virtual work. Then, the linear element is used to solve the problem. Of course, it reduced the amount of calculation while the accuracy is ensured. At last, the results of the inter-laminar stresses are given for different ply conditions of laminated composite plates. The strength and stiffness of a composite build-up depends on the orientation sequence of the plies. The practical range of strength and stiffness of carbon fibre extends from values as low as those provided by fiberglass to as high as those provided by titanium. This range of values is determined by the orientation of the plies to the applied load. Proper selection of ply orientation in advanced composite materials is necessary to provide a structurally efficient design. The part might require 0° plies to react to axial loads, ±45° plies to react to shear loads, and 90° plies to react to side loads. Because the strength design requirements are a function of the applied load direction, ply orientation and ply sequence have to be correct. It is critical during a repair to replace each damaged ply with a ply of the same material and ply orientation.
Finite Element Method
Introduction
the boundaries (or edges) of the region the value of the department variables (or their derivatives) are prescribed. Basic concept of Finite Element Method
The most distinctive feature of the finite element method that separate it from others is the given of a given domain into a set of simple sub domains, called ‘Finite Elements’. Any geometric shape that allow the computation of the solution or its approximation, or provides necessary relations among the values of solution at selected points called nodes of the sub domain, qualifies as a finite element. Other features of the method include, seeking continuous often polynomial approximations of the solution each element in terms of solution and balance of inter element forces. Exact method provides exact solution to the problem, but the limitation of this method is that all practical problems cannot be solved and even if they can be solved, they may have complex solution. Approximate Analytical Methods are alternative to the exact methods, in which certain functions are assumed to satisfy the geometric boundary conditions, but not necessary the governing equilibrium equations. These assumed functions, which similar, are then solved by any conventional available method. The solutions obtained from this methods have limited range of values of variables for which the approximate solution is nearer to the exact solution. Nodes of the sub domain, qualifies as a finite element. Other features of the method include, seeking continuous often polynomial approximation of the solution over each in terms of solution and balance of their element of inter element forces. Exact method provide exact solution to the problem, the limitation of this method is that all practical problems cannot be solved and even if they can be solved, they may have complex solution. Approximate Analytical Methods are alternative to the methods, in which certain function are assumed to satisfy the geometric boundary conditions, but not necessary the governing equilibrium equation. These assumed functions, in which are simpler are then solved by any conventional method available. The solutions obtained from these methods have limited range of values of variables for which the approximate solution is nearer to the exact solution. Finite difference method, the differential equations are approximated by finite difference equation. Thus the given governing equation is converted to a set of algebraic equation. These simultaneous equations can be solved by any simple method such as gauss Elimination, Gauss-Seidel iteration method, Crout’smethod etc. the method of finite difference yield fairly good results and are relatively easy to program. Hence, they are popular in solving heat transfer and fluid flow problems. However, it is not suitable for problems with awkward irregular geometry and suitable for problems of rapidly changing variable suchas stress concentration problems Finite Element approaches
These two difference Finite element approaches to analyse structures namely
1. Force method 2. Displacement method Force method
The number of forces (shear forces, axial forces & bending moment) is the basic unknown in the system of equations
Displacement method
The nodal displacement is the basic unknown in the system of equations. The fundamental concept of finite element method is that is a discrete model can approximate any continuous quantity such as temperature, pressure and displacement. These are many problems where analytical solutions are difficult or impossible to obtain. In such cases finite element method provides an approximate and a relatively easy solutions. Finite Element method becomes more powerful when combined rapid processing capabilities of computers.
The basic of finite element method is to discrete the entire structure into small element. Nodes or grids define each element and the nodes serve as a link between the two elements. Then the continuous quantity is approximated over each element by a polynomial equation. The gives a system of equations, in which is solved by using matrix techniques to get the values of the values of the desired quantities.
The basic equation for the static analysis is: [K] [Q] = [F] Where [K] = Structural stiffness matrix [F] = Loads Applied
[Q] = Nodal displacement vector
The global stiffness matrix is assembled from the element stiffness matrices.
Using these equations the modal displacement, the element stresses and strains can be determined.
Advantages of FEM
The advantages of finite element method are listed below: 1. Finite element method is applicable to any field
problem: heat transfer, stress analysis, magnetic and etc.
