An Approximate Thermo-Mechanical Solution of a Functionally Graded Cylinder Using Hybrid Integral Transform and Finite Element Method

Subject Areas : Engineering

M Dehghan ¹ , A Moosaie ² , M Zamani Nejad ³

1 - Department of Mechanical Engineering, Yasouj University, Yasouj, Iran
2 - Department of Mechanical Engineering, Yasouj University, Yasouj, Iran
3 - Department of Mechanical Engineering, Yasouj University, Yasouj, Iran

Received: 2021-09-02 Accepted : 2021-11-19 Published : 2022-03-30

Keywords:

References:

1.  Obata Y., Noda N., 1994, Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material, Journal of Thermal Stresses 17(3): 471-487.


2.  Jabbari M., Sohrabpour S., Eslami M., 2002, Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads, International Journal of Pressure Vessels and Piping 79(7): 493-497.


3.  Jabbari M., Sohrabpour S., Eslami M., 2003, General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisymmetric steady-state loads, Journal of Applied Mechanics 70(1): 111-118.


4.  Ootao Y., Akai T., Tanigawa Y., 2008,Transient piezothermoelastic analysis for a functionally graded thermopiezoelectric hollow cylinder, Journal of Thermal Stresses 31(10): 935-955.


5. Malekzadeh P., Heydarpour Y., 2012, Response of functionally graded cylindrical shells under moving thermo-mechanical loads, Thin-Walled Structures 58: 51-66.


6. Moosaie A., 2012, Steady symmetrical temperature field in a hollow spherical particle with temperature-dependent thermal conductivity, Archives of Mechanics 64(4): 405-422.


7.  Moosaie A., 2015, Axisymmetric steady temperature field in FGM cylindrical shells with temperature-dependent heat conductivity and arbitrary linear boundary conditions, Archives of Mechanics 67(3): 233-251.


8.  Moosaie A., 2016, A nonlinear analysis of thermal stresses in an incompressible functionally graded hollow cylinder with temperature-dependent material properties, European Journal of Mechanics-A/Solids 55: 212-220.


9.  Dehghan M., Nejad M.Z., Moosaie A., 2016, Thermo-electro-elastic analysis of functionally graded piezoelectric shells of revolution: Governing equations and solutions for some simple cases, International Journal of Engineering Science 104: 34-61.


10.  Nejad M.Z., Rahimi G., Ghannad M., 2009, Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system, Mechanics 77(3): 18-26.


11.  Jabbari M., Nejad M.Z. , Ghannad M., 2015, Thermo-elastic analysis of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading, International Journal of Engineering Science 96: 1-18.


12.  Gharibi M., Nejad M.Z., Hadi A., 2017, Elastic analysis of functionally graded rotating thick cylindrical pressure vessels with exponentially-varying properties using power series method of Frobenius, Journal of Computational Applied Mechanics 48(1): 89-98.


13.  Zamani Nejad M., Jabbari M., Hadi A., 2017, A review of functionally graded thick cylindrical and conical shells, Journal of Computational Applied Mechanics 48(2): 357-370.


14.  Dehghan M., Baradaran G.H., 2011, Buckling and free vibration analysis of thick rectangular plates resting on elastic foundation using mixed finite element and differential quadrature method, Applied Mathematics and Computation 218(6): 2772-2784.


15.  Lin J.-Y., Chen H.-T., 1992, Radial axisymmetric transient heat conduction in composite hollow cylinders with variable thermal conductivity, Engineering Analysis with Boundary Elements 10(1): 27-33.


16.  Ebrahimi M., Vakilipour S., Shahverdi M., 2017, A novel computational procedure based on league championship algorithm for solving an inverse heat conduction problem, Journal of Computational Applied Mechanics 48(2): 285-296.


17.  Ozkan G., Mengi Y., 1997, On the use of FFT algorithm for the circumferential coordinate in boundary element formulation of axisymmetric problems, International Journal for Numerical Methods in Engineering 40(13): 2385-2412.


18.  Liu T.-W., Xu H.-H., Qiu X.-L., 2012, A combination method of mixed multiscale finite-element and laplace transform for flow in a dual-permeability system, International Scholarly Research Notices 2012:


19.  Noor A.K., Peters J.M., 1988, Stress and vibration analyses of anisotropic shells of revolution, International Journal for Numerical Methods in Engineering 26(5): 1145-1167.


