ORIGINAL_ARTICLE
Mechanical Properties of Graphene/Epoxy Nanocomposites under Static and Flexural Fatigue Loadings
In the present study, the effect of various weight fractions of graphene nanoplatelet (GPL) on flexural fatigue behavior of epoxy polymer has been investigated at room temperature and generally the temperature was monitored on the surface of specimen during each test. The flexural stiffness of grapheme nano-platelet/epoxy nanocomposites at 0.1, 0.25 and 0.5 wt. % as a main effective parameter on flexural bending fatigue was considered. The samples were implemented to different displacement fatigue amplitudes and it led to the known bending strength ratio. Finally, the flexural fatigue responses of graphene nano-platelet/epoxy nanocomposites at mentioned graphene contents were taken into account. The experimental results show that the addition of 0.25 wt. % of graphene nano-platelet on fatigue life was more effective in comparison with 0.1 and 0.5 wt. % epoxy graphene nanocomposites. According to the addition of graphene nano-platelets, a remarkable increase in fatigue life of epoxy was observed. For instance, at the bending strength ratio equal to 43% by adding 0.1, 0.25 and 0.5 wt. % of graphene into epoxy resin, 22.4, 27.4 and 17 times improvement in flexural bending fatigue life of the neat epoxy were observed, respectively.
http://macs.journals.semnan.ac.ir/article_274_3311cbba13d2b2091b06edbc824fa159.pdf
2014-04-01T11:23:20
2017-11-19T11:23:20
1
7
10.22075/macs.2014.274
Mechanical properties
boundary layer
Flexural bending fatigue
Displacement control
Graphene nano-platelets
Nanocomposites
Mahmood
Shokrieh
shokrieh@iust.ac.ir
true
1
Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran.
Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran.
Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran.
LEAD_AUTHOR
Masood
Esmkhani
esmkhani@iust.ac.ir
true
2
Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran.
Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran.
Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran.
AUTHOR
Amir
Haghighatkhah
ahaqiqatkhah@mecheng.iust.ac.ir
true
3
Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran.
Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran.
Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran.
AUTHOR
[1] Paepegem VW, Degrieck J. Experimental Setup for and Numerical Modeling of Bending Fatigue Experiments on Plain Woven Glass/epoxy Composites. Compos Struct 2001; 51: 1-8.
1
[2] Paepegem VW, Degrieck J. A New Coupled Approach of Residual Stiffness and Strength for Fatigue of Fibre-reinforced Composites, Int J Fatigue 2002; 24: 747-762.
2
[3] Paepegem VW, Degrieck J. Fatigue Degradation Modelling of Plain Woven Glass/epoxy Composites. Compos Part A 2001; 32: 1433-1441.
3
[4] Ramkumar A, Gnanamoorthy R. Effect of nanoclay addition on the displacement-controlled flexural fatigue behaviour of a polymer. Mater Sci 2010; 45: 4180–87.
4
[5] Rajeesh AK, Gnanamoorthy R, Velmurugan R. Effect of humidity on the indentation hardness and flexural fatigue behavior of polyamide 6 nanocomposite. Mater Sci and Eng 2010; 527: 2826–2830.
5
[6] Timmaraju MV, Gnanamoorthy R, Kannan K. Effect of environment on flexural fatigue behavior of polyamide 66/hectorite nanocomposites. Int J Fatigue 2011; 33: 541–48.
6
[7] Timmaraju MV, Gnanamoorthy R, Kannan K. Effect of initial imbibed moisture content on flexural fatigue behavior of polyamide 66/hectorite nanocomposites at laboratory condition. Mater Sci and Eng 2011; 528: 2960–2966.
7
[8] Shokrieh MM, Esmkhani M, Haghighatkhah AR. Flexural fatigue behaviour of carbon nanofiber/epoxy nanocomposites. Fatigue Fract Eng Mater Struct 2014; 37: 553-560.
8
[9] Shokrieh MM, Esmkhani M, Haghighatkhah AR. Displacement-controlled flexural bending fatigue behaviour of graphene/epoxy nanocomposites. Compos Mater DOI: 10.1177/0021998313503483 (in press)
9
[10] Shokrieh MM, Esmkhani M, Haghighatkhah AR. Zhao Z. Flexural fatigue behaviour of synthesized graphene/carbon-nanofiber/epoxy hybrid nanocomposites. Mater Des 2014; 62: 401-408.
10
[11] Böger L, Sumfleth J, Hedemann H, Schulte K. Improvement of fatigue life by incorporation of nanoparticles in glass fibre reinforced epoxy. Compos Part A-APPL. S 2010; 41: 1419–1424.
11
[12] Fritzschen J, Lorenz H, Klüppel M. CNT Based Elastomer-Hybrid-Nanocomposites with Promising Mechanical and Electrical Properties. Macrmol Mater and Eng 2009; 294: 551–560.
12
[13] Li J, Wong PS, Kim JK. Hybrid nanocomposites containing carbon nanotubes and graphite nanoplatelets. Mater Sci Eng A 2008; 484: 660–663.
13
[14] ASTM B593-96. Standard Test Method for Bending Fatigue Testing for Copper-Alloy Spring Materials (2003).
14
[15] Berchem K, Hocking MG. A simple plane bending fatigue and corrosion fatigue testing machine, Measurement Sci and Technol 2006;17: 60–66.
15
[16] ASTM D 790–10, Standard test methods for flexural properties of unreinforced and reinforced plastics and electrical insulating materials, 2010.
16
[17] Shokrieh MM, M. Esmkhani, Shokrieh Z., Zhao Z. Stiffness prediction of grapheme nanoplatelet/epoxy nanocomposites by a combined molecular dynamics–micromechanics method, Comput Mater Sci 2014; 92: 444–450.
