ORIGINAL_ARTICLE
Solution of Nonlinear Hardening and Softening type Oscillators by Adomian’s Decomposition Method
A type of nonlinearity in vibrational engineering systems emerges when the restoring force is a nonlinear function of displacement. The derivative of this function is known as stiffness. If the stiffness increases by increasing the value of displacement from the equilibrium position, then the system is known as hardening type oscillator and if the stiffness decreases by increasing the value of displacement, then the system is known as softening type oscillator. The restoring force as a nonlinear polynomial function of order three, can describe a wide variety of practical nonlinear situations by proper choosing of constant multipliers. In this paper, a spring-mass system is considered by the restoring force of the introduced type. Choosing suitable values for a, b and n, a hardening and softening type oscillators are constructed and related equations of motion are introduced as second order nonlinear differential equations. The equations are solved directly, using the Adomian’s decomposition method (ADM). In another approach, the equations are converted to systems of first order differential equations and then solved using the same method. The results show that the ADM gives accurate results in both approaches, beside it shows that converting the equation to a system of equations of lower order, tends to more accurate solutions when ADM applies.
http://jsme.iaukhsh.ac.ir/article_515272_6e5b40e90d4167d12447d3c361111969.pdf
2013-06-22
1
10
Hardening and Softening Oscillator
Nonlinear
Adomian’s Method
Bahraam
Golmohammadi
1
Lecturer, Islamic Azad University, Salmas Branch, Engineering Faculty
AUTHOR
Ghasem
Asadi Cordshooli
g.asadi@iausr.ac.ir
2
Lecturer,Islamic Azad University, Shahr e Rey Branch, Science Faculty
LEAD_AUTHOR
A. R.
Vahidi
3
Assistant Professor, Islamic Azad University, Shahr e Rey Branch, Science Faculty
AUTHOR
[1]Adomian G., Applied Stochasti, Processes, Academic Press, 1983.
1
[2] Adomian G. Bellman R., Partial Differential Equations, D.Reidel Publishing Co., 1985.
2
[3] Adomian G., “Nonlinear Stochastic Systems Theory and Applications to Physics”, Kluwer, 1989.
3
[4] Adomian G., Solving Frontier Problems of physics: The Decomposition Method, Kluwer, 1994.
4
[5] Cherruault Y., Convergence of Adomin’s method, Kybernetes,Vol. 9 (2), 1988, pp. 31-38.
5
[6] Cherruault Y., Adomian G., Decomposition method: A new proof of convergence, Mathematical and ComputerModeling,Vol. 18(12), 1993, pp. 103-106.
6
[7] Babolian E.,Biazar J., Solving Concrete Examples by Adomian Method, Application mathematics And Computation, Vol. 135, 2003, pp. 161-167.
7
[8] Babolian E., Vahidi A.R.,AsadiCordshooliGh., Solving differential equations by decomposition Method, Application mathematics And Computation, Vol. 167, 2005, pp. 1150-1155.
8
[9] Wazwaz A.M., The modified decomposition method and Pade approximations for solving Thomas Fermi equations, Application mathematics And Computation, Vol. 105 ,1999, pp. 11-19.
9
[10] Wazwaz A.M., A comparison between Adomian decomposition method and Taylor series metod in the series solution, Application mathematics And Computation, Vol. 97,1998, pp. 37-44.
10
[11] BellomoN.,SarafyanD., On a Comparison between Adomian’sDecomposision Method and Picard Iteration, JournalMathematics and Analysis Application, Vol. 123, 1987, pp. 389–400.
11
[12] Vahidi A.R., AsadiCordshooliGh., Modifying Adomian Decomposition Method for Ordinary Differential Equations, Journal of Applied Mathematics, Vol. 3(10), 2006, pp. 49-54.
12
[13]Vahidi A.R., AsadiCordshooliGh., AzimzadehZ., Comparing numerical methods for the solution of the damped forced oscillator problem, Iranian Journal of Optimization, Vol. 2,2009, pp. 1-12.
