We Have Numbers Of Free Samples

Abstract:

Here in this paper we have done an analysis on the structural aspects of a composite material. The composite laminated sheet is taken into consideration as a symmetric lamination. The desired thing is to find out the mathematical modeling as well as the theoretical calculations on this part. Since, we have all the dimensions in our hand the basic requirements are very easy to find out. Along with the theoretical calculations we have also performed the analysis in software tools to visualize the nature of the composite laminated sheet on compressive loading. We have defined the ply setting or the ply configuration according to their properties and arrangement. As the sequential parameter is given in the assignment brief we have made the modeling of that particular part according to the sequence and arrangement of fiber laminations. The software tool we have used here for modeling and finite element analysis is CATIA V5R20. All the dimensions are properly taken into consideration. Before simulation the material selection was one of the most important tasks to do this job. The material selection was done by the composite material selection tool in CATIA. As we can see the problem statement is given by specifying the ply arrangement. So to make sure the appropriate calculation it is the toughest part of the simulation otherwise it is depends only on the parameters inserted on it. If we go through this report it will be clear to all of us about the structural strength of composite material laminated sheet.

Introduction:

The material we are discussing here is the composite material. There is an extensive use of this kind of material from the running world. The reason of its extensive use is not only the high strength to wait ratio. There are so many reasons behind its acceptance. At that time the comparison takes place on this kind of material with some metals like steel and aluminum. Along with its high strength it is very less weight compared to any structural material available in structural analysis. Like any metal available and used in so many bending works it can be used by making a prominent replica of the desired model. Since, the material made up of some kind of cloth type fiber texture it can bend itself for any purpose. The feasibility and compatibility of its kind of material discussed in this report in terms of their mechanical load test reports.

Now a day, in most of the cases for manufacturing the air craft body paneling and inside structural beams this kind of composite materials are using, due to its high strength-to-weight ratio. It has strength almost equal steel but the weigh is half of the steel. It is nothing but a revolution in the field of structural material establishment. Since woven roving fibers are there inside the sheet it has high shear strength. As much we have done in our report it is all about the buckling or the deformation due to axial or bi-axial compressive loadings. For our assumption we have worked on this topic only by considering the one directional compressive load application on the sheet. For a better abbreviation on this topic we have searched so many researched papers and learned so many things from it. Due to the same reason we have performed three steps of result analysis one is based on Eigen value approach another one is non linear approach and the most effective and prominent one is the finite element analysis using software tools. The term we are using here is critical buckling load. It is the maximum load on which the buckling effect can be observed. After that critical point of loading, fracture will occur on the structure. So, on this point of view we need to check the maximum buckling deformation till it breaks, on that time the maximum load application will be considered as the maximum or critical buckling load.

Aims and Objectives:

The aims and objectives of presenting this experiment are,

• To become familiar with the theory as well as the practical aspects of finite element analysis of composite material.
• To get the clear vision on the software analysis methodologies for deformation maximum stress and buckling to its critical value.
• To get a basic idea about the terminologies of theory related to finite element analysis and to become familiar with simulation software.
• To get a clear view on the lamination technique and the ply arrangements as per requirements and to analyze them also.
• To use the general methods in virtual simulation software for analyzing fiber reinforced plastic materials.
• To know the proper usage of such kind of products in real life observation and implementation.

Part: 1

A. What is buckling and why it is important in engineering?

Answer:

Buckling is a structural failure of any structure occurred if a sudden compressive load is applied on that particular structure. Basically it is the sideways deflection occurred mainly observed in vertical column structures.

The observation of buckling in engineering is very important, the reason behind it is, any engineering service is based on the safety standard. The most important thing is safety standard which have to maintain at all kind of structure. At the time of designing and manufacturing the structural arrangement if we do not consider the buckling then a safe structure may not be available. For any kind of vertical column design if we apply the load on the structure then we can get the buckling on that particular column. If the buckling is permissible for that column, then only we can consider the structure as a safe one. These are the main importance of study of buckling in structural analysis and engineering.

