Abstract
A thermo-elastic analysis of a multi-directional functionally graded thick rectangular plate with different boundary conditions is carried out in this study. Some material properties are assumed to be temperature dependent and graded in all three spatial directions following a power law function. The differential quadrature method (DQM) is employed to obtain the temperature distribution throughout the 3D-FGM plate. The governing partial differential equations based on the three-dimensional thermo-elasticity theory are obtained, and the DQM is employed to discretize the resulting equations. Comparisons are made with the available results of 1D-FGM and 2D-FGM plates in the literature and an Abaqus model. Numerical results are obtained for different gradient indices, plate dimensions, and various thermal and mechanical boundary conditions.
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References
Koizumi, M.: FGM activities in Japan. Compos. Part B 28B, 1–4 (1997)
Alinaghizadeh, F., Kadkhodayan, M.: Large deflection analysis of moderately thick functionally graded annular sector plates fully and partially rested on two-parameter elastic foundations by GDQ method. Aerosp. Sci. Technol. 39, 260–271 (2014)
Qian, L.F., Batra, R.C.: Transient thermoelastic deformations of a thick functionally graded plate. J. Therm. Stress. 27, 705–740 (2004)
Parveen, G.N., Reddy, J.N.: Nonlinear transient thermoelastic analysis of functionally graded ceramic–metal plates. Int. J. Solids Struct. 35, 4457–4476 (1998)
Ootao, Y., Tanigawa, Y.: Three-dimensional solution for transient thermal stresses of functionally graded rectangular plate due to nonuniform heat supply. Int. J. Mech. Sci. 47, 1769–1788 (2005)
Ootao, Y., Tanigawa, Y.: Three-dimensional solution for transient thermal stresses of an orthotropic functionally graded rectangular plate. Compos. Struct. 80, 10–20 (2007)
Noda, N.: Thermal stresses in functionally graded materials. J. Therm. Stress. 22, 477–512 (1999)
Reddy, J.N.: Analysis of functionally graded plates. International 47, 663–684 (2000)
Vel, S.S., Batra, R.C.: Exact solution for thermoelastic deformations of functionally graded thick rectangular plates. Am. Inst. Aeronaut. Astronaut. J. 40, 1421–1433 (2002)
Vel, S.S., Batra, R.C.: Three-dimensional analysis of transient thermal stresses in functionally graded plates. Int. J. Solids Struct. 40, 7181–7196 (2003)
Zafarmand, H., Kadkhodayan, M.: Three-dimensional static analysis of thick functionally graded plates using graded finite element method. Proc. Inst. Mech. Eng. Part C 228, 1275–1285 (2014)
Nemat-Alla, M.: Reduction of thermal stresses by developing two-dimensional functionally graded materials. Int. J. Solids Struct. 40, 7339–7356 (2003)
Lü, C.F., Lim, C.W., Chen, W.Q.: Semi-analytical analysis for multi-directional functionally graded plates: 3-D elasticity solutions. Int. J. Numer. Methods Eng. 79, 25–44 (2009)
Birman, V., Chona, R., Byrd, L.W., Haney, M.A.: Response of spatially tailored structures to thermal loading. J. Eng. Math. 61, 201–217 (2008)
Qian, L.F., Batra, R.C.: Design of bidirectional functionally graded plate for optimal natural frequency. J. Sound Vib. 280, 415–424 (2005)
Xu, Y., Wang, L., Du, H.: Analysis of heating steady temperature field in an Al1100/Ti–6Al–4V/SiC 2D-FGM plane plate by FEM. Key Eng. Mater. 450, 235–238 (2011)
Nemat-Alla, M., Ahmed, K.I.E., Hassab-Allah, I.: Elastic–plastic analysis of two-dimensional functionally graded materials under thermal loading. Int. J. Solids Struct. 46, 2774–2786 (2009)
Tahouneh, V., Naei, M.H.: A novel 2-D six-parameter power-law distribution for three-dimensional dynamic analysis of thick multi-directional functionally graded rectangular plates resting on a two-parameter elastic foundation. Meccanica 49, 91–109 (2014)
Yang, Y.Z.: The symplectic solution for the bi-directional functionally graded piezoelectric materials. Appl. Mech. Mater. 174–177, 131–134 (2012)