13
[14] Vahidi A.R., Babolian E., AsadiCordshooliGh., Samiee F., Restarted Adomian’s Decomposition Method for Duffing’s Equation, InternationalJournal of Mathematics Analysis, Vol. 3(15), 2009, pp. 711-717.
14
[15] Vahidi A.R., Babolian E., AsadiCordshooliGh., Numerical solutions of Duffing’s oscillator problem, Indian Journal Physics, Vol. 86(4),2012, pp. 311-315.
15
[16] AsadiCordshooliGh., Vahidi A.R., Solutions of Duffing - van der Pol equation using Decomposition Method, Adv. Studies Theorist Physics, Vol. 5) 3(, 2011, pp. 121-129.
16
[17] Siddiqui A.M., Hameed M., Siddiqui B.M., Ghori Q.K., Use of Adomian decomposition method in the study of parallel plate flow of a third grade fluid, Communications in Nonlinear Science and Numerical Simulation, Vol. 15(9), 2010, pp. 2388-2399.
17
[18] Wu Guo-cheng, Adomian decomposition method for non-smooth initial value problems, Mathematical and Computer Modeling, Vol. 54(9-10), 2011, pp. 2104-2108.
18
[19] Sweilam N.H., Khader M.M., Approximate solutions to the nonlinear vibrations of multiwalled carbon nanotubes using Adomian decomposition method, Applied Mathematics and Computation, Vol. 217 (2), 2010, pp. 495-505.
19
[20] Duan J., ChaoluT., Rach R., Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the Rach–Adomian–Meyers modified decomposition method, Applied Mathematics and Computation, Vol. 218(17), 2012, pp. 8370-8392.
20
[21] Mao Qibo, Free vibration analysis of multiple-stepped beams by using Adomian decomposition method, Mathematical and Computer Modelling, Vol. 54, (1-2), 2011, pp. 756-764.
21
[22] Srinivasan P., Nonlinear Mechanical Vibrations, New Age International Publishers, 2008
22
ORIGINAL_ARTICLE
Study of the size-dependant vibration behavior of an AFM microcantilever with a sidewall probe
In this paper, the resonant frequency and sensitivity of an atomic force microscope (AFM) with an assembled cantilever probe (ACP) are analyzed utilizing the modified couple stress theory. The proposed ACP comprises a horizontal microcantilever, an extension and a tip located at the free end of the extension, which make AFM capable of scanning the sample sidewall. First, the governing differential equation and boundary conditions for dynamic analysis are obtained by a combination of the basic equations of the modified couple stress theory and Hamilton principle. Then, a closed form expression for the resonant frequency are derived, and using this expression the sensitivity are also investigated. The results of the proposed model are compared with those of the classic beam theory. The comparison shows that the difference between the results predicted by these two theories becomes significant when the horizontal cantilever thickness comes approximately close to the material length scale parameter, in which for some values of contact stiffness the difference reaches its maximum. It can also be inferred that a decrease in the microcantilever thickness could have a knock on effect on the shifts of first frequency and first sensitivity caused by an increase in the extension length.
http://jsme.iaukhsh.ac.ir/article_515274_fbceaf94e486d097a8b0711a2a3d75d2.pdf
2013-06-22
11
22
M.
Abbasi
1
Lecturer, , Mech. Eng., Islamic Azad Univ., Shahrood Branch
AUTHOR
A.
Karami Mohammadi
akaramim@shahroodut.ac.ir
2
Assis. Prof., Mech. Eng., Shahrood Univ. of Tech., Shahrood, Iran
LEAD_AUTHOR
[1] Garcia R., Perez R., Dynamic atomic force microscopy methods, Surface Science Report, Vol. 47, 2002, pp. 197–301.
