Hybrid integral transform and p-version FEM for thermo-mechanical analysis of a functionally graded piezoelectric hollow cylinder subjected to asymmetric loads

Document Type : Article

Authors

Department of Mechanical Engineering, Yasouj University, Yasouj, P.O. Box 75914-353, Iran

Abstract

As the first endeavor, a combination of fast Fourier transform and p-version of finite element method is proposed for electro-thermo-elastic analysis of a thick hollow cylinder under asymmetric thermal loadings. Especially in shells of revolution, the proposed FFT-pFE method is accompanied by a significant decrease in the computational costs. Due to the problem periodicity in such structures, the fast Fourier transform technique is used to discretize the governing equations into a set of harmonics in circumferential direction. Each harmonic is then partitioned using higher order finite elements. Hierarchical finite elements based on Legendre polynomial interpolation functions are utilized to discretize 2D governing equations of a functionally graded piezoelectric (FGP) cylinder. 3D governing equations of a FGP hollow cylinder are then discretized by using the higher-order Lagrangian finite elements. The effects of FFT grid-size as well as the order of the interpolation functions are investigated on convergence behavior of the proposed mixed FFT-pFE method. The piezoelectric material properties, with the exception of the Poisson’s ratio, are considered to vary along the radius of the cylinder and pursue the power function. The governing equations are derived using the principle of virtual displacements. For a 3D FGP hollow cylinder, the influence of ...