17
ORIGINAL_ARTICLE
Predicting Young’s Modulus of Aggregated Carbon Nanotube Reinforced Polymer
Prediction of mechanical properties of carbon nanotube-based composite is one of the important issues which should be addressed reasonably. A proper modeling approach is a multi-scale technique starting from nano scale and lasting to macro scale passing in-between scales of micro and meso. The main goal of this research is to develop a multi-scale modeling approach to extract mechanical properties of CNT based nanocomposites emphasizing on meso-scale parameters. Agglomeration and non-straight shapes of CNTs have to be captured in this specific scale. The representative volume element (RVE) for meso-scale is identified considering local concentration of CNTs as the main source of inhomogeneity in the investigated material region. Irregular tessellation technique on the basis of Voronoi method and Bayes algorithm is employed to partition the RVE at meso scale into constitutive polygons containing one single aggregate. A MATLAB code is written to perform this stage on the basis of random pattern. Mechanical properties of the tasseled regions are extracted by a combination of micromechanics rule addressing local position and aggregates in the material region. A bounding technique accounting for non-straight shape of CNT is utilized to consider the any arbitrary shape of wavy CNT. Investigated material region at macro scale is divided into constitutive blocks assigning random volume fractions of CNT to each block implying non-uniformed dispersion of CNT. The results demonstrate the importance of considering the position of local aggregates in modeling procedure. The obtained results of modeling are compared with experimentally measured mechanical properties.
http://macs.journals.semnan.ac.ir/article_275_7f19f550ecd32822c30d1f775d1a048d.pdf
2014-04-01T11:23:20
2017-11-19T11:23:20
9
16
10.22075/macs.2014.275
Carbon nanotube
Multi-scale modeling
Irregular tessellation
Stochastic modeling
Roham
Rafiee
roham.rafiee@ut.ac.ir
true
1
Composites Research Laboratory, Faculty of New Sciences and Technologies, University of Tehran, Tehran, 1439955941 Iran
Composites Research Laboratory, Faculty of New Sciences and Technologies, University of Tehran, Tehran, 1439955941 Iran
Composites Research Laboratory, Faculty of New Sciences and Technologies, University of Tehran, Tehran, 1439955941 Iran
LEAD_AUTHOR
Vahid
Firouzbakht
firouzbakht@ut.ac.ir
true
2
Composites Research Laboratory, Faculty of New Sciences and Technologies, University of Tehran, Tehran, 1439955941 Iran
Composites Research Laboratory, Faculty of New Sciences and Technologies, University of Tehran, Tehran, 1439955941 Iran
Composites Research Laboratory, Faculty of New Sciences and Technologies, University of Tehran, Tehran, 1439955941 Iran
AUTHOR
[1] Dai H. Carbon nanotubes: opportunities and challenges. Surf Sci 2002; 500(1-3): 218–41
1
[2] Kang, Heung YY, Kim JH, Lee JW, Gollapudi R, Subramaniam S, et al. Introduction to carbon nanotube and nanofiber smart materials, Compos. Part B-Engineering 2006; 37(6): 382–94
2
[3] Salvetat-Delmotte JP, Rubio A. Mechanical properties of carbon nanotubes: a fiber digest for beginners. Carbon 2002; 40(10) 1729–734
3
[4] Lau KT, Gu C, Hui D. A critical review on nanotube and nanotube/nanoclay related polymer composite materials, Compos Part B-Engineering 2006; 37(6): 425–36
4
[5] Qian D, Dickey E, Andrews R, Rantell T. Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites, Appl Phys Lett 2000; 76(20): 2868-870
5
[6] Schadler L, Giannaris SC, Ajayan PM. Load transfer in carbon nanotube epoxy composites, Appl Phys Lett 2000; 73(26): 3842-844
6
[7] Zhu J, Peng H, Rodriguez-Macias F, Margrave J, Khabashesku V, Imam A, Lozano K, Barrera E. Reinforcing epoxy polymer composites through covalent integration of functionalized nanotubes, Adv Funct Mater 2004; 14(7): 643–48
7
[8] Odegard GM, Gates TS, Wise KE, Park C, Siochi EJ. Constitutive modeling of nanotube–reinforced polymer composites, Compos Sci Technol 2003; 63(11): 1671–687
8
[9] Ashrafi B, Hubert P. Modeling the elastic properties of carbon nanotube array/polymer composites, Compos Sci Technology 2006; 66(3-4): 387–96
9
[10] Han Y, Elliott J. Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites, Compos Mater Sci 2007; 39 :315–23.