1
[2] Holmberg K., Matthews A., Coatings Tribology: Properties, Techniques and Applications in Surface Engineering, Second Ed., New York, Elsevier, 1994.
2
[3] Mahdavi M.H., Farshidianfar A., Tahani M., Mahdavi S., Dalir H., A more comprehensive modeling of atomic force microscope cantilever, Ultra microscopy, Vol. 109, 2008, pp. 54–60.
3
[4] Turner J.A., Hirsekorn S., Rabe U., Arnold W., High-frequency response of atomic-force microscope cantilevers, Journal of Applied Physics, Vol. 82(3), 1997, pp. 966-979.
4
[5] Wu T.S., Chang W.J., Hsu J.C., Effect of tip length and normal and lateral contact stiffness on the flexural vibration responses of atomic force microscope cantilevers, Micro electron Engineering, Vol. 71, 2004, pp. 15–20.
5
[6] Chang W.J., Fang T.H., Chou H.M., Effect of interactive damping on sensitivity of vibration modes of rectangular AFM cantilevers, Physics Letters A, Vol. 312, 2003, pp. 158–165.
6
[7] Shen K., Hurley D.C., Turner J.A., Dynamic behaviour of dagger-shaped cantilevers for atomic force microscopy, Nanotechnology, Vol. 15, 2004, pp. 1582-1589.
7
[8] Abbasi M., Mohammadi A.K., A new model for investigating the flexural vibration of an atomic force microscope cantilever, Ultramicroscopy, Vol. 110, 2010, pp. 1374–1379.
8
[9] Lee H.L., Chang W.J., Dynamic response of a cracked atomic force microscope cantilever used for nanomachining, Nanoscale Research Letters, Vol.7, 2012, pp. 131.
9
[10] Dai G., Wolff H., Pohlenz F., Danzebrink U.H., Wilkening G., Atomic force probe for sidewall scanning of nano- and microstructures, Applied Physics Letters, Vol. 88, 2006; pp. 171908.
10
[11] Chang W.J., Lee H.L., Chen T.Y.F., Study of the sensitivity of the first four flexural modes of an AFM cantilever with a sidewall probe, Ultra microscopy, Vol. 108, 2008, pp. 619-624
11
[12] Kahrobaiyan M.H., Ahmadian M.T., Haghighi P., Haghighi A., Sensitivity and resonant frequency of an AFM with sidewall and top-surface probes for both flexural and torsional modes, International Journal ofMechanical Science, Vol. 52, 2010, pp.1357-1365.
12
[13] Dai G., Wolff H., Weimann T., Xu M., Pohlenz F., Danzebrink H.U., Nanoscale surface measurements at sidewalls of nano- and micro-structures, Measurement Science and technology, Vol. 18, 2007, pp. 334.
13
[14] Fleck N.A., Muller G.M., Ashby M.F., Hutchinson J.W., Strain gradient plasticity: theory and experiment, Acta Metallurgical et Materialia, Vol. 42, No. 2, 1994, pp. 475–487.
14
[15] Stolken J.S., Evans A.G., Microbend test method for measuring the plasticity length scale, Acta Materialia, Vol. 46, No. 14, 1998, pp. 5109–5115.
15
[16] Lam D.C.C., Yang F., Chong A.C.M., Wang J., Tong P., Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, Vol. 51(8), 2003 pp. 1477 1508.
16
[17] Mindlin R.D., Micro-structure in linear elasticity, Archive for Rational Mechanics and Analysis, Vol. 16(1), 1964, pp. 51–78.
17
[18] Toupin R.A., Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, Vol. 11(1), 1962, pp. 385–414.
18
[19] Fleck N.A., Hutchinson J.W., Strain gradient plasticity, Advances in Applied Mechanics, Vol. 33, 1997, pp. 296–358.
19
[20] Yang F., Chong A.C.M., Lam D.C.C., Tong, P., Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, Vol. 39, 2002, pp. 2731.
