ORIGINAL_ARTICLE
Numerical and Experimental Study of Effect of Scan Velocity in Laser Forming by Temperature Gradient Mechanism
In this paper the process of laser forming has been investigated using an analytical and an experimental method for three levels scans velocity. A coupled analysis has been performed in ANSYS®. Also in order to prove the predictive methods, experiments on thin sheet metals have been done when a laser of a fair power was used. Before done, experiments were designed with full factorial chosen as the experiment scheme planning. For performing experiments a CO2 laser a maximum power of 200 watt is used. A CMM is used to measuring the bending angle of the workspice. Finally, a statistical analysis on the experimental data was performed. The comparison between numerical and experimental results shows the bending angle decreased by increasing the scan velocity also rate of the bending angle decreased by increasing the scan velocity.
http://jsme.iaukhsh.ac.ir/article_515538_877ab8f6197a16194758af2e5022f506.pdf
2008-06-21
1
8
Laser
Sheet metal
TGM
Thermal–mechanical coupling problem
H.
Moslemi Naeni
moslemi@modares.ac.ir
1
- Professor, University of Tarbiat Modares
LEAD_AUTHOR
V.
Panahizadeh
2
Ph.D. Student, University of Tarbiat Modares
AUTHOR
M. Hossein
pour Gollo
3
Ph.D. Student, University of Tarbiat Modares
AUTHOR
S.
Mazdak
4
Ph.D. Student, University of Tarbiat Modares
AUTHOR
[1] Shi Y.J., Shen H., Yao Z.Q. and Hu J., Numerical Investigation of Straight-Line laser forming under the temperature gradient mechanism, Acta Metallurgica Sinica, Vol. 19 No. 2 , 2006, pp. 144-150
1
[2] Magee J., Watkins K.G. & Steen W.M., Advances in Laser Forming, J. Laser Applications, Vol. 10, Issue 6, 1998, pp. 235-246
2
[3] Hoseinpour Gollo M., Moslemi Naeini H., Liaghat G.H., Torkamany M. J., Jelvani S., Panahizadeh V., An experimental study of sheet metal bending by pulsed Nd:YAG laser with DOE method, Int. J. Mater Form, Springer-online (In press)
3
[4] Wegener K. & Adelhardt M., Shipbuilding experiences a revolution, Industrial Laser Solutions, Pennwell Corporation, Tulsa ,Vol. 17, No.12, , 2002 , pp. 9-12.
4
[5] Panahizadeh V., Moslemi Naeini H., Mehreban M. and Mazdak S., Investigation of Bending Angle in TGM Laser Forming Process Using DOE Method, Tehran International Congress on Manufacturing Engineering (TICME2007), Tehran, Iran, Dec. 2007.
5
[6] Yongjun Shi, Hong Shen, Zhenqiang Yao, Jun Hu, Temperature gradient mechanism in laser forming of thin plates, Optics & Laser Technology , Vol. 39, 2006, pp. 858–863.
6
[7] Moslemi Naeini H., Panahizadeh V., Mazdak S., Mousavi H., TGM Laser Forming Process for Sheet Metals –an FEM Analysis Approach, Turkey Int. Congress on Manufacturing Eng. (Diemold2007), Turkey, 2007.
7
[8] Z. Hu, R. Kovacevic, M. Labudovic, Experimental and numerical modeling of buckling instability of laser sheet forming, Int. J. Machine Tools & Manufacture Vol. 42, 2002, pp.1427–1439
8
[9] ASM Metals Handbook, ASM International, 10th Ed. 1990.
9
ORIGINAL_ARTICLE
Vibration Suppression of Smart FGM Cylindrical Shells Using Magnetostrictive Layers
In the present work, FGM shells integrated with magnetostrictive layers acting as distributed sensors and actuators are modeled to control vibration attenuation of FGM shells with simply supported boundaryconditions. To achieve a mechanism for actively control of the oscillation amplitude of the integrated structure, a negative velocity proportional feedback control law is implemented in the study. Theoretical formulation is based on the first order shear deformation shell theory, taking into consideration transverse shear deformation and rotary inertia effects. Material properties are assumed to be temperature-dependent and graded in the thickness direction according to different volume fraction functions. A FGM cylindrical shell made up of a mixture of ceramic and metal is considered. The magnetostrictive layers are also considered to be made of Terfenol-D. The influence of vibration attenuation characteristics of magnetostrictive layers, the location of these layers and control parameters on vibration suppression is investigated.
http://jsme.iaukhsh.ac.ir/article_515539_16b3d65258e0a6fa57b947351fea8ab3.pdf
2008-06-21
9
18
Vibration attenuation
FGM Shells
Magnetostrictive layers
Velocity feedback control
M.
