2016
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Free Vibration of Annular Plates by Discrete Singular Convolution and Differential Quadrature Methods
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2
Plates and shells are significant structural components in many engineering and industrial applications. In this study, the free vibration analysis of annular plates is investigated. To this aim, two different numerical methods including the differential quadrature and the discrete singular convolution methods are performedfor numerical simulations. Moreover, the Frequency values are obtained via these two methods and finally, the performance of these methods is investigated.
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128
133


Kadir
Mercan
Akdeniz University Civil ENG.DEPT.
Akdeniz University Civil ENG.DEPT.
Iran
mercankadir32@gmail.com


Hakan
Ersoy
Akdeniz University Mechanical Engineering Dept.
Akdeniz University Mechanical Engineering
Iran
hakanersoy@akdeniz.edu.tr


Omer
Civalek
Civil Engineering Dept.
Civil Engineering Dept.
Iran
civalek@yahoo.com
Differential quadrature
discrete singular convolution
annular plate
free vibration
[[1] Qatu, M., Vibration of Laminated Shells and Plates, Academic Press, U.K., 2004. ##[2] Soedel, W., Vibrations of shells and plates, Third Edition, CRC Press, 2004. ##[3] Leissa, A.W., Vibration of shells, Acoustical Society of America, 1993. ##[4] Reddy, J.N., Mechanics of laminated composite plates and shells: theory and analysis. (2nd ed.) New York: CRC Press, 2003. ##[5] Tornabene, F., Fantuzzi, N., “Mechanics of laminated composite doublycurved shell structures, the generalized differential quadrature method and the strong formulation finite element method”, Società Editrice Esculapio, 2014. ##[6] Leissa AW., Vibration analysis of plates. NASA, SP160, 1969. ##[7] Blevins R.D., “Formulas for natural frequency and mode shapes.” MalaburFlorida: Robert E. Krieger, 1984. ##[8] Vogel, S.M. and Skinner, D.W., “Natural frequencies of transversely vibrating uniform annular plates”, J. Appl. Meh., Vol. 32, pp. 926931, 1965. ##[9] Civalek, Ö., “Finite Element analyses of plates and shells”. Elazığ: Fırat University, (in Turkish) 1998. ##[10] Wei, G.W., 2001, “Vibration analysis by discrete singular convolution, Journal of Sound and Vibration”, Vol. 244, pp. 535553, 2001. ##[11] Wei, G.W., “Discrete singular convolution for beam analysis, Engineering Structures”, Vol. 23, pp.10451053, 2001. ##[12] Wei, G.W., Zhou Y.C., Xiang, Y., “Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm”, Int J Numer Methods Eng., Vol. 55, pp.913946, 2002. ##[13] Wei, G.W., Zhou Y.C., Xiang, Y., “The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution”, Int J Mechanical Sciences, Vol. 43, pp.17311746, 2001. ##[14] Wei, G.W., “A new algorithm for solving some mechanical problems”, Comput. Methods Appl. Mech. Eng., Vol. 190, pp. 20172030, 2001. ##[15] Lim, C.W., Li Z.R., and Wei, G.W., “DSCRitz method for highmode frequency analysis of thick shallow shells”, International Journal for Numerical Methods in Engineering, Vol. 62, pp.205232, 2005. ##[16] Civalek, Ö., “An efficient method for free vibration analysis of rotating truncated conical shells”, Int. J. Pressure Vessels and Piping, Vol. 83, pp. 112, 2006. ##[17] Civalek, Ö., Gürses, M. “Free vibration analysis of rotating cylindrical shells using discrete singular convolution technique”. Int J Press Vessel Pip, Vol. 86, No. 10, pp. 677683, 2009. ##[18] Civalek, Ö., “Vibration analysis of laminated composite conical shells by the method of discrete singular convolution based on the shear deformation theory”, Compos Part B Eng, Vol. 45, No. 1, pp. 10011009, 2013. ##[19] Civalek, Ö., “Free vibration analysis of composite conical shells using the discrete singular convolution algorithm”, Steel Compos Struct, Vol. 6, No. 4, pp.353366, 2006. ##[20] Civalek, Ö., “The determination of frequencies of laminated conical shells via the discrete singular convolution method”, J Mech Mater Struct, Vol. 1, No. 1, pp. 163182, 2006. ##[21] Civalek, Ö., “A fournode discrete singular convolution for geometric transformation and its application to numerical solution of vibration problem of arbitrary straightsided quadrilateral plates”, Appl Math Model, Vol. 33, pp. 300–314, 2009. ##[22] Civalek, Ö., “Threedimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method”, Int J Mech Sci, Vol. 49, No.6, pp.752765, 2007. ##[23] Demir, Ç., Mercan, K., Civalek, Ö., “Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel”, Compos Part B: Eng Vol. 94, pp. 110, 2016. ##[24] Civalek, Ö., “Fundamental frequency of isotropic and orthotropic rectangular plates with linearly varying thickness by discrete singular convolution method”, Appl Math Model, Vol. 33, No. 10, pp. 38253835, 2009. ##[25] Civalek, Ö., “Free vibration analysis of symmetrically laminated composite plates with firstorder shear deformation theory (FSDT) by discrete singular convolution method”, Finite Elem Anal Des Vol. 44, pp. 725731, 2008. ##[26] Civalek, Ö., “Vibration analysis of conical panels using the method of discrete singular convolution”, Commun Numer Methods Eng, Vol. 24, pp. 169181, 2008. ##[27] Civalek, Ö., Korkmaz, A, Demir, Ç., “Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two opposite edges”. Adv Eng Softw, Vol. 41, pp. 557560, 2010. ##[28] Civalek, Ö., “Analysis of thick rectangular plates with symmetric crossply laminates based on firstorder shear deformation theory”, J Compos Mater, Vol. 42, pp. 2853–2867, 2008. ##[29] Seçkin, A., Sarıgül, A.S., “Free vibration analysis of symmetrically laminated thin composite plates by