Finite Element Analysis of Composite Water Buffer Drum

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FINITE ELEMENT ANALYSIS OF COMPOSITE WATER BUFFER DRUM

Abstract

Composite materials offer many advantages for oil and gas developments based on their low density, corrosion resistance, and excellent fatigue performance.  In addition, the use of composites allows for greater design flexibility for tailoring the properties to meet specific design requirements, thus promoting better system oriented and cost-effective solutions. However, on a performance equated basis, the economic incentive to use composite components can often be demonstrated based on their capability to reduce system and life cycle costs.

Water buffer drum which is a pressure vessel holds a specified volume of fluid with desired temperature and pressure. Its function is to provide water with certain temperature to equipment facility. For smooth working large number of piping is attached to this. These conditions create critical nozzle loading on the pressure vessel. This paper gives an idea about comparative study between carbon steel and combination of carbon steel and composites. Composites such as Glass fibered reinforced are used for the study. Pressure vessel with a combination of different boundary conditions such as Pressure, Nozzle loading, Wind, Seismic is analyzed for carbon steel and the combination of carbon steel and composites. Various thickness combinations of composite and carbon steel are used for design study. While analyzing water buffer drum components stress induced in various components are compared. By replacing some thickness of carbon steel there will be % reduction in weight which will save many costs related to the weight of water buffer drum.

Table of Contents

Acknowledgement

Abstract

List of Illustrations

List of Tables

Chapter 1 Introduction

1.1 What is water buffer drum

1.2 Research Objective

1.3 Composites

Chapter 2 Geometry

Chapter 3 Design Parameters

3.1 Design conditions

3.2 Material Properties

Chapter 4 Design Calculations & Loading Conditions

4.1 Weight

4.2 Pressure & Static Head

4.3 Nozzle Loads

4.4 Seismic Loading

4.5 Wind Loading

4.6 Loading Combinations

Chapter 5 Carbon Steel Results

5.1 Load Case 1

5.2 Load Case 2

5.3 Load Case 3

5.4 Load Case 4

5.5 Comparison of Load cases

Chapter 6 Composites

6.1 E-glass properties

6.2 Simulation

Chapter 7 Composite Results

7.1 Results for shell

7.2 Results for Support Leg

7.3 Results for RF Pad

7.4 Results for E-glass

7.5 Weight Difference

Chapter 8 Conclusion

Future Work

References

Biographical Information

List of Illustrations

Figure 1‑1 Chilled water buffer drum

Figure 1‑2 Hot water buffer drum

Figure 1‑3 Composites

Figure 2‑1 Overall Dimensions

Figure 2‑2 Overall Geometry

Figure 2‑3 Nozzle orientation

Figure 2‑4 Water buffer drum with nozzles

Figure 2‑5 Leg support with reinforcement pad

Figure 2‑6 Leg cross section

Figure 2‑7 Baseplate cross section

Figure 4‑1 Direction of applied nozzle Loads

Figure 4‑2 Seismic Loads & Reactions for a vessel with unbraced legs

Figure 4‑3 Coefficient Rw

Figure 4‑4 Coefficients Ca & Cv

Figure 4‑5 Structure Category & Exposure Categories from Moss

Figure 4‑6 (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

Figure 5‑1 Case 1 Results (a) Total Deformation (b) Overall Stress
(c) Legs (d) RF Pad

Figure 5‑2 Case 2 Results (a) Total Deformation (b) Overall Stress
(c) Legs (d) RF Pad

Figure 5‑3 Case 3 Results (a) Total Deformation (b) Overall Stress
(c) Legs (d) RF Pad

Figure 5‑4 Case 4 Results (a) Total Deformation (b) Overall Stress
(c) Legs (d) RF Pad