B. What is a ‘Degree of Freedom’?

Answer:

Degree of Freedom is a term used in so many cases for engineering aspects as well as statistical data analysis also. In engineering it is defined as the minimum numbers of independent variables are needed for defining the position or the motion of a particular coordinate or a system. It is a property of kinematics arrangement. It decides the minimum possibilities of the movement of a system in different ways described by its motion.

For 3D and 2D space it is defined by two formats these are,

DOF_3D= 6 – Restraints

DOF_2D= 3 – Restraints

C. What is a “mesh Independent result”?

Answer:

For this question first we need to understand what mesh is. The mesh is actually a very small segment that has been segmented from a continuous body. It is the discrete part of a continuous part to calculate its characteristics at that position and from that we will be able to generate the whole structure analysis. Due to that reason the meshing is done for finite element analysis at any structure to get the appropriate outcome from FEA. It is also known as grid generation to approximate the geometry.

Now coming to the question mesh independent analysis is kind of a solution that we get form any finite element analysis without considering the meshing. The consideration of meshing is done actually in this topic but the independent says that if we rearrange the sizes of the mesh then it will not distract the outcome of the FEA result. That is the independency of the mesh solution. The main finding is that; a further meshing will not hamper the FEA result on any structure is known as mesh independent solution or result.

D. How can the critical buckling load of a plate be computed using a “FEA – Eigen value analysis”?

Answer:

The finite element analysis is completely based on two parameters one is the linear analysis and another one is the nonlinear analysis. For linear analysis the Eigen value approach is the way to find out the solution of FEA. It is also known as Euler buckling analysis. It is the most effective way to mathematically calculate buckling for a linear analysis on any elastic structure. Since the phenomenon buckling is nonlinear quantity in nature but the Eigen value approach is a linear one so it is not that much trusted method for finding out buckling. Instead of this we can find out the buckling in Eigen value approach.

The Eigen value method is applicable only when the value of having a value of more than 1.4 then the Eigen value will be applicable for determining the FEA analysis for our model.

For linear buckling calculation we have to follow the below assumption for any structure,

E. How can the critical buckling load of a plate be computed using a “FEA – Non-linear analysis”?

Answer:

The nonlinear buckling calculation is one of the most efficient techniques to measure the buckling due to the applied compressive load. The importance of this kind of analysis is, it can be used at some condition where the material and the product geometry is kind of nonlinear in nature. For that kind of nonlinear structures, the nonlinear approach to calculate the critical buckling is very much necessary.

For finding out a plate buckling in nonlinear approach we can use the formula given below for a perfect result or else alternatively we can direct apply some software tools to find out the correct FEA analysis report from that. The related expression given here,

Where,

F. What is laminated composite plate?

Answer:

It is basically a special type of material in material science. It is made of lamination process with the help of special kind of fiber materials on layers. These are mainly composite materials. To make a strong, stiff and load carrying capability is high on its weight ratio this are made. This are made of various fiber materials and resin based for a complete structure. The most important feature of such kind of material is high load to weight ratio. The most common composite materials are fiber and carbon fiber. These are used to make FRP type of material.

G. What are the main assumptions of Classical Laminated Plate Theory (CLPT)?

Answer:

The assumptions are stated below,

1. The composite material lamination should not contain any slip between the adjacent layers of the main material.
2. For every lamination of the composite material the layers are to be considered as a homogeneous to predict the property of the property of the material entirely.
3. For every layer the laminations should contain a plane stress alongside.
4. Every lamina used in this plate should be isotropic in nature.
5. The laminate always deforms on the basis of Kirchhoff- love assumption.

H. What are the main assumptions for the first order shear deformation theory (FSDT)?

Answer:

The assumptions are stated below,

1. Only pure bending can occur.
2. Only isotropic orthotropic homogeneous materials can be considered in this case.
3. The linear elasticity between proportionality limit can be analyzed in this.
4. Cross section of the beam is still plane after bending occurs in this case.

I. How can the results from the FE analysis of a laminated composite plate be validated?

Answer:

To validate the finite element analysis result of the composite laminated structure we just need to be make sure that, the values inserted at the time of FEA analysis are correct or not. Sometime FEA may not be correct at that time we just need to calculate the same with the help of manual calculations and to check whether the values we are getting in FEA are matching with the manual calculation results or not. If we get some result in our manual calculation varying a lot with the FEA value, then we need to check the percentage of error. By this method we can make a table to show the approximation of our result.