using discrete singular convolution (DSC) approach: algorithm and verification”, J Sound Vib, Vol. 315, pp. 197211, 2008. ##[30] Seçkin, A., “Modal and response bound predictions of uncertain rectangular composite plates based on an extreme value model”, J Sound Vib, Vol. 332, pp.13061323, 2013. ##[31] Xin, L., Hu, Z., “Free vibration of layered magnetoelectroelastic beams by SSDSC approach”, Compos Struct, Vol. 125, pp. 96103, 2015. ##[32] Xin. L., Hu, Z., “Free vibration of simply supported and multilayered magnetoelectroelastic plates”, Comp Struct, Vol. 121, pp. 344350, 2015. ##[33] Wang, X., Xu, S., “Free vibration analysis of beams and rectangular plates with free edges by the discrete singular convolution”, J Sound Vib, Vol. 329, pp. 17801792, 2010. ##[34] Wang, X., Wang, Y., Xu, S., “DSC analysis of a simply supported anisotropic rectangular plate”, Compos Struct, Vol. 94, pp. 25762584, 2012. ##[35] Duan, G., Wang, X., Jin, C., “Free vibration analysis of circular thin plates with stepped thickness by the DSC element method”, Thin Walled Struct, Vol. 85, pp. 2533, 2014. ##[36] Baltacıoğlu, A.K., Civalek, Ö., Akgöz, B., Demir, F., “Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution”, Int J Pres Vessel Pip, Vol. 88, pp. 290300, 2011. ##[37] Civalek, Ö., Akgöz, B., “Vibration analysis of microscaled sector shaped graphene surrounded by an elastic matrix”, Comp. Mater. Sci., Vol. 77, pp. 295303, 2013. ##[38] Gürses, M., Civalek, Ö., Korkmaz, A., Ersoy, H., “Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on firstorder shear deformation theory”, Int J Numer Methods Eng, Vol.79, pp. 290313, 2009. ##[39] Baltacıoglu, A.K., Akgöz, B., Civalek, Ö., “Nonlinear static response of laminated composite plates by discrete singular convolution method”, Compos Struct, Vol. 93, pp. 153161, 2010. ##[40] Gürses, M., Akgöz, B., Civalek, Ö., “Mathematical modeling of vibration problem of nanosized annular sector plates using the nonlocal continuum theory via eightnode discrete singular convolution transformation”, Appl Math Comput, Vol. 219, pp. 3226–3240, 2012. ##[41] Mercan, K., Civalek, Ö., “DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix”, Comp Struct, Vol. 143, pp. 300309, 2016. ##[42] Akgöz, B., Civalek, O., “A new trigonometric beam model for buckling of strain gradient microbeams”, Int J Mech Sci Vol. 81, pp. 8894, 2014. ##[43] Civalek, Ö., Akgöz, B., “Static analysis of single walled carbon nanotubes (SWCNT) based on Eringen’s nonlocal elasticity theory”, Int J Eng Appl Sci, Vol. 1, pp. 4756, 2009. ##[44] Demir, Ç., Civalek, Ö., “Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models”, Appl Mathl Model, Vol. 37, pp. 93559367, 2013. ##[45] Akgöz, B., Civalek, Ö., “Shear deformation beam models for functionally graded microbeams with new shear correction factors”, Comp Struct, Vol. 112, pp. 214225, 2014. ##[46] Xin, L., Hu, Z., “Free vibration analysis of laminated cylindrical panels using discrete singular convolution”, Comp Struct, Vol. 149, pp. 362368, 2016. ##[47] Tornabene, F., Fantuzzi, N., Viola, E., Ferreira, A.J.M., “Radial basis function method applied to doublycurved laminated composite shells and panels with a General Higherorder Equivalent Single Layer formulation”, Compos Part B: Eng, Vol. 55, pp. 642–659, 2013. ##[48] Tornabene, F., Viola, E., “Inman DJ. 2D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures”, J Sound Vib, Vol. 328, pp. 259–290, 2009. ##[49] Civalek, Ö., “Application of Differential Quadrature (DQ) and Harmonic Differential Quadrature (HDQ) For Buckling Analysis of Thin Isotropic Plates and Elastic Columns”, Eng Struct, Vol. 26, No. 2, pp. 171186,2004. ##[50] Civalek, Ö., “Geometrically nonlinear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ)”, PhD. Thesis, Fırat University, (in Turkish), Elazığ, 2004. ##[51] Liew, K.M., Han, JB, Xiao, Z.M., and Du, H., “Differentiel Quadrature Method for Mindlin plates on Winkler foundations”, Int. J. Mech. Sci., Vol. 38, No. 4, pp. 405421, 1996. ##[52] Striz, A.G., Wang, X., Bert, C.W., “Harmonic differential quadrature method and applications to analysis of structural components”, Acta Mechanica, Vol. 111, pp. 8594, 1995. ##[53] Bert, C.W., Wang, Z., Striz, A.G., “Static and free vibrational analysis of beams and plates by differential quadrature method”, Acta Mechanica, Vol. 102, pp. 1124, 1994. ##[54] Du, H., Lim, M.K., Lin, R.M., “Application of generalized differential quadrature method to vibration analysis”, J Sound Vib,Vol. 181, No. 2, 27993, 1995. ##[55] Mercan, K, Demir, Ç., Civalek, Ö., "Vibration analysis of FG cylindrical shells with powerlaw index using discrete singular convolution technique." Curv Layer Struct, Vol. 3, No.1, pp. 8290, 2016.##]
Springbackward Phenomenon of a Transversely Isotropic Functionally Graded Composite Cylindrical Shell
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2
This study provides an approach to predict the springback phenomenon during postsolidification cooling in a functionally graded hybrid composite cylindrical shell with a transverse isotropic structure. Here, the material properties are given with a general parabolic powerlaw function. During the theoretical analysis, an appropriate transformation is introduced in the equilibrium equation, which is resulting in a hypergeometrical differential equation. Thermoelastic solutions are obtained and analyzed for a homogeneous, nonhomogeneous, and elasticplastic state. The solution is validated by applying it to the multilayered functionally graded cylindrical shell using the transfer or propagator matrix method.
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134
143