Figure 5‑5 Stress comparison chart

Figure 6‑1 0° Fiber direction

Figure 6‑2 Lay up direction

Figure 7‑1 Stress generated in shell for combination 4+2

Figure 7‑2 Stress generated in shell for combination 4+4

Figure 7‑3 Stress generated in shell for combination 6+2

Figure 7‑4 Stress comparison for shell

Figure 7‑5 Stress generated in leg for combination 4+2

Figure 7‑6 Stress generated in leg for combination 4+4

Figure 7‑7 Stress generated in leg for combination 6+2

Figure 7‑8 Stress comparison for Leg

Figure 7‑9 Stress generated in RF Pad for combination 4+2

Figure 7‑10 Stress generated in RF Pad for combination 4+4

Figure 7‑11 Stress generated in RF Pad for combination 6+2

Figure 7‑12 Stress comparison for RF Pad

Figure 7‑13 Stress & MOS in solid composite for combination 4+2

Figure 7‑14 Stress & MOS in solid composite for combination 4+4

Figure 7‑15 Stress & MOS in solid composite for combination 6+2

Figure 7‑16 Comparison of MOS for ply sequence

Figure 7‑17 Weight Comparison with a different combination

List of Tables

Table 2‑1 Nozzle properties

Table 3‑1 Design Parameters

Table 3‑2 Material List

Table 3‑3 Material Properties

Table 4‑1 Empty weight distribution

Table 4‑2 Static head

Table 4‑3 Nozzle Loads

Table 4‑4 Wind calculation coefficient from Moss

Table 5‑1 Comparison of stress-induced for all load cases

Table 6‑1 E-glass Properties

Table 7‑1 Comparison of stress generated in shell

Table 7‑2 Comparison of stress generated in Leg

Table 7‑3 Comparison of stress generated in Leg

Table 7‑4 Margin of safety for Ply sequence

Table 7‑5 Weight Comparison

Chapter 1  Introduction

The pressure vessel is one most important equipment for the smooth functioning of many industries such as oil and gas, pharmaceutical, healthcare, HVAC. The pressure vessel is nothing but equipment to hold the desired volume of gas or liquid at required temperature and pressure. The pressure vessel is generally made of carbon steel, stainless steel or metals. There are very few cases where non-metal is used for manufacturing of pressure vessel. Pressure vessel construction is very costly for its service time considered. Corrosion is one of a factor that cost many lots in construction. But there are ways to reduce the overall cost of the pressure vessel.

To reduce pressure vessel cost, the weight of pressure vessel should decrease, and lifespan should increase. The decrease in weight will affect vessel transportation, operation, and maintenance cost. Reducing weight is very tedious job due to complexity in pressure vessel operation. For this new material with low density and high strength and stiffness can be used.

In recent years, composite materials with these properties are evolved. Also, extensive research on various materials and improvising their properties are going on.

Many materials with such properties are easily available in the market.

 

1.1 What is water buffer drum

Water buffer drum is pressure vessel used for water flow circulation to increase system efficiency in chillers, reactors, boilers. Depending upon application temperature range of fluid in water buffer drum is decided. As per process requirement capacity of the drum, more factors are taken into consideration for design. It is used in fluid circulation vessel so the major piping system is attached to this.

Chilled water buffer drums are designed for use of chilled water system with insufficient water volume capacity, in relation to chiller capacity. Chilled water buffer drum increases system volume and reduces the rate of temperature change in return water, resulting in improved temperature control, consistent system operation and controlled compressor cycling.

Figure 1‑1 Chilled water buffer drum

Hot water buffer drum is designed for use of high temperature, a high-efficiency system that incorporates small, modular low mass boiler. It adds necessary thermal mass to the system to dampen fast transitions and minimize boiler cycling that occurs during zero or low domestic load conditions.

Figure 1‑2 Hot water buffer drum[1]

1.2 Research Objective

The objective of this study is to analyze water buffer drum which is used in industry for storing water with desired temperature and pressure. For smooth functioning of the drum, piping is attached to it. For most of the cases, piping loads are affecting design thickness of drum. In this study, we are analyzing buffer drum with various thickness combination of composite and carbon steel. We will be keeping same design conditions for the composite model as that of original carbon steel model to withstand combined loads like internal pressure, nozzle load, wind load, seismic load.

We aim to show stress generated due to loading condition various parts with variation in a combination of thickness with carbon steel and composite. As using composite will be beneficial for weight reduction of whole geometry.

1.3 Composites

A composite material is made by combining two or more materials – often ones that have very different properties. The two materials work together to give the composite unique properties. However, within the composite, you can easily tell the different materials apart as they do not dissolve or blend into each other. Most composites are made of just two materials. One is the matrix or binder. It surrounds and binds together fibers or fragments of the other material, which is called the reinforcement. Composite materials are high in strength to weight ratio[2]. Composites are a combination of two or more constituent materials with significantly different physical and chemical properties. When two or more materials combine it give other material which is completely different from individual materials.

