Cylindrical Bending of Power Law Varied Functionally Graded Laminate Subjected to Thermo-Mechanical Loading

Document Type : Original Article


1 Structural Engineering Department, Research Scholar, Veermata Jijabai Technological Institute, Mumbai, Maharashtra, India

2 Associate Professor Structural Engineering Department, VJTI Mumbai, India


In this paper, efforts have devoted to developing heat conduction formulation to determine the exact temperature for power law varied functionally graded (FG) laminate. Further, the semi-analytical approach has re-invented for displacement and stress analysis of FG laminate. This way of analysis involves solving of two-point boundary value problem (BVP) ruled by first-order ordinary differential equations (ODE's). Here material properties such as modulus of elasticity, coefficient of thermal expansion, and heat conductivity have considered being varied as per power law, whereas Poisson’s ratio kept constant. The effect has undergone examination for applied transverse thermal loading and mechanical loading with the developed semi-analytical formulation. The observation of the effect of variation of volume fraction as per power law on through thickness temperature distribution along with consideration of exact temperature and with assumed power law temperature has carried out. Further corresponding thermal stress analysis and its comparison with numerical parametric studies lead to productive output in this area of research.


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[1]     Chakraborty A, Gopalakrishnan S, Reddy JN. A new beam finite element for the analysis of functionally graded materials. Int J Mech Sci 2003;45:519–39. doi:10.1016/S0020-7403(03)00058-4.
[2]     Benatta MA, Mechab I, Tounsi A, Adda Bedia EA. Static analysis of functionally graded short beams including warping and shear deformation effects. Comput Mater Sci 2008;44:765–73. doi:10.1016/j.commatsci.2008.05.020.
[3]     Kadoli R, Akhtar K, Ganesan N. Static analysis of functionally graded beams using higher order shear deformation theory. Appl Math Model 2008;32:2509–25. doi:10.1016/j.apm.2007.09.015.
[4]     Ben-Oumrane S, Abedlouahed T, Ismail M, Mohamed BB, Mustapha M, El Abbas AB. A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams. Comput Mater Sci 2009;44:1344–50. doi:10.1016/j.commatsci.2008.09.001.
[5]     Mahi A, Adda Bedia EA, Tounsi A, Mechab I. An analytical method for temperature-dependent free vibration analysis of functionally graded beams with general boundary conditions. Compos Struct 2010;92:1877–87. doi:10.1016/j.compstruct.2010.01.010.
[6]     Kiani Y, Eslami MR. Thermal buckling analysis of functionally graded material beams. Int J Mech Mater Des 2010;6:229–38. doi:10.1007/s10999-010-9132-4.
[7]     Wattanasakulpong N, Gangadhara Prusty B, Kelly DW. Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams. Int J Mech Sci 2011;53:734–43. doi:10.1016/j.ijmecsci.2011.06.005.
[8]     Giunta G, Crisafulli D, Belouettar S, Carrera E. Hierarchical theories for the free vibration analysis of functionally graded beams. Compos Struct 2011;94:68–74. doi:10.1016/j.compstruct.2011.07.016.
[9]     Ma LS, Lee DW. A further discussion of nonlinear mechanical behavior for FGM beams under in-plane thermal loading. Compos Struct 2011;93:831–42. doi:10.1016/j.compstruct.2010.07.011.
[10]   Thai H-T, Vo TP. Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. Int J Mech Sci 2012;62:57–66. doi:10.1016/j.ijmecsci.2012.05.014.
[11]   Thai H-T, Vo TP. A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams. Int J Eng Sci 2012;54:58–66. doi:10.1016/j.ijengsci.2012.01.009.
[12]   Ma LS, Lee DW. Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading. Eur J Mech - A/Solids 2012;31:13–20. doi:10.1016/j.euromechsol.2011.06.016.
[13]   Şimşek M, Reddy JN. Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory. Int J Eng Sci 2013;64:37–53. doi:10.1016/j.ijengsci.2012.12.002.
[14]   Li S-R, Cao D-F, Wan Z-Q. Bending solutions of FGM Timoshenko beams from those of the homogenous Euler–Bernoulli beams. Appl Math Model 2013;37:7077–85. doi:10.1016/j.apm.2013.02.047.
[15]   Lezgy-Nazargah M. Fully coupled thermo-mechanical analysis of bi-directional FGM beams using NURBS isogeometric finite element approach. Aerosp Sci Technol 2015;45:154–64. doi:10.1016/j.ast.2015.05.006.
[16]   El-Ashmawy AM, Kamel MA, Elshafei MA. Thermo-mechanical analysis of axially and transversally Function Graded Beam. Compos Part B Eng 2016;102:134–49. doi:10.1016/j.compositesb.2016.07.015.
[17]   Trinh LC, Vo TP, Thai H-T, Nguyen T-K. An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads. Compos Part B Eng 2016;100:152–63. doi:10.1016/j.compositesb.2016.06.067.
[18]   De Pietro G, Hui Y, Giunta G, Belouettar S, Carrera E, Hu H. Hierarchical one-dimensional finite elements for the thermal stress analysis of three-dimensional functionally graded beams. Compos Struct 2016;153:514–28. doi:10.1016/j.compstruct.2016.06.012.
[19]   Hui Y, Giunta G, Belouettar S, Huang Q, Hu H, Carrera E. A free vibration analysis of three-dimensional sandwich beams using hierarchical one-dimensional finite elements. Compos Part B Eng 2017;110:7–19. doi:10.1016/j.compositesb.2016.10.065.
[20]   Rajasekaran S, Khaniki HB. Bi-directional functionally graded thin-walled non-prismatic Euler beams of generic open/closed cross section Part I: Theoretical formulations. Thin-Walled Struct 2019;141:627–45. doi:10.1016/j.tws.2019.02.006.
[21]   Pendhari SS, Kant T, Desai YM, Venkata Subbaiah C. On deformation of functionally graded narrow beams under transverse loads. Int J Mech Mater Des 2010;6:269–82. doi:10.1007/s10999-010-9136-0.
[22]   Kantrovich LV, Krylov VI. Approximate Methods of Higher Analysis, 3rd Edition, Noordhoff, Groningen,. 1958.