V. R.
Manthena
Department of Mathematics, RTM Nagpur University, Nagpur, India.
Department of Mathematics, RTM Nagpur University,
Iran
vkmanthena@gmail.com


N. K.
Lamba
Deptt. of Mathematics, Shri Lemdeo Patil Mahavidyalya, Nagpur, India.
Deptt. of Mathematics, Shri Lemdeo Patil
Iran
navneetkumarlamba@gmail.com


G. D.
Kedar
Deptt. of Mathematics, RTM Nagpur University, Nagpur, India.
Deptt. of Mathematics, RTM Nagpur University,
Iran
gdkedar2013@gmail.com
Thermoelasticity
Functionally Graded Hybrid Composites
Cylindrical shell
Spring Backward Effect
[[1] O’Neill, J. M., Rogers, T. G., and Spencer, A. J. M., “Thermally induced distortions in the moulding of laminated channel sections”, Math. Engg. Ind., Vol. 2, pp. 6572, 1988. ##[2] Wawner, T. O., and Gundel, D. B., “Investigation of the Reaction Kinetics between SiC Fibers and selectively Alloyed Titanium Matrices”, School of Engineering and Applied Science Technical Repot (Grant No. NAG1745, Department of Materials Science, University of Virginia, Charlottesville, VA, 1991. ##[3] Birman, V., “Stability of functionally graded hybrid composite plates”, Composites Engineering, Vol. 5, pp. 913921, 1995. ##[4] Ootao, Y., and Tanigawa, Y., “Threedimensional transient thermal stresses of functionally graded rectangular plate due to partial heating”, Journal of Thermal Stresses, Vol. 22, pp. 3555, 1999. ##[5] Reddy, J.N., “Analysis of functionally graded plates”, Int. J. Numer. Meth. Engg. , Vol. 47, pp. 663–684, 2000. [6] Ye, G. R., Chen, W. Q., and Cai, J. B., “A uniformly heated functionally graded cylindrical shell with transverse isotropy”, Mechanics Research Communications, Vol. 28, pp. 535542, 2001. ##[7] Kieback, B., Neubrand, A., and Riedel, H., “Processing techniques for functionally graded materials”, Mater Sci. Engg., A362, pp. 81105, 2003. ##[8] Sugano, Y., Chiba, R., Hirose, K., and Takahashi, K.,, “Material design for reduction of thermal stress in a functionally graded material rotating disk”, JSME International Journal Series A Solid Mechanics and Material Engineering, Vol. 47, pp. 189197, 2004. ##[9] Eraslan, A. N., and Akis, T., “Elastoplastic response of a long functionally graded tube subjected to internal pressure”, Turkish J. Eng. Env. Sci., Vol. 29, pp. 361368, 2005. ##[10] Ohmichi, M., and Noda, N., “The effect of oblique functional gradation to thermal stresses in the functionally graded infinite strip”, Acta Mechanica, Vol. 196, pp. 219237, 2007. ##[11] Huang, Y. H., and Han, X., “Transient Analysis of Functionally Graded Materials Plate using ReducedBasis Methods”, Computational Mechanics, Proceedings of International Symposium on Computational Mechanics, China, 2007. ##[12] Bobaru, F., “Designing optimal volume fractions for functionally graded materials with temperature dependent material properties”, J. Appl. Mech, Vol. 74, pp. 861875, 2007. ##[13] You, L. H., Wang, J. X., and Tang, B. P., “Deformations and stresses in annular disks made of functionally graded materials subjected to internal and/or external pressure”, Meccanica, Vol. 44, pp. 283292, 2008. ##[14] Paulino, G.H., “Multiscale and functionally graded materials”, In: Proceedings of the international conference FGM IX, Hawaii, 2008. ##[15] ChienChing Ma, and YiTzu Chen, “Theoretical analysis of heat conduction problems of nonhomogeneous functionally graded materials for a layer sandwiched between two halfplanes”, Acta Mechanica, Vol. 221, Number 34, Page 223, 2011. ##[16] Birman, V., Keil, T., and Hosder, S., “Functionally graded materials in Engineering, In: Structural interfaces and attachments in Biology”, Springer, New York, 2012. ##[17] Chiba, R., and Sugano, Y., “Optimisation of material composition of functionally graded materials based on multiscale thermoelastic analysis”, Acta Mechanica, Vol. 223, pp. 891909, 2012. ##[18] Lamba, N. K., Khobragade, N. W., “Uncoupled thermoelastic analysis for a thick cylinder with radiation”, Theoretical and Applied Mechanics Letters, Vol. 2, pp. 2135, 2012. ##[19] Gaikwad, K., “Twodimensional steadystate temperature distribution of a thin circular plate due to uniform internal energy generation”, Cogent Mathematics, Vol. 3, 1135720, 2016. ##[20] Matveenko, V. P., Fedorov, A. Yu., and Shardakov, I. N., “Analysis of stress singularities at singular points of elastic solids made of functionally graded materials”, Doklady Physics, Vol. 61, pp. 24 28, 2016. [21] Williams, T. O., Arnold, S. M., and Pindera, M. J., “An analytical/Numerical correlation study of the multiple concentric cylinder model for the thermoplastic response of metal matrix composites”, NASA Contractor Report 191142, Lewis Research Center, Cleveland, Ohio, 1993. ##[22] Spencer, A. J. M., Watson, P., and Rogers, T. G., “Thermoelastic Distortions in laminated anisotropic tubes and channel section”, Journal of Thermal Stresses, Vol. 15, pp. 129141, 1992. ##[23] Varghese V., and Khobragade, N.W., “Mathematical analysis of functionally graded hybrid composite channel section in the interfacial zone during postsolidification cooling”, Adv. And Appl in fluid Mechanics, Vol. 3, pp. 4155, 2008. ##[24] Arnold, S. M., Arya, V. K., and Melis, M. E., “Elastic/Plastic analysis of advanced composites investigating the use of the complaint layer concept in reducing residual stresses resulting from processing”, NASA Technical Memorandum 103204, Lewis Research Center, 1990. ##[25] Abramowitz, M., and Stegun, I. A., (Editors), “Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables”, National Bureau of Standards Applied Mathematics, Washington, 1964. ##]
Conjugate and Directional Chaos Control Methods for Reliability Analysis of CNT–Reinforced Nanocomposite Beams under Buckling Forces; A Comparative Study
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The efficiency and robustness of reliability methods are two important factors in the firstorder reliability method (FORM). The conjugate choice control (CCC) and directional chaos control method (DCC) are developed to improve the robustness and efficiency of the FORM formula using the stability transformation method. In this paper, the CCC and DCC methods are applied for the reliability analysis of a nanocomposite beam as a complex engineering problem, which is reinforced by carbon nanotubes (CNTs) under buckling force. The probabilistic model for nanocomposite beam is developed through the buckling failure mode which is computed by using the EulerBernoulli beam model. The robustness and efficiency CCC and DCC are compared using the stable solution and a number of call limit state functions. The results demonstrate that the CCC method is more robust than the DCC in this case, while the DCC method is simpler than the CCC.
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144
151


Behrooz
Keshtegar
University of Zabol
University of Zabol
Iran
bkeshtegar@uoz.ac.ir