Figure 1‑3 Composites[3]

In this study we considering E-glass fiber. E-glass fiber is having some distinct properties to be considered, those properties are listed below:

  • High stiffness
  • Low cost
  • Corrosion resistant
  • Thermal resistance
  • Low density
  • Design flexibility
  • Low manufacturing constraints

Also, while analyzing composite some factors should consider:

  • Delamination in ply
  • In Plane shear due to deflection
  • Shear due to out of plane deformation

Chapter 2  Geometry

In this chapter, we will discuss about water buffer drum geometry used for analysis. Overall length of 7150 mm with TL to TL length 4100 mm and internal diameter of 1450 mm. 8 mm thickness is used for geometry for shell and head. For this study, carbon steel material is used for preliminary analysis.

Figure 2‑1 Overall Dimensions

Figure 2‑2 Overall Geometry

For working of water buffer drum various nozzles are attached to water buffer drum. Nozzle orientation with nozzle properties is mentioned below.

Figure 2‑3 Nozzle orientation

Figure 2‑4 Water buffer drum with nozzles

Form nozzle table other details for nozzles like nozzle projection, nozzle size, nozzle thickness, reinforcement pad can be obtained. Nozzle thickness is nothing but nozzle schedule. Nozzle is a pipe, so thickness of nozzle varies with schedule, but the outer diameter remains the same for every size. Nozzle table is mentioned below.

Description Pipe size

(inch)

Schedule RF Pad

(mm)

Projection

(mm)

Water Inlet 3” Sch 160 t8 x 210 550 from TTL
Drain 2” t13.6 t8 x 165 550 from BTL
Minimum flow 2” Sch 160 t8 x 165 910 from CL
Water Outlet 4” Sch 160 t8 x 250 910 from CL
Vent 3” Sch 120 t8 x 210 550 from TTL
Overflow 3” Sch xxs t8 x 300 910 from CL
Handhole 8” Sch 60 600 from TTL
Recirculation Line 4” Sch 120 t8 x 250 550 from TTL

Table 2‑1 Nozzle properties

Nozzles are welded to the pressure vessel and then mentioned thickness reinforcement pads are welded to pressure vessel.

According to pressure vessel, elevation and functioning type of supports are decided. Supports types for vertical pressure vessel are generally Leg, Lug, and Skirt. Legs are nothing but typical cross sections like I beam, angle beam, channel beam or pipe. In this study cross-section of leg is I beam. Water buffer drum is supported by legs which are welded to reinforcement pad on pressure vessel shell. Legs are welded to baseplate which is attached to foundation with help of foundation anchor bolts. Reinforcement pad with width of 285 mm and height of 450 mm is welded on shell with 45°, 135°, 225°, 315° orientation. For baseplate foundation bolts BCD is 1724 mm.

Figure 2‑5 Leg support with reinforcement pad

Figure 2‑6 Leg cross section

Figure 2‑7 Baseplate cross section

Chapter 3  Design Parameters

Pressure vessel design generally based on functioning, surrounding conditions, working zone and many more. In this chapter, we will discuss about design conditions, material properties of carbon steel.

3.1 Design conditions

Factors affecting the design of water buffer drum are:

  • Internal pressure
  • External pressure
  • Design temperature
  • Corrosion allowance
  • Welding joint type & efficiency
  • Materials
  • Insulation
  • Testing conditions

Depending upon these conditions pressure vessel manufacturing constraints can be obtained. In this case, we are considering basic design parameters to obtain pressure vessel basic geometry. Pressure vessel consists of various parts which are welded to shell and head. Welding details are a very important criterion in the manufacturing of pressure vessel. Most of the time welding details are defined by the manufacturer. In this case, required design parameters are listed below:

Parameter Value Unit
Internal Pressure Atmospheric Pressure

(101325)

Pa
External Pressure Atmospheric Pressure

(101325)

Pa
Design Temperature 75 °C
Density of fluid 997 Kg/m3
Corrosion Allowance 1.5 mm
Joint Efficiency 1.0
Radiography 100%

