ORIGINAL_ARTICLE
Local and Global Approaches to Fracture Mechanics Using Isogeometric Analysis Method
The present research investigates the implementations of different computational geometry technologies in isogeometric analysis framework for computational fracture mechanics. NURBS and T-splines are two different computational geometry technologies which are studied in this work. Among the features of B-spline basis functions, the possibility of enhancing a B-spline basis with discontinuities by means of knot insertion makes isogeometric analysis method a suitable candidate for modeling discrete cracks. Also, the repetition of two different control points between two patches can create a discontinuity in and demonstrates a singularity in the stiffness matrix. In the case of a pre-defined interface, non-uniform rational B-splines are used to obtain an efficient discretization. T-splines constitute a type of computational geometry technology with the possibility of local refinement and with no topologically rectangular arrangement of control points. Therefore, T-splines can decrease superfluous control points which do not have any major effects on the geometry. Various numerical simulations demonstrate the suitability of the isogeometric approach in fracture mechanics.
http://jacm.scu.ac.ir/article_11237_6e78c51216bf17ef960003a0c08445e3.pdf
2015-12-01T11:23:20
2018-12-10T11:23:20
168
180
10.22055/jacm.2015.11237
Fracture mechanics
Isogeometric analysis method
Knot insertion
NURBS
T-spline
Abdolghafoor
Khademalrasoul
ag.khadem@yahoo.com
true
1
Ph.D. Student of Civil Engineering, Shahrood University of technology, Iran.
Ph.D. Student of Civil Engineering, Shahrood University of technology, Iran.
Ph.D. Student of Civil Engineering, Shahrood University of technology, Iran.
LEAD_AUTHOR
Reza
Naderi
rz_naderi@yahoo.com
true
2
Department of Civil Engineering. Shahroud University of technology.
Department of Civil Engineering. Shahroud University of technology.
Department of Civil Engineering. Shahroud University of technology.
AUTHOR
[1] Bhardwaj G., Singh I.V., Mishra B.K., Bui T.Q., “Numerical simulation of functionally graded cracked plates using NURBS based XIGA under different loads and boundary conditions”, Composite Structures, Vol. 126, pp. 347-359, 2015.
1
[2] Singh I.V., Bhardwaj G., Mishra B.K., “A new criterion for modeling multiple discontinuities passing through an element using XIGA”, Journal of Mechanical Science and Technology, Vol. 29, No. 3, pp. 1131-1143, 2015.
2
[3] Rabczuk T., Belytschko T., Cracking particles: a simplified meshfree method for arbitrary evolving cracks, International Journal for Numerical Methods in Engineering, Vol. 61 No. 13, pp. 2316-2343, 2004.
3
[4] Naderi R., Khademalrasoul A., “Fully Automatic Crack Propagation Modeling in Interaction with Void and Inclusion without Remeshing” Modares Mechanical Engineering, Vol. 15 No. 7, pp. 261-273, 2015. (In Persian)
4
[5] Zhuang Z., Liu Z., Cheng B., Liao J., “Chapter 2 - Fundamental Linear Elastic Fracture Mechanics.In”: Zhuang Z, Liu Z, Cheng B, Liao J, editors. Extended Finite Element Method. Oxford: Academic Press, pp. 13-31, 2014.
5
[6] Daxini S.D., Prajapati J.M., “A Review on Recent Contribution of Meshfree Methods to Structure and Fracture Mechanics Applications”, The Scientific World Journal, 2014.
6
[7] Chen T., Xiao Z.-G., Zhao X.-L., Gu X.-L., “A boundary element analysis of fatigue crack growth for welded connections under bending”, Engineering Fracture Mechanics, Vol. 98, pp. 44-51, 2013.
7
[8] Hughes T.J.R., Cottrell J.A., Bazilevs Y., “Isogeometric Analysis Toward integration of CAD and FEM”, 2009.
8
[9] Cottrell J.A., Hughes T.J.R., Bazilevs Y., “Isogeometric Analysis: Toward Integration of CAD and FEA”, Wiley, 2009.
9
[10] Hughes T.J.R., Cottrell J.A., Bazilevs Y., “Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering, Vol. 194, No. 39–41, pp. 4135-4195, 2005.
10
[11] Bazilevs Y., Calo V.M., Cottrell J.A., Evans J.A., Hughes T.J.R., Lipton S., et al., “Isogeometric analysis using T-splines”, Computer Methods in Applied Mechanics and Engineering, Vol. 199, No. 5–8, pp. 229-263, 2010.
11
[12] Ghorashi S.S., Valizadeh N., Mohammadi S., “Extended isogeometric analysis for simulation of stationary and propagating cracks”, International Journal for Numerical Methods in Engineering, Vol. 89, No. 9, pp. 1069-1101, 2012.