Zeng
meng
hefei university of technology
hefei university of technology
Iran
mengz@hfut.edu.cn
Reliability analysis
Nanocomposite beam
Conjugate chaos control
Directional chaos control
[[1] Keshtegar, B., Limited Conjugate Gradient Method for Structural Reliability Analysis, Engineering with Computers, doi:10.1007/s0036601604937, pp. 19, 2016. ##[2] Rashki, M., Miri, M. and Moghaddam, M.A., A New Efficient Simulation Method to Approximate the Probability of Failure and Most Probable Point. Structural Safety, Vol. 39, pp. 229, 2012. ##[3] Keshtegar, B. and Miri, M., An Enhanced HLRF Method for the Computation of Structural failure probability Based on Relaxed Approach, Civil Engineering Infrastructures, Vol. 1:, pp. 6980, 2013. ##[4] Keshtegar, B. and Miri, M., Introducing Conjugate Gradient Optimization for Modified HLRF Method, Engineering Computations, Vol. 31, pp. 775790, 2014. ##[5] Yang, D., Chaos Control for Numerical Instability of First Order Reliability Method, Commun. Nonlinear Sci. Numer. Simulat., Vol. 15, pp. 3131–3141, 2010. ##[6] Gong, J.X. and Yi, P., A Robust Iterative Algorithm for Structural Reliability Analysis, Struct. Multidisc. Optim., Vol. 43, pp. 519–527, 2011. ##[7] Liu, P.L. and Kiureghian, A.D., Optimization Algorithms for Structural Reliability, Struct. Saf., Vol. 9, pp. 161–177, 1991. ##[8] Meng, Z., Li, G., Yang, D. and Zhan, L., A New Directional Stability Transformation Method of Chaos Control for First Order Reliability Analysis, Struct. Multidiscipl. Optim., DOI: 10.1007/s001580161525z, pp. 112, 2016. ##[9] Keshtegar, B., Stability Iterative Method for Structural Reliability Analysis Using a Chaotic Conjugate Map, Nonlinear Dyn., Vol. 84, No. 4, pp. 21612174, 2016. ##[10] Keshtegar, B., Chaotic Conjugate Stability Transformation Method for Structural Reliability Analysis, Computer Methods in Applied Mechanics and Engineering, Vol. 310, pp. 866885, 2016. ##[11] Keshtegar, B. and Miri, M., Reliability Analysis of Corroded Pipes Using Conjugate HL–RF Algorithm Based on Average Shear Stress Yield Criterion, Engineering Failure Analysis, Vol. 46, pp. 104–117, 2014. ##[12] Vodenitcharova, T. and Zhang, L., Bending and Local Buckling of a Nanocomposite Beam Reinforced by a SingleWalled Carbon Nanotube, International journal of solids and structures, Vol. 43, pp. 30063024, 2006. ##[13] Thai, HT and Vo, T.P., A Nonlocal Sinusoidal Shear Deformation Beam Theory with application to Bending, Buckling, and Vibration of Nanobeams, International Journal of Engineering Science, Vol. 54, pp. 5866, 2012. ##[14] Arani, A.G., Maghamikia, S., Mohammadimehr, M. and Arefmanesh, A., Buckling Analysis of Laminated Composite Rectangular Plates Reinforced by SWCNTs Using Analytical and Finite Element Methods, Journal of Mechanical Science and Technology, Vol. 25, pp. 809820, 2011. ##[15] Rafiee, M., Yang, J. and Kitipornchai, S., Thermal Bifurcation Buckling of Piezoelectric Carbon Nanotube Reinforced Composite Beams, Computers & Mathematics with Applications, Vol. 66, pp. 11471160, 2013. ##[16] Wattanasakulpong, N. and Ungbhakorn, V., Analytical Solutions for Bending, Buckling and Vibration Responses of Carbon NanotubeReinforced Composite Beams Resting on Elastic Foundation, Computational Materials Science, Vol. 71, pp. 201208, 2013. ##[17] Kolahchi, R., Bidgoli, M.R., Beygipoor, G. and Fakhar, M.H., A Nonlocal Nonlinear Analysis for Buckling in Embedded FGSWCNTReinforced Microplates Subjected to Magnetic Field, Journal of Mechanical Science and Technology, Vol. 29, pp. 36693677, 2015. ##[18] Mosharrafian, F. and Kolahchi, R., Nanotechnology, Smartness and Orthotropic Nonhomogeneous Elastic Medium Effects on Buckling of Piezoelectric Pipes, Struct Eng Mech., Vol. 58, pp. 931947, 2016. ##[19] Barzoki, A.M., Arani, A.G., Kolahchi, R. and Mozdianfard, M., ElectroThermoMechanical Torsional Buckling of a Piezoelectric Polymeric Cylindrical Shell Reinforced by DWBNNTs with an Elastic core, Applied Mathematical Modelling, Vol.;36, 29832995, 2012. ##[20] Kolahchi, R., Hosseini, H. and Esmailpour, M., Differential Cubature and QuadratureBolotin Methods for Dynamic Stability of Embedded Piezoelectric Nanoplates Based on ViscoNonlocalPiezoelasticity Theories, Composite Structures, Vol. 157, pp. 174186, 2016. ##[21] Tan, P. and Tong, L., MicroElectromechanics Models for PiezoelectricFiberReinforced Composite Materials, Composites science and technology, Vol. 61, pp. 759769, 2001.##]
Generalized Warping In FlexuralTorsional Buckling Analysis of Composite Beams
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2
The finite element method is employed for the ﬂexuraltorsional linear buckling analysis of beams of arbitrarily shaped composite crosssection taking into account generalized warping (shear lag effects due to both ﬂexure and torsion). The contacting materials, that constitute the composite cross section, may include a finite number of holes. A compressive axial load is applied to the beam. The influence of nonuniform warping is considered by the usage of one independent warping parameter for each warping type, i.e. shear warping in each direction and primary as well as secondary torsional warping, multiplied by the respective warping function. The calculation of the four aforementioned warping functions is implemented by the solution of a corresponding boundary value problem (longitudinal local equilibrium equation). The resulting stress field is corrected through a shear stress correction. The equations are formulated with reference to the independent warping parameters additionally to the displacement and rotation components.
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152
173


Amalia
Argyridi
Institute of Structural Analysis &amp; Aseismic Research
School of Civil Engineering
National Technical University of Athens
Zografou Campus
Athens 157 80, Greece
Institute of Structural Analysis &amp;
Iran
a.argyridi@gmail.com