Table 3‑1 Design Parameters

3.2 Material Properties

In pressure vessel design various components are included which can be manufactured from various manufacturing procedures like casting, machining, forming, forging etc. Materials are of various types like a plate, rod, pipe. As the strength of a material depends on its manufacturing process. According to process requirement material for various components to be decided. Also, while choosing materials there is one more factor to be considered. That factor is the type of fluid pressure vessel will hold. Fluid inside is also causing corrosion. By considering all these factors materials needed to be considered for design. Generally, standard materials are considered for design from ASME section II part A & B. Material properties are taken from ASME section II part D. Material list and material properties considered for this case are mentioned below:

Component Material
Shell & Head SA 516 Gr.70
Reinforcement Pad SA 516 Gr.70
Support Leg SA 36
Baseplate SA 36

Table 3‑2 Material List [4][5]

Properties Value
SA 516 Gr.70 SA 36
Young’s Modulus 200 GPa 200 GPa
Yield Tensile Strength 260 MPa 250 MPa
Ultimate Tensile Strength 485 MPa 400 MPa
Poisson’s Ratio 0.29 0.26
Density 7800 kg/m3 7800 kg/m3
Allowable stress 138 MPa 114 MPa

Table 3‑3 Material Properties[6][7][8]

Chapter 4  Design Calculations & Loading Conditions

The loadings to be considered in designing a vessel shall include those from:

  1. Internal or External pressure
  2. the weight of the vessel and normal contents under operating or test conditions
  3. superimposed static reactions from the weight of attached equipment, such as motors, machinery, other vessels, piping, linings, and insulation
  4. cyclic and dynamic reactions due to pressure or thermal variations, or from equipment mounted on a vessel and mechanical loadings
  5. wind, snow, and seismic reactions
  6. impact reactions such as those due to fluid shock
  7. temperature gradients and differential thermal expansion
  8. abnormal pressures, such as those caused by deflagration
  9. test pressure and coincident static head acting during the test[9]

These are several loading conditions that one should take into consideration while designing the pressure vessel. In every pressure vessel according to surrounding or process conditions types of loadings vary. Multiple loadings can simultaneously act on the pressure vessel. While designing pressure vessel multiple loading cases should be considered. First, we will find individual loads acting on pressure vessel according to design parameters. In this design study, we are considering Pressure, Piping, Wind and seismic loading. In this chapter, we are discussing detail load calculations for factors mentioned.

4.1 Weight

Weight is a most important factor while designing pressure vessel especially supports the vessel. Empty weight and operating weight needs to be considered for load cases. For this case, empty weight of water buffer drum is 2220 kg. This weight is obtained from ANSYS properties. Component wise weight distribution is given below:

Component Material Density (kg/m3) Weight (kg)
Shell SA 516 Gr.70 7800 1524
RF Pads SA 516 Gr.70 7800 36
Support Leg with Base plate SA 36 7800 660

Table 4‑1 Empty weight distribution

For designing pressure vessel, we must consider the real-time scenario. Real time scenario for a pressure vessel is nothing but an operating condition. To obtained operating weight we need to add fluid weight enclosed by water buffer drum to empty weight. First, we need to find volume enclosed by pressure vessel.

Water buffer drum volume = Cylinder volume + Head volume

Cylinder volume =

z) =0.00256 Kz Kzt V2 I [12]

qz = 0.00256 (1.12) (1.0) (72)2 (1.15)

= 17.09 pound per square feet

F = (17.09) (0.85) (0.9) (64.7)

= 846 lb

The overturning moment at the base,

M = 121400 lb in

Effective overturning moment per leg,

Mw = 30350 lb in OR 3435 Nm

4.6 Loading Combinations

In this analysis, a combination of mentioned loadings is used as load cases. While combining load case mainly testing, transportation and operating conditions are considered. While transportation of buffer drum or for maintenance all nozzle will be blinded. In that case, there will be a vacuum created inside buffer drum. On that note, external atmospheric pressure will act on drum. We considered wind and seismic loadings for drum. Ideally, it should be designed for worst case like wind and seismic loads at same time. But it is not needed to consider such a rare case. In all the cases there is fixed support is considered on anchor bolt surface on base plate. Typically, we are analyzing four cases with load combination mentioned as below:

Case 1: Internal Pressure + Static Head + Operating Weight + Nozzle Loads

Case 2: External Pressure + Empty weight

Case 3: Internal Pressure + Static Head + Operating Weight + Nozzle Loads + Seismic Load

Case 4: Internal Pressure + Static Head + Operating Weight + Nozzle Loads + Wind Load

Actual ANSYS applied load case is shown below:

   

  1.                                                       (b)

    

(c)                                                       (d)

Figure 4‑6 (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4

Chapter 5  Carbon Steel Results

From loading conditions, results for four cases are obtained. In this chapter, we will compare all load case results. All the results are obtained with simulation software ANSYS 17.2 For each case we are comparing overall stress, stress induced in support leg, stress induced in reinforcement pad. By comparing results, we can obtain most stringent case for the pressure vessel.