10
[11] Villoria RG, Miravete A. Mechanical model to evaluate the effect of the dispersion in nanocomposites, Acta Mater 2007; 55(9) 3025–031
11
[12] Tserpes KI, Panikos P, Labeas G, Panterlakis SpG, Multi-scale modeling of tensile behavior of carbon nanotube-reinforced composites, Theor Appl Fract mech 2008; 49(1): 51-60
12
[13] Frankland SJV, Harik VM, Odegard GM, Brenner DW, Gates TS. The stress–strain behavior of polymer–nanotube composites from molecular dynamics simulation, Compos Sci Technol 2003; 63(11): 1655–661
13
[14] Mokashi VV, Qian D, Liu Y. A study on the tensile response and fracture in carbon nanotube-based composites using molecular mechanics, Compos Sci Technol 2007; 67(3-4): 530–40
14
[15] Shokrieh MM, Rafiee R. On the tensile behavior of an embedded carbon nanotube in polymer matrix with non-bonded interphase region, Compos Struct 2010; 92(3): 647-52
15
[16] Selmi A, Friebel C, Doghri I, Hassis H. Prediction of the elastic properties of single walled carbon nanotube reinforced polymers: A comparative study of several micromechanical models, Compos Sci Technol 2007; 67(10): 2071–084
16
[17] Seidel GD, Lagoudas DC. Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites, Mech Mater 2006; 38(8-10): 884–907
17
[18] Liu Y, Nishimura N, Otani Y. Large-scale modeling of carbon-nanotube composites by a fast multipole boundary element method, Comput Mater Sci 2005; 34(2): 173-87
18
[19] Thostenson ET, Ren Z, Chou TW. Advances in the science and technology of carbon nanotubes and their composites: a review, Compos Sci Technol 2001; 61(13): 1899–912
19
[20] Anumandla V, Gibson RF. A comprehensive closed form micromechanics model for estimating the elastic modulus of nanotube-reinforced composites, Compos Part A 2006; 37(12):2178–185
20
[21] Yeh MK, Tai NH, Liu JH. Mechanical peroperties of phenolic-Based nanocomposites reinforced by multi-walled carbon nanotubes and carbon fibers, Compos Part A 2008; 39(4):677–84
21
[22] Shao LH, Luo RY, Bai SL,Wang J. Prediction of effective moduli of carbon nanotube-reinforced composites with waviness and debonding. Compos Struct 2009; 87(3): 274-281
22
[23] Montazeri A, Javadpour J, Khavandi A, Tcharkhtchi A, Mohajeri A. Mechanical properties of multi-walled carbon nanotube/epoxy composites, Mater Des 2010; 31: 4202–208
23
[24] Shady E, Gowayed Y. Effect of nanotube geometry on the elastic properties of nanocomposites, Compos Sci Technol 2010; 70(10): 1476–481
24
[25] Omidi M, Rokni DTH, S.Milani A, Seethaler RJ, Arasteh R. Prediction of the mechanical characteristics of multi-walled carbon nanotube/epoxy composites using a new form of the rule of mixtures, Carbon 2010; 48(11): 3218–228
25
[26] Fisher FT, Bradshaw RD, Brinson LC. Fiber waviness in nanotube-reinforced polymer composites—I: modulus predictions using effective nanotube properties, Compos Sci Technol 2003; 63(11): 1689–1703
26
[27] Bradshaw RD, Fisher FT, Brinson LC. Fiber waviness in nanotube-reinforced polymer composites: II. Modeling via Numerical approximation of the dilute strain concentration tensor. Compos Sci Technol 2003; 63(11): 1689–1703
27
[28] Ayatollahi MR, et al. Effect of multi-walled carbon nanotube aspect ratio on mechanical and electrical properties of epoxy-based nanocomposites. Polym Test 2011; 30(5): 548-56.
28
[29] Martone A, Faiella G, Antonucci V, Giordano M, Zarrelli M. The effect of the aspect ratio of carbon nanotubes on their effective reinforcement modulus in an epoxy matrix, Compos Sci Technol 2011; 71(8): 1117–1123
29
[30] Srivastava VK, Singh S. A Micro-Mechanical model for elastic modulus of multi-walled Carbon-Nanotube/Epoxy resin composites, Int J of Composite Materials 2012; 2(2): 1-6.
30
[31] Li C, Chou TW. Multiscale modeling of carbon nanotube reinforced polymer composites, Nanosci Nanotechnol 2003; 3(5): 423-30.
31
[32] Tsai JL, Tzeng SH, Chiu YT, Characterizing elastic properties of carbon nanotubes/polyimide nancomposites using multi-scale simulation, Compos. Part B-Engineering 2010; 41: 106-115
32
[33] Luo D, Wang WX, Takao Y. Effects of the distribution and geometry of carbon nanotubes on the macroscopic stiffness and microscopic stresses of nanocomposites, Compos Sci Technol 2007; 67(14): 2947–2958
33
[34] Spanos PD, Kontsos A. A multiscale monte carlo finite element method for determining mechanical properties of polymer nanocomposites, Probabilis Eng Mech 2007; 23(4): 456-70
34
[35] Shokrieh MM, Rafiee R. Development of a full range multi-scale model to obtain elastic properties of CNT/polymer composites. Iran Polym J 2012; 21: 397–402
35
[36] Okabe A, Boots B, Kokichi Sugihara K, Chiu SN. Spatial Tessellations – Concepts and Applications of Voronoi Diagrams. 2nd edition. John Wiley; 2000
36
[37] Mishnaevsky Jr. Computational esomechanics of composites. John Wiley; 2007
37
[38] Shokrieh MM, Rafiee R. Investigation of nanotube length effect on the reinforcement efficiency in carbon nanotube based composites, Compos Struct 2010; 92 (10): 2415-420
38
[39] Shokrieh MM, Rafiee R. Prediction of mechanical properties of an embedded carbon nanotube in polymer matrix based on developing equivalent long fiber, Mech Res Commun 2010; 37(2):235-240
39
[40] Shokrieh MM, Rafiee R. On the tensile behavior of an embedded carbon nanotube in polymer matrix with non-bonded interphase region, Compos Struct 2010; 92(3): 647-652
40
[41] Hashin,Z. The elastic moduli of heterogeneous materials, Appl Mech 1962; 29: 143–150
41
[42] Christensen, RM. Mechanics of Composite Materials. New York: Wiley-Interscience; 1979
42
[43] Shi DL, Feng XQ, Huang YY, Hwang KC, Gao H. The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composite, Eng Mater Technol 2004; 126: 250-57
43
[44] Rafiee R. Influence of carbon nanotube waviness on the stiffness reduction of CNT/polymer composites, Compos Struct 2013; 97: 304-09.
44
[45] Ogasawara T, Ishida Y, Ishikawa T, Yokota R. Characterization of multi-walled carbon nanotube/phenylethynyl terminated polyimide composites. Compos Part A 2004; 35(1): 67–74.
45
[46] Kanagaraj S, Varanda FR, Zhiltsova TV, Oliveira MSA, Simoes JAO. Mechanical properties of high density polyethylene/carbon nanotube composites. Compos Sci Technol 2007; 67(15-16): 3071-3077
46
[47] Xiao SP, Zhang LC, Zarudi I. Mechanical and rheological properties of carbon nanotube-reinforced polyethylene composites. Compos Sci Technol 2007; 67(2): 177-82.