12
[13] De Luycker E., Benson D.J., Belytschko T., Bazilevs Y., Hsu M.C., “X-FEM in isogeometric analysis for linear fracture mechanics”, International Journal for Numerical Methods in Engineering, Vol. 87, No. 6, pp. 541-565, 2011.
13
[14] Evans J.A., Bazilevs Y., Babuška I., Hughes T.J.R., “n-Widths, sup–infs, and optimality ratios for the k-version of the isogeometric finite element method”, Computer Methods in Applied Mechanics and Engineering, Vol. 198 No. 21–26, pp. 1726-1741, 2009.
14
[15] Cottrell J.A., Hughes T.J.R., Reali A., “Studies of refinement and continuity in isogeometric structural analysis”, Computer Methods in Applied Mechanics and Engineering, Vol. 196, No. 41–44, pp. 4160-4183, 2007.
15
[16] Cottrell J.A., Reali A., Bazilevs Y., Hughes T.J.R., “Isogeometric analysis of structural vibrations, Computer Methods in Applied”, Mechanics and Engineering, Vol. 195, No. 41–43, pp. 5257-5296, 2006.
16
[17] Akkerman I., Bazilevs Y., Kees C.E., Farthing M.W., “Isogeometric analysis of free-surface flow”, Journal of Computational Physics, Vol. 230, No. 11, pp. 4137-4152, 2011.
17
[18] Bazilevs Y., Akkerman I., “Large eddy simulation of turbulent Taylor–Couette flow using isogeometric analysis and the residual-based variational multiscale method”, Journal of Computational Physics, Vol. 229, No. 9, pp. 3402-3414, 2010.
18
[19] Bazilevs Y., Calo V.M., Cottrell J.A., Hughes T.J.R., Reali A., Scovazzi G., “Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows”, Computer Methods in Applied Mechanics and Engineering, Vol. 197, No. 1–4, pp. 173-201, 2007.
19
[20] Bazilevs Y., Hsu M.C., Scott M.A., “Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines”, Computer Methods in Applied Mechanics and Engineering, Vol. 249–252, pp. 28-41, 2012.
20
[21] Li K., Qian X., “Isogeometric analysis and shape optimization via boundary integral”, Computer-Aided Design, Vol. 43, No. 11, pp. 1427-1437, 2011.
21
[22] Hassani B., Tavakkoli S.M., Moghadam N.Z., “Application of isogeometric analysis in structural shape optimization”, Scientia Iranica, Vol. 18, No. 4, pp. 846-852, 2011.
22
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[25] Simo J.C., Oliver J., Armero F., “An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids”, Computational Mechanics, Vol. 12, No. 5, pp. 277-296, 1993.
25
[26] Oliver J., “Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 2: numerical simulation”, International Journal for Numerical Methods in Engineering, Vol. 39, No. 21, pp. 3601-3623, 1996.
26
[27] Belytschko T., Black T., “Elastic crack growth in finite elements with minimal remeshing”, International Journal for Numerical Methods in Engineering, Vol. 45, No. 5, pp. 601-620, 1999.
27
[28] Babuška I., Zhang Z., “The partition of unity method for the elastically supported beam”, Computer Methods in Applied Mechanics and Engineering, Vol. 152, No. 1–2, pp. 1-18, 1998.
28
[29] Babuska I., Melenk, J, “The Partition of unity method”, International Journal for Numerical Methods in Engineering, Vol. 40, pp. 727–758, 1997.
29
[30] Bhardwaj G., Singh I.V., Mishra B.K., “Stochastic fatigue crack growth simulation of interfacial crack in bi-layered FGMs using XIGA”, Computer Methods in Applied Mechanics and Engineering, Vol. 284, pp. 186-229, 2015.
30
[31] Bhardwaj G., Singh I.V., Mishra B.K., Kumar V., “Numerical Simulations of Cracked Plate using XIGA under Different Loads and Boundary Conditions”, Mechanics of Advanced Materials and Structures, 2015.
31
[32] Scott M.A., Li X., Sederberg T.W., Hughes T.J.R., “Local refinement of analysis-suitable T-splines”, Computer Methods in Applied Mechanics and Engineering, Vol. 213–216, pp. 206-222, 2012.
32
[33] Piegl L.A., Tiller W., The Nurbs Book, Springer-Verlag GmbH, 1997.
33
[34] Rogers D.F., “An introduction to NURBS: with historical perspective”, Morgan Kaufmann Publishers, 2001.
34
[35] De Boor C., “On calculating with B-splines”, Journal of Approximation Theory, Vol. 6, No.1, pp. 50-62, 1972.
