Analytical and Numerical Bending Solutions for Thermoelastic Functionally Graded Rotating Disks with Nonuniform Thickness Based on Mindlin’s Theory

Document Type : Original Research Paper

Authors

Mechanical Engineering Department, Babol Noshirvani University of Technology, Babol, Iran.

Abstract

In this paper, analytical and numerical solutions for thermoelastic functionally graded (FG) rotating disks with non-uniform thickness under lateral pressure are studied. The study is performed based on Mindlin’s theory. Considering the fact that bending and thermal loadings in analysis of rotating disk are necessary to study the components such as brake and clutch disks. The governing differential equations arising from FG rotating disk are firstly extracted. Then, Liao’s homotopy analysis method (HAM) and Adomian’s decomposition method (ADM) are applied as two analytical approaches. Calculation of stress components and then comparison of the results of HAM and ADM with Runge-Kutta’s and FEM are performed to survey compatibility of their results. The distributions of radial and circumferential stresses of rotating disks are studied and discussed. Finaly, the effects of temperature, grading index, angular velocity and lateral loading on the components of displacement and stresses are presented and discussed, in detail.

Keywords

References

[1] M. Bayat, B.B. Sahari, M. Saleem, A. Ali, S.V. Wong, Bending analysis of a functionally graded rotating disk based on the first order shear deformation theory, Appl. Math. Model., 33 (2009) 4215-4230.
[2] A.N. Eraslan, Y. Orcan, Elasticplastic deformation of a rotating solid disk of exponentially varying thickness. Mech. Mater., 34 (2002) 423-32.
[3] S.A.H. Kordkheili, R. Naghdabadi, Thermoelastic analysis of a functionally graded rotating disk, Compos. Struct., 79 (2006) 508-16.
[4] M. Bayat, M. Saleem, B.B. Sahari, A.M.S. Hamouda, E. Mahdi, Mechanical and thermal stresses in a functionally graded rotating disk with variable thickness due to radially symmetry loads, Int. J. Pres. Ves. Pip., 86 (2009) 357-372.
[5] M.H. Hojjati, S. Jafari, Variational iteration solution of elastic non uniform thickness and density rotating disks, Far. East. J. Appl. Math., 29 (2007) 185-200.
[6] M.H. Hojjati, S. Jafari, Semi-exact solution of elastic non-uniform thickness and density rotating disks by homotopy perturbation and Adomian’s decomposition methods. Part I: Elastic solution, Int. J. Pres. Ves. Pip., 85 (2008) 871-879.
[7] M.H. Hojjati, S. Jafari, Semi-exact solution of nonuniform thickness and density rotating disks. Part II: Elastic strain hardening solution, Int. J. Pres. Ves. Pip., 86 (2009) 307-18.
[8] M.H. Hojjati, A. Hassani, Theoretical and numerical analyses of rotating discs of nun-uniform thickness and density, Int. J. Pres. Ves. Pip., 25 (2008) 695-700.
[9] A. Hassani, M.H. Hojjati, G. Farrahi, R.A. Alashti, Semi-exact elastic solutions for thermo-mechanical analysis of functionally graded rotating disks, Compos. Struct., 93 (2011) 3239-3251.
[10] A. Hassani, M.H. Hojjati, G. Farrahi, R.A. Alashti, Semi-exact solution for thermo-mechanical analysis of functionally graded elastic-strain hardening rotating disks, Commun. Nonlinear. Sci. Num. Simulat., 17 (2012) 3747-3762.
[11] A. Hassani, M.H. Hojjati, E. Mahdavi, R.A. Alashti, G. Farrahi, Thermo-mechanical analysis of rotating disks with non-uniform thickness and material properties, Int. J. Pres. Ves. Pip., 98 (2012) 95-101.
[12] A. Hassani, M.H. Hojjati, A.R. Fathi, In-Plane free vibrations of annular elliptic and circular elastic plates of non-uniform thickness under classical boundary conditions, Int. Rev. Mech. Eng., 4 (2010) 112-119.
[13] G. Adomian, Solving frontier problems of physics: the decomposition method. Boston: Kluwer Academic; 1994.
[14] S.J. Liao, Beyond perturbation: introduction to the homotopy analysis method. Boca Raton: Chapman and Hall/CRC Press; 2003.
[15] S.A. Hosseini Kordkheili, M. Livani, Thermoelastic creep analysis of a functionally graded various thickness rotating disk with temperaturedependent material properties, Int. J. Pres. Ves. Pip., (2013) 63-74.
[16] M. Bayat, M. Rahimi, M. Saleem, A.H. Mohazzab, I. Wudtke, H. Talebi, One-dimensional analysis for magneto-thermo-mechanical response in a functionally graded annular variable-thickness rotating disk, Appl. Math. Model., 38 (2014) 4625-4639.
[17] D. Ting, D. Hong-Liang, Thermo-elastic analysis of a functionally graded rotating hollow circular disk with variable thickness and angular speed, Appl. Math. Model., 40 (2016) 7689-7707.
[18] Hong-Liang Dai, Zhen-Qiu Zheng, Ting Dai, In vestigation on a rotating FGPM circular disk under a coupled hygrothermal field, Appl. Math. Model., 46 (2017) 28-47.
[19] D. Ting, D. Hong-Liang, An analysis of a rotating (FGMEE) circular disk with variable thickness under thermal environment, Appl. Math. Model., 45 (2017) 900-924.
[20] R. Szilard, Theories and applications of plate analysis: Classical, Numerical and Engineering Methods, John Wiley & Sons, Inc; 2004.
[21] S. Chakraverty, Vibration of plates, New York: CRC Press; Taylor & Francis group; 2009.
[22] S.S. Rao, Vibration of continuous systems, John Wiley & Sons, Inc; 2007.
[23] J.N. Reddy, C.M. Wang, S. Kitipornchai, Axisymmetric bending of functionally graded circular and annular plate, Eur. J. Mech. A/Solids 18 (1999) 185-199.
[24] A.M. Wazwaz, Partial differential equations and solitary waves theory, Higher education Press, 2009.
[25] C.F. Gerald, P.O. Wheatley. Applied numerical analysis. 6th ed. California: Addison-Wesley; 2002.
[26] User’s Manual of ANSYS 16.2, ANSYS Inc.; 2015.
Journal of Stress Analysis
Volume 2, Issue 1
September 2017
Pages 35-49

Files

Share

How to cite

Statistics