Wang, Y.Z., Kuna, M.: Time-harmonic dynamic Green’s functions for two-dimensional functionally graded magneto electro elastic materials. J. Appl. Phys. 115, 043518 (2014)
Asemi, K., Salehi, M., Akhlaghi, M.: Three dimensional static analysis of two dimensional functionally graded plates. Int. J. Recent Adv. Mech. Eng. (IJMECH) 2, 21–32 (2013)
Asgari, M., Akhlaghi, M.: Transient thermal stresses in two-dimensional functionally graded thick hollow cylinder with finite length. Arch. Appl. Mech. 80, 353–376 (2010)
Davoodi Kermani, I., Ghayour, M., Mirdamadi, H.R.: Free vibration analysis of multi-directional functionally graded circular and annular plates. J. Mech. Sci. Technol. 26, 3399–3410 (2012)
Nie, G.J., Zhong, Z.: Dynamic analysis of multi-directional functionally graded annular plates. Appl. Math. Model. 34, 608–616 (2010)
Lu, C.F., Chen, W.Q., Xu, R.Q., Lim, C.W.: Semi-analytical elasticity solutions for bi-directional functionally graded beams. Int. J. Solids Struct. 45, 258–275 (2008)
Nie, G., Zhong, Z.: Axisymmetric bending of two directional functionally graded circular and annular plates. Acta Mech. Solida Sin. 20, 289–295 (2007)
Behravan Rad, A.: Static analysis of two directional functionally graded circular plate under combined axisymmetric boundary conditions. Int. J. Eng. Appl. Sci. 4, 36–48 (2012)
Asgari, M., Akhlaghi, M., Hosseini, S.M.: Dynamic analysis of two-dimensional functionally graded thick hollow cylinder with finite length under impact loading. Acta Mech. 208, 163–180 (2009)
Sobhani Aragh, B., Hedayati, H.: Static response and free vibration of two-dimensional functionally graded metal/ceramic open cylindrical shells under various boundary conditions. Acta Mech. 223, 309–330 (2012)
Shariyat, M., Alipour, M.M.: Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations. Arch. Appl. Mech. 81, 1289–1306 (2011)
Asemi, K., Salehi, M., Akhlaghi, M.: Elastic solution of a two-dimensional functionally graded thick truncated cone with finite length under hydrostatic combined loads. Acta Mech. 217, 119–134 (2011)
Malekzadeh, P.: Three-dimensional free vibrations analysis of thick functionally graded plates on elastic foundations. Compos. Struct. 89, 367–373 (2009)
Zenkour, A.M., Ashraf, M.: The refined sinusoidal theory for FGM plates on elastic foundations. Int. J. Mech. Sci. 51, 869–880 (2009)
Amini, M.H., Soleimani, M., Rastgoo, A.: Three-dimensional free vibration analysis of functionally graded material plates resting on an elastic foundation. Smart Mater. Struct. 18, 1–9 (2009)
Benyoucef, S., Mechab, I., Tounsi, A., Fekrar, A., Ait Atmane, H., Abbas Adda Bedia, E.I.: Bending of thick functionally graded plates resting on Winkler-Pasternak elastic foundations. Mech. Compos. Mater. 46, 425–434 (2010)
Zenkour, A.M.: Hygro-thermo-mechanical effects on FGM plates resting on elastic foundations. Compos. Struct. 93, 234–238 (2010)
Thai, H.T., Choi, D.H.: A refined plate theory for functionally graded plates resting on elastic foundation. Compos. Sci. Technol. 71, 1850–1858 (2011)
Thai, H.T., Choi, D.H.: Zeroth-order shear deformation theory for functionally graded plates resting on elastic foundation. Int. J. Mech. Sci. 78, 35–43 (2014)
Zenkour, A.M., Sobhy, M.: Dynamic bending response of thermoelastic functionally graded plates resting on elastic foundations. Aerosp. Sci. Technol. 29, 7–17 (2013)
Malekzadeh, P., Monajjemzadeh, S.M.: Dynamic response of functionally graded plates in thermal environment under moving load. Compos. Part B 45, 1521–1533 (2013)
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Adineh, M., Kadkhodayan, M. Three-dimensional thermo-elastic analysis of multi-directional functionally graded rectangular plates on elastic foundation. Acta Mech 228, 881–899 (2017). https://doi.org/10.1007/s00707-016-1743-x
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DOI: https://doi.org/10.1007/s00707-016-1743-x