Darvizeh
darvizeh@guilan.ac.ir
1
Professor, Guilan University, Technology Faculty.
LEAD_AUTHOR
R.
Ansari
guilan.ac.ir@r_ansari
2
Assistant Porfessor, Guilan University, Technology Faculty
AUTHOR
A.
Darvizeh
3
Professor, Guilan University, Technology Faculty
AUTHOR
R.
Rajabieh Fard
4
M.Sc. Student, Islamic Azad University, Tehran Jonoub Branch.
AUTHOR
[1] Ansari R., Darvizeh M., Prediction of Dynamic Behaviour of FGM Shells Under Arbitrary Boundary Conditions, J. Composite Structures, (Article in press).
1
[2] Kumar J.S., Ganesan N., Swarnamani S. and Padmanabhan, C., Active control of cylindrical shell with magnetostrictive layer, J. Sound & Vibration, 262, pp. 577-589.
2
[3] Reddy J.N., Mechanics of laminated composite plates and shells, 2004, CRC Press LLC.
3
Pradhan S.C, Vibration suppression of FGM shells using embedded magnetostrictive layers, Int. J. Solid and Structures, Vol. 42, pp. 2465-2488
4
ORIGINAL_ARTICLE
Investigation of the Effectiveness of Using a CVT in Samand Automobile
This paper investigates the effectiveness of using CVT (Continuous Variable Transmission) in Samand automobile. For this analysis, the conventional Samand and a Samand equipted with CVT are modeled and simulated by using Simulink based software (ADVISOR) and the performances are compared. This analysis includes the effect of driving cycle, fuel consumption and the efficiency of components of the power train. The results show that the fuel economy is increased while using CVT. Finally, the overall cost analysis for incorporating CVT is done and the economical advantage is discussed.
http://jsme.iaukhsh.ac.ir/article_515540_196f8905e59766683db24df396f5d0ba.pdf
2008-06-21
19
30
CVT
ADVISOR
FTP
Fuel consumption
Mohsen
Esfahanian
mesf1964@cc.iut.ac.ir
1
Assistant Professor, Isfahan University of Technology, Mechanical Engineering Faculty.
LEAD_AUTHOR
Mohsen
Nikbin
2
M.Sc., Islamic Azad University, Khomeini Shahr Branch
AUTHOR
[1] Birch, Stuart, Audi takes CVT from 15th century to 21st century (English), Automotive Engineering International Magazine, SAE International, Retrieved on Nov. 2007.
1
[2] Harris, William, How CVTs work (English) article, How Stuff Works, Inc. online resource (auto.howstuffworks.com, Retrieved on Dec. 2007.
2
[3] Iran Khodro archive, Samand owner’s handbook, Published by Iran Khodro Industrial Group (English), , 1st Edition, October 2002.
3
[4] شرکت ساپکو، جزوه مکانیک خودرو- بخش ترمودینامیک، انتشارات ساپکو،، 1382.
4
[5] نیکبین، م.، پایاننامه کارشناسی ارشد، بررسی استفاده از CVT برروی خودروهای داخلی، دانشگاه آزاد اسلامی، واحد خمینی شهر، 1387.
