Word Files
Reference for Downloading Educational Files
  2. Facilities - Mechanics
  3. Buckling analysis of graphene multilayer composite nanosheets placed on elastic substrate by non-local theory and DQ method

Buckling analysis of graphene multilayer composite nanosheets placed on elastic substrate by non-local theory and DQ method

Number of pages: 76 File Format: word File Code: 32352
Year: Not Specified University Degree: Master's degree Category: Facilities - Mechanics
Tags/Keywords: Buckling analysis - Composite - Composite nano sheets - DQ method - Elastic bed - Graffen - High order shear theory - Non-local theory
  • Part of the Content
  • Contents & Resources

  • Summary of Buckling analysis of graphene multilayer composite nanosheets placed on elastic substrate by non-local theory and DQ method

    Dissertation for Master's Degree in Mechanics

    Applied Design Orientation

    Abstract:

    Composites have been receiving a lot of attention in recent decades due to their high strength and light weight. Such materials can be subjected to static, impact, dynamic loading and to be subjected to failure that the various failures that occur will cause a strong drop in strength in the structure. Always with the progress of different sciences, engineers think of using different materials in that field. In recent years, with the advent of nanotechnology, engineers felt the need to use different materials in this field. Therefore, it is necessary to conduct research on existing nanoscale compounds such as multilayered nanotubes, multilayered graphene nanobeams, multilayered graphenes, and multilayered nanosheets. In recent years, a lot of research has been done on multilayer nanotubes, but research on multilayer composite nanosheets is limited. In the investigation of these nanomaterials at the nanoscale, there are various theories, one of which is the non-local theory. In this theory, by entering the size parameter, the effects of small dimensions on the nano scale can be well expressed. In this project, we intend to investigate the buckling of graphene multilayer composite nanosheet. Graphene sheets can be considered as orthotropic sheets whose properties are different in both longitudinal and transverse directions. Due to the fact that graphene nanosheets are usually found in elastic environments, we placed the nanosheet on the elastic substrate to consider the effects of the elastic environment. Because nanoplates are usually used in small length-to-thickness ratios and in these conditions, shear effects become important, for this reason, the third-order shear theory has been used so that we can consider these effects well. By using the virtual work method, the balance equations are obtained, and these balance equations are coupled to each other and cannot be solved by analytical methods, so it is necessary to use a numerical method to solve these equations. One of the useful methods in this field is the differential quadratic method, which has high convergence speed in addition to high accuracy. In order to be able to investigate the effects of layer rotation and their arrangement in non-local theory, various numerical analyzes have been performed. Also, the influence of different parameters such as plate dimensions, thickness, elastic bed coefficient and non-local parameter on the non-local behavior of nano-plate is investigated. rtl;">

    1. Chapter 1: General Research

    1-1-Introduction

    Nanotechnology deals with various materials and their application in areas such as materials engineering, electronics, computers, sensors, operators and machines on a nano scale. Atoms and molecules are considered as the building blocks of engineering materials and electronic devices of the future. At the nanoscale, many fields of science and theory merge because they are based on atoms and molecules. To put it more simply, the subject of nanotechnology is the knowledge and technology of direct or indirect use of atoms and molecules in structures in order to carry out specific missions. The prefix nano indicates a length scale unit equal to meters, which is hundreds to thousands of times smaller than a biological cell or a bacterium. In the nanoscale, the dimensions of the structure reach 10 or 100 atoms and completely new physical and chemical phenomena are observed. Therefore, one of the interesting and effective aspects is the use of an atomic pattern suitable for the specific function desired by the designer and the creation of the material based on the designer's wishes. The first mention of the scientific and technical possibility of making new materials based on stacking atoms together was presented by the Nobel Prize-winning physicist Richard Feynman [1] in his lecture on "Infinite Space at the End".. In that speech that was held at the American Society of Physicists in 1959, he stated that if our ability to observe what we do at the nano scale and the ability to do things at the atomic scale is developed, great help can be given to the problems of chemistry and biology, a development that I think is inevitable. Manufactured products are generally made of atomic composition, and the characteristics of each one depend on how its atoms are arranged together. If we change the composition of atoms in coal, we can make diamonds. If we change the composition of atoms in sand and use a little bit of other elements in it, we can make a computer chip. Today's molecular scale production methods are in their infancy. Molding, milling, turning, and even lithography move atoms in statistically large batches. Just like stacking children's toy blocks with punching gloves. You can only move these blocks around and stack them on top of each other. But you won't be able to make them in any orderly way you want. In the future, nanotechnology will allow us to remove the boxing gloves from our hands. We will be able to take nature's building blocks (atoms and molecules) individually, easily and cheaply, and put them together in almost any way we like. This issue is considered essential and fundamental in order to continue the revolution in hardware in the next decade, and it makes it possible to create a new generation of products that are cleaner, stronger and more accurate. It is worth noting that these days, the word "new technology" has received a lot of attention and is used to express all kinds of research works that have dimensional characteristics less than one nano (one millionth of a millimeter).