Evangelos
Sapountzakis
Institute of Structural Analysis & Aseismic Research
School of Civil Engineering
National Technical University of Athens
Zografou Campus
Athens 157 80, Greece
Institute of Structural Analysis &
Iran
cvsapoun@central.ntua.gr
Nonuniform warping
Shear lag
Shear deformation
Composite beams
Flexuraltorsional buckling
[[1] Reissner, E., “Analysis of shear lag in box beams by the principle of minimum potential energy.” Q. Appl. Math., Vol. 41, pp. 268 – 278, 1946. ##[2] Dikaros I.C. and Sapountzakis E.J., “Generalized Warping Analysis of Composite Beams of an Arbitrary Cross Section by BEM. I: Theoretical Considerations and Numerical Implementation”, Journal of Engineering Mechanics, ASCE, Vol. 140, Issue 9, DOI: 10.1061/(ASCE)EM.19437889.0000775, 04014062, 2014. ##[3] Bradford, M.A. and Liu, X., “Flexuraltorsional buckling of highstrength steel beams”, Journal of Constructional Steel Research,Vol. 124, pp. 122131, 2016. ##[4] Szymczak, C. and Kujawa, M., “On local buckling of coldformed channel members”, ThinWalled Structures, Vol. 106, pp. 93101, 2016. ##[5] Wang, Q. and Li, W.Y., “Lateral buckling of thinwalled members with shear lag using spline ﬁnite member element method”, Computers and Structures, Vol. 75, pp. 8191, 2000. ##[6] Wang, Q. and Li, W.Y., “Buckling of thinwalled compression members with shear lag using spline finite member element method “, Computational Mechanics, Vol. 18, pp.139146, 1996. ##[7] Wang, Q., “Lateral buckling of thinwalled open members with shear lag using optimization techniques”, International Journal of Solids and Structures, Vol. 11, pp. 13431352, 1997. ##[8] Wang, Q. and Li, W.Y., “A closedform approximate solution of lateral buckling of doubly symmetric thinwalled members considering shear lag”, International Journal of Mechanical Sciences, Vol. 39, No. 5, pp. 523535, 1997. ##[9] Wang, Q. and Li, W.Y., “Spline finite member element method for buckling of thinwalled members with any cross sections in pure bending”, Computer Methods in Applied Mechanics and Engineering, Vol. 136, pp. 259271, 1996. ##[10] Jetteur, P., “A New Design Method for Stiffened Compression Flanges of Box Girders”, ThinWalled Structures, Vol. 1, pp. 189210, 1983. ##[11] Salaheldin M. and Schmidt L. C., “Linear and Nonlinear Response of a Simple Box Girder”, Journal of Constructional Steel Research, Vol. 13, pp. 4359, 1989. ##[12] Macháček, J., Studnička, J. and Křístek, V. (1994), “Coupled Instability and Negative Shear Lag Phenomenon in Box Girders”, ThinWalled Structures, Vol. 20, pp. 7382. ##[13] Salim, H.A., Davalos, J.E., Qia, P. and Kigel, S.A., “Analysis and design of fiber reinforced plastic composite deckandstringer bridges”, Composite Structures, Vol. 38, Issues14, pp. 295307, 1997. ##[14] Andreassen, M.J. and Jönsson, J., “A distortional semidiscretized thinwalled beam element”, ThinWalled Structures, Vol. 62, pp. 142157, 2013. ##[15] Henriques, D., Gonçalves, R. and Camotim, D., “GBTbased ﬁnite element to assess the buckling behaviour of steel–concrete composite beams”, ThinWalled Structures, Vol. 107, pp. 207220, 2016. ##[16] Kolakowski, Z., Krolak, M. and KowalMichalska, K., “Modal interactive buckling of thinwalled composite beamcolumns regarding distortional deformations”, International Journal of Engineering Science, Vol. 37, pp. 15771596, 1999. ##[17] Kolakowski, Z. and Teter, A., “Interactive buckling of thinwalled beamcolumns with intermediate stiffeners or/and variable thickness”, International Journal of Solids and Structures, Vol. 37, pp. 33233344, 1999. ##[18] Teter, A. and Kolakowski, Z., “Lower bound estimation of loadcarrying capacity of thinwalled structures with intermediate stiffeners”, ThinWalled Structures, Vol. 39, pp. 649669, 2001. ##[19] Teter, A. and Kolakowski, Z., “Natural frequencies of a thinwalled structures with central intermediate stiffeners or/and variable thickness”, ThinWalled Structures, Vol. 41, pp. 291316, 2003. ##[20] Teter, A. and Kolakowski, Z., “Interactive buckling and load carrying capacity of thinwalled beam–columns with intermediate stiffeners”, ThinWalled Structures, Vol. 42, pp. 211254, 2004. ##[21] Kolakowski, Z. and Krolak, M., “Modal coupled instabilities of thinwalled composite plate and shell structures”, Composite Structures, Vol. 76, pp. 303313, 2006. ##[22] Kolakowski, Z. and Kubiak T., “Interactive dynamic buckling of orthotropic thinwalled channels subjected to inplane pulse loading”, Composite Structures, Vol. 81, pp. 222232, 2007. ##[23] Kolakowski, Z., “Some aspects of dynamic interactive buckling of composite columns”, ThinWalled Structures, Vol. 45, pp. 866871, 2007. ##[24] Kolakowski, Z. and KowalMichalska, K., “Interactive buckling regarding the axial extension mode of a thinwalled channel under uniform compression in the ﬁrst nonlinear approximation”, International Journal of Solids and Structures, Vol. 49, pp. 119125, 2011. ##[25] Kolakowski, Z. and Teter A., “Load carrying capacity of functionally graded columns with open crosssections under static compression”, Composite Structures, Vol. 129, pp. 17, 2015. ##[26] Kolakowski, Z., “Some aspects of interactive dynamic stability of thinwalled trapezoidal FGM beamcolumns under axial load”, ThinWalled Structures, Vol. 98, pp. 431442, 2016. ##[27] Kolakowski, Z. and Kubiak T., “Some aspects of the longitudinaltransverse mode in the elastic thinwalled girder under bending moment”, ThinWalled Structures, Vol. 102, pp. 197204, 2016. ##[28] Schardt, R., Eine erweiterung der technischen biegetheorie zur berechnung prismatischer faltwerke, Stahlbau Vol. 35, pp. 161–171, 1966 (German). ##[29] Schardt, R., Verallgemeinerte Technische Biegetheorie, Springer Verlag, Berlin, Germany, 1989(German). ##[30] Michell, A.G.M., “Elastic stability of long beams under transverse forces” Philos. Mag. Vol. 48, 5th Series, pp. 298309, 1899. ##[31] Prandtl, L., Kipperscheinungen, Dissertation der Universitat Munchen, 1899. ##[32] Vlasov, V. Z., Thinwalled elastic beams, Israel Program for Scientific Translations, Jerusalem, 