47
ORIGINAL_ARTICLE
Biaxial Buckling and Bending of Smart Nanocomposite Plate Reinforced by CNTs using Extended Mixture Rule Approach
In this research, the buckling and bending behaviour of smart nanocomposite plate reinforced by single- walled carbon nanotubes (SWCNTs) under electro-magneto-mechanical loadings is studied. The extended mixture rule approach is used to determine the elastic properties of nanocomposite plate. Equilibrium equations of smart nanocomposite plate are derived using the Hamilton’s principle based on the classical plate theory (CPT). The nonlocal critical biaxial buckling load and the nonlocal deflection of smart nanocomposite plate are obtained by applying the Eringen’s theory and Navier’s method. In this article, the influences of applied voltage, magnetic field, aspect ratios, nonlocal parameter, and elastic foundation coefficients on the critical buckling load and deflection of smart nanocomposite plate are investigated. The nonlocal critical biaxial buckling load of smart nanocomposite plate increases with the increase in applied voltage and magnetic field intensity. The nonlocal deflection of smart nanocomposite plate decreases with an increase in the magnetic field intensity. Also, the stability of smart nanocomposite plate increases in the presence of elastic foundation.
http://macs.journals.semnan.ac.ir/article_276_b5abae97c9bf4162d5a91192e6d55682.pdf
2014-04-01T11:23:20
2017-11-19T11:23:20
17
26
10.22075/macs.2014.276
Biaxial buckling and bending
Smart nanocomposite plate
Electro-magneto-mechanical loadings
The extended mixture rule approach
Classical plate theory
Mehdi
Mohammadimehr
mmohammadimehr@kashanu.ac.ir
true
1
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
LEAD_AUTHOR
Borhan
Rousta-Navi
borhanrousta@yahoo.com
true
2
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
AUTHOR
Ali
Ghorbanpour-Arani
aghorban@kashanu.ac.ir
true
3
Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan,Iran
Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan,Iran
Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan,Iran
AUTHOR
[1] Fukuda H, Kawata K, On Young’s modulus of short fibre composites. Sci Technol 1974; 7(20): 22-7.
1
[2] Jin Y, Yuong FG, Simulation of elastic properties of single-walled carbon nanotubes. Compos Sci Technol 2003; 63 (15): 15-7.
2
[3] Chang T, Gao H, Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model. Mech Phys Sol2003; 51 (10): 74-59.
3
[4] Griebel M, Hamaekers J, Molecular dynamics simulations of the elastic moduli of polymer–carbon nanotube composites. Mech Eng, 2004; 193 (17): 88-73.
4
[5] Han Y, Elliott J, Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Comput Mater Sci 2007; 39 (31): 23–5.
5
[6] Zhu R, Pan E, Roy AK, Molecular dynamics study of the stress–strain behavior of carbon-nanotube reinforced, composites. Mater Sci Eng 2007; 447: 51–7.
6
[7] Li X, Gao H, Scrivens WA, Fei D, Xu X, Sutton MA, Reynolds AP, Myrick ML, Reinforcing mechanisms of single-walled carbon nanotubereinforced polymer composites. Nanosci Nanotechnol 2007; 7(17): 23-9.
7
[8] Joshi P, Upadhyay SH, Evaluation of elastic properties of multi walled carbon nanotube reinforced composite, Comput Mater Sci 2014; 81: 338-332.
8
[9] Salehi-Khojin A, Jalili N, Buckling of boron nitride nanotube reinforced piezoelectric polymeric composites subject to combined electro-thermo-mechanical loadings, Compos Sci Technol 2008; 68: 1501–1489.
9
[10] Vodenitcharova T, Zhang LC, Bending and local buckling of a nanocomposite beam reinforced by a single-walled carbon nanotube. Int J Sol Struct 2006; 43 (30): 24-6.
10
[11] Shen HS, Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments. Part II: Pressure-loaded shells. Compos Struct 2011; 93: 2496-503.
11
[12] ShaatM, MahmoudFF, GaoXL, FaheemAF, Size-dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects, Int J Mech Sci 2014; 79: 37-31. [13] Golmalani ME, Rezataleb J, Nonlinear bending analysis of orthotropic nanoscale plates in an elastic matrix based on nonlocal continuum mechanics, Compos Struct2014; 111:97- 85. [14] Malekzade P, a Shojaee M, Buckling analysis of quadrilateral laminated plates with CNT reinforced composite layers, Thin-Walled Struct 2013; 71: 118-108. [15] Mohammadimehr M, Mohandes M, Moradi M, size dependent effect on the buckling and vibration analysis of double bonded nanocomposite piezoelectric plate reinforced by BNNT based on modified couple stress theory, Vib Control, first published on August 5, 2014 as doi:10.1177/1077546314544513.
12
[16] Mohammadimehr M, Rousta Navi B, Ghorbanpour Arani A, Surface stress effect on the nonlocal biaxial buckling and bending analysis of piezoelectric nano plate reinforced by CNT using Eshelby-Mori-Tanaka approach, Sol Mech, Accepted 6 August 2014.
13
[17] Ghorbanpour Arani A, Kolahchi R, Vossough H, Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory. Physica B 2012; 407: 4465–4458.
14
[18] Murmu T, Pradhan SC, Buckling of biaxially compressed orthotropic plates at small scales, Mech Res Commun2009; 36: 938–933.
15
[19] Zhu p, Lei ZX, Liew KM, Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory. Compos Struct 2012; 94: 1460– 1450.
16
[20] Lei ZX, Liew KM, Yu JL, Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method. Compos Struct 2013; 98: 168– 160.
17
[21] Jafari Mehrabadi S, Sobhani Aragh B, Khoshkhahesh V, Taherpour A, Mechanical buckling of rectangular nanocomposite plate reinforced by aligned and straight single-walled carbon nanotubes. Compos: Part B 2012; 43: 2040– 2031.
18
[22] Alzahrani EO, Zenkour AM, Sobhy M, Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium. Compos Struct2013; 105: 172– 163.
19
[23] Alibeigloo A, Static analysis of functionally graded carbon nanotube-reinforced composite plate embedded in piezoelectric layers by using theory of elasticity. Compos Struct 2013; 95: 622– 612.