We can follow some steps to get a perfect result from FEM, these are,

1. The solution we are getting from the software tool should be meshing independent so that for re meshing we don’t get another analyzing result.
2. The analysis we are doing in our software tool must follow all the basic laws of physics. Since the model a very simple there is no need to be worried about the clear result.
3. The material selection is a very important topic in finite element analysis. At the time of manual calculation, we will not face any problem but if we go through the software calculation then a mistake in material selection may vary our result.

If we consider all this thing, then we will be able to validate our result properly and can make a comparison with the manual calculation to prove the correct result.

Part: 2

In this part of the report we are calculating the critical buckling for the given structure and the given data. The point is that we have been given a data for a composite plate having a particular dimension. All the parameters related to the material property is given in the theory section of the assignment brief from that we have taken them into consideration. The process of finding out the critical buckling is a manual one. Only mathematical tools are used in this part of the report. It is beneficial to the reader as well as the performer so that we can make a proof to relate our maximum buckling in terms of translational displacement in software tool to our mathematical result. Here for this calculation we have also considered the lamination code also. The lamination code is the feature of the fiber matting technique at the time of reinforcement. Two different ply technique is being considered here for the below calculation. In this part we have also shown the matrixes we need to show as per our marking scheme. If we read it carefully then we will definitely get the things we have in our assignment brief.

Here we need to calculate the critical buckling load with the values n = m =1, the plate is a simply supported rectangular plate having a size of a = b = 200 mm. modulus of elasticity E₁= 172 Gpa and E₂= 6.9 Gpa, shear modulus is G₁₂= 3.45 Gpa, Poisson’s ratio v₁₂= v₁₂= 0.25, thickness of each or lamina equal to 0.5 mm and density = 1750 kg/m³.

According to the problem statement the composite laminated plate is subjected to apply a liner bi directional compressive load from its two side or edges as shown in the figure. Here we need to find out the load critical value amplitude.

Where, m and n are the number of half waves in the acting lode to maximize the critical buckling load. To maximize the critical buckling load, we have to vary the parameters m and n respectively. Here the,,, are the stiffness factors can be expressed as the function of three variables like V₀, V₁ and V₃ and the material properties U_i, i= 1,2,…………,5.

where,

Here h is the total thickness of the laminated sheet or plate; z is the perpendicular distance from the plane of symmetry and is the angle of ply orientation, = is a variable that is equal to the k _th ply occupied and is equal to zero is the ply is empty.

Therefore, we have found the Q values of the asked in the problem statement.

Q11	183.466 Gpa
Q22	7.36 Gpa
Q13	1.84 Gpa
Q66	3.45 Gpa

 

Since the load application is here is only in one direction that is x axis. There is not any load application on the y direction.  So at the time of calculating maximum or critical buckling we can neglect the y component of normal load application to the edge of the composite plate.

Now, for finding out the [ABD] we need to take the Q values into consideration and also here is a matter of concerning the ply orientation and coding.

For both the cases if the thickness of the ply is same in nature, then it is known as regular anti symmetric angle ply laminate.

At that time the matrixes will be,

The maximum buckling for this simply supported plate considered as a beam,

Part: 3

Here in this part of this report we are calculating the critical buckling in terms of the translational displacement of a particular structure. The structural parameters are given here in this assignment brief and the requirement is to calculate the critical buckling. The buckling is the phenomena of any kind of beam type structure subjected to application of compressive load in different direction. We can make this calculation mathematically but the requirement is to virtually analyze them so that we can understand the displacement vector. The approach is Eigen value approach with consecutive meshing on the main structure.

The basic information we got from the assignment brief we are supposed to design the same replica model of that composite plate and then we need to analyze the plate considering a beam. Since, we have already found out the mathematical calculation in the previous part of the report so we can apply the load on the plate accordingly. We can visualize the buckling effect on the given structure and the deformation after applying all the boundary conditions we will be able to find out the translational displacement for that particular composite laminated plate.