  • Contents & References of Buckling analysis of graphene multilayer composite nanosheets placed on elastic substrate by non-local theory and DQ method

    List:

    Abstract: 1.

    1.  Chapter 1: General research. 2

    1-1-Introduction. ..2

    1-2-micro/nanoelectromechanical systems. 4

    1-3-Research objectives and project implementation process. 5

    2.  Second chapter: Research literature. 8

    2-1-Theoretical discussions. 8

    2-2-Different methods of modeling at different scales. 8

    2-2-1- Atomic modeling method. 8

    2-2-2- multi-scale methods. 9

    2-2-3- continuous atomic method. 9

    2-2-4- Quantum mechanics. 11

    2-2-5- molecular dynamics. 12

    2-2-6- Monte Carlo method. 12

    2-2-7- Dislocation dynamics. 13

    2-2-8- Molecular mechanics method. 13

    2-2-9- high-order theories of continuous environment. 14

    2-2-9-1-Theory of Fractions and Theory of Coupled Stresses. 16

    2-3-Nonlocal elasticity. 18

    2-4-Introducing sheet theories. 21

    2-5-Classical sheet theory. 22

    2-6-first order shear deformation theory. 23

    2-7-3rd order shear theory. 23

    2-8-Nano structures. 24

    2-9-carbon nanotubes can be divided into five categories. 24

    2-10-elastic environment. 26

    2-11-Research background. 27

    2-12- Summary of the second chapter. 31

    3. Chapter 3: Relationships and Formulas 32

    3-1-Nano plate modeling and numerical solution presentation. 32

    3-2-non-local elasticity theory. 32

    3-3-extracting the equations of motion. 35

    3-4- Analytical solution. 51

    3-5-Numerical solution. 52

    3-5-1- GDQ numerical method. 52

    3-5-1-1 determining the coordinates of the nodes. 55

    3-5-1-2 determining the weight coefficients. 56

    4.  Chapter 4:: Simulating the results. 59

    4-1-Numerical results. 59

    4-2-Authentication. 61

    4-3-Nano plate buckling. 63

    4-3-1- Effect of plate dimensions on buckling force. 64

    4-3-2- Effect of dimensional parameters and boundary conditions on buckling force. 67

    4-4-The effect of the dimensional parameter on different modes. 68

    4-4-1- The effect of Winkler modulus on buckling force. 70

    4-4-2- Examining the effect of the Winkler coefficient on different modes. 72

    4-5-Effect of Winkler coefficient on buckling force for different lengths. 73

    4-5-1- Effect of Pasternak shear coefficient on buckling force. 75

    4-5-2- Effect of Pasternak shear coefficient on different modes of buckling force. 75

    5.  Chapter Five: Conclusion and suggestions. 77

    5-1- Proposal for future research. 78

    6.  Resources. 80

    Source:

    1. 

    [1].     Li, C. and T.-W. Chou, A structural mechanics approach for the analysis of carbon nanotubes. International Journal of Solids and Structures, 2003. 40(10): p. 2487-2499.

    [2].       Cosserat, E., et al., Théorie des corps déformables. 1909: A. Hermann Paris.

    [3].      Eringen, A.C., On the foundations of electroelastostatics. International Journal of Engineering Science, 1963. 1(1): p. 127-153.

    [4].      Eringen, A.C., Linear theory of micropolar viscoelasticity. International Journal of Engineering Science, 1967. 5(2): p. 191-204.