20
[24] Mohammadimehr M, Rahmati A, Small scale eﬀect on electro-thermo-mechanical vibration analysis of single-walled boron nitride nanorods under electric excitation, Turkis J Env Sci 2013; 37: 15-1.
21
[25] Malekzadeh P, Setoodeh AR, Alibeygi Beni A, Small scale effect on the thermal buckling of orthotropic arbitrary straight-sided quadrilateral nanoplates embedded in an elastic medium. Compos Struct 2011; 93: 2083– 9.
22
[26] Rahmati A H, Mohammadimehr M, Vibration analysis of non-uniform and non-homogeneous boron nitride nanorods embedded in an elastic medium under combined loadings using DQM, Physica B: Condensed Matter 2014, 440: 98-88.
23
[27] Mohammadimehr M, Saidi A R, Ghorbanpour Arani A, Arefmanesh A, Han Q, Buckling analysis of double-walled carbon nanotubes embedded in an elastic medium under axial compression using non-local Timoshenko beam theory, Proc. J of IMech E Part C: Mech Eng Sci2011, 225: 506-498.
24
[28] Kraus J, Electromagnetics. USA: McGrawHill Inc., 1984.
25
[29] Ghorbanpour Arani A, Maghamikia Sh, Mohammadimehr M, Arefmanesh A, Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods. Mech Sci Technol 2011; 25 (3): 820-809
26
ORIGINAL_ARTICLE
An Analytical Study on Effects of adding Nanoparticles to Water and Enhancement in Thermal Properties Based on Falkner-Skan Model
In the age of technology, it is vital to cool down different parts of a device to use it more beneficially. Using nanofluids is one of the most common methods which has shown very effective results. In this paper, we have rephrased a classic equation in fluid mechanics, i.e. the Falkner-Skan boundary layer equation, in order to be used for nanofluid. This nonlinear equation, which was presented by Liao, has been solved by Homotopy Analysis Method (HAM). This method is very capable to solve a wide range of nonlinear equations. The physical interpretation of results which are velocity and temperature profiles are explained in details and they are parallel with experimental outcomes of previous researchers.
http://macs.journals.semnan.ac.ir/article_277_7960faef55166c0dd9e8e9f3ec2ea7c9.pdf
2014-04-01T11:23:20
2017-11-19T11:23:20
27
35
10.22075/macs.2014.277
Falkner-skan
boundary layer
nanofluids
HAM
Y.
Rostamiyan
y.rostamiyan@yahoo.com
true
1
Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
LEAD_AUTHOR
M.
Abbasi
true
2
Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
AUTHOR
F.
Aghajani
true
3
Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
AUTHOR
F.
Hedayati
true
4
Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran
AUTHOR
S.M.
Hamidi
true
5
Department of Electrical and Energy Engineering, University of Vaasa, Vaasa 65200, Finland
Department of Electrical and Energy Engineering, University of Vaasa, Vaasa 65200, Finland
Department of Electrical and Energy Engineering, University of Vaasa, Vaasa 65200, Finland
AUTHOR
[1] Lee S, Choi SUS, Li S, Eastman JA. Measuring thermal conductivity of fluids containing oxidenanoparticles. ASME J Heat Transfer 1999; 121: 280–9.
1
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[3] Das SK, Putra N, Roetzel W. Pool boiling characteristics of nano-fluids. Int J Heat Mass Transfer 2003; 46: 851–62.
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[4] Lee S, Choi SUS, Li S, Eastman JA. Measuring thermal conductivity of fluids containing oxidenanoparticles. ASME J Heat Transfer 1999; 121: 280–9.
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[5] Xuan Y, Li Q.: Heat transfer enhancement of nanofluids. Int J Heat Fluid Flow 2000; 21: 58–64.
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[6] Das SK, Putra N, Roetzel W. Pool boiling characteristics of nano-fluids. Int J Heat Mass Transfer 2003; 46: 851–62.
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[8] Das SK, Putra N, Thiesen P, Roetzel W. Temperature dependence of thermal conductivity enhancement for nanofluids. ASME J Heat Transfer 2003; 125: 567–74.
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[10] Eastman JA, Choi SUS, Li S, Yu W, Thomson LJ. Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl Phys Lett 2001; 78: 718–20.
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[11] Xie H, Wang J, Xi T, Liu Y, Ai F, Wu Q. Thermal conductivity enhancement of suspensions containing nanosized alumina particles. Appl Phys 2002; 91: 4568–72.
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[13] Wang BX, Zhou LP, Peng XF. A fractal model for predicting the effective thermal conductivity of liquid with suspension of nanoparticles. Int J Heat Mass Transfer 2003; 46: 2665–72.
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[14] Xue QZ. Model for effective thermal conductivity of nanofluids.PhysLett A 2003; 307: 313–7.
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[15] Yu W, Choi SUS. The role of interfacial layers in the enhanced thermal conductivity of nanofluids: arenovated Maxwell model. Nanoparticle Res 2003; 5: 167–71.
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[18] Pade. On the solution of Falkner–Skan equations, J Math Anal Appl 2003; (285): 264–274.
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[19] Liao, S. J. On the Homotopy Analysis Method for Nonlinear Problems. Appl Math Comput 2004; 47 (2)
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[20] Liao, S. J. An Explicit, Totally Analytic Approximation of Blasius’s Viscous Flow Problems. Int J Non-Linear Mech 1999; 34 (4)
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[22] Domairry, G. and N. Nadim. Assessment of Homotopy Analysis Method and Homotopy Perturbation Method in Non-Linear Heat Transfer Equation. Int Commun Heat Mass Transfer 2008; 35 (1):
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[29] Ziabakhsh Z, Domairry G, Ghazizadeh HR. Analytical solution of the stagnation-point flow in a porous medium by using the homotopy analysis method, Taiwan Institute Chem Eng 2009; 40(1): 91-97.