For this case we have calculated the buckling in software tool to visualize it properly. Since, this is the linear calculation is being done so there will be more similarity with the manual calculation we have done earlier. The linear finite element analysis is being done on the context of mesh sensitivity by means of which, it is used such a manner that the meshing played an important role in this part. Since, it is a mesh sensitivity analysis therefore if we vary the meshing size automatically we will get difference in result. The difference in result is not that much higher but a smaller size of mesh depicts a higher accuracy in result.

Table: showing the ply sequence of the 1^st case described in the assignment brief [0/90/+45/-45]₂

Ply Group	Sequence	Ply	Material	Direction	Rosette	Surface	Draping	Ply ID
Plies Group.1	Sequence.1	Ply.1	Fibre (carbon)	0	Axis System.1	Fill.1	F	1
Plies Group.1	Sequence.2	Ply.2	Fibre (carbon)	90	Axis System.1	Fill.1	F	2
Plies Group.1	Sequence.3	Ply.3	Fibre (carbon)	0	Axis System.1	Fill.1	F	3
Plies Group.1	Sequence.4	Ply.4	Fibre (carbon)	90	Axis System.1	Fill.1	F	4
Plies Group.1	Sequence.5	Ply.5	Fibre (carbon)	0	Axis System.1	Fill.1	F	5
Plies Group.1	Sequence.6	Ply.6	Fibre (carbon)	90	Axis System.1	Fill.1	F	6
Plies Group.1	Sequence.7	Ply.7	Fibre (carbon)	0	Axis System.1	Fill.1	F	7
Plies Group.1	Sequence.8	Ply.8	Fibre (carbon)	90	Axis System.1	Fill.1	F	8

 

As the above table we have got the auto generated ply orientation and sequence of the composite sheet according to this we have performed the static load distribution and from that we are getting the deformation in terms of linear displacement.

This above figure showing the ply orientation done in Catia for reference it is just showing the normal procedure of selecting composite material. Since all other composite material are stated as their code name that is why here the glass fibre is just shown in the screen shot. For understand. In calculation part we have used the carbon fibre reinforced plastic. The reason is just to visualize the plying technique.

The above figure shows the visualization of ply arrangements.

Since, the buckling is a failure analysis of a model of structure. So, here we are performed the analysis such that the load application carried out on the model and it is done till it fails structurally that is just beyond buckling of the composite plate.

The critical buckling load specifies the maximum limit of compressive load applied on a structure on which point it buckles. After that critical value the elastic property of that material changes into plastic property. That means the failure occurring describes the plastic deformation. We have applied the load on the normal to its edge surface by grounding its opposite surface. After that we increased the load step by step until the failure occurs.

As we have found out the general buckling mechanism in this field where we have the ply sequence like [0/90] the process and the result are shown above in the figures.

In this section we got the critical buckling as followed by the figures. This is about 2.7 Gpa. And for that buckling the deformation or displacement is about 0.00263 mm at the critical buckling point.

Mathematical buckling load	Software buckling load
3.94 *10^6 N_m2	2.7 *10^4 N_m2

 

For the second case we have followed the same rule for making a virtual model of the composite sheet having the ply sequence of [0/30/90/-30]₂

Ply Group	Sequence	Ply	Material	Direction	Rosette	Surface	Draping	Ply ID
Plies Group.1	Sequence.1	Ply.1	Fibre (carbon)	0	Axis System.1	Fill.1	F	1
Plies Group.1	Sequence.2	Ply.2	Fibre (carbon)	0	Axis System.1	Fill.1	F	2
Plies Group.1	Sequence.3	Ply.3	Fibre (carbon)	90	Axis System.1	Fill.1	F	3
Plies Group.1	Sequence.4	Ply.4	Fibre (carbon)	90	Axis System.1	Fill.1	F	4
Plies Group.1	Sequence.5	Ply.5	Fibre (carbon)	0	Axis System.1	Fill.1	F	5
Plies Group.1	Sequence.6	Ply.6	Fibre (carbon)	0	Axis System.1	Fill.1	F	6
Plies Group.1	Sequence.7	Ply.7	Fibre (carbon)	90	Axis System.1	Fill.1	F	7
Plies Group.1	Sequence.8	Ply.8	Fibre (carbon)	90	Axis System.1	Fill.1	F	8

 

And for that we have applied the same procedure to find out the buckling at the structural composite material sheet. Since, we have the same number of layers compared to the 1^st case we don’t need to take the thickness into consideration. Just we have changed the ply sequence according to their arrangement code given and checked the same.