    [5].      Tauchert, T., W. Claus, and T. Ariman, The linear theory of micropolar thermoelasticity. International Journal of Engineering Science, 1968. 6(1): p. 37-47.

    [6].      Eringen, A.C., Screw dislocation in non-local elasticity. Journal of Physics D: Applied Physics, 1977. 10(5): p. 671.

    [7].      Eringen, A.C., Microcontinuum field theories: foundations and solids. Vol. 487. 1999: Springer New York.

    [8].      Mindlin, R. and H. Tiersten, Effects of couple-stresses in linear elasticity. Archive for Rational Mechanics and Analysis, 1962. 11(1): p. 415-448.

    [9].      Mindlin, R., Influence of couple-stresses on stress concentrations. Experimental Mechanics, 1963. 3(1): p. 1-7.

    [10].    Banks Jr., C.B. and M. Sokolowski, On certain two-dimensional applications of the couple stress theory. International Journal of Solids and Structures, 1968. 4(1): p. 15-29.

    [11].    Weitsman, Y., Couple-stress effects on stress concentration around a cylindrical inclusion in a field of uniaxial tension. Journal of Applied Mechanics, 1965. 32: p.

    [12].    Murmu, T. and S. Pradhan, Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Physica E: Low-dimensional Systems and Nanostructures, 2009. 41(7): p. 1232-1239.

    [13].    Xiang, Y., C. Wang, and S. Kitipornchai, Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations. International journal of mechanical sciences, 1994. 36(4): p. 311-316.

    [14].    Liew, K., X. He, and S. Kitipornchai, Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix. Acta Materialia, 2006. 54(16): p. 4229-4236.

    [15].    Bever, M. and P. Duwez, Gradients in composite materials. Materials Science and Engineering, 1972. 10: p. 1-8.

    [16].    Richly, W., Treatise on powder metallurgy, Vol. 4: Classified and annotated bibliography 1950-1960. Cl. G. Goetzel. Part. I: Literature Survey Interscience Publishers, J. Wiley & Sons, New York/London, 1963, 837 S., oa. 16 x 24 cm, geb. sh. 300,—. Materials and Corrosion, 1964. 15(10): p. 883-883.

    [17].    Markworth, A.J. and J.H. Saunders, A model of structure optimization for a functionally graded material. Materials Letters, 1995. 22(1): p. 103-107. [18].    Gasik, M.M., Micromechanical modeling of functionally graded materials. Computational Materials Science, 1998. 13(1): p. 42-55.

    [19].    Grujicic, M. and Y. Zhang, Determination of effective elastic properties of functionally graded materials using Voronoi cell finite element method. Materials Science and Engineering: A, 1998. 251(1): p. 64-76.

    [20].    Aboudi, J., M.-J. Pindera, and S.M. Arnold, Higher-order theory for functionally graded materials. Composites Part B: Engineering, 1999. 30(8): p. 777-832.

    [21].    Fleck, N. and J. Hutchinson, A phenomenological theory for strain gradient effects in plasticity. Journal of the Mechanics and Physics of Solids, 1993. 41(12): p. 1857-1825.

    [22].    Lam, D., et al., Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids, 2003. 51(8): p. 1477-1508.

    [23].    Kong, S., et al., Static and dynamic analysis of micro beams based on strain gradient elasticity theory. International Journal of Engineering Science, 2009. 47(4): p. 487-498.

    [24].    Wang, B., J. Zhao, and S. Zhou, A micro scale Timoshenko beam model based on strain gradient elasticity theory. European Journal of Mechanics-A/Solids, 2010. 29(4): p. 591-599.

    [25].    Sahmani, S. and R. Ansari, On the free vibration response of functionally graded higher-order shear deformable microplates based on the strain gradient elasticity theory. Composite Structures, 2012. [26].    Hu, Y.-G., et al., Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes. Journal of the Mechanics and Physics of Solids, 2008. 56(12): p. 3475-3485.

    [27].    Peddieson, J., G.R. Buchanan, and R.P. McNitt, Application of nonlocal continuum models to nanotechnology. International Journal of Engineering Science, 2003. 41(3): p. 305-312.

    [28].    Aydogdu, M., A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration. Physica E: Low-dimensional Systems and Nanostructures, 2009. 41(9): p. 1651-1655.