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36
ORIGINAL_ARTICLE
Optimization of Hybrid Composite Laminate Based on the Frequency using Imperialist Competitive Algorithm
Imperialist competitive algorithm (ICA) is a new socio-politically motivated global search strategy. The ICA is applied to hybrid composite laminates to obtain minimum weight and cost. The approach which is chosen for conducting the multi-objective optimization was the weighted sum method (WSM). The hybrid composite Laminates are made of glass/epoxy and carbon/epoxy to combine the lightness and economical attributes of the first with high-stiffness property of the second in order to make trade-off between the cost and weight as the objective functions and natural flexural frequency as a constraint. The results were evaluated for different weighting factors (a) including optimum stacking sequences, and number of plies made of either glass or carbon fibers using the ICA, and were compared with those using the genetic algorithm (GA) and ant colony system (ACS). The comparisons confirmed the advantages of hybridization and revealed that the ICA outperformed the GA and ACS in terms of function’s value and constraint accuracy.
http://macs.journals.semnan.ac.ir/article_278_63be65d1a83cfab4d5d464f2378cda4e.pdf
2014-04-01T11:23:20
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37
48
10.22075/macs.2014.278
Composite laminate
Hybridization
Stacking sequence
Imperialist competitive algorithm
Frequency
Hossein
Hemmatian
hoseinhemmatian@gmail.com
true
1
Departement of Mechanical Engineering, Semnan Branch, Islamic Azad University, Semnan, Iran
Departement of Mechanical Engineering, Semnan Branch, Islamic Azad University, Semnan, Iran
Departement of Mechanical Engineering, Semnan Branch, Islamic Azad University, Semnan, Iran
LEAD_AUTHOR
Abdolhossein
Fereidoon
afereidoon@semnan.ac.ir
true
2
Faculty of Mechanical Engineering, Semnan University, Semnan, 19111-35131, Iran
Faculty of Mechanical Engineering, Semnan University, Semnan, 19111-35131, Iran
Faculty of Mechanical Engineering, Semnan University, Semnan, 19111-35131, Iran
AUTHOR
Hadi
Shirdel
hoseinhemmatian@yahoo.com
true
3
Faculty of Mechanical Engineering, Semnan University, Semnan, 19111-35131, Iran
Faculty of Mechanical Engineering, Semnan University, Semnan, 19111-35131, Iran
Faculty of Mechanical Engineering, Semnan University, Semnan, 19111-35131, Iran
AUTHOR
[1] Ghasemi H, Roberto Brighenti R, Xiaoying Zhuang X, Jacob Muthu J, Timon Rabczuk T. Optimiza-tion of fiber distribution in fiber reinforced composite by using NURBS functions. Comput Mater Sci 2014; 83: 463-473.
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[2] Blasques J P, Stolpe M. Maximum stiffness and minimum weight optimization of laminated composite beams using continuous fiber angles. Struct Multidiscip O 2011; 43(4): 573-588.
2
[3] Sadollah A, Bahreininejad A, Hamdi M, Purbolak-sono J. Optimum mechanical behavior of calci-um phosphate cement/hydroxyl group function-alized multi-walled carbon nanotubes/bovine serum albumin composite using metaheuristic algorithms. Neural Comput Appl 2014; 24(1): 193-200.
3
[4] Zuo Z H, Xie Y M. Maximizing the effective stiff-ness of laminate composite materials. Comput Mater Sci 2014; 83: 57-63.
4
[5] Hemmatian H, Fereidoon A, Sadollah A, Bah-reininejad A. Optimization of laminate stacking sequence for minimizing weight and cost using elitist ant system optimization. Adv Eng Softw 2013; 57: 8-18.
5
[6] Sobey AJ, Blake JIR, Shenoi RA. Implications of failure criteria choices on the rapid concept de-sign of composite grillage structures using mul-tiobjective optimisation. Struct Multidiscip O 2013; 47: 735-747.
6
[7] Omkar SN, Venkatesh A, Mudigere M. MPI-based parallel synchronous vector evaluated particle swarm optimization for multi-objective design optimization of composite structures. Eng Appl Artif Intel 2012; 25: 1611-1627.
7
[8] Rahul, S G, Chakraborty D, Dutta A. Multi-objective optimization of hybrid laminates subjected to transverse impact. Compos Struct 2006; 73(3): 360-369.
8
[9] Javidrad F, Nouri R. A simulated annealing method for design of laminates with required stiffness properties. Compos Struct 2011; 93: 1127-35.
9
[10] Gubran HBH, Gupta K. The effect of stacking se-quence and coupling mechanisms on the natural frequencies of composite shafts. Sound Vib 2012; 282: 231-248.
10
[11] Banerjee JR. Explicit analytical expressions for frequency equation and mode shapes of compo-site beams. Sol Struct 2001; 38: 2415-2426.
11
[12] Shun F H, Chao SC. Determination of elastic con-stants of materials by vibration testing. Compos Struct 2000; 49(2): 183-190.
12
[13] Abachizadeh M, Tahani M. An ant colony optimi-zation approach to multi objective optimal de-sign of symmetric hybrid laminates for maxi-mum fundamental frequency and minimum cost. Struct Multidisc Optim 2009; 37: 367-376.
13
[14] Abdalla MM, Setoodeh S, Gürdal Z. Design of var-iable stiffness composite panels for maximum fundamental frequency using lamination param-eters. Compos Struct 2007; 81: 283-291.
14
[15] Bert CW. Optimal design of a composite-material plate to maximize its fundamental frequency. Sound Vib 1977; 50: 229-237.
15
[16] Reiss R, Ramachandran S. Maximum frequency design of symmetric angle-ply laminates. Com-pos Struct 1987; 4: 1476-1487.
16
[17] Grenestedt JL. Layup optimization and sensitivity analysis of the fundamental eigenfrequency of composite plates. Compos Struct 1989. 12: 193-209.