1961. ##[33] Timoshenko, S.P. and Gere, J.M., Theory of Elastic Stability, McGrawHill, Tokyo, 1961. ##[34] Rao, J. S. and Carnegie, W., “Solution of the Equations of Motion of CoupledBending Torsion Vibrations of Turbine Blades by the Method of RitzGalerkin”, International Journal of Mechanical Science, Vol. 12, pp. 875882, 1970. ##[35] Mei, C., “Coupled Vibrations of ThinWalled Beams of OpenSection Using the Finite Element Method”, International Journal of Mechanical Science, Vol. 12, pp. 883891, 1970. ##[36] Hodges, D.H. and Peters, D.A., “On the lateral buckling of uniform slender cantilever beams”, Interational Journal of Solids and Structures, Vol. 11, pp. 12691280, 1975. ##[37] Reissner, E., “On lateral buckling of endloaded cantilever beams”, ZAMP, Vol. 30, pp. 3140, 1979. ##[38] Milisavljevic, B.M., “On lateral buckling of a slender cantilever beam”, International Journal of Solids and Structures, Vol. 32, Issue 16, pp. 23772391, 1995. ##[39] Hodges, D.H., “Lateraltorsional flutter of a deep cantilever loaded by lateral follower force at the tip”, Journal of Sound and Vibration, Vol. 247, Issue 1, pp. 175183, 2001. ##[40] Orloske, K., Leamy, M.J. and Parker, R.G. (2006), “Flexuraltorsional buckling of misaligned axially moving beams. I. Threedimensional modeling, equilibria, and bifurcations”, International Journal of Solids and Structures, Vol. 43, pp. 42974322. ##[41] Lee, J. and Kim, SE. “Flexuraltorsional buckling of thinwalled Isection composites”, Computers and Structures, Vol. 79, pp. 987995, 2001. ##[42] Sapkás, A. and Kollár, L. P., “Lateraltorsional buckling of composite beams”, International Journal of Solids and Structures, Vol. 39, pp. 2939–2963, 2002. ##[43] Kollár, L. P., “Flexuraltorsional buckling of open section composite columns with shear deformation”, International Journal of Solids and Structures, Vol. 38, pp. 75257541, 2001. ##[44] Machado S.P. and Cortínez V.H., “Lateral buckling of thinwalled composite bisymmetric beams with prebuckling and shear deformation”, Engineering Structures, Vol. 27, pp. 1185–1196, 2005. ##[45] Yu, W., Hodges, D. H., Volovoi, V., Cesnik, C.E.S, “On Timoshenkolike modeling of initially curved and twisted composite beams”, International Journal of Solids and Structures, Vol. 39, pp. 5101–5121, 2002. ##[46] Cortínez, V. H. and Piovan, M. T., “Stability of composite thinwalled beams with shear deformability”, Computers and Structures, Vol. 84, pp. 978990, 2006. ##[47] Le Grognec, P., Nguyen, Q.H., Hjiaj, M., “Exact buckling solution for twolayer Timoshenko beams with interlayer slip”, International Journal of Solids and Structures, Vol. 49, pp. 143150, 2012. ##[48] Rodman, U., Saje, M., Planinc, I. and Zupan, D., “Exact buckling analysis of composite elastic columns including multiple delamination and transverse shear”, Vol. 30, pp. 1500–1514, 2008. ##[49] Kim N.I and Lee J., “Lateral buckling of shear deformable laminated composite Ibeams using the ﬁnite element method”, International Journal of Mechanical Sciences, Vol. 68, pp. 246–257, 2013. ##[50] MagnuckaBlandzi, E., Magnucki, K. and Wittenbeck, L., “Mathematical modeling of shearing effect for sandwich beam with sinusoidal corrugated cores”, Applied Mathematical Modelling, Vol. 39, pp. 2796–2808, 2015. ##[51] Wattanasakulpong, N., Prusty, G. and Kelly, D., “Thermal buckling and elastic vibration of thirdorder shear deformable functionally graded beams”, Vol. 53, Issue 9, pp. 734–743, 2011. ##[52] Batista, M. (2016), “A ClosedForm Solution for Reissner Planar FiniteStrain Beam Using Jacobi Elliptic Functions”, International Journal of Solids and Structures, doi:10.1016/j.ijsolstr.2016.02.020. ##[53] Murin, J., Aminbaghai, M., Hrabovsky, J., Gogola, R., Kugler, S., “Beam finite element for modal analysis of FGM structures”, Engineering Structures, Vol. 121, pp. 118, 2016. ##[54] Sapountzakis E.J. and Dourakopoulos J.A., “Flexural – Torsional Buckling Analysis of Composite Beams by BEM Including Shear Deformation Effect”, Mechanics Research Communications, Vol 35, pp 497516, 2008. ##[55] V.J.Tsipiras, E.J. Sapountzakis, Secondary Torsional Moment Deformation Effect in Inelastic Nonuniform Torsion of Bars of Doubly Symmetric Cross Section by BEM. International Journal of Nonlinear Mechanics, Vol. 47, pp. 6884, 2012. ##[56] MSC/NASTRAN for Windows, Finite element modeling and postprocessing system. Help System Index,Version 4.0, USA, 1999. ##[57] Ansys Mechanical APDL Release 15.0 UP20131014. ##[58] NX Nastran User’s Guide, Siemens PLM Software Inc; 2007.##]
Deformation Characteristics of Composite Structures
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2
The composites provide design flexibility because many of them can be moulded into complex shapes. The carbon fibrereinforced epoxy composites exhibit excellent fatigue tolerance and high specific strength and stiffness which have led to numerous advanced applications ranging from the military and civil aircraft structures to the consumer products. However, the modelling of the beams undergoing the arbitrarily large displacements and rotations, but small strains, is a common problem in the application of these engineering composite systems. This paper presents a nonlinear finite element model which is able to estimate the deformations of the fibrereinforced epoxy composite beams. The governing equations are based on the EulerBernoulli beam theory (EBBT) with a von Kármán type of kinematic nonlinearity. The anisotropic elasticity is employed for the material model of the composite material. Moreover, the characterization of the mechanical properties of the composite material is achieved through a tensile test, while a simple laboratory experiment is used to validate the model. The results reveal that the composite fibre orientation, the type of applied load and boundary condition, affect the deformation characteristics of the composite structures. The nonlinearity is an important factor that should be taken into consideration in the analysis of the fibrereinforced epoxy composites.
1