5
ORIGINAL_ARTICLE
Investigation on Buckling of Orthotropic Circular and Annular Plates of Continuously Variable Thickness by Optimized Ritz Method
This paper investigates symmetrical buckling of orthotropic circular and annular plates of continuous variable thickness. Uniform compression loading is applied at the plate outer boundary. Thickness varies linearly along radial direction. Inner edge is free, while outer edge has different boundary conditions: clamped, simply and elastically restraint against rotation. The optimized RayLeigh-Ritz method is applied for buckling analysis. In this method, a polynomial function that is based on static deformation of orthotropic circular plates in bending is used. Also, byemploying an exponential parameter in deformation function, eigenvalue is minimized in respect to that parameter. The advantage of this procedure is simplicity in comparison with other methods, while whole algorithm for solution can be coded for computer programming. The effect of variation of radius, thickness, different boundary conditions, ratio of radial Young Modulus to circumferential one, ratio of outer radius to inner one in annular plates on critical buckling coefficient are investigated. The obtained results show that in plate with identical thickness, increasing of outer radius decreases the critical buckling coefficient. In addition increasing of thickness of the plates results in increase of critical buckling coefficient.
http://jsme.iaukhsh.ac.ir/article_515542_f61b43d09753ab3e5f024a3031e657fa.pdf
2008-06-21
31
40
Buckling
Optimized Rayleigh-Ritz Method
Orthotropic plate
Variable thickness
Fatemeh
Farhatnia
farhatnia@iaukhsh.ac.ir
1
Assistant Professor, Islamic Azad University, Khomeinishahr Branch
LEAD_AUTHOR
Arash
Golshah
2
M.Sc. Student, Islamic Azad University, Khomeinishahr Branch
AUTHOR
[1] Woinowski-Krieger, S., Buckling stability of circularplates with circular cylindrical Aeolotropy, Ingenieur-Archiv, Vol. 26, 1958, pp. 129-131
1
[2] Meink T., Huybrechts S., Ganley J., “The Effect of varying thickness on the buckling of orthotropic plates, J. Composite Materials, Vol. 33, 1999, pp. 1048-1061.
2
[3] Laura P.A.A, Gutierrez R.H., Sanzi H.C., Elvira G., buckling of circular, solid and annular plates with an intermediate circular support, J. Ocean Engineering, Vol. 27, 2000, pp.749-755
3
[4] Ciancio P.M, Reyes J.A., Buckling of circular annular plates of continuously variable thickness used as internal bulkheads in submersibles, J. Ocean engineering, Vol. 30, 2003, pp. 1323-1333
4
[5] Bostjan B., Kosel F., Thickness optimization of circular annular plates at buckling, Thin-Walled Structures, Vol. 32, 2006,74-81.
5
[6] Gutierrez R.H., Romanlli E., Laura P.A.A., Vibration and elastic stability of thin circular plates with variable profile, J. Sound and Vibration, Vol. 195, 1996, 391-399.
6
[7] Liang B., Zhang Sh, Dian-Yun Chen, Natural frequencies of circular annular plates with variable thickness by a new method, J. Pressure Vessels and Piping, Vol. 84, 2007, 293-297.
7
[8] Timoshenko, S. P., Gere, J. M., Theory of elastic stability, 2nd Ed, McGraw-Hill, New York, 1961.
8
[9] Venstel E., Thin plates and shells, Dekker Publication, 2001.
9
[10] Chuen-Yuan Chia, Nonlinear Analysis of Plates, McGraw-Hill, 1980.
10
11
12
13
14
ORIGINAL_ARTICLE
Investigation of Manufacturing Processes of the Metallic
CNG Pressure Vessels
CNG vessels are used in many vehicles. Mass production of CNG pressure vessels requires exact understanding of process effective parameters. In this paper, the numerical analysis has been used to study the manufacturing parameters. The entire manufacturing processes, including deep drawing, redrawing and ironing, of an aluminum liner sample of CNG pressure vessel (without spinning) have been simulated by Finite Element technique. The deep drawing process has been modeled by using flat dies. Then, drawing force and wall thickness variations have been studied. In order to achieve the final diameter of the liner, the redrawing process has been implemented in a flat die. To obtain a uniform wall thickness, the ironing process has been simulated in two stages, and the required force and the change of wall thickness for each process have been recorded. The results of this paper have been compared with the published results obtained by other researcher and found a good correlation between them.
http://jsme.iaukhsh.ac.ir/article_515545_e2b50cad8c905b84c7ae9a9587458640.pdf
2008-06-21
41
50
Deep drawing
Redrawin
Ironing
Simulatio
CNG liner
M.