In this section we got the critical buckling as followed by the figures. This is about 3.04 Gpa. And for that buckling the deformation or displacement is about 0.00276 mm at the critical buckling point.

Mathematical buckling load	Software buckling load
3.94 *10^6 N_m2	3.04 *10^4 N_m2

Part: 4

This part of the report consists of some nonlinear approach to the finite element analysis we need to do in the simulation software. In linear bodies symmetric in shape the analysis is easier one compared to the nonlinear non symmetric bodies. For both cases linear and nonlinear analysis, the stress and strain concentration are same for their behavior. But the change in the deformation in case of linear is quite desirable and symmetric in nature. In case of nonlinear composite sheets, the material properties are not same throughout the sheet. For that reason, the deformation in terms of buckling is not same throughout the body.

So here the laminations are to be taken into consideration carefully. And the ply sequence is also very much important for the nonlinear analysis. And for analysis we have to make the ply sequence as the laminate 1 and laminate 2 described in part 2.

The ply sequences we need to consider here is the [0/90]₄ and [0₂/90₂]₂ and we have checked the analysis in software on static simulation case study.

Since the structure is kind of nonlinear in nature that means the strain and stress concentration are same with the linear analysis but the deformation is not same in nature. A massive change in the buckling in terms of deformation is showing in this nonlinear finite element analysis. As on the von mises stress we can see some peak stress concentration on the structure, which shows the nonlinearity of the given structure and the nonlinear analysis result. In this method we have used the ply sequence for lamination is given below in the table.

Ply Group	Sequence	Ply	Material	Direction	Rosette	Surface	Draping	Ply ID
Plies Group.1	Sequence.1	Ply.1	Fibre (Carbon)	0	Axis System.1	Fill.1	F	1
Plies Group.1	Sequence.2	Ply.2	Fibre (Carbon)	90	Axis System.1	Fill.1	F	2
Plies Group.1	Sequence.3	Ply.3	Fibre (Carbon)	0	Axis System.1	Fill.1	F	3
Plies Group.1	Sequence.4	Ply.4	Fibre (Carbon)	90	Axis System.1	Fill.1	F	4
Plies Group.1	Sequence.5	Ply.5	Fibre (Carbon)	0	Axis System.1	Fill.1	F	5
Plies Group.1	Sequence.6	Ply.6	Fibre (Carbon)	90	Axis System.1	Fill.1	F	6
Plies Group.1	Sequence.7	Ply.7	Fibre (Carbon)	0	Axis System.1	Fill.1	F	7
Plies Group.1	Sequence.8	Ply.8	Fibre (Carbon)	90	Axis System.1	Fill.1	F	8

 

For the second case of the nonlinear analysis we just need to do the same thing but the difference is that, we have to change the ply sequence of the composite sheet lamination. Here the composite lamination has a laminate code of [0₂/90₂]₂ it implies that there are two 0 and two 90 segment in one layer and that total layer multiplied by two makes the whole lamination configuration of the composite sheet.

Ply Group	Sequence	Ply	Material	Direction	Rosette	Surface	Draping	Ply ID
Plies Group.1	Sequence.1	Ply.1	Fibre (Carbon)	0	Axis System.1	Fill.1	F	1
Plies Group.1	Sequence.2	Ply.2	Fibre (Carbon)	0	Axis System.1	Fill.1	F	2
Plies Group.1	Sequence.3	Ply.3	Fibre (Carbon)	90	Axis System.1	Fill.1	F	3
Plies Group.1	Sequence.4	Ply.4	Fibre (Carbon)	90	Axis System.1	Fill.1	F	4
Plies Group.1	Sequence.5	Ply.5	Fibre (Carbon)	0	Axis System.1	Fill.1	F	5
Plies Group.1	Sequence.6	Ply.6	Fibre (Carbon)	0	Axis System.1	Fill.1	F	6
Plies Group.1	Sequence.7	Ply.7	Fibre (Carbon)	90	Axis System.1	Fill.1	F	7
Plies Group.1	Sequence.8	Ply.8	Fibre (Carbon)	90	Axis System.1	Fill.1	F	8