174
191


Theddeus T.
AKANO
Department of Systems Engineering, University of Lagos, NIGERIA
Department of Systems Engineering, University
Iran
takano@unilag.edu.ng


Omotayo. A
FAKINLEDE
Department of Systems Engineering, University of Lagos, NIGERIA
Department of Systems Engineering, University
Iran
oafak@unilag.edu.ng


Patrick
Olayiwola
Bells University of Technology
Bells University of Technology
Iran
olayiwola_patrickshola@yahoo.com
Anisotropic elasticity
composite material
large displacement
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S., “BendingUnbending Analysis of Anisotropic Sheet under Plane Strain Condition”, Esteghlal Journal of Engineering, Vol. 26, No. 2, pp. 187196, 2008. ##[14] Vora, M. R., Matlock, H., “A discreteelement analysis for anisotropic skew plates and grids”, Ph.D Thesis, University of Texas at Austin, 1970. ##[15] Panak, J. J., Matlock, H., “A DiscreteElement Method of Analysis for Orthogonal Slab and Grid Bridge Floor Systems, No. 5625 Res Rpt, Center for Highway Research, University of Texas at Austin, 1972. ##[16] Noor, A. K., Rarig, P. L., “Threedimensional solutions of laminated cylinders”, Computer Methods in Applied Mechanics and Engineering, Vol. 3, No. 3, pp. 319334, 1974. ##[17] Malik, M., “Differential quadrature method in computational mechanics: new development and applications”, Ph.D. Dissertation, University of Oklahoma, Oklahoma, 1994. ##[18] Malik, M., Bert, C. W., “Differential quadrature analysis of free vibration of symmetric crossply laminates with shear deformation and rotatory inertia”, Shock and Vibration, Vol. 2, No. 4, pp.321338, 1995. ##[19] Liew, K. M., Han, J. B., Xiao, Z. M., “Differential quadrature method for thick symmetric crossply laminates with firstorder shear flexibility”, International Journal of Solids and Structures, Vol. 33, No. 18, pp. 26472658, 1996. ##[20] Davi, G., “Stress fields in general composite laminates”, AIAA journal, Vol. 34, No. 12, pp. 26042608, 1996. ##[21] Davı̀, G., Milazzo, A., “Bending stress fields in composite laminate beams by a boundary integral formulation”, Computers & structures, Vol. 71, No. 3, pp. 267276, 1999. ##[22] Milazzo, A., “Interlaminar stresses in laminated composite beamtype structures under shear/bending”, AIAA journal, Vol. 38, No. 4, pp. 687694, 2000. ##[23] Noor, A. K., Burton, W. S., “Stress and free vibration analyses of multilayered composite plates”, Composite Structures, Vol. 11, No. 3, pp. 183204, 1989. ##[24] Noor, A. K., Peters, J. M., “A posteriori estimates for the shear correction factors in multilayered composite cylinders”, Journal of engineering mechanics, Vol. 115, No. 6, pp. 12251244, 1989. ##[25] Noor, A. K., Burton, W. S., Peters, J. M., “Predictorcorrector procedures for stress and free vibration analyses of multilayered composite plates and shells”, Computer Methods in Applied Mechanics and Engineering, Vol. 82, No. 1, pp. 341363, 1990. ##[26] Vel, S. S., Batra, R. C., “Analytical solution for rectangular thick laminated plates subjected to arbitrary boundary conditions”, AIAA journal, Vol. 37, No. 11, pp. 14641473. 1999. ##[27] Vel, S. S., Batra, R. C., “The generalized plane strain deformations of thick anisotropic composite laminated plates”, International Journal of Solids and Structures, Vol. 37, No. 5, pp. 715733, 2000. ##[28] Machado, S. P., Filipich, C. P. Rosales, M. B., “Plane Anisotropic Beams with Shear Deformation via a Generalized Solution”, Santa FeParaná, Argentina, October 2002, S. R. Idelsohn, V. E. Sonzogni and A. Cardona (Eds.), Mecánica Computational, Vol. 20, pp. 775785, 2000. ##[29] Machado, S. P., Cortínez, V. H., “Nonlinear model for stability of thinwalled composite beams with shear deformation”, ThinWalled Structures, Vol. 43, No. 10, pp. 16151645. 2005. ##[30] Filipich, C. P., Rosales, M. B., “Arbitrary precision frequencies of a free rectangular thin plate”, Journal of Sound and Vibration, Vol. 230, No. 3, pp. 521539, 2000. ##[31] Rosales, M. B., Filipich, C. P., “Time integration of nonlinear dynamic equations by means of a direct variational method”, Journal of sound and vibration, Vol. 254, No. 4, pp. 763775, 2002. ##[32] Vnučec, Z., “Analysis of the Laminated Composite Plate under Combined Loads”, Analysis, Vol. 2, No. 2, 2005. ##[33] Morandini, M., Chierichetti, M., Mantegazza, P., “Characteristic behaviour of prismatic anisotropic beam via generalized eigenvectors”, International Journal of Solids and Structures, Vol. 47, No. 10, pp. 13271337, 2010. ##[34] Kim, T., Hansen, A. M., Branner, K., “Development of an anisotropic beam finite element for composite wind turbine blades in multibody system”, Renewable Energy, Vol. 59, pp. 172183, 2013. ##[35] Reddy, J. N., & Robbins, D. H., “Theories and computational models for composite laminates”, Applied mechanics reviews, Vol. 47, No. 6, pp. 147169, 1994. ##[36] Varadan, T. K., Bhaskar, K., “Review of different laminate theories for the analysis of composites”, JournalAeronautical Society of India, Vol. 49, pp. 202208, 1997. ##[37] Carrera, E., “An assessment of mixed and classical theories for the thermal stress analysis of orthotropic multilayered plates. Journal of Thermal Stresses, Vol. 23, No. 9, pp. 797831, 2000. ##[38] Battini, J. M., Nguyen, Q. H., Hjiaj, M., “Nonlinear finite element analysis of composite beams with interlayer slips”, Computers and structures, Vol. 87, No. 13, pp. 904912, 2009. ##[39] Ranzi, G., Dall’Asta, A., Ragni, L., Zona, A., “A geometric nonlinear model for composite beams with partial interaction”, Engineering Structures, Vol. 32, No. 5, pp. 13841396, 2010. ##[40] Zona, A., Ranzi, G., “Finite element models for nonlinear analysis of steel–concrete composite beams with partial interaction in combined bending and shear”, Finite Elements in Analysis and Design, Vol. 47, No. 2, pp. 98118, 2011. ##[41] Abass, M. K., Elshafei, M. A., “Linear and Nonlinear Finite Element Modelling of Advanced Isotropic and Anisotropic Beams Part I: Euler Bernoulli Theory”, 13th International conference on aerospace sciences & aviation technology, Cairo, Egypt, 2009. ##[42] Vanegas, J. D., Patiño, I. D., “Linear and NonLinear Finite Element Analysis of ShearCorrected Composites Box Beams”, Latin American Journal of Solids and Structures, Vol. 10, No. 4, pp. 647673, 2013. ##[43] Zhang, Y., and Lin, X., “Nonlinear finite element analyses of steel/FRPreinforced concrete beams by using a novel composite beam element”, Advances in Structural Engineering, Vol. 16, No. 2, pp. 339352, 2013. ##[44] Rahman, M., Aktaruzzaman, F. N. U., Absar, S., Mitra, A., Hossain, A., “Finite Element Analysis of Polyurethane Based Composite Shafts Under Different Boundary Conditions”, In ASME 2014 International Mechanical Engineering Congress and Exposition (pp. V010T13A014V010T13A014). American Society of Mechanical Engineers, 2014. ##[45] Mahmoud, A. M., “Finite element modeling of steel concrete beam considering double composite action”, Ain Shams Engineering Journal, 2015. ##[46] Li, Z. M., Qiao, P., “Buckling and postbuckling behaviour of shear deformable anisotropic laminated beams with initial geometric imperfections subjected to axial compression”, Engineering Structures, Vol. 85, pp. 277292, 2015. ##[47] Li, Z. M., Qiao, P., Thermal postbuckling analysis of anisotropic laminated beams with different boundary conditions resting on twoparameter elastic foundations”, European Journal of MechanicsA/Solids, Vol. 54, pp. 3043, 2015. ##[48] Reddy, J. N., “An Introduction to Nonlinear Finite Element Analysis: with applications to heat transfer, fluid mechanics, and solid mechanics”, OUP Oxford, 2014. ##[49] Heinbockel, J. H., Introduction to tensor calculus and continuum mechanics, Vol. 52. 2001. ##[50] Gibson, Ronald F., “A simplified analysis of deflections in shear deformable composite sandwich beams”, Journal of sandwich structures and materials, Vol. 13, No. 5, pp. 579588, 2011. ##[51] Bower, A. F., Applied mechanics of solids. CRC press, 2010. ##[52] Reddy, J. N., Mechanics of laminated composite plates and shells: theory and analysis. CRC press, 2004. ##[53] Jones, R. M., Morgan, H. S., “Analysis of Nonlinear StressStrain Behaviour of FiberReinforced Composite Materials”, AIAA Journal, Vol. 15, No. 12, pp. 16691676, 1997. ##[54] Wang, X., Chung, D. D. L., “Continuous carbon fibre epoxymatrix composite as a sensor of its own strain”, Smart materials and structures, Vol. 5, No. 6, 796, 1996. ##[55] Nye, J. F., “Physical properties of crystals: their representation by tensors and matrices”, Oxford university press, 1985.##]
Modified Rectangular Patch Antenna Loaded With Multiple C Slots for Multiple Applications
2
2
A new multiple Cslotted microstrip patch antenna is proposed in the present study. A patch antenna is a widebeam narrowband antenna. The microstrip patch antenna consists of a very thin metallic strip (patch) placed a small fraction of a wavelength above a ground plane. The patch can be designed in any possible shape and normally made of conducting materials such as copper or gold. This study presents a design of a CSlotted microstrip patch antenna for multiple applications. The proposed antenna's characteristics include a low cost, easy fabrication and good isolation along with Quad different frequency bands which are centered at 1.60 GHz, 2.50 GHz, 4.70 GHz and 5.50 GHz for parameter S11. The antenna is designed, simulated, and optimized for Quad band performance by using IE3D software. The Cshapeslotted patch antenna is designed on a FR4 substrate with the thickness of 1.59 mm and the relative permittivity of 4.4. The proposed patch dimension is 16*16 mm and it utilizes the microstrip line feed. The simulated results parameter S11 and S12, shows that the antenna can cover the bands of several applications including GPS (1.21.6 GHz), GSM (1.81.9 GHz) and WiMAX (2.35.8 GHz). Simulation results are presented in terms of Resonant Frequency, Return Loss, Voltage Standing Wave Ratio (VSWR) and Radiation Pattern.
1