20
[21] Kong S., Zhou S., Nie Z., Wang K., The size-dependent natural frequency of Bernoulli–Euler micro-beams, International Journal of Engineering science, Vol. 46, 2008, pp. 427.
21
[22] M.H. Kahrobaiyan, M. Asghari, M. Rahaeifard, M.T. Ahmadian, Investigation of the size-dependent dynamic characteristics of atomic force microscope microcantilevers based on the modified couple stress theory, International Journal of Engineering Science, Vol. 48, 2010, pp.1985–1994.
22
[23] Lee H.W., Chang W.J., Sensitivity of V-shaped atomic force microscope cantilevers based on a modified couple stress theory, Microelectronic Engineering, Vol. 88, 2011, pp. 3214.
23
[24] Sommerhalter C.h., Glatzel T.h., Mattes T.W., Waldau A.J., Steiner M.C., Applied Surface Science, Vol. 157, 2000, pp. 32.
24
[25] Lin S.M., Liauh C.T., Wang W.R., Ho S.H., Analytical solutions of the first three frequency shifts of AFM non-uniform probe subjected to the Lennard–Jones force, Ultra microscopy, Vol. 106, 2006, pp. 508–515.
25
ORIGINAL_ARTICLE
Free and Forced Vibration Analysis of Composite Laminated Conical Shells under Different Boundary Conditions Via Galerkin Method
In this paper, natural frequency and response of forced vibration of composite laminated conical shells under different boundary conditions are investigated. To this end, equations of Donnell's thin shell theory are used as governing equations. The analytical Galerkin method together with beam mode shapes as weighting functions is employed to solve the problem. Due to importance of boundary conditions upon the mechanical behavior of conical shells, the analysis is carried out for all possible boundary conditions. The response of forced vibration is calculated via the modal participation factor method. Numerical comparisons of free vibration with the results in the open literature are made to validate the present methodology.
http://jsme.iaukhsh.ac.ir/article_515275_87be74c9d4159a753435b11278765918.pdf
2013-06-22
23
36
Free vibration
Forced vibration
Conical shell
Composite laminated
Galerkin Method
A.
Nasiri Rad
1
M.Sc., Islamic Azad University, Takestan Branch
AUTHOR
R.
Ansari
r_ansari@guilan.ac.ir
2
Associate Professor, Department of Mechanical Engineering, University of Guilan
LEAD_AUTHOR
H.
Rouhi
3
Ph.D. Student, Department of Mechanical Engineering , University of Guilan
AUTHOR
[1] Wilkins D. J., Bert C. W., Egle D. M., Free vibrations of orthotropic sandwich conical shells with various boundary conditions, Journal of Sound and Vibration, Vol. 13, 1970, pp. 211-228.
1
[2] Irie T., Yamada G., Muramoto Y., Free vibration of joined conical-cylindrical shells, Journal of Sound and Vibration, Vol. 95, 1984, pp. 31-39.
2
[3] Thambiratnam, D. P., Zhuge Y., Axisymmetric free vibration analysis of conical shells, Engineering Structures, Vol. 15, 1993, pp. 83-89.
3
[4] Shu C., An efficient approach for free vibration analysis of conical shells, International Journal of Mechanical Sciences, Vol. 38, 1996, pp. 935-949.
4
[5] Lam K. Y., Hua L., On free vibration of a rotating truncated circular orthotropic conical shell, Composites Part B: Engineering, Vol. 30, 1999, pp. 135-144.
5
[6] Hu H. T., Ou S. C., Maximization of the fundamental frequencies of laminated truncated conical shells with respect to fiber orientations, Composite Structures, Vol. 52, 2001, pp. 265-275.
6
[7] Wu C. P., Lee C. Y., Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness, International Journal of Mechanical Sciences, Vol. 43, 2001, pp. 1853-1869.