 

The sequence or the orientation is somehow different from the first case we have studied here. But the number of layer is same, so we can assume the thickness id same as the previous composite sheet. The basic design and their ply sequence for lamination made as per the requirement. The steps followed in this just same as described in the part 3 of this report. Since, the thickness is same only lamination code is difference we will get a very few difference in analysis result.

Here we have calculated the buckling in terms of deflection in translational displacement. That will be considered as the critical buckling at which there we can visualize the most deflection after there will be plastic deformation that is the flexure.

[0/90]4	0.00652 mm at 1.18*10^5 N_m2
[02/902]2	0.00579 mm at 1.22*10^5 N_m2

 

Part: 5

Here in this part of the report we are discussing about the variation of the report results we have got in different analysis cases. In the second part of this report we have calculated the critical buckling load manually. In third part of the report we have done the simulation in software tool as directed by the ply settings and found out the load application and the buckling displacement. In the fourth part of the report we have done the same thing and visualized the buckling of the composite material laminated sheet.

The mathematical modeling and simulation was done by two methods with considering the requirements on the assignment brief. In the first analysis we analyzed them in linear mode. That is the method where we assumed the material property as a symmetric one. On the next part we have calculated the same but the only difference is here we have taken the material property as an unsymmetrical quantity. The ply sequence was also taken into consideration for both these cases as we have attached the tables with the report automatically generated by Catia in excel format. For evidence we have also attached a figure with the report to show how the sequencing is done. Firstly, we are discussing on the difference in the values we got. A comparative table is given below to understand it clearly.

Type of measurement	Lamination #1	Lamination#2
Theoretical	3.94 *10^6 N_m2	3.94 *10^6 N_m2
Analytical	2.7 *10^4 N_m2	3.04 *10^4 N_m2

 

The lamination 1 and lamination 2 shown on above table are the laminations described on the assignment brief part 3. This table shows the difference between the buckling loads experienced by the composite material sheet. The difference is not that much higher because both the manual and analytical calculation done on the basis of linear analysis.

At the time of measuring the same thing with two different ply sequence lamination by using nonlinear analysis methodology we have also found out the knuckling loads. Here we can observe a higher difference between the manual calculated value and the analysis value because the manual calculation based on the Eigen value approach. That was linear in nature but we are comparing it with the nonlinear analysis. And we all know for this kind of material based analysis the nonlinear analysis is more appropriate compared to the linear analysis.

Type of measurement	Lamination #1	Lamination#2
Theoretical	7.887*10^6 N_m2	7.887*10^6 N_m2
Analytical	1.18*10^5 N_m2	1.22*10^5 N_m2

 

Here the laminations are taken into consideration as per the assignment brief 4^th part.

For the discussion required about the non-conservative Eigen value. We all know that the buckling analysis is not an appropriate analysis for finding out the buckling load. For a very few threshold value of load the buckling may occur. And the critical buckling can vary with various aspects like temperature, position. Among them the conservation of Eigen value solution is very difficult. Because the Eigen value approach is completely based on the matrix method and for this kind of matrix method we won’t be able to get an appropriate result. Moreover, of which we will only be able to get a clear vision on the problem statement along with their coefficients. That is the only statement can be followed with the problem statement given like non conservative Eigen solution. The Eigen solution can never find a correct answer for a particular finite element analysis instead of this a nonlinear analysis is one of the best technique to get the proper outcome.

Part: 6

Here in this part of the report we have discussed the various aspects of buckling loads and there buckling according to their lamination. We are supposed to make three different case studies. On both of them we have applied a same amount of compressive load and for that compressive load we have found out the buckling in terms of the translational displacement. Since we have considered the three types of laminations and the thickness are used as a changing variable. The motive of such kind of analysis is to make a comparatively best solution in terms of compressive load sustainability. In the assignment brief we need to find out the optimum solution from the structures.