2. In finite element method there is no geometric restriction. The body or region analysed may have any shape.
3. Boundary conditions and loading are not restricted. For example, in a stress analysis any portion of the body may be supported, while distributed or concentrated forces may be applied to any other portion.
4. Material properties are not restricted to isotropy and may change from one element to another or even within an element.
5. Components that have different behaviour and different mathematical description can be combined together. Thus single finite element model might contain bar, bean, plate, cable and friction elements. 6. A finite element model closely resembles the actual
body or region to be analysed.
7. The approximation is easily improved by regarding the mesh so that more elements appear where field gradients are high and more resolution is required. Limitations of FEM
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analysis by FEA is prohibitive. Stress values may vary from fine mesh to average mesh.
Problem Statement and Methodology
Introduction
In the previous section, the relevant literature available has been reviewed and the scope for the present work has been identified in this section, the statements of the problem of present work and methods used for the solution for the problem has been explained selection of materials in designing the structural and/or mechanical components play an important role and is fixed based on the strength, stiffness, cost and other mechanical properties such as hardness ,toughness, wear resistance etc. Materials selected in view of the above requirements may not have internal damping capacity.
Problem statement
The objective of the present research problem is to study the static and dynamic response of laminate simply boundary conditions. Static and dynamic response of the laminate is studied by varying the thickness. The analysis is carried out for carbon-carbon, carbon polyimide, boron aluminium materials are used.
Methodology
The problem is analyzed using 3-dimensional finite element method and is modeled in ANSYS software.
Static and dynamic response of the laminate is studied by varying the parameters of the layers such as its thickness. Problem Modeling
The present analysis the following assumptions are made for the present analysis.
1. 1.The laminate is thin and wide (width is far greater than thickness)
2. A perfect interlaminar bond adjusts between the various laminas.
3. The strain distribution in the thickness direction is linear.
4. All laminas are microscopically homogeneous and behave in a linear elastic manner.
5. Fibers are perfectly aligned. 6. All loads are within elastic limit.
7. The plane cross section remains plane during and after loading.
Element type
Static analysis
For static analysis SOLID 185 ELEMENT is used and their features explained in the following.
SOLID185 is used for 3-Dimensional modelling of solid structures. It is defined by eight nodes having three degrees of freedom at each node are translations in the nodal x,y and z directions. The element has plasticity, stress stiffening, creep, large deflection and large strain capabilities. It also has mixed formulation capability for simulating deformations of nearly incompressible elastoplastic materials, and fully incompressible hyper elastic materials.SOLID185 is available in two forms are Homogeneous Structural Solid is called as “Solid 185
Homogenous Structural Solid Element Description”. Layered Structured Solid is called as “Solid 185 Homogenous Structural Solid Element Description”.
Element Description
SOLID185 Structural Solid is suitable for modeling general 3-D solid structures. It allows for prism and tetrahedral degenerations when used in irregular regions. Various element technologies such as B-bar, uniformly reduced integration and Element Reference Contains proprietary and confidential information of ANSYS.
Figure 1 1SOLID185 Homogenous structural solid geometry
The geometry and node locations for this element are shown in figure. The element is defined by eight nodes and the orthotropic material properties. The default element coordinate system is along global directions. You may define an element coordinate system using ANSYS which forms the basis for orthotropic material directions.
Element loads are described in nodes and element loads. Pressures may be input as surface loads on the element faces as shown by the circled numbers in figure. Positive pressures act into the element. Temperatures may be input as element body loads at the nodes.
Dynamic analysis
For dynamic analysis SHELL281 is used and their features are explained in the following
SHELL281 is suitable for analyzing thin to moderately-thick shell structures. The element has eight nodes with six degrees of freedom at each node: translations in the x, y, and z axes, and rotations about the x, y, and z-axes. (When using the membrane option, the element has translational degrees of freedom only.) SHELL281 is well-suited for linear, large rotation, and/or large strain nonlinear applications. Change in shell thickness is accounted for in nonlinear analyses. The element accounts for follower load stiffness effects of distributed pressures.
Figure 2 SHELL 281 geometry
The shell section commands allow for layered shell definition. Options are available for specifying the thickness, material, orientation, and number of integration points
thickness of the layers. Designate the number of integration points located through the thickness of each layer when using section input. When only one, the point is always located midway between the top and bottom surfaces.