Zohoor
mzohoor@kntu.ac.ir
1
Assistant Professor, K. N. Toosi University of Technology, Faculty of Mechanical Engineering
LEAD_AUTHOR
M.
Rahimian
2
M.Sc., K. N. Toosi University of Technology, Faculty of Mechanical Engineering
AUTHOR
[1] WWW. ENGINEERING AND TECHNOLOGY.COM
1
[2] Choi Chul Kim J.C., Jung S.Y., Development of an automated design system of a CNG composite vessel using a steel liner manufactured using the DDI process. Int. J. Adv. Mfg. Tech., Vol. 24, , 2004, pp. 781–788.
2
[3] Vardga L., Nagy A., Kovacs A., Design of CNG tank made of Aluminum and Reinforced Plastic, Composites, Vol. 26, Issue 6, , 1995, pp. 457-463.
3
[4] Allen S.j., Mahdavian S.M., The effect of lubrication on die expansion during the deep drawing of axisymmetrical steel cups, J. Material Processing Technology, Vol. 199, 2008, pp. 102-107.
4
[5] Sedighi M. & Rasti M. , An investigation on manufacturing process parameters of CNG pressure vessels, Int. J. Adv. Mfg. Tech.,
5
Vol. 38, No. 9-10, 2008, pp. 958-964.
6
[6] Hrivnak A., Sobotova L., The influence of the deformation aging and the conditions of stress on the properties of the deep drawing steel sheet, J. Material Processing Technology,Vol. 34, 1992, pp. 425-430.
7
[7] Date P.P., Padmanabhan K.A., On the prediction of the forming limit diagram of sheet metals, Int. J. Mechanical Science , Vol. 34 (5), 1992, pp. 363-374.
8
[8] Yossifon S., Tirosh J., On the dimensional accuracy of deep drawing products by hydroforming processes, Int. J. Mech. Sci. 33 (4), pp. 279-295, 1991
9
[9] Thiruvarudchelvan S., N.H. Loh, Drawing of cylindrical and hemispherical cups using an improved tooling for friction-actuated blank holding, J. Material Processing Technology, Vol. 37, pp. 267–280, 1993
10
[10] WWW.MATWEB.COM
11
[11] NAM J. & Seop HAN K., Finite Element Analysis of deep Drawing and Ironing Process in the Steel D&I Canmaking, ISIJ.
12
[12] ABAQUS Version 6.7 Documentation, ABAQUS Analysis User’s Manual, 2007.
13
ORIGINAL_ARTICLE
Nonlinear Finite Element Analysis of Thermoelastic Stresses of FGM Rotating Disk Considering Temperature-Dependency of Material Properties
In the present paper, nonlinear radial and hoop thermoelastic stresses analysis of a disk made of FGMs material is investigated. According to this purpose, finite element method is used. In the present method, second-order one-dimensional element (with three node points) is proposed. The geometrical and stress boundary conditions are defined in the state of non-existence of external pressure and then zero radial stress in the outer layer of the disk, and zero displacement in the center of the disk. Also the temperature distribution is assumed as linear. The material properties changes including temperature-dependency are modeled. Finally, a numerical example is proposed to show the radial displacements, radial and hoop thermoelastic stresses versus radius of the disk for different power (N) from Power-law and different angular velocities. The results show that by increasing both two parameters, N and angular velocity of the disk, the amounts of displacement and stress are increased. At last, temperature-dependency and temperature-independency of material properties is investigated.
http://jsme.iaukhsh.ac.ir/article_515551_7c53c573149f2082341eff0128a8c572.pdf
2008-06-21
51
58
Rotating disk
Finite Element Method
FGM
Thermoelastic stress
Temperature-dependency
nonlinear analysis
Mehrnoosh
Damircheli
damirchi@kvoushco.com
1
Ph.D Student of mechanical engineering, Islamic Azad University, Science and Technology branch
LEAD_AUTHOR
Mohammad
Azadi
m.azadi.1983@gmail.com
2
Ph.D Student of mechanical engineering, Sharif University of Technology
AUTHOR
[1] Suresh S., Mortensen A., Fundamental of Functionally Graded Materials, Barnes and Noble Pub, 1998.
1
[2] Koizumi M., Nino M., Overview of FGM research in Japan, MRS Bulletin, Vol. 20, 1995, pp. 19-21.