Keywords


[1]        Moosaie, A. "Axisymmetric steady temperature field in FGM cylindrical shells with temperature-dependent heat conductivity and arbitrary linear boundary conditions", Archives of Mechanics,  67(3), pp. 233-251 (2015).
[2]        Jabbari, M., Nejad, M. Z., and Ghannad, M. "Thermo-elastic analysis of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading", International journal of engineering science,  96, pp. 1-18 (2015).
[3]        Moosaie, A. and Panahi-Kalus, H. "Thermal stresses in an incompressible FGM spherical shell with temperature-dependent material properties", Thin-Walled Structures,  120, pp. 215-224 (2017).
[4]        Takagi, K., Li, J.-F., Yokoyama, S. et al. "Design and fabrication of functionally graded PZT/Pt piezoelectric bimorph actuator", Science and Technology of Advanced Materials,  3(2), pp. 217-224 (2002).
[5]        Ootao, Y., Akai, T., and Tanigawa, Y. "Transient piezothermoelastic analysis for a functionally graded thermopiezoelectric hollow cylinder", Journal of Thermal Stresses,  31(10), pp. 935-955 (2008).
[6]        Wu, C.-P. and Syu, Y.-S. "Exact solutions of functionally graded piezoelectric shells under cylindrical bending", International Journal of Solids and Structures,  44(20), pp. 6450-6472 (2007).
[7]        Alashti, R. A., Khorsand, M., and Tarahhomi, M. "Thermo-elastic analysis of a functionally graded spherical shell with piezoelectric layers by differential quadrature method", Scientia Iranica,  20(1), pp. 109-119 (2013).
[8]        Dehghan, M., Nejad, M. Z., and Moosaie, A. "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, pp. 34-61 (2016).
[9]        Nejad, M. Z., Jabbari, M., and Ghannad, M. "A general disk form formulation for thermo-elastic analysis of functionally graded thick shells of revolution with arbitrary curvature and variable thickness", Acta Mechanica,  228(1), pp. 215-231 (2017).
[10]      Santos, H., Soares, C. M. M., Soares, C. A. M. et al. "A semi-analytical finite element model for the analysis of laminated 3D axisymmetric shells: bending, free vibration and buckling", Composite structures,  71(3), pp. 273-281(2005).
[11]      Santos, H., Soares, C. M. M., Soares, C. A. M. et al. "A finite element model for the analysis of 3D axisymmetric laminated shells with piezoelectric sensors and actuators", Composite structures,  75(1), pp. 170-178 (2006).
[12]      Santos, H., Soares, C. M. M., Soares, C. A. M. et al. "A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials under thermal shock", Composite Structures,  86(1), pp. 10-21(2008).
[13]      Santos, H., Soares, C. M. M., Soares, C. A. M. et al. "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), pp. 940-947 (2008).
[14]      Santos, H., Soares, C. M. M., Soares, C. A. M. et al. "A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials", Composite Structures,  91(4), pp. 427-432 (2009).
[15]      Noor, A. K. and Peters, J. M. "Stress and vibration analyses of anisotropic shells of revolution", International journal for numerical methods in engineering,  26(5), pp. 1145-1167 (1988).
[16]      Sheinman, I. and Weissman, S. "Coupling between symmetric and antisymmetric modes in shells of revolution", Journal of composite materials,  21(11), pp. 988-1007 (1987).
[17]      Sivadas, K. and Ganesan, N. "Effect of coupling between symmetric and antisymmetric modes in composite thick shells of revolution", Finite elements in analysis and design,  11(1), pp. 9-18 (1992).
[18]      Loghman, A., Nasr, M., and Arefi, M. "Nonsymmetric thermomechanical analysis of a functionally graded cylinder subjected to mechanical, thermal, and magnetic loads", Journal of Thermal Stresses, pp. 1-18 (2017).
[19]      Chen, W., Bian, Z., Lv, C. et al. "3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid", International Journal of Solids and Structures,  41(3-4), pp. 947-964 (2004).
[20]      Liang, X., Deng, Y., Cao, Z. et al. "Three-dimensional dynamics of functionally graded piezoelectric cylindrical panels by a semi-analytical approach", Composite Structures, p. 111176 (2019).
[21]      Gao, W., Qin, Z., and Chu, F. "Wave propagation in functionally graded porous plates reinforced with graphene platelets", Aerospace Science and Technology, p. 105860 (2020).
[22]      Canuto, C. G., Hussaini, M. Y., Quarteroni, A. et al., Spectral methods: Fundamentals in single domains. springer, (2010).
[23]      Dehghan, M. and Baradaran, G. H. "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), pp. 2772-2784 (2011).
[24]      Malekzadeh, P. and Karami, G. "A mixed differential quadrature and finite element free vibration and buckling analysis of thick beams on two-parameter elastic foundations", Applied Mathematical Modelling,  32(7), pp. 1381-1394 (2008).
[25]      Lin, J.-Y. and Chen, H.-T. "Radial axisymmetric transient heat conduction in composite hollow cylinders with variable thermal conductivity", Engineering analysis with boundary elements,  10(1), pp. 27-33 (1992).
[26]      Liu, T.-W., Xu, H.-H., and Qiu, X.-L. "A combination method of mixed multiscale finite-element and laplace transform for flow in a dual-permeability system", International Scholarly Research Notices,  2012 (2012).
[27]      Entezari, A., Filippi, M., Carrera, E. et al. "3D-wave propagation in generalized thermoelastic functionally graded disks", Composite Structures,  206, pp. 941-951 (2018).
[28]      Heydarpour, Y., Malekzadeh, P., Dimitri, R. et al. "Thermoelastic Analysis of Functionally Graded Cylindrical Panels with Piezoelectric Layers", Applied Sciences,  10(4), p. 1397 (2020).
[29]      Qin, Z., Pang, X., Safaei, B. et al. "Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions", Composite Structures,  220, pp. 847-860 (2019).
[30]      Qin, Z., Yang, Z., Zu, J. et al. "Free vibration analysis of rotating cylindrical shells coupled with moderately thick annular plates", International Journal of Mechanical Sciences,  142, pp. 127-139 (2018).
[31]      Qin, Z., Zhao, S., Pang, X. et al. "A unified solution for vibration analysis of laminated functionally graded shallow shells reinforced by graphene with general boundary conditions", International Journal of Mechanical Sciences,  170, pp. 105341 (2020).
[32]      Safaei, B. "The effect of embedding a porous core on the free vibration behavior of laminated composite plates", Steel Compos. Struct,  35(5), pp. 659-670 (2020).
[33]      Safaei, B., Ahmed, N., and Fattahi, A. "Free vibration analysis of polyethylene/CNT plates", The European Physical Journal Plus,  134(6), pp. 271 (2019).
[34]      Cho, C. and Ahn, S. "Transient thermoelastic analysis of disk brake using the fast Fourier transform and finite element method", Journal of thermal stresses,  25(3), pp. 215-243 (2002).
[35]      Floquet, A. and Dubourg, M. "Nonaxisymmetric effects for three-dimensional analysis of a brake", Journal of Tribology,  116(3), pp. 401-407 (1994).
[36]      Floquet, A. and Dubourg, M.-C. "Realistic braking operation simulation of ventilated disk brakes", Journal of Tribology,  118(3), pp. 466-472 (1996).
[37]      Jin, G., Ma, X., Shi, S. et al. "A modified Fourier series solution for vibration analysis of truncated conical shells with general boundary conditions", Applied Acoustics, 85, pp. 82-96 (2014).
[38]      Mohazzab, A. H. and Dozio, L. "Prediction of natural frequencies of laminated curved panels using refined 2-D theories in the spectral collocation method", Curved Layer Struct,  2, pp. 1-14 (2015).
[39]      Mohazzab, A. H. and Dozio, L. "A spectral collocation solution for in-plane eigenvalue analysis of skew plates", International Journal of Mechanical Sciences,  94, pp. 199-210 (2015).
[40]      Xie, X., Zheng, H., and Jin, G. "Integrated orthogo nal polynomials based spectral collocation method for vibration analysis of coupled laminated shell structures", International Journal of Mechanical Sciences,  98, pp. 132-143 (2015).
[41]      Szabó, B. and Babuska, I., Introduction to finite element analysis. John Wiley and Sons, (2011).
[42]      Adjerid, S., Aiffa, M., and Flaherty, J. "Hierarchical finite element bases for triangular and tetrahedral elements", Computer Methods in Applied Mechanics and Engineering,  190(22), pp. 2925-2941 (2001).
[43]      Yu, Z., Guo, X., and Chu, F. "A multivariable hierarchical finite element for static and vibration analysis of beams", Finite Elements in Analysis and Design,  46(8), pp. 625-631 (2010).
[44]      Tai, C.-Y. and Chan, Y. "A hierarchic high-order Timoshenko beam finite element", Computers & Structures,  165, pp. 48-58 (2016).
[45]      Wang, H. and Qin, Q. H. "FE approach with Green’s function as internal trial function for simulating bioheat transfer in the human eye", Archives of Mechanics,  62(6), pp. 493-510 (2010).
[46]      Cao, C., Qin, Q.-H., and Yu, A. "A new hybrid finite element approach for three-dimensional elastic problems", Archives of Mechanics,  64(3), pp. 261-292 (2012).
[47]      Zienkiewicz, O. C. and Taylor, R. L., The finite element method: solid mechanics. Butterworth-heinemann, (2000).
[48]      Duda, P. "Finite element method formulation in polar coordinates for transient heat conduction problems", Journal of Thermal Science,  25(2), pp. 188-194 (2016).
[49]      Jabbari, M., Sohrabpour, S., and Eslami, M. "Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads", International Journal of Pressure Vessels and Piping,  79(7), pp. 493-49 (2002).
[50]      Alashti, R. A. and Khorsand, M. "Three-dimensional thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers by differential quadrature method", International Journal of Pressure Vessels and Piping,  88(5-7), pp. 167-180 (2011).