From ANSYS, we have obtained equivalent von misses stress at every component. As legs are welded to RF pad and RF pad is welded on the shell. So, we are considering stress values of these components. As near welding connection, there will be more stress concentration. For results in each case, the maximum point of stress generation for each component are shown in results.

Results for deformation, Maximum Stress induced, Stress-induced in legs and RF pad for every case is shown.

5.1 Load Case 1

Results for load case 1 are shown below:

           

(a)                                                      (b)

          

(c)                                                     (d)

Figure 5‑1 Case 1 Results (a) Total Deformation (b) Overall Stress (c) Legs (d) RF Pad

5.2 Load Case 2

Results for load case 2 are shown below:

          

(a)                                                        (b)

          

(c)                                                         (d)

Figure 5‑2 Case 2 Results (a) Total Deformation (b) Overall Stress (c) Legs (d) RF Pad

5.3 Load Case 3

Results for Load Case 3 are shown below:

          

  1.                                                    (b)

         

  1.                                                   (d)

Figure 5‑3 Case 3 Results (a) Total Deformation (b) Overall Stress (c) Legs (d) RF Pad

5.4 Load Case 4

Results for Load Case 4 are shown below:

          

  1.                                                        (b)

           

(c)                                                          (d)

Figure 5‑4 Case 4 Results (a) Total Deformation (b) Overall Stress (c) Legs (d) RF Pad

5.5 Comparison of Load cases

From all load cases comparing data of stress induced in shell, Leg, RF pad to find dominant case amongst all. Stress-induced by various components are tabulated below:

Stress (MPa) Case 1 Case 2 Case 3 Case 4
Shell 112.68 21.57 112.68 112.68
Leg 77.82 4.74 92.87 100.53
RF Pad 84.35 8.11 86.97 88.17

Table 5‑1 Comparison of stress-induced for all load cases

Figure 5‑5 Stress comparison chart

From above comparison, we have noticed that value on shell remains same in almost all the cases as nozzle loading is a critical factor for causing maximum stress around nozzle reinforcement pad on shell. And stress generated in legs and RF pad varies with each load case. From above data, we can say load case 4 which is Internal Pressure + Static Head + Nozzle load + Wind load is critical case for water buffer drum.

Chapter 6  Composites

In this chapter, we will discuss material properties, how composite analysis is done in ANSYS. This study includes comparison between carbon steel and combination of carbon steel and composites. Various cases with different thickness combinations are considered for this study.  For this study, we are replacing some part of shell thickness by composite material. Support leg and RF pad remain same as that of carbon steel.

In this case we are considering three thickness combinations. These combinations are:

  1. 4 mm of carbon steel + 2 mm of E-glass
  2. 4 mm of carbon steel + 4 mm of E-glass
  3. 6 mm of carbon steel + 2 mm of E-glass

6.1 E-glass properties

Mainly E-glass is used for this study due to its extensive properties for this type of application. As mentioned earlier, E-glass is orthotropic in nature. As its material properties are not same in every direction. We need to mention every single property required for analysis. E-glass unidirectional material is used for simulation. Default E- glass UD material mentioned in ANSYS in used. Material properties Material properties of E-glass are mentioned in the table below:

Properties Value
E11 45000 MPa
E22 10000 MPa
E33 10000 MPa
V12 0.3
V23 0.4
V31 0.3
G12 5000 MPa
G23 3847 MPa
G31 5000 MPa
Tensile strength in X direction 1100 MPa
Tensile strength in Y direction 35 MPa
Tensile strength in Z direction 35 MPa
Compressive strength in X direction -675 MPa
Compressive strength in Y direction -120 MPa
Compressive strength in Z direction -120 MPa
Shear strength in XY 80 MPa
Shear strength in YZ 47 MPa
Shear strength in XZ 80 MPa

Table 6‑1 E-glass Properties

6.2 Simulation

ANSYS Processing is divided into three steps:

Pre-processing: In this step, the material is defined and assigned to geometry. Model is generated. Also, the meshing of the model with different mesh parameters is done.