2
[3] Kaysser W.A., Ilschner B., FGM research activities in Europe, MRS Bulletin, Vol. 20 1995, pp. 22-26.
3
[4] Research on the basic technology for the development of functionally graded materials for relaxation of thermal stress, Science on Technology Agency of Japanese Government Report, 1987.
4
[5] Timoshenko S.P., Goodier J.N., Theory of Elasticity, McGraw-Hill, New York, 1987
5
[6] Lekhnitskii S.G. , Anisotropic Plates, Gordon and Breach, London, 1968.
6
[7] Seireg A., Surana K.S., Optimum design of rotating disks, J. Engineering, Vol. 92, 1970, pp. 1–10.
7
[8] Murthy D.N.S., Sherbourne A.N., Elastic stresses in anisotropic disks of variable axial, J. Mechanical Science, Vol. 12,1970, pp. 627–640.
8
[9] Yeh K.Y., Han R.P.S., Analysis of high-speed rotating disks with variable axial and in-homogeneity, J. Applied Mechanics, Vol. 61, 1994, pp. 186–191.
9
[10] Leissa A.W., Vagins M., The design of orthotropicmaterials for stress optimization, J. Solids Structures, Vol. 14,1978, pp. 517–526.
10
[11] Jain R., Ramachandra K., Simha K.R.Y., Rotating anisotropic disc of uniform strength, J. Mechanical Science, Vol. 41, 1999, pp. 639–648.
11
[12] Jain R., Ramachandra K., Simha K.R.Y., Singularity in rotating orthotropic discs and shells, J. Solids Structures, Vol. 37, 2000,
12
pp. 2035–58
13
[13] Zhou F., Ogawa A., Elastic solutions for a solid rotating disk with cubic anisotropy, J. Applied Mechanics, Vol. 69 , 2002, pp. 81–83
14
[14] Ramu S.A., Iyengar K.J., Quasi-three dimensional elastic stresses in rotating disks, J. Mechanical Science, Vol. 16 ,1974, pp. 473–477
15
[15] Chen W.Q., Lee K.Y., Stresses in rotating cross-ply laminated hollow cylinders with arbitrary axial, J. Strain Analysis, Vol. 39, 2004,
16
pp. 437–445
17
[16] Mian M.A, Spencer A.J.M., Exact solutions for functionally graded and laminated elastic materials, J. Solid Mechanics, Vol. 46, 1998, pp. 2283–95.
18
[17] Chen J., Ding H., Chen W., Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy, J. Applied Mechanics, Vol. 77, 2007, pp. 241–251.
19
[18] Hosseini Kordkheili S.A., Naghdabadi R., Thermoelastic analysis of a functionally graded rotating disk, J. Composite Structures, Vol. 79, 2007, pp. 508-516.
20
[19] Zenkour A.M., Stress distribution in rotating composite structures of functionally graded solid disks, J. Materials Processing Technology, Vol. 209(7), 2009, pp. 3511-17.
21
[20] Bayat M., Sahari B.B., Saleem M., Ali A., Wong S.V., Thermoelastic solution of a functionally graded variable thickness rotating disk with bending based on the first-order shear deformation theory, J. Thin-walled Structure, Vol. 47, Issue 5, 2009, Pages 568-582 .
22
[21] Reddy J.N., Chin C.D., Thermomechanical analysis of functionally graded cylinders and plates, J. Thermal Stresses, Vol. 21,1998,
23
pp. 593-626.
24
[22] Budynas R.G., Advanced Strength And Applied Stress Analysis, McGraw-Hill Kogakusha, Ltd., Tokyo, 1977.
25
[23] T.J.R. Hughes, The Finite Element Method, Prentice-Hall International Inc., 1987.