7
[8] Hu X. X., Sakiyama T., Matsuda H., Morita C., Vibration of twisted laminated composite conical shells, International Journal of Mechanical Sciences, Vol. 44, 2002, pp. 1521-1541.
8
[9] Civalek O., An efficient method for free vibration analysis of rotating truncated conical shells, International Journal of Pressure Vessels and Piping, Vol. 83, 2006, pp. 1-12.
9
[10] Liang S., Chen H. L., Chen T., Wang M. Y., The natural vibration of a symmetric cross-ply laminated composite conical-plate shell, Composite Structures, Vol. 80, 2007, pp. 265-278.
10
[11] Tripathi V., Singh B. N., Shukla K. K., Free vibration of laminated composite conical shells with random material properties, Composite Structures, Vol. 81, 2007, pp. 96-104.
11
[12] Civalek O., Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: Discrete singular convolution (DSC) approach, Journal of Computational and Applied Mathematics, Vol. 205, 2007, pp. 251-271.
12
[13] Sofiyev A. H., Korkmaz K. A., Mammadov Z., Kamanli M., The vibration and buckling of freely supported non-homogeneous orthotropic conical shells subjected to different uniform pressures, International Journal of Pressure Vessels and Piping, 86, Vol. 2009, pp. 661-668.
13
[14] Sofiyev A. H., The vibration and stability behavior of freely supported FGM conical shells subjected to external pressure, Composite Structures, Vol. 89, 2009, pp. 356-366.
14
[15] Sofiyev A. H., Kuruoglu N., Halilov H. M., The vibration and stability of non-homogeneous orthotropic conical shells with clamped edges subjected to uniform external pressures, Applied Mathematical Modeling, Vol. 34, 2010, pp. 1807-1822.
15
[16]conical shells - A finite element approach, Composite Structures, Vol. 94, 2012, pp. 2188-2196.
16
[17] Sofiyev A. H., Kuruoglu N., Vibration analysis of FGM truncated and complete conical shells resting on elastic foundations under various boundary conditions, Journal of Engineering Mathematics, Vol. 77, 2012, pp. 131- 145.
17
[18]Malekzadeh P., Heydarpour Y., Free vibration analysis of rotating functionally graded truncated conical shells, Composite structures, Vol. 97, 2013, pp. 176-188.
18
[19]Civalek O., Vibration analysis of laminated composite conical shells by the method of discrete singular convolution based on the shear deformation theory, Composites Part B: Engineering, Vol. 45, 2013, pp. 1001-1009.
19
[20] Qatu M. S., Sullivan R. W., Wang W., Recent research advances on the dynamic analysis of composite shells: 2000-2009, Composite structures, Vol. 93. 2010, pp. 14-31.
20
[21] Soedel W., Vibrations of Shells and Plates, 2004, Marcel Dekker, Inc., New York.
21
[22] Loy, C. T., Lam, K. Y., Vibration of Cylindrical Shells with Ring Support, International Journal of Mechanical Sciences, Vol. 39, 1997, pp. 445–471.
22
[23] Irie T., Yamada G., Tanaka K., Natural frequencies of truncated conical shells, Journal of Sound and Vibration, Vol. 92, 1984, pp. 447-453.
23
[24] Lam K. Y., Li H., On free vibration of rotating truncated orthotropic conical shell, Composite, Vol. 30, 1999, pp. 135-44.
24
[25] Li F. M., Kishimoto K., Huang W. H., The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh-Ritz method, Mechanics Research Communications, Vol. 36, 2009, pp. 595-602
25
[26] Shu C., Free vibration analysis of composite laminated conical shells by generalized differential quadrature, Journal of Sound and Vibration, Vol. 194, 1996, pp. 587-604.