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[36] Cox M.G., “The Numerical Evaluation of B-Splines”, IMA Journal of Applied Mathematics, Vol. 10, No. 2, pp. 134-149, 1972.
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[37] Sederberg T.W., Zheng J., Bakenov A., Nasri A., T-splines and T-NURCCs, ACM SIGGRAPH 2003 Papers, San Diego, California, 882295: ACM, pp. 477-484, 2003.
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[38] Buffa A., Cho D., Sangalli G., “Linear independence of the T-spline blending functions associated with some particular T-meshes”, Computer Methods in Applied Mechanics and Engineering, Vol. 199, No. 23–24, pp. 1437-1445, 2010.
38
[39] Buffa A., Cho D., Kumar M., “Characterization of T-splines with reduced continuity order on T-meshes”, Computer Methods in Applied Mechanics and Engineering, Vol. 201–204, pp. 112-126, 2012.
39
[40] Scott M.A., Simpson R.N., Evans J.A., Lipton S., Bordas S.P.A., Hughes T.J.R., et al., “Isogeometric boundary element analysis using unstructured T-splines”, Computer Methods in Applied Mechanics and Engineering, Vol. 254, pp. 197-221, 2013.
40
ORIGINAL_ARTICLE
Vibration analysis of a rotating closed section composite Timoshenko beam by using differential transform method
This study introduces the Differential Transform Method (DTM) in the analysis of the free vibration response of a rotating closed section composite, Timoshenko beam, which features material coupling between flapwise bending and torsional vibrations due to ply orientation. The governing differential equations of motion are derived using Hamilton’s principle and solved by applying DTM. The natural frequencies are calculated and the effects of the bending-torsion coupling, the slenderness ratio and several other parameters on the natural frequencies are investigated using the computer package, Mathematica. Wherever possible, comparisons are made with the studies in open literature.
http://jacm.scu.ac.ir/article_11256_03281b99be3d5ae2b2cb443990f44fe6.pdf
2015-12-01T11:23:20
2018-12-10T11:23:20
181
186
10.22055/jacm.2015.11256
Rotating beam
composite
Natural frequency
Mode shape
DTM
Saeed
Talebi
saeed.talebi68@gmail.com
true
1
Department of Mechanical
Engineering, University of
Isfahan
Department of Mechanical
Engineering, University of
Isfahan
Department of Mechanical
Engineering, University of
Isfahan
LEAD_AUTHOR
Hamed
Uosofvand
mr.uosofvand@gmail.com
true
2
department of mechanical engineering, university of kashan, Kashan, Iran
department of mechanical engineering, university of kashan, Kashan, Iran
department of mechanical engineering, university of kashan, Kashan, Iran
AUTHOR
Alireza
Ariaei
ariaei@eng.ui.ac.ir
true
3
Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, isfahan, iran
Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, isfahan, iran
Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, isfahan, iran
AUTHOR
[1] Thakkar D., Ganguli R., “Helicopter vibration reduction in forward ﬂight with induced shear based piezoceramic actuation”, Smart Mater. Struct., 30 (3), pp. 599-608, 2004.
1
[2] Kumar S., Roy N., Ganguli R., “Monitoring low cycle fatigue damage in turbine blades using vibration characteristics”, Mech. Syst. Signal Process, 21 (1), pp.480–501, 2007.
2
[3] Zhou J.K., “Differential Transformation and its Application for Electrical Circuits”, Wuhan, Huazhong University Press, Wuhan, China, 1986.
3
[4] Ozdemir O.O., Kaya M.O., “Flap wise bending vibration analysis of a rotating tapered cantilever Bernoulli-Euler beam by differential transform method”, Journal of Sound and Vibration, 289, pp.413–420, 2006.
4
[5] Mei C., “Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam”, Computers and Structures, 86, pp.1280–1284, 2008.
5
[6] Kaya M. O., Ozdemir Ozgumus O., “Flexural–Torsional Coupled Vibration Analysis of Axially Loaded Closed Section Composite Timoshenko Beam by Using DTM”, Journal of Sound and Vibration, (3-5), pp. 495-506, 2007.
6
[7] Li J., Shen R., Hua H., Jin X., “Bending-torsional coupled vibration of axially loaded composite Timoshenko thin-walled beam with closed cross-section”, Composite Structures 64, pp. 23-35, 2004.