26
ORIGINAL_ARTICLE
Differential Quadrature Method for the Analysis of Hydrodynamic Thrust Bearings
This paper presents the application of the method of generalized differential quadrature (GDQ) for the analysis of hydrodynamic thrust bearings. GDQ is a simple, efficient, high-order numerical technique and it uses the information on all grid points to approach the derivatives of the unknown function. The effectiveness of the solution technique is verified by comparing the GDQ computed results with the results of analytical solutions, FEM and FDM results from the published literature. It's seen from the results that GDQ method can easily compete with the existing methods of solution of lubrication problems in respect to its analytical simplicity, smaller computer storage requirements and capability of producing accurate results with very high computational efficiency.
http://jsme.iaukhsh.ac.ir/article_515552_ca115047ad31510152a262c7d40f75a2.pdf
2008-06-21
59
68
Numerical Solution
GDQ Method
Hydrodynamic Lubrication
Thrust Bearing
M.
Zare-Mehrjardi
1
M.Sc. Student, Yazd University, Mechanical Engineering Department
AUTHOR
A.D.
Rahmatabadi
dashti@yazduni.ac.ir
2
Assistant Professor, Yazd University, Mechanical Engineering Department
LEAD_AUTHOR
M.R.
Fazel
3
Lecturer, Yazd University, Mechanical Engineering Department
AUTHOR
[1] Raimondi A A. and Boyd J., A solution for the finite journal bearing and its application to analysis and design, ASLE Trans, Vol.1, 1959, pp.159-209.
1
[2] Raimondi A A., A numerical solution for the gas lubricated full journal bearing of finite length, ASLE Trans, Vol.4, 1961, pp.131-155
2
[3] Reddi M M., Finite Element Solution for Incompressible Lubrication Problem, ASME J. Lubrication Technology, Vol. 91, 1969, pp. 524-533
3
[4] Kato T. and Hori Y., A Fast Method for Calculating Dynamic Coefficients of a Finite Width Journal Bearing With Quasi Reynolds Boundary Condition, ASME J. Tribology, Vol.110, 1988, pp.387-393
4
[5] Sharma R.K. and Pandey R.K., 2008, Influence of surface profile on slider bearing performance,In. J. Surface Science and Engineering, Vol. 2, No. 34, pp. 265 – 280.
5
[6] Bellman R. and Casti J., 1971, Differential quadrature and long –term integration, J. Math Anal Appl 34, pp.235-238
6
[7] Mingle J., The method of Differential Quadrature for transient non-linear diffusion, J. Math Anal Appl , Vol.60, 1977, pp.559-569
7
[8] Bert CW., Jang SK., Striz AG., Two New Approximate Methods for Analyzing Free Vibration of Structural Components, AIAA J.26, 1988, , pp.612-618
8
[9] Shu C., Richards B E., Application of Generalized Differential Quadrature to Solve Two-dimensional Incompressible Navier-stokes Equation, Int. J. Numer Methods Fluids,Vol. 15, 1992, pp.791-798
9
[10] Malik M., Bert C W., Differential quadrature solution for steady-state incompressible and compressible lubrication problems, J. Tribology, Vol.116, 1994, pp.296-302
10
[11] Zhang Q., Guo G., Winoto S H., Analysis of Hydrodynamic Journal Bearing With GDQ Method, Magnetic Recording Conference, TU06, 2002, pp.1-2
11
[12] Shu C., Richards B E., Parallel Simulation of Incompressible Viscose Flows by Generalized Differential Quadrature, Compute System in Eng. Vol. 3, 1992,, pp.271-281
12
[13] Constantinescu V.N., Sliding Bearing, New York: Allerton Press, 1985, Ch.2.
13
ORIGINAL_ARTICLE
The new version of Differential Quadrature Buckling Analyses of FGM Rectangular Plates Under Non-Uniform Distributed In-Plane Loading
In this paper the buckling coefficient of FGM rectangular plates calculated by the new version of differential quadrature method (DQM). At the first the governing differential equation for plate has been calculated and then according to the new version of differential quadrature method (DQM) the existence derivatives in equation , convert to the amounts of function in the grid points inside of the region is solved .With doing this , The equation will be converted to an eigen value problem and the buckling coefficient is obtained .
In the solving of this problem two kinds of loading for all edges are simply supported or clamped are considered and also the effect of power law index over the buckling coefficient is considered . For the case Isotropic the results are compared well with finite element and finite difference results.This fact indicates that the new version of DQ method can be employed for obtaining buckling loads of plates subjected to non–uniform distributed loading for other boundary conditions.
http://jsme.iaukhsh.ac.ir/article_515553_f9dec04ec9fdd3f98d25ec40293a9407.pdf
2008-06-21
69
78
Buckling
FGM materials
Isotropic plate
The new version of DQ
Mohammad Mehdi
Najafizadeh
m-najafizadeh@iau-arak.ac.ir
1
Assistant Professor, Islamic Azad University, Arak Branch.