26
ORIGINAL_ARTICLE
Finite element simulation of the clinching process of steel sheets and study on influence of anisotropy on the mechanical behavior of joint
This article describes a numerical study on the TOX-clinching process of the steel sheets. In addition, the influence of plastic anisotropy of the material on joining parameters is analyzed by evolution of the joint parameters such as undercut and neck thickness and punch force-displacement curve. Finite element analysis with ABAQUS/CAE-Explicit program is used to simulate two dimensional and three dimensional model of clinching process based on the above objectives. This work mainly represents the comparison between experimental and the simulation results with respect to process which gives the validation of the simulation results.Three-dimentional simulation of clinching process is used to study the effect of anisotropy. Results indicate that the clinching punch force-displacement curve for connection of anisotropic sheets is higher than that for isotropic sheets. In addition, results indicate that neck thickness increases with the effect of plastic anisotropy and the undercut decreases with it.
http://jsme.iaukhsh.ac.ir/article_515276_42db9f1d271fa0bdb7466a71758601d5.pdf
2013-06-22
37
46
M.R.
Dorri
1
M.Sc. Student, Islamic Azad University, Khomeinishahr Branch.
AUTHOR
M.
Loh-mousavi
loh-mousavi@iaukhsh.ac.ir
2
Assistant Professor, Islamic Azad University, Khomeinishahr Branch
LEAD_AUTHOR
S.
Saberi
3
Assistant Professor, Islamic Azad University, Najafabad Branch.
AUTHOR
[1] Mizanur R., Experiment and Numerical Simulation of TOX Clinching Process for galvanized thin steel sheets using ABAQUS Program, Institute of Materials Science, Welding and Forming, Graz University of Technology, Graz, Austria, 2007
1
[2] Saberi S., Enzinger N., Vallant R., Cerjak, H., Hinterdorfer,J., Rauch R., Influence of plastic anisotropy on the mechanical behavior of clinched joint of different coated thin steel sheets, International journal of material forming, volume1, supplement1, 2008, pp. 273–276
2
[3]Akbarzadeh-paydar O., Analyse der Verbindungsfestigkeit von Clinchpunkten für beschichtete Stahlfeinbleche unter quasistatischer Belastung mittels experimentellen Untersuchungen und FE-Simulation, Institute of Materials Science, Welding and Forming, Graz University of Technology, Graz, Austria, 2007
3
[4] Varis J., Lepisto J., A simple testing-based procedure and simulation of the clinching process using finite element analysis for establishing clinching parameters, Thin-Walled Structures, Vol. 41, 2003, pp. 691–709
4
[5] Carboni M., Beratta S., Monno M., Fatigue behavior of tensile-shear loaded clinched joints, Engineering Fracture Mechanics, Engineering Fracture Mechanics, Vol. 73, 2006, pp. 178–190
5
[6] جانسون، و.، ملور، پ.، ترجمه ابرینیا، ک.، پلاستیسیته مهندسی، انتشارات یامهدی (عج)، تهران، گروه صنایع یامهدی (عج)، 1378،122-120
6
[7] Banabic D., Plastic behavior of sheet metal, sheet metal forming process, Springer, 2010, pp. 27-140
7
[8] ABAQUS Inc. (2009). ABAQUS User's Manual, Version 6.9.
8
ORIGINAL_ARTICLE
Bending analysis of composite sandwich plates using generalized differential quadrature method based on FSDT
Nowadays, the technology intends to use materials such as magnesium alloys due to their high strength to weight ratio in engine components. As usual, engine cylinder heads and blocks has made of various types of cast irons and aluminum alloys. However, magnesium alloys has physical and mechanical properties near to aluminum alloys and reduce the weight up to 40 percents. In this article, a new low cycle fatigue lifetime prediction model is presented for a magnesium alloy based on energy approach and to obtain this objective, the results of low cycle fatigue tests on magnesium specimens are used. The presented model has lower material constants in comparison to other criteria and also has proper accuracy; because in energy approaches, a plastic work-lifetime relation is used where the plastic work is the multiple of stress and plastic strain. According to cyclic softening behaviors of magnesium and aluminum alloys, plastic strain energy can be proper selection, because of being constant the product value of stress and plastic strain during fatigue loadings. In addition, the effect of mean stress is applied to the low cycle fatigue lifetime prediction model by using a correction factor. The results of presented models show proper conformation to experimental results
http://jsme.iaukhsh.ac.ir/article_515277_8a37bb8f7320b3878f20871c464588e1.pdf
2013-06-22
47
62
Bending
Generalized differentialmethod
Composite sandwich plates
First Order Shear Deformation Theory
M.