If three or more points, two points are located on the top and bottom surfaces respectively and the remaining points are distributed at equal distances between the two points. The default number of integration points for each layer is three; however, when a single layer is defined and plasticity is present, the number of integration points is changed to a minimum of five during solution.
Geometry
The considered problem is modelled with the following geometry is 100*100*10 for both static and dynamic analysis.
Figure 3 Laminate geometry
Loading Conditions
On the laminate they are two loading they are: 1. Pressure loads
2. Displacement loads
The shell section commands allow for layered shell definition. Options are available for specifying the thickness, material, orientation, and number of integration points through the Designate the number of integration points located through the thickness of each layer when using section input. When only one, the point is always located midway between the top and bottom surfaces.
points, two points are located on the top and bottom surfaces respectively and the remaining points are distributed at equal distances between the two points. The default number of integration points for each layer is three; s defined and plasticity is present, the number of integration points is changed to a minimum of
The considered problem is modelled with the following geometry is 100*100*10 for both static and dynamic analysis.
On the laminate they are two loading they are:
Figure 4 Figure shows the loading condition under displacements
Figure 5 Fig shows the loading conditions under pressure
Material Properties
Carbon
We are using carbon-carbon and carbon plyimide in those the carbon is a fiber. Carbon fibers are very stiff and strong, 3 to 10 times stiffer than glass fibers. Carbon fibre is used for structural aircraft applications, such as
controls, and primary fuselage and wing structure. Advantages include its high strength and corrosion resistance. Disadvantages include lower conductivity than aluminium therefore, a lightning protection mesh or coating is
aircraft parts that are prone to lightning strikes. Another disadvantage of carbon fibre is its high cost. Carbon fibre is gray or black in colour and is available as dry fabric and prepreg material. Carbon fibers have a high potential for c galvanic corrosion when used with metallic fasteners and structures.
Boron
Another material which is using in our analysis is boron aluminium. Boron fibers are very stiff and have a high tensile and compressive strength. The fibers have a relative
diameter and do not flex well; therefore, they are available only as a prepreg tape product. An epoxy matrix is often used with the boron fibre. Boron fibers are used to repair cracked aluminium aircraft skins, because the thermal expansion of boron is close to aluminium and there is no galvanic corrosion potential. The boron fibre is difficult to use if the parent material surface has a contoured shape. The boron fibers are very
Figure shows the loading condition under displacements
Fig shows the loading conditions under pressure
carbon and carbon plyimide in those the carbon is a fiber. Carbon fibers are very stiff and strong, 3 to 10 times stiffer than glass fibers. Carbon fibre is used for structural aircraft applications, such as floor beams, stabilizers, flight controls, and primary fuselage and wing structure. Advantages include its high strength and corrosion resistance. Disadvantages include lower conductivity than aluminium therefore, a lightning protection mesh or coating is necessary for aircraft parts that are prone to lightning strikes. Another disadvantage of carbon fibre is its high cost. Carbon fibre is gray or black in colour and is available as dry fabric and prepreg material. Carbon fibers have a high potential for causing galvanic corrosion when used with metallic fasteners and
International Journal of Recent Scientific Research Vol. 10, Issue, 09(G), pp. 34978-34985, September, 2019
expensive and can be hazardous for personnel. Boron fibers are used primarily in military aviation applications.
Polyimide
Polyimide resins excel in high-temperature environments where their thermal resistance, oxidative stability, low coefficient of thermal expansion, and solvent resistance benefit the design. Their primary uses are circuit boards and hot engine and airframe structures. A polyimide may be either a thermo set resin or a thermoplastic. Polyimides require high cure temperatures, usually in excess of 550 °F (290 °C). Consequently, normal epoxy composite bagging materials are not usable, and steel tooling becomes a necessity. Polyimide bagging and release films, such as Kapton are used. It is extremely important that Upilex replace the lower cost nylon bagging and polytetrafluoroethylene (PTFE) release films common to epoxy composite processing.