    [29].    Civalek, ?. and C. Demir, Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory. Applied Mathematical Modeling, 2011. 35(5): p. 2053-2067.

    [30].    Reddy, J., Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science, 2007. 45(2): p. 288-307.

    [31].    Reddy, J. and S. Pang, Nonlocal continuum theories of beams for the analysis of carbon nanotubes. Journal of Applied Physics, 2008. 103(2): p. 023511-023511-16.

    [32].    Reddy, J.

Buckling analysis of graphene multilayer composite nanosheets placed on elastic substrate by non-local theory and DQ method
How To Access The File
Related Contents:
Number of pages: 95 Category: Facilities - Mechanics

Dissertation for Master's Degree in Mechanical Engineering (Applied Design) Abstract In this research, the analysis of vibrations, buckling and wave propagation of wrapped nano beam under axial load on Pasternak substrate is discussed. First, the displacement and displacement field of the wrapped beam is obtained. Then, using the obtained displacement field, strain-displacement ...

Number of pages: 108 Category: Facilities - Mechanics

Master's Thesis in Mechanical Engineering-Applied Design Abstract In this thesis, classical sheet theories, first-order shear deformation theory and refined two-variable theory for the free vibration problem are investigated using standard finite element and hierarchical finite element methods. The refined two-variable theory is an equivalent single-layer theory, in which two ...

Number of pages: 124 Category: Facilities - Mechanics

Master's Thesis on Car Structure and Body Abstract In recent years, many researchers have allocated their attention to a special category of materials, memory materials. The ability to absorb and control vibrations actively or passively, respectively, is affected by the features of shape memory and hysteresis energy loss caused by the pseudo-elastic characteristics of these ...

Number of pages: 64 Category: Facilities - Mechanics

Master's Thesis of Mechanical Engineering-Applied Design Abstract In many applications, graphene (monolayer or multilayer) is used in the polymer matrix as a composite. In this research, ideal graphene with a hexagonal bond shape between atoms, located in a polymer matrix, with different boundary conditions, including gripped and simple, under biaxial external compressive ...

Number of pages: 107 Category: Civil Engineering

Dissertation for Master's Degree in Civil Engineering, Structures, Abstract: This thesis is the results of a numerical and parametric study on the effect of reinforcing reinforced concrete shear wall with FRP composite and applying the results of the finite element method. The finite element program is compared and calibrated against experimental data. Then, the numerical ...

Number of pages: 117 Category: Civil Engineering

Civil Engineering Master's Thesis, Soil and Foundation Engineering Abstract In this thesis, in order to analyze the behavior of surface foundations based on reinforced soil, a simple physical method based on the resistance of materials called ""cone method"" is used, which is actually used as an alternative to the exact solution methods that are based on the three-dimensional ...

Number of pages: 107 Category: Facilities - Mechanics

Dissertation for M.Sc Master's Degree, Mechanical Engineering - Applied Design Abstract Modern wind turbines today tend to vibrate a lot due to their elastic, long and narrow structure. Therefore, all components of wind turbines should be subjected to vibration and modal analysis in the design stages, and their natural frequencies should be reviewed with turbine excitation ...

Number of pages: 140 Category: Facilities - Mechanics

Master's Thesis in Mechanical Engineering (Applied Design): Abstract of the analysis of leading damage in pin connections of composite materials. The purpose of this research is to analyze the leading damage in pin connections of composite materials. To do this, finite element software ABAQUS and FORTRAN programming have been used. The contact between the composite plate with ...

Number of pages: 76 Category: Facilities - Mechanics

Dissertation for Master's Degree in Mechanical Engineering Field: Applied Design Abstract In this thesis, stability analysis of composite beam reinforced with carbon nanotubes on elastic support under axial force is investigated. The distribution of nanotubes is assumed to be uniform[1]. To determine the properties of materials reinforced with nanotubes, the results of molecular ...

Number of pages: 129 Category: Facilities - Mechanics

Dissertation for Master's Degree in Mechanical Engineering (Applied Design) Abstract: Electromechanical micro and nano systems have been noticed due to their distinctive features and unique characteristics, mainly in the two fields of sensors and sensors, in various sciences such as mechanics, aerospace and medicine. Electrostatic stimulation is one of the simplest and most ...