7
ORIGINAL_ARTICLE
Dynamical Behavior of a Rigid Body with One Fixed Point (Gyroscope). Basic Concepts and Results. Open Problems: a Review
The study of the dynamic behavior of a rigid body with one fixed point (gyroscope) has a long history. A number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior) – stable, periodic, quasi-periodic or chaotic. The main objectives of this review are: 1) to outline the characteristic features of the theory of dynamical systems and 2) to reveal the specific properties of the motion of a rigid body with one fixed point (gyroscope).This article consists of six sections. The first section addresses the main concepts of the theory of dynamical systems. Section two presents the main theoretical results (obtained so far) concerning the dynamic behavior of a solid with one fixed point (gyroscope). Section three examines the problem of gyroscopic stabilization. Section four deals with the non-linear (chaotic) dynamics of the gyroscope. Section five is a brief analysis of the gyroscope applications in engineering. The final section provides conclusions and generalizations on why the theory of dynamical systems should be used in the study of the movement of gyroscopic systems.
http://jacm.scu.ac.ir/article_11949_d960168e6836b18dcb446814e81f298c.pdf
2015-12-01T11:23:20
2018-12-10T11:23:20
187
206
10.22055/jacm.2015.11949
Gyroscopic systems
theory of dynamical systems
dynamical behavior
Svetoslav
Nikolov
s.nikolov@imbm.bas.bg
true
1
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. BonchevStr., Bl. 4, Bulgaria
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. BonchevStr., Bl. 4, Bulgaria
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. BonchevStr., Bl. 4, Bulgaria
LEAD_AUTHOR
Nataliya
Nedkova
nataliya_nedkova@abv.bg
true
2
University of Transport, G. Milev Str., 158, 1574 Sofia, Bulgaria
University of Transport, G. Milev Str., 158, 1574 Sofia, Bulgaria
University of Transport, G. Milev Str., 158, 1574 Sofia, Bulgaria
AUTHOR
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[2] Alligood, K., Sauer, T. and Yorke, J., Chaos. An Introduction to Dynamical Systems, Springer, NewYork, 1996.
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[51] Idowu, B., Vincent, U. and Njah, A., “Synchronization of Chaos in Non-identical Parametrically Excited Systems”, Chaos, Solitons and Fractals, Vol. 39, pp. 2322-2331, 2009.
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[52] Kirillov, O., “Gyroscopic Stabilization in the Presence of Nonconservative Forces”, Dokl. Acad. Nauk, Vol. 416, pp. 451-456, 2007.
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99
ORIGINAL_ARTICLE
Buckling Analysis of Cantilever Nanoactuators Immersed in an Electrolyte: A Close Form Solution Using Duan-Rach Modified Adomian Decomposition Method
A new modified Adomian Decomposition Method (ADM) was utilized to obtain an analytical solution for the buckling of the nanocantilever actuators immersed in liquid electrolytes. The nanoactuators in electrolytes are subject to different nonlinear forces including ionic concentration, van der Waals, external voltage and electrochemical forces. The Duan–Rach modified Adomian decomposition method was used to obtain a full explicate solution for the buckling of nanoactuators free of any undetermined coefficients. The results were compared with those of Wazwas ADM and of a finite element method available in the literature and excellent agreement was found between them.
http://jacm.scu.ac.ir/article_12024_46bf28975511f8c180458d56cdffc012.pdf
2015-12-01T11:23:20
2018-12-10T11:23:20
207
219
10.22055/jacm.2015.12024
Nanoactuator
Duan and Rach ADM
Analytic Solution
Electrolyte
Mohammad
Ghalambaz
m.ghalambaz@gmail.com
true
1
Department of Mechanical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran.
Department of Mechanical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran.
Department of Mechanical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran.
LEAD_AUTHOR
Mehdi
Ghalambaz
ghalambaz.mehdi@gmail.com
true
2
Department of Mechanical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran.
Department of Mechanical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran.
Department of Mechanical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran.
AUTHOR
Mohammad
Edalatifar
m.edalatifar@gmail.com
true
3
Department of Electrical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran.
Department of Electrical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran.
Department of Electrical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran.
AUTHOR
[1] Martin, O. Gouttenoire, V. Villard, P. Arcamone, J. Petitjean, M. Billiot, G., G., Philippe, J., Puget, P., Andreucci, P., Ricoul, F. and Dupré, C., “Modeling and design of a fully integrated gas analyzer using a μGC and NEMS sensors”, Sensors and Actuators B: Chemical, Vol. 194, pp.220-8, 2014.
1
[2] Jóźwiak, G. Kopiec, D. Zawierucha, P. Gotszalk, T. Janus, P. Grabiec, P., and , and Rangelow, I. W., “The spring constant calibration of the piezoresistive cantilever based biosensor”, Sensors and Actuators B: Chemical, Vol. 170, pp. 201-206, 2012.
2
[3] Ekinci, K. L. and Roukes, M. L.,” Nanoelectromechanical systems”., Review of Scientiﬁc Instruments, Vol. 76, No.6, 061101, 2005.