20.  Sheinman I. , Weissman S., 1987, Coupling between symmetric and antisymmetric modes in shells of revolution, Journal of Composite Materials 21(11): 988-1007.


21.  Sivadas K., Ganesan N., 1992, Effect of coupling between symmetric and antisymmetric modes in composite thick shells of revolution, Finite Elements in Analysis and Design 11(1):9-18.


22. Correia I.P., Barbosa J., Soares C.M.M., Soares C.A.M., 2000, A finite element semi-analytical model for laminated axisymmetric shells: statics, dynamics and buckling, Computers & Structures 76(1-3): 299-317.


23.  Santos, C. M. M. Soares, C. A. M. Soares , J. Reddy, A semi-analytical finite element model for the analysis of laminated 3D axisymmetric shells: bending, free vibration and buckling, Composite Structures 71(3): 273-281.


24.  Santos H., Soares C.M.M., Soares C.A.M., Reddy J., 2006, A finite element model for the analysis of 3D axisymmetric laminated shells with piezoelectric sensors and actuators, Composite Structures 75(1): 170-178.


25.  Santos H., Soares C.M.M., Soares C.A.M., Reddy J., 2008, A finite element model for the analysis of 3D axisymmetric laminated shells with piezoelectric sensors and actuators: bending and free vibrations, Computers & Structures 86(9): 940-947.


26.  Santos H., Soares C.M.M., Soares C.A.M., Reddy J., 2009, A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials, Composite Structures 91(4): 427-432.


27.  Heinrich B., 1996, The Fourier-finite-element method for Poisson’s equation in axisymmetric domains with edges, SIAM Journal on Numerical Analysis 33(5): 1885-1911.


28.  Kim Y.P., Kweon J.R., 2009, The Fourier-finite element method for the Poisson problem on a non-convex polyhedral cylinder, Journal of Computational and Applied Mathematics 233( 4): 951-968.


29.  Bakr S.A., Pardo D., Mannseth T., 2013, Domain decomposition Fourier finite element method for the simulation of 3D marine CSEM measurements, Journal of Computational Physics 255: 456-470.


30.  Lai J., Booker J.R., 1991, Application of discrete Fourier series to the finite element stress analysis of axi‐symmetric solids, International Journal for Numerical Methods in Engineering 31(4): 619-647.


31.  Cho C., Ahn S., 2002,Transient thermoelastic analysis of disk brake using the fast Fourier transform and finite element method, Journal of Thermal Stresses 25(3): 215-243.


32.  Floquet A., Dubourg M., 1994, Nonaxisymmetric effects for three-dimensional analysis of a brake, Journal of Tribology 116(3): 401-407.


33.  Floquet A., Dubourg M., 1996, Realistic braking operation simulation of ventilated disk brakes, Journal of Tribology 118(3): 466-472.


34.  Jin G., Ma X., Shi S., Ye T., Liu Z., 2014, A modified Fourier series solution for vibration analysis of truncated conical shells with general boundary conditions, Applied Acoustics 85: 82-96.


35.  Jin G., Ye T., Jia X., Gao S., 2014, A general Fourier solution for the vibration analysis of composite laminated structure elements of revolution with general elastic restraints, Composite Structures 109: 150-168.


36.  Mohazzab A.H., Dozio L., 2015, Prediction of natural frequencies of laminated curved panels using refined 2-D theories in the spectral collocation method, Curved Layer Structures 2: 1-14.


37.  Mohazzab A.H., Dozio L., 2015, A spectral collocation solution for in-plane eigenvalue analysis of skew plates, International Journal of Mechanical Sciences 94: 199-210.


38.  Xie X., Zheng H., Jin G., 2015, Integrated orthogonal polynomials based spectral collocation method for vibration analysis of coupled laminated shell structures, International Journal of Mechanical Sciences 98: 132-143.


39.  Trefethen L.N., 2000, Spectral Methods in MATLAB, Siam.


40. Hetnarski R.B., Eslami M.R., Gladwell G., Thermal Stresses: Advanced Theory and Applications, Springer.