17
[18] Duffy KJ, Adali S. Maximum frequency design of pre-stressed symmetric, cross-ply laminates of hybrid construction. Adv Des Auto 1991; 2: 477-484.
18
[19] Adali S. Design of shear-deformable antisymmet-ric angle-ply laminates to maximize the funda-mental frequency and frequency separation. Compos Struct 1984; 2: 349-369.
19
[20] Apalak MK, Yildirim M, Ekici R. Layer optimiza-tion for maximum fundamental frequency of laminated composite plates for different edge conditions. Compos Sci Technol 2008; 68: 537-550.
20
[21] Fukunaga H, Sekine H, Sato M. Optimal design of symmetric laminated plates for fundamental frequency. Sound Vib 1994; 171: 219-229.
21
[22] Narita Y. Layerwise optimization for the maxi-mum fundamental frequency of laminated com-posite plates. Sound Vib 2003; 263: 1005-1016.
22
[23] Narita Y, Hodgkinson JM. Layerwise optimisation for maximizing the fundamental frequencies of point-supported rectangular laminated compo-site plates. Compos Struct 2005; 69: 127-135.
23
[24] Adali S, Duffy KJ. Minimum cost design of vibrat-ing laminates by hybridization. Eng Optim 1992; 19: 255-267.
24
[25] Farshi B, Rabiei R. Optimum design of composite laminates for frequency constraints. Compos Struct 2007; 81(4): 87-597.
25
[26] Adali S, Verijenko VE. Optimum stacking se-quence design of symmetric hybrid laminates undergoing free vibrations. Compos Struct 2001; 54: 131-138.
26
[27] Tahani M, Kolahan F, Sarhadi A. Genetic algo-rithm for multi-objective optimal design of sandwich composite laminates with minimum cost and maximum frequency. ICMPM, Sath-yamangalam, India, 2005. p. 741-748.
27
[28] Kolahan F, Tahani M, Sarhadi A. Optimal design of sandwich composite laminates for minimum cost and maximum frequency using simulated annealing. TICME, Tehran, Iran, 2005.
28
[29] Hao W, Ying Y, Yujia L. Reliability Based Optimi-zation of Composite Laminates for Frequency Constraint. Chinese Journal of Aeronautics 2008; 21: 320-327.
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[30] Grosset L, Venkataraman S, Haftka RT. Genetic optimization of two-material composite lami-nates. In: 16th ASC Technical Meeting, Blacks-burg, Virginia, 2001.
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[31] Abachizadeh M, Tahani M. Ant colony optimiza-tion of hybrid laminates for minimum cost and weight. In: Saravanos DA (ed) Proceedings of 6th international symposium on advanced compo-sites COMP’07, Corfu, Greece, 2007.
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[32] Atashpaz-Gargari E, Lucas C. Imperialist competi-tive algorithm: An algorithm for optimization in-spired by imperialistic competition. In: IEEE Congress on Evolutionary Computation, Singa-pore, 2007. p. 4661-67.
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[33] Atashpaz-Gargari E, Hashemzadeh F, Rajabioun R, Lucas C. Colonial competitive algorithm: A novel approach for PID controller design in MIMO distillation column process. Int J Intel Comput Cyber 2008; 3: 337-55.
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[34] Kaveh A, Talatahari S. Imperialist competitive algorithm for engineering design problems. Asian J Civil Eng 2010; 11: 675-697.
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[36] Abdi B, Mozafari H, Ayob A, Kohandel R. Imperi-alist Competitive Algorithm and its Application in Optimization of Laminated Composite Struc-tures. European J Sci Res 2011; 55: 174-187.
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[37] Mozafari H, Abdi B, Ayob A. Optimization of Composite Plates Based on Imperialist Competi-tive Algorithm. Int J Comput Sci Eng 2010; 2: 2816-2819.
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[38] Mozafari H, Alias A, Kamali F. Optimum Design of Composite Plates under Thermal Buckling Loads using Imperialist Competitive Algorithm. Int J Comput Sci Eng Technol 2010; 1: 54-58.
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45
[46] Herakovich CT. Mechanics of fiberous compo-sites, New York: John Whiley and Sons, 1998
46
ORIGINAL_ARTICLE
Elasticity Solution of Functionally Graded Carbon Nanotube Reinforced Composite Cylindrical Panel
Based on three-dimensional theory of elasticity, static analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical panel subjected to mechanical uniformed load with simply supported boundary conditions is carried out. In the process, stress and displacement fields are expanded according to the Fourier series along the axial and circumferential coordinates. From constitutive law, stress-displacement relations and equilibrium equations, state space equation is obtained. The obtained first order governing differential equations can be solved analytically. The effects of CNT distribution cases, the volume fraction of CNT, length to mid radius ratio, span of the cylindrical panel, variation of mechanical load and radius to thickness ratio on the bending behaviour of the cylindrical panel are examined. It should be noted that by using Fourier series solution it is possible only to solve the static behaviour of cylindrical panel with simply supported for all of edges and for the non-simply supported boundary conditions it is possible to solve numerically. The obtained analytical solution can be used to validate the results of approximate two dimensional conventional theories.
http://macs.journals.semnan.ac.ir/article_279_36187dcdc15631bb992187b8858b1e1e.pdf
2014-04-01T11:23:20
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49
60
10.22075/macs.2014.279
Carbon nanotube
Cylindrical panel
boundary layer
Static
Elasticity
Akbar
Alibeigloo
abeigloo@modares.ac.ir
true
1
Department of Mechanical Engineering, Tarbiat Modares University, Tehran, 14115-143, Iran
Department of Mechanical Engineering, Tarbiat Modares University, Tehran, 14115-143, Iran
Department of Mechanical Engineering, Tarbiat Modares University, Tehran, 14115-143, Iran
LEAD_AUTHOR
[1] Thostenson, ET, Ren,ZF, Chou, TW. Advances in the science and technology of carbon nanotubes and their composite: a review, Compos Sci Thecnol 2001; 61:1899-912.