3
[4] Guthy, C., Belov, M. Janzen, A. Quitoriano, N. J. Singh, A. Guthy, C., Belov, M., Janzen, A., Quitoriano, N.J., Singh, A., Wright, V.A., Finley, E., Kamins, T.I. and Evoy, S., “Large-scale arrays of nanomechanical sensors for biomolecular fingerprinting. Sensors and Actuators B” Chemical, Vol. 187, pp. 111-117, 2013.
4
[5] Choi, W.Y., Osabe, T., and Liu, T. J. K., “Nano-electro-mechanical nonvolatile memory (NEMory) cell design and scaling, Electron Devices” IEEE Transactions on, Vol. 55, No.2, pp. 3482-3488, 2008.
5
[6] Dumas, N., Trigona, C. Pons, P. Latorre, L., and Nouet, P, “Design of smart drivers for electrostatic MEMS switches”, Sensors and Actuators A: Physical, Vol. 167, pp. 422-432, 201.
6
[7] Boyd, J. G., and Kim, D.,”Nanoscale electrostatic actuators in liquid electrolytes”, Journal of colloid and interface science, Vol. 301, No. 2, pp. 542-548, 2006.
7
[8] Noghrehabadi, A., Eslami, M., and Ghalambaz, M., “Influence of size effect and elastic boundary condition on the pull-in instability of nano-scale cantilever beams immersed in liquid electrolytes”, International Journal of Non-Linear Mechanics, Vol. 52, pp. 73-84, 2013.
8
[9] Boyd, J. G. and Lee, J., “Deflection and pull-in instability of nanoscale beams in liquid electrolytes”, Journal of colloid and interface science, Vol. 356, pp. 387-94, 2011.
9
[10] Wazwaz, A. M., “The numerical solution of sixth-order boundary value problems by the modiﬁed decomposition method”, Applied Mathematics and Computation, Vol.118, pp. 311-325, 2001.
10
[11] Alam, M. K., Rahim, M. T., Avital, E. J., Islam, S., Siddiqui, A. M., & Williams, J. J. R., “Solution of the steady thin film flow of non-Newtonian fluid on vertical cylinder using Adomian Decomposition Method”, Journal of the Franklin Institute, Vol. 350, No. 4, pp. 818-839, 2013.
11
[12] Koochi, A., Kazemi, A. S., Tadi Beni, Y., Yekrangi, A., and Abadyan, M., “Theoretical study of the effect of Casimir attraction on the pull-in behavior of beam-type NEMS using modified Adomian method. Physica”, E: Low-dimensional Systems and Nanostructures, Vol. 43, No. 2, pp. 625-632, 2010.
12
[13] Koochi, A. L. I., Hosseini-Toudeshky, H. Ovesy, H. R., and Abadyan, M.,” Modeling the Influence of Surface Effect on Instability of Nano-Cantilever in Presence of Van Der Waals Force”, International Journal of Structural Stability and Dynamics, Vol. 13, pp. 1250072, 2013.
13
[14] Soroush, R. Koochi, A. L. I. Kazemi, A. S., and Abadyan, M., “Modeling the Effect of Van Der Waals Attraction on the Instability of Electrostatic Cantilever and Doubly-Supported Nano-Beams Using Modified Adomian Method”, International Journal of Structural Stability and Dynamics, Vol. 12, 1250036, 2012.
14
[15] Kuang, J. H., and Chen, C. J., “Adomian decomposition method used for solving nonlinear pull-in behavior in electrostatic micro-actuators”, Mathematical and Computer Modelling, Vol. 41, pp. 1479-1491, 2005.
15
[16] Koochi, A. Kazemi, A. S. Noghrehabadi, A. Yekrangi, A., and Abadyan, M., “New approach to model the buckling and stable length of multi walled carbon nanotube probes near graphite sheets”, Materials & Design, Vol. 32, 2949-2955, 2011.
16
[17] Noghrehabadi, A., Ghalambaz, M., and Ghanbarzadeh, A.,” A new approach to the electrostatic pull-in instability of nanocantilever actuators using the ADM–Padé technique”, Computers & Mathematics with Applications, Vol. 64, pp. 2806-2815, 2012.
17
[18] Duan, J. S. and Rach, R., “A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations”, Applied Mathematics and Computation, Vol. 218, pp. 4090-41118, 2011.
18
[19] Duan, J. S., Rach, R., Wazwaz, A. M., Chaolu, T., and Wang, Z.,” A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with Robin boundary conditions”, Applied Mathematical Modelling, Vol. 37, pp. 8687-8708, 2013.