LEAD_AUTHOR
Reza
Kazemi Mehrabadi
2
M.Sc. Mechanical Engineering, Islamic Azad University, Arak Branch.
AUTHOR
[1] Bellman RE, Casti J., Differential quadrature and long-term integration, J. Mathematical Analysis and Applications, Vol. 34, 1971, pp. 235-238.
1
[2] Wang X, Gu H, Liu B., on buckling analysis of beam and frame structures by differential quadrature element method, Proceedings of Engineering Mechanics, Vol. 1, 1996, pp. 382-385.
2
[3] Liu GR, Wu TY., Vibration analysis of beam using the generalized differential quadrature rule and domain decomposition, J. Sound and Vibration, Vol. 246, 2001, pp. 461-481.
3
[4] Bert CW, Devarakonda KK., Buckling of rectangular plates subjected to nonlinearly distributed in-plane loading, Int. J. Solids Structures, Vol. 40, 2003, pp. 4097–4106.
4
[5] Sherbourne AN, Pandey MD., differential quadrature method in the buckling analysis of beams and composite plates, Computers and Structures, Vol. 40, 1991, pp. 903–913.
5
[6] Bert CW, Wang X, Striz AG., Differential quadrature for static and free vibration analyses of anisotropic plates. Int. J. Solids Structures, Vol. 30(13), 1993, pp. 1737–44.
6
[7] Wang X, Bert CW., A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates, J Sound & Vibration, Vol. 162(3), 1993, pp. 566–72.
7
[8] Wang X, Gu H, Liu B., On buckling analysis of beams and frame structures by the differential quadrature element method, Proc Eng Mech, Vol. 1, 1996, pp.382–5.
8
[9] Wang X, Differential quadrature for buckling analysis of laminated Plates, Comput Struct, Vol. 57(4), 1995, pp.715–9.
9
[10] Wang X, Tan M, Zhou Y., Buckling analyses of anisotropic plates and isotropic skew plates by the new version differential quadrature method, Thin-Walled Structures, Vol. 41, 2003, pp.15–29.
10
[11] Wang X., Shi X., Applications of differential quadrature method for solutions of rectangular plates subjected to non-uniformly distributed in-plane loadings, (unpublished manuscript).
11
[12] Wang. X., Xinfeng W., Differential quadrature buckling analyses of rectangular plates subjected to non–uniform distributed in–plane loadings, Thin-walled structures, Vol. 44, 2006, pp. 837-843.
12
[13] Koizumi M., FGM activities in Japan, Composites, Vol. 28 (1-2), 1997, pp. 1-4.
13
[14] Reddy J. N., Wang C. M., Kitipornachi, axisymmetric bending of functionally graded circular annular plates, Eur. J. Mech A/Solid, Vol. 20, 2001, pp. 841-855.
14
[15] Brush D.O., Almroth B.O., Buckling of bars, plates and shells, McGraw Hill, New York, 1975.
15
[16] Xinwei W., Feng L., Xinfeng W. and Lifei G., New approaches in application of differential quadrature method to fourth – order differential equations, Communication In Methods In Engineering, Vol. 21, 2005, pp. 61-71.
16
[17] Praveen G.N., Reddy J.N., Nonlinear Transient thermoelastic analysis of functionally graded Ceramic-metal plates, Int. J. solids and structures, Vol. 35(33), 1998, pp. 4457-4476.
17
[18] Van der Neut A., Buckling caused by thermal stresses, High temperature effects in aircraft structures, AGARDograph, Vol. 28, 1958, pp.215–47.
18
[19] Benoy M.B., An energy solution for the buckling of rectangular plates under non-uniform in-plane loading, Aeronaut J, Vol. 73, 1969, pp. 974–7.
19
[20] Young WC, Budynas RG., Roarks formulas for stress & strain, 7th ed., New York, USA, McGraw-Hill, 2002.
20
21