yazdani
1
Master student, Mechanical engineering Department, Hamadan Branch, Islamic Azad University Science and research Campus , Hamadan, Iran
AUTHOR
A.
Ghassemi
_ghassemi@pmc.iaun.ac.ir
2
Assistant professor, Mechanical engineering Department, Branch, Islamic Azad University, Isfahan, Iran
LEAD_AUTHOR
M.
Hedatati
3
Master student Mechanical engineering Department, Isfahan University of Technology, Isfahan, Iran
AUTHOR
[1] Pandit M.K., Singh B.N., Sheikh A.H., Buckling of laminated sandwich plates with soft core based on an improved higher order zigzag theory, Journal of Thin-Walled Structures, Vol. 46, 2008, pp. 1183– 1191.
1
[2] Leissa A.W., Review of laminated composites plate buckling, Applied Mechanical Rev, Vol. 40, 1987.
2
[3] Levy M., Sur L’equilibrie Elastique d’une Plaque Rectangulaire, Compt Rend, Vol. 129, 1899, pp. 535-539.
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[4] Timoshenko S.P., woinowsky – Krieger.S., Theory of plates and shells , 2d ed., McGraw Hill, New York, 1959.
4
[5] هنرجو ، ب،" آنالیز صفحات لایه لایه مرکب به روش differential quadrature "، دانشگاه شیراز ، 1378.
5
[6] Whitney J.M., Pagano.N J, Shear deformation in heteogeneous anisotropic plates, ASME Journal of Applied Mechanical, Vol. 37,1970, pp. 1031-1036.
6
[7] Bert C.W., Chen T.L.C., Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular plates, International Journal of Solids Structure, Vol. 14, 1978, pp. 465-473.
7
[8] Reddy J.N., Chao W.C., A comparison of closed-form and finite-element solutions of thick, laminated, anisotropic rectangular plates, Nuclear Engineering and Design, Vol. 64, 1981, pp. 153-167.
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[9] Kant T., Numerical analysis of thick plates, Computation and Mathematics Applied Mechanical Engineering, Vol. 31, 1982, pp.1–18.
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[10] Pandya B science N., Kant T., A consistent refined theory for flexure of a symmetric laminate, Mechanics Research Communications, Vol, 14, 1987, pp.107–113.
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[11] Pandya BN., Kant T., Higher order shear deformable theories for flexure of sandwich plates –finite element evaluations.InternationalJournal of Solids Structures, Vol. 24(12), 1988, pp. 1267–86.
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[12] Pandya BN., Kant T., Flexure analysis of laminated composites using refined higher order C_ plate bending elements Computation and Mathematics Applied Mechanical Engineering, Vol. 66, 1988, pp. 173–98.
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[13] Pandya BN., Kant T., A refined higher order generally orthotropic C_ plate bending element. Composite Structures, Vol. 28, 1988, pp. 119–133.
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[14] Pandya BN., Kant T., Finite element stress analysis of laminated composites using higher order displacement model, Composite science Technology, Vol. 32, 1988, pp. 137–155.
14
[15] Kant T., Manjunatha BS., An unsymmetric FRC laminate C_ finite element model with 12 degrees of freedom per node. Eng Comput, Vol. 5(3), 1988, pp. 300–308.