19
[20] Adomian, G. and Rach, R., “Inversion of nonlinear stochastic operators”, J Math Anal Appl, Vol. 91, pp. 39–46, 1983.
20
[21] Duan, J. S., Rach, R., and Wang, Z.,” On the effective region of convergence of the decomposition series solution”, Journal of Algorithms & Computational Technology, Vol. 7, pp. 227-248, 2013.
21
[22] Yazdanpanahi, E., Noghrehabadi, A., and Ghalambaz, M.,” Pull-in instability of electrostatic doubly clamped nano actuators: Introduction of a balanced liquid layer (BLL)”, International Journal of Non-Linear Mechanics, Vol. 58, pp. 128-138, 2014.
22
ORIGINAL_ARTICLE
Analytical Solution of Linear, Quadratic and Cubic Model of PTT Fluid
An attempt is made for the first time to solve the quadratic and cubic model of magneto hydrodynamic Poiseuille flow of Phan-Thein-Tanner (PTT). A series solution of magneto hydrodynamic (MHD) flow is developed by using homotopy perturbation method (HPM). The results are presented graphically and the effects of non-dimensional parameters on the flow field are analyzed. The results reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena.
http://jacm.scu.ac.ir/article_12047_812e9e73d9bd80ef37b22977eaa26b04.pdf
2015-12-01T11:23:20
2018-12-10T11:23:20
220
228
10.22055/jacm.2015.12047
Phan-Thein-Tanner (PTT) model
Homotopy perturbation method
Nonlinear
Naeem
Faraz
nfaraz_math@yahoo.com
true
1
Shanghai University, Shanghai China
Shanghai University, Shanghai China
Shanghai University, Shanghai China
LEAD_AUTHOR
Hou
Lei
houlei@staff.shu.edu.cn
true
2
Shanghai University, Shanghai China
Shanghai University, Shanghai China
Shanghai University, Shanghai China
AUTHOR
Yasir
Khan
yasirmath@yahoo.com
true
3
Hafr al Batin Saudia Arabia
Hafr al Batin Saudia Arabia
Hafr al Batin Saudia Arabia
AUTHOR
[1] L-M. Maria, M. Hana, N. Sarka, Global existence and uniqueness result for the diffusive peterlin viscoelastic model, Nonlin. Anal. Meth. Appl.120 (2015) 154-170.
1
[2] Z. Ting, Global strong solutions for equations related to the incompressible viscoelastic fluids with a class of large initial data, Nonlin. Anal. Meth. Appl. 100 (2014) 59-77.
2
[3] G. Matthias, G. Dario, N. Manuel, L-p-theory for a generalized nonlinear viscoelastic fluid model of differential type in various domains, Nonlin. Anal. Meth. Appl. 75 (2012) 5015-5026.
3
[4] F. Ettwein, M. Ruzicka, B. Weber, Existence of steady solutions for micropolar electrorheological fluid flows, Nonlin. Anal. Meth. Appl. 125 (2015) 1-29.
4
[5] F. J. Suarez-Grau, Asymptotic behavior of a non-Newtonian flow in a thin domain with Navier law on a rough boundary, Nonlin. Anal. Meth. Appl. 117 (2015) 99-123.
5
[6] Y. Ye, Global existence and blow-up of solutions for higher-order viscoelastic wave equation with a nonlinear source term, Nonlin. Anal. Meth. Appl.112 (2015) 129-46.
6
[7] R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of polymeric liquids, 1Fluid Mechanics second edition, John Wiley & Sons, Inc. 1987.
7
[8] N. Phan-Thien and R. I. Tanner, A new constitutive equation derived from network theory, J. Non-Newtonian Fluid Mech. 2(1977) 353–365.
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[9] L. Quinzani, R. Armstrong, R. Brown, Use of coupled birefringence and LDV studies of flow through a planar contraction to test constitutive equations for concentrated polymer solutions. J. Rheolm. 39 (1955) 1201–1228.
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[10]A. Baloch, P. Townsend, M. Webster, On vortex development in viscoelastic expansion and contraction flows. J Non Newton Fluid Mech. 65 (1996) 133–149.
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[11]J. Tichy, B. Bou-Said B, (2008) The Phan-Thien and Tannermodel applied to thin film spherical coordinates: applications for lubrication of hip joint replacement. J Biomech Eng, 130 (2008) 021012.
11
[12]A. M. Siddiqui, Q. A. Azim, A. Ashraf et al, Exact Solution for Peristaltic Flow of PTT Fluid in an Inclined Planar Channel and Axisymmetric Tube, Int.J. Nonlin. Sci. Num. Sim. 10 (2009) 75-91
12
[13]L. Ferras, J. Nobrega, F. Pinho, Analytical solutions for channel flows of Phan-Thien-Tanner and Giesekus fluids under slip. J. Non Newton Fluid Mech. 171 (2012) 97–105
13
[14]P. J. Oliveira and F. T. Pinho, Analytical solution for fully-developed channel and pipe flow of Phan-Thien, Tanner fluids, J. Fluid Mech. 387 (1999) 271–280.