192
199


Amit
Jain
Poorima College of Engineering, Jaipur, Rajasthan, India
Poorima College of Engineering, Jaipur, Rajasthan,
Iran
jain.2102@gmail.com


Monika
Surana
Poorima College of Engineering, Jaipur, Rajasthan, India
Poorima College of Engineering, Jaipur, Rajasthan,
Iran
suranamonika@gmail.com
Microstrip antenna
Slotted patch
GPS
GSM
WiMAX
[[1] C.A.Balanis “Antenna Theory, Analysis and Design” JOHN WILEY & SONS, INC, NEW YORK 1997. ##[2] K. F. Lee, Ed., “Advances in Microstrip and Printed Antennas” John Wiley, 1997. ##[3] Mamta Devi Sharma, Abhishek Katariya, Dr. R. S. Meena, “E Shaped Patch Microstrip Antenna for WLAN Application Using Probe Feed and Aperture Feed” IEEE conference publications, 2012. ##[4] M. J. Kim, C. S. Cho, and J. Kim, “A dual band printed dipole antenna with spiral structure for WLAN application,” IEEE Microw. Wireless Compon. Lett., Vol. 15, no. 12, pp. 910–912, Dec. 2005. ##[5] A.D.Yaghjian and S. R. Best, "Impedance, Bandwidth, and Q of Antennas," IEEE Transactions on Antennas and Propagation, AP53, 4, April 2005, pp. 1 298 1 324. ##[6] Bhardwaj, Dheeraj, et al. "Design of square patch antenna with a notch on FR4 substrate." Microwaves, Antennas & Propagation, Vol.51, No.3, 880885, 2008. ##[7] Zaker, Reza, Changiz Ghobadi, and Javad Nourinia,"Bandwidth enhancement of novel compact single and dual bandnotched printed monopole antenna with a pair of Lshaped slots." Antennas and Propagation, IEEE Transactions on Vol.57, No.12, 2009. ##[8] S. Imran Hussain Shah, Shahid Bashir, Syed Dildar Hussain Shah, “Compact Multiband microstrip patch antenna using Defected Ground structure (DGS)”, The 8th European Conference on Antennas and Propagation (EuCAP 2014), IEEE Transactions, 97888907018, pp. 23672370, September 2014. ##[9] T. H. Kim and D. C. Park, “Compact dualband antenna with double Lslits for WLAN operations,” IEEE Antennas Wirel. Propag. Lett., Vol. 4, no. 1, pp. 249–252, 2005. ##[10] Abutarboush. H.F., Sharmim. A., “Wide frequency indepeııdently controlled dualband inkjet printed antenna.” Microwaves, Antennas & Propagation, lET , Vol.8, no.1, pp.52,56, January 8 2014 ##[11] Kaya A., Kaya, I and Karaca E. H. “ Radio Frequency Ushape slot Antenna Design with NiTi shape Memory Alloys” Microwave and Optical Technology Letters, 55, 29762984, (2013) ##[12] Bhardwaj, Dheeraj, et al. "Design of square patch antenna with a notch on FR4 substrate." Microwaves, Antennas & Propagation, Vol.51, No.3, 880885, 2008. ##[13] IE3D Simulation Software, Zealand, version 14.05.2008.##]