15
[16] Swaminathan K., Patil S.S., Nataraja M.S, Mahabaleswara K.S., Bending of sandwich plates with anti-symmetric angle-ply face sheets – Analytical evaluation of higher order refined computational models, Composite Structures, Vol. 75, 2006, pp. 114–120.
16
[17] Bellman R., Casti J., Differential quadrature and long-term integration, Journal of Mathematical Analysis and Applications, Vol. 34, 1971, pp. 235–238.
17
[18] Bellman R.E., Kashef B.G., Casti J., Differential quadrature: a technique for a rapid solution of nonlinear partial differential equations, Journal Computational Physics, Vol. 10, 1972, pp. 40–52.
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[19] Bert C.W., S.K. Jang., Striz A.G., Two new approximate methods for analyzing free vibration of structural components, AIAA Journal, Vol. 26, 1988, pp. 612-618.
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[20] Bert C.W., Malik M., Differential quadrature in computational mechanics: a review, Applied Mechanical Review, Vol. 49, 1996, pp. 1–27.
20
[21] Chen W., Shu C., He W., Zhong, T., The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates, Composite Structures, Vol. 74, 2000, pp. 65–76.
21
[22] Chen W., Tanaka M.A., Study on time schemes for DRBEM analysis of elastic impact wave, Computational Mechanics, Vol. 28, 2002, pp. 331–338.
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23
[24]. Bert C.W., Wang X., Striz, A.G., Differential quadrature for static and free vibration analyses of anisotropic plates, International Journal of Solids Structures, Vol. 30, 1993, pp.1737–1744.
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[25] Wang X., Bert C.W., A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates, Journal of Sound Vibration, Vol. 162, 1993, pp. 566–572.
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[26] Wang X., Gu H., Static analysis of frame structures by the differential quadrature element method. International Journal Numer Mechanical Eng, Vol. 40, 1997, pp. 759–772.
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[27] Wang X., Wang Y., Free vibration analyses of thin sector plates by the new version of differential quadrature method. Computation and Mathematics Applied Mechanical Engineering, Vol. 193, 2004, pp. 3957–3971.
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[28] Wang X., Differential quadrature for buckling analysis of laminated plates. Computers and Structures, Vol. 57, 1995, pp. 715–719.
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ORIGINAL_ARTICLE
A new low cycle fatigue lifetime prediction model for magnesium alloy based on modified plastic strain energy approach
Nowadays, the technology intends to use materials such as magnesium alloys due to their high strength to weight ratio in engine components. As usual, engine cylinder heads and blocks has made of various types of cast irons and aluminum alloys. However, magnesium alloys has physical and mechanical properties near to aluminum alloys and reduce the weight up to 40 percents. In this article, a new low cycle fatigue lifetime prediction model is presented for a magnesium alloy based on energy approach and to obtain this objective, the results of low cycle fatigue tests on magnesium specimens are used. The presented model has lower material constants in comparison to other criteria and also has proper accuracy; because in energy approaches, a plastic work-lifetime relation is used where the plastic work is the multiple of stress and plastic strain. According to cyclic softening behaviors of magnesium and aluminum alloys, plastic strain energy can be proper selection, because of being constant the product value of stress and plastic strain during fatigue loadings. In addition, the effect of mean stress is applied to the low cycle fatigue lifetime prediction model by using a correction factor. The results of presented models show proper conformation to experimental results.
http://jsme.iaukhsh.ac.ir/article_515278_54fbcb5264c42d83991560b982d454ef.pdf
2013-06-22
63
76
cylinder head
low cycle fatigue
fatigue lifetime prediction model
Magnesium alloy
energy approach
Mohammad
Azadi
m.azadi.1983@gmail.com
1
PhD, Fatigue and Wear in Materials Workgroup, Irankhodro Powertrain Company (IPCO), Tehran, Iran
LEAD_AUTHOR
Gholam Hossein
Farrahi
2
Professor, Materials Life Estimation and Improvement, Sharif University of Technology, Tehran, Iran
AUTHOR
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