14
[15]F. T. Pinho and P. J. Oliveira, Analysis of forced convection in pipes and channels with simplified Phan-Thien Tanner Fluid, Int. J. Heat Mass Transfer. 43(2000) 2273–2287.
15
[16]Hou Lei, V. Nassehi, Evaluation of stress effecting flow in rubber mixing, Nonlin. Anal. Meth. Appl. 47 (2001) 1809-1820.
16
[17]Hou Lei, Member, IAENG, D.Z. Lin, B.Wang, H.L. Li, L. Qiu,Computational Modelling on the Contact Interface with Boundary-layer Approach , Pro. Worl. Cong. Eng., I (2011) July 6 – 8, London, U.K.
17
[18]Hou Lei, H. L. Li, H. Wang , L. Qiu, Stochastic Analysis in the Visco-Elastic Impact Condition, Conference on Chemical Engineering and Advanced Materials (CEAM) VIRTUAL FORUM Naples 2009
18
[19]Hou Lei, J. Zhao and L. Qiu, The non-Newtonian fluid in the collision, Appl. Mech. Mat. 538 (2014) 72-75.
19
[20]Z. Shaoling, Hou Lei, Decoupled algorithm for solving Phan-Thien-Tanner viscoelastic fluid by finite element method, Comp. Math. App. 69 (2015) 423-437.
20
[21]Hou Lei, Li, Han-ling, Zhang Jia-jian; et al Boundary-layer eigen solutions for multi-field coupled equations in the contact interface, App. Math. Mech., 31 (2010) 719-732.
21
[22]N. Faraz, Study of the effects of the Reynolds number on circular porous slider via variational iteration algorithm-II, Comp. Math. App. 61 (2011) 1991-1994.
22
[23]N. Faraz, Y. Khan, D. S. Shankar, Decomposition-transform method for Fractional Differential Equations, Int. J. Nonl. Sci. Num. Sim. 11 (2010) 305-310.
23
[24]Y. Khan, N. Faraz, S. Kumar, et al, A Coupling Method of Homotopy Perturbation and Laplace Transformation for Fractional Models, Uni. Pol. Buch. Sci. Bull.-Ser. A-App. Math. Phy. 74 (2012) 57-68.
24
[25]N. Faraz, Hou Lei, Y. Khan, Homotopy Perturbation Method for Thin Film Flow of a Maxwell Fluid over a Shrinking/Stretching Sheet with Variable Fluid Properties International Conference On Mechanics And Control Engineering, MCE (2015) 52-57.
25
[26]N. Faraz, Y. Khan, Study of the Rate Type Fluid with Temperature Dependent Viscosity, Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences. 67 (2011) 460-468.
26
[27]Y. Khan, Q. Wu, N. Faraz; et al, Heat Transfer Analysis on the Magnetohydrodynamic Flow of a Non-Newtonian Fluid in the Presence of Thermal Radiation: An Analytic Solution, Zeitschrift Fur Naturforschung Section A-A Journal Of Physical Sciences. 67 (2012) 147-152.
27
[28]Y. Khan, N. Faraz, Y. Ahmet; et al. A Series Solution of the Long Porous Slider, Tribology Transactions. 54 (2011)187-191.
28
[29]F. Talay Akyildiz, K. Vajravelu, Magnetohydrodynamic flow of a viscoelastic fluid, Physics Letters A. 372 (2008) 3380-3384.
29
ORIGINAL_ARTICLE
Pull-in behavior of a bio-mass sensor based on an electrostatically actuated cantilevered CNT with consideration of rippling effect
This paper examines the pull-in behavior of a bio-mass sensor with a cantilevered CNT actuated electrostatically by considering rippling deformation. Although this phenomenon can remarkably change the behavior of CNT, its effect on the performance of a CNT-based mass sensor has not been investigated thus far. This investigation is based on modified Euler-Bernoulli beam theory and rippling effect is entered into the equations related to the cantilevered CNT-bases sensor. The impact of other properties like different masses, mechanical damping and intermolecular force is studied in this paper, as well. The results reveal that rippling deformation decreases the pull-in voltage and tip deflection of CNT but enhances the pull-in time. Results related to the impact of other mentioned properties are presented, too. The results are compared with other pull-in sensor equations in the literature and “molecular dynamics”, in both of which an excellent agreement is seen, to verify the soundness of this study.