The optimum solution is the structure that has the highest compressive load sustaining capacity. From here if we found the solution like a particular structure has lowest translational displacement that will be considered as the optimum solution.

For the 30 degree of the stringer,

For [0/30/90/-30]

For [-45/60/45/60]

For the 45 degree of the stringer,

For, [0/90/+45/-45]

For [0/30/90/-30]

For [-45/60/45/60]

For the 60 degree of the stringer,

For, [0/90/+45/-45]

 

 

For [0/30/90/-30]

For [-45/60/45/60]

Sl no	Degree orientation	Samples	Thickness	Strain energy von mises stress (N_m2)	Deflection (mm)
1	30	[0/90/+45/-45]	0.4	4.75*109	8.31
2	30	[0/90/+45/-45]	0.5	4.38*109	7.68
3	30	[0/90/+45/-45]	0.6	4.19*109	7.52
4	30	[0/30/90/-30]	0.4	4.85*109	8.41
5	30	[0/30/90/-30]	0.5	4.33*109	8.00
6	30	[0/30/90/-30]	0.6	4.21*109	7.80
7	30	[-45/60/45/60]	0.4	5.31*109	8.74
8	30	[-45/60/45/60]	0.5	4.75*109	8.31
9	30	[-45/60/45/60]	0.6	4.38*109	7.68
10	45	[0/90/+45/-45]	0.4	3.61*109	7.34
11	45	[0/90/+45/-45]	0.5	3.17*109	6.37
12	45	[0/90/+45/-45]	0.6	2.88*109	5.79
13	45	[0/30/90/-30]	0.4	4.41*109	8.84
14	45	[0/30/90/-30]	0.5	4.26*109	8.53
15	45	[0/30/90/-30]	0.6	4.05*109	8.10
16	45	[-45/60/45/60]	0.4	4.72*109	9.44
17	45	[-45/60/45/60]	0.5	4.20*109	8.41
18	45	[-45/60/45/60]	0.6	3.90*109	7.80
19	60	[0/90/+45/-45]	0.4	3.96*109	7.92
20	60	[0/90/+45/-45]	0.5	3.04*109	6.09
21	60	[0/90/+45/-45]	0.6	2.74*109	5.48
22	60	[0/30/90/-30]	0.4	4.14*109	8.29
23	60	[0/30/90/-30]	0.5	3.65*109	7.31
24	60	[0/30/90/-30]	0.6	3.32*109	6.64
25	60	[-45/60/45/60]	0.4	4.02*109	8.04
26	60	[-45/60/45/60]	0.5	3.90*109	7.80
27	60	[-45/60/45/60]	0.6	3.59*109	7.19

 

From the above table we can see the buckling in terms of translational displacement. The design is said to be optimum if the deflection is less. The deflection is less signifying the strong structural strength of the part we are observing. For our observation we can say the first lamination sequence making a composite sheet is having a optimum design the reason behind it is the less amount of deflection for same applied compressive load. On the same load application if we can find out the minimum translational displacement then we can conclude it as an optimum solution.

Conclusion:

As we have gone through several steps to perform this analysis we have a very clear view on the composite sheet structural strength. The most important topic is being found out throughout the report is buckling and the buckling load. The buckling is the phenomena of all structural body which is experiencing a compressive load on it. First of all, we have found the manual calculations on buckling on the basis of Eigen value approach. The Eigen value approach is the linear analysis. It is the easiest way to find out the buckling but in manual calculation for linear analysis we cannot find out exactly buckling. In Eigen value approach we can only find out the matrixes related to the analysis. But if there is any kind of unsymmetrical in the part then a linear analysis will not be able to give the correct result. For that reason, the nonlinear analysis is incorporated in this report as the assignment brief given. From those values we have compared and observed a very high difference in the outcome for Eigen approach and nonlinear approach. And the error is also calculated. At the last of the report we have also analyzed three types of composite sheets for a relatively complex structure and got the results from them. Among these three combinations the first one is the most optimal solution which can sustain a higher load with low buckling. This is all about the report we have made on this topic.

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