Solution: In this step, all loading conditions to geometry such as forces, moments are defined and applied. Solution control tool is available to control various steps in solution module.

Post-processing: In this step desired results can be produced. There are multiple options to generate results.

ANSYS composite PrePost is a tool for analyzing composite models ply by ply. As composite solid consists of several plies to make one solid model. This creates engineering complexity to define a thickness, orientation, materials. Ply angle or fiber orientation is one of the major factors in a composite layup. In this module, positive or negative fiber direction angle can be given to ply as per layup requirement. Numerous layer with different orientation and thickness can be set one below other to generate thickness.

Engineering layered composites involve complex definitions that include numerous layers, materials, thicknesses, and orientations. The engineering challenge is to predict how well the finished product will perform under real-world working conditions. Simulation is ideal for this when considering stresses and deformations as well as a range of failure criteria. ANSYS Composite PrepPost software provides all necessary functionalities for finite element analysis of layered composite structures. You can choose to work with either shell theory (thin-composites) or move to modeling solid composites in the case of thicker parts.[14]

Figure 6‑1 0° Fiber direction

In Figure 6-1, 0° Ply fiber direction is shown for this case. Apart from 0°, we can give any angle for fiber direction of ply. With same or varying ply thickness we can generate a solid model of the required thickness. For generating the solid model, we should give layup direction to generate thickness.[14][15][16]

Figure 6‑2 Lay up direction

Nozzle loading is most critical loading for this case. Resultant force and moment for all nozzles vary because of difference in x, y, z component of each nozzle. For this type of loading, we are considering quasi-isotropic ply sequence.

Ply sequence for all the cases remains same which is [0/90/45/-45/-45/45/90/0].

Ply thickness for each case is different. For case (a) & (c), ply thickness is 0.25 mm and for case (b), ply thickness is 0.5 mm.

References

[1] “buffertanks.pdf.” [Online]. Available: https://westank.com/wp-content/docs/brochures/buffertanks.pdf.

[2] Composite, “No Title.” [Online]. Available: http://www.rsc.org/Education/Teachers/Resources/Inspirational/resources/4.3.1.pdf.

[3] “Composite.” [Online]. Available: http://www.keyshone.com/9-interesting-facts-know-aircraft-composite-materials/.

[4] B. ASME, Sec. II Part A Ferrous Material Specifications (Begining to SA-450). 2014.

[5] A. Boiler, “Part A Ferrous Material Specifications (SA-451 to End),” 2014.

[6] P. V. Code, “Part D Properties (Metric),” 2013.

[7] “SA 516 Gr 70 Material Properties.” [Online]. Available: http://www.matweb.com/search/DataSheet.aspx?MatGUID=9ccee2d0841a404ca504620085056e14&ckck=1.

[8] “SA 36 Material Properties.” [Online]. Available: http://www.matweb.com/search/datasheet.aspx?matguid=afc003f4fb40465fa3df05129f0e88e6.

[9] P. V. Code, “Rules for Construction of Pressure Vessels,” 2013.

[10] A. V. Barderas and B. S. S. G. Rodea, “HOW TO CALCULATE THE VOLUMES OF PARTIALLY FULL TANKS,” vol. 2, no. 1, pp. 1–7, 2016.

[11] “Nozzle loads.” [Online]. Available: http://www.piping-engineering.com/nozzle-loads-part-1.html.

[12] D. Moss, Pressure vessel design manual. .

[13] P. D. B. S. Mr. Jiger Modia, Prof. S J Joshib, “Pressure Vessel Design against Wind and Seismic Load,” no. November 2013, 2014.

[14] “ANSYS Composite PrePost.” [Online]. Available: https://www.ansys.com/Products/Structures/ANSYS-Composite-PrepPost.

[15] “Robert M. Jones Mechanics of Composite Materials.pdf.” .

[16] V. Valery and I. Evgeny, Mechanics and Analysis of Composite Materials. .

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