http://jacm.scu.ac.ir/article_12006_9adc81349880a9abe9be76b9d8b6b934.pdf
2016-06-10T11:23:20
2018-12-10T11:23:20
229
239
10.22055/jacm.2016.12006
Bio-mass sensor
Rippling Deformation
CNT
Pull-in instability
Nazanin
Farjam
nazanin.farjam@gmail.com
true
1
Shahid Chamran University of Ahvaz
Shahid Chamran University of Ahvaz
Shahid Chamran University of Ahvaz
LEAD_AUTHOR
[1] Keivan Kiani, Hamed Ghaffari, Bahman Mehri, Application of elastically supported single-walled carbon nanotubes for sensing arbitrarily attached nanoobjects, Current Applied Physics 13 (2013) 107-120.
1
[2] Ho Jung Hwang, Jeong Won Kang, Carbon-nanotube-based nanoelectromechanical switch, Physica E: Low-dimensional Systems and Nanostructures 27 (2005) 163-175.
2
[3] K. Azizi, S. Majid Hashemianzadeh, Sh. Bahramifar, Density functional theory study of carbon monoxide adsorption on the inside and outside of the armchair single-walled carbon nanotubes, Current Applied Physics 11 (2011) 776-782.
3
[4] Muhammad A. Hawwa, Hussain M. Al-Qahtani, Nonlinear oscillations of a double-walled carbon nanotube, Computational Materials Science 48 (2010) 140-143.
4
[5] S.K. Georgantzinos, N.K. Anifantis, Carbon nanotube-based resonant nanomechanical sensors: a computational investigation of their behavior, Physica E: Low-dimensional Systems and Nanostructures 42 (2010) 1795-1801.
5
[6] M.Z. Atashbar, B. Bejcek, S. Singamaneni, Carbon nanotube based biosensors. Vienna, Austria, in: IEEE Sensor Conference (October 24th-27th, 2004), pp.1048-1105.
6
[7] R.F. Gibson, E.O. Ayorinde, Y.F. Wen, Vibrations of carbon nanotubes and their composites: a review, Composites Science and Technology 67 (2007) 1-28.
7
[8] T. Murmu, S. Pradhan, Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory, Computational Materials Science 46 (2009) 854e859.
8
[9] S. Gupta, R. Batra, Continuum structures equivalent in normal mode vibrations to single walled carbon nanotubes, Computational Materials Science 43 (2008) 715-723.
9
[10]K. Tonisch, V. Cimalla, F. Will, F. Weise, M. Stubenrauch, A. Albrecht, M. Hoffmann, O. Ambacher, Nanowire-based electromechanical biomimetic sensor, Physica E: Low-dimensional Systems and Nanostructures 37 (2007) 208-211.
10
[11]J. Zhu, Pull-in instability of two opposing microcantilever arrays with different bending rigidities, International Journal of Mechanical Sciences 50 (2008) 55-68.
11
[12]M. Rasekh, S.E. Khadem, Pull-in analysis of an electrostatically actuated nanocantilever beam with nonlinearity in curvature and inertia, International Journal of Mechanical Sciences 53 (2011) 108-115.
12
[13]Dequesnes, M., Tang, Z., Aluru, N.R., Static and Dynamic Analysis of Carbon Nanotube-Based Switches,Journal of Engineering Materials and Technology, 126(3) (2004) 230-237.
13
[14]I. Mehdipour, A. Erfani-Moghadam, C. Mehdipour Application of an electrostatically actuated cantilevered carbon nanotube with an attached mass as a bio-mass sensor, Current Applied Physics 13 (7), 1463-1469.
14
[15]Wang, X.Y., Wang, X., Numerical simulation for bending modulus of carbon nanotubes and some explanations for experiment, Composites: Part B, 35 (2004) 79–86.
15
[16]Payam Soltani, D. D. Ganji, I. Mehdipour1 and A. Farshidianfar, Nonlinear vibration and rippling instability for embedded carbon nanotubes, Journal of Mechanical Science and Technology 26 (4) (2012) 985-992.
16
[17]Koochi, A., Kazemi, A.S., Noghrehabadi, A., Yekrangi, A., Abadyan, M., New approach to model the buckling and stable length of multi walled carbon nanotube probes near graphite sheets, Materials and Design, 32 (2011) 2949-2955.
17
[18]Hayt, W.H., Buck, J.A., Engineering electromagnetic, 6th ed. New York: McGrawHill, (2001).
18
[19]Abbasnejad, B., Rezazadeh, G., Shabani, R., Stability analysis of a capacitive fgm micro-beam using modified couple stress theory, Acta Mechanica Solida Sinica, 26(4) (2013) 427-440.
19