Mechanical properties which are used in both static and dynamic analysis are:
Table 1 Properties of materials
Properties Carbon/
Polyimide
Boron/
Aluminum Carbon/Carbon
EX 151GPa 235GPa 70.7GPa
EY 9.65GPa 137GPa 73.4GPa
EZ 9.65GPa 137GPa 73.4GPa
PRXY 0.34 0.30 0.04
PRYZ 0.02 0.17 0.04
PRXZ 0.34 0.17 0.04
GXY 6.34GPa 47GPa 23.46GPa
GYZ 3.17GPa 23.5GPa 12.23GPa
GXZ 3.17GPa 23.5GPa 12.23GPa
RESULTS AND DISCUSSIONS
Introduction
The analysis of result for both static and dynamic analysis are obtained and shown in the below.
Static Analysis
The finite element mesh is refined until the results are satisfactory and then static and dynamic analysis are performed on composite laminate. The figures show the static deformation of the laminate with layer having equal thickness. It is observed that there is a linear increase of the deflection which is due to the reduction in stiffness of the structure.
In static analysis the stresses in x, y and z direction, displacements in x, y and z directions and shear modulus in x, y and z direction are obtained and are shown in figures below.
Figure 6 Figure shows the maximum shear modulus in MPA
Figure 7 Figure shows the maximum stresses in N/mm
Figure 8 Figure shows the maximum displacements in mm
Plots for Static Analysis
Plots are obtained for displacements, stresses and shear modulus are shown in the following.
Figure 9 Plot shows the displacements in Uz direction
Figure 10 Plot shows the displacements in Uy direction
Stresses
Figure 11 Plot shows the stresses in Sx direction
Figure 12 Plot shows the stresses in Sy direction
Shear Modulus
Plot shows the displacements in Uz direction
Plot shows the displacements in Uy direction
Plot shows the stresses in Sx direction
Plot shows the stresses in Sy direction
Figure 13 Plot shows the shear modulus in Sxz direction
Figure 14 Plot shows the shear modulus in Sxy direction
Dynamic Analysis
In dynamic analysis we use three types of materials for each material the frequencies are varying with respect to thickness of the layers. Natural frequencies of the laminate for the mode shapes are obtained. These are shown with help of plots in the following for different materials
Carbon-Polyimide
Figure 15 Plot shows the frequency distribution for carbon
Boran-Alluminium
Plot shows the shear modulus in Sxz direction
Plot shows the shear modulus in Sxy direction
In dynamic analysis we use three types of materials for each material the frequencies are varying with respect to thickness of the layers. Natural frequencies of the laminate for the mode shapes are obtained. These are shown with help of plots in the following for different materials.
International Journal of Recent Scientific Research Vol. 10, Issue, 0
Figure 16 Plot shows the frequencies for Boran
Carbon-Carbon
Figure 17 Plot shows the frequencies of
carbon-These are the plots which are obtained from static and dynamic analysis of composite laminates.
CONCLUSION AND FUTURE SCOPE
Conclusion
Based on static analysis done on the three different laminates.
Boron/Aluminum shows excellent properties than other two materials.
It has less displacement and moderate strain and high shear modulus compared to other laminates.
Based on Dynamic analysis done the frequency of Boron/Aluminum is greater than carbon
carbon-carbon materials. Future Scope
The present work can be extended for the analysis of hollow structures and angle ply laminates
Can be extended for analysis of columns.
De-lamination effects on the structure.
Can extend for different innovative layer arrangement.
References
1. X. Zhang, C.H. Yang, “Recent developments of FEA for laminated composite plates”, journal of Elsevier 88(2009) 147-157.
2. A.Chan, W.K.Chiu, X.L.Liu, “Determining the elastic interlaminar shear modulus of composite laminates”, journal of Elsevier
How to cite this article:
Prasanna Kumar T J, K Venkata, Mastan Rao P and Venkatesh B., Analysis of Composite Laminate Using Finite Element Technique DOI: http://dx.doi.org/10.24327/ijrsr.2019.1009
International Journal of Recent Scientific Research Vol. 10, Issue, 09(G), pp. 34978-34985
Plot shows the frequencies for Boran-Aluminium
-carbon material
These are the plots which are obtained from static and dynamic
CONCLUSION AND FUTURE SCOPE
Based on static analysis done on the three different laminates. Boron/Aluminum shows excellent properties than It has less displacement and moderate strain and high
ther laminates.
Based on Dynamic analysis done the frequency of Boron/Aluminum is greater than carbon-polymide and
The present work can be extended for the analysis of hollow structures and angle ply laminates
extended for analysis of columns. lamination effects on the structure.
Can extend for different innovative layer arrangement.
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