1
[2] Gou J, Minaie B, Wang B, Liang Z, Zhang C. Com-putational and experimental study of interfacial bonding of single-walled nanotube reinforced composites stiffness, Comp Mater Sci 2004;31:225–236.
2
[3] Wuite J, Adali S. Deflection and stress behavior of nanocomposite reinforced beams using a mul-ti scale analysis, Compos Struct 2005;71:388–396.
3
[4] Vodenitcharova T, Zhang C. Bending and local buckling of a nanocomposite beam reinforced by a single-walled carbon nanotube, Int J Sol Struct 2006; 43:3006–3024.
4
[5] Shen HS. Nonlinear bending of functionally grad-ed carbon nanotube-reinforced composite plates in thermal environments, Compos Struct 2009;91:9–19.
5
[6] Formica G, Lacarbonara W, Alessi R. Vibrations of carbon nanotube-reinforced composites, Sound Vib 2010;329:1875–1889.
6
[7] Shen HS, Zhang C. Thermal buckling and post buckling behavior of functionally grade carbon nanotube-reinforced composite plates, Mater De-sign 2010;31:3403–3411.
7
[8] Ke LL, Yang J, Kitipornchai S. Nonlinear free vi-bration of functionally graded carbon nanotube-reinforced composite beams, Compos Struct 2010;92:676-683.
8
[9] Shen HS. Post buckling of nanotube-reinforced composite cylindrical shells in thermal envi-ronments, Part I: Axially-loaded shells, Compos Struct 2011; 93: 2096–2108.
9
[10] Shen HS. Post buckling of nanotube-reinforced composite cylindrical shells in thermal envi-ronments, Part II: Pressure-loaded shells, Com-pos Struct 2011;93: 2496–2503.
10
[11] Wang ZX, Shen HS. Nonlinear vibration of nano-tube-reinforced composite plates in thermal en-vironments, Comp Mater Sci 2011;50: 2319–2330.
11
[12] Mehrabadi SJ, Sobhani Aragh B, Khoshkhahesh V, Taherpour A. Mechanical buckling of nano-composite rectangular plate reinforced by aligned and strait single-walled carbon nano-tubes, Compos Part B-Eng 2012;43(4):2031-2040.
12
[13] Zhu P, Lei ZX, Liew KM. Static and free vibration analyses of carbon nanotube-reinforced compo-site plates using finite element method with first order shear deformation plate theory, Compos Struct 2012;94:1450–1460.
13
[14] Wang ZX, Shen HS. Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets, Compos Part B-Eng 2012;43:411–421.
14
[15] Yas MH, Heshmati M. Dynamic analysis of func-tionally graded nanocomposite beam reinforced by randomly oriented carbon nanotube under the action of moving load, Appl Math Model 2012;36:1371–1394.
15
[16] Alibeigloo A. Static analysis of functionally grad-ed carbon nanotube-reinforced composite plate embedded in piezoelectric layers by using theo-ry of elasticity, Compos Struct 2013;95:612-622.
16
[17] Bhardwaj G, Upadhyay AK, Pandey R, Shukla KK. Non-linear flexural and dynamic response of CNT reinforced laminated composite plate, Compos Part B-Eng 2013;45:89-100.
17
[18] Shen HS. Thermal buckling and post buckling behavior of functionally graded carbon nano-tube-reinforced composite cylindrical shells, Compos Part B-Eng 2012; 43:1030-1038.
18
[19] Shen HS, Xiang Y. Nonlinear vibration of nano-tube-reinforced composite cylindrical shells in thermal environments, Comput. Methods Appl. Mech. Eng 2012; 213-216:196–205.
19
[20] Moradi-Dastjerdi R, Foroutan M, Pourasgha A. Dynamic analysis of functionally graded nano-composite cylinders reinforced by carbon nano-tube by a mesh-free method, Mater Design 2013;44:256–266.
20
[21] Moradi-Dastjerdi R, Foroutan A, Pourasgha A. Eshelby–Mori–Tanaka approach for vibrational behavior of continuously graded carbon nano-tube-reinforced cylindrical panels. Compos Part B-Eng 2012;43:1943–1954.
21
ORIGINAL_ARTICLE
Free Vibration Analysis of Composite Plates with Artificial Springs by Trigonometric Ritz Method
In this paper free vibration analysis of two rectangular isotropic plates, which are connected to each other by two translational and rotational springs along the edges, are investigated. The equation of motion and associated boundary and continuity conditions are derived using the extended Hamilton principle. To solve the eigenvalue problem, the Ritz method is utilized. Numerical investigations are presented to show some applications of this method. In this research two types of problems are investigated: first, vibration of a continuous plate and second, free vibration of two hinged plates. This approach is usually referred to as the artificial spring method, which can be regarded as a variant of the classical penalty method. In order to validate the results, the achieved results are compared to results which are presented in literatures.
http://macs.journals.semnan.ac.ir/article_280_aa4762b28ed401e6548a090f10de624e.pdf
2014-04-01T11:23:20
2017-11-19T11:23:20
61
70
10.22075/macs.2014.280
Vibration analysis
Composite plates
Artificial spring
Trigonometric Ritz method
Hossein
Ghadirian
dhghadirian@yahoo.com
true
1
Faculty of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran
Faculty of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran
Faculty of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran
LEAD_AUTHOR
Mohammad
Ghazavi
dhghadirian1@yahoo.com
true
2
Faculty of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran
Faculty of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran
Faculty of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran
AUTHOR
Korosh
Khorshidi
k-khorshidi@araku.ac.ir
true
3
Department of Mechanical Engineering, Faculty of Engineering, Arak University, 3815688349, Arak, Iran
Department of Mechanical Engineering, Faculty of Engineering, Arak University, 3815688349, Arak, Iran
Department of Mechanical Engineering, Faculty of Engineering, Arak University, 3815688349, Arak, Iran
AUTHOR
Leissa AW, Vibration of plates ,DTIC Document, 1969.
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