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Three-dimensional thermomechanical deformations of functionally graded rectangular plates. (English) Zbl 1002.74061
Summary: Using an asymptotic method, we study three-dimensional thermomechanical deformations of simply supported, functionally graded rectangular plates. The locally effective material properties are estimated by Mori-Tanaka scheme. The temperature, displacements and stresses of the plate are computed for different volume fractions of ceramic and metallic constituents, and they could serve as benchmark results to assess approximate two-dimensional plate theories.

MSC:
74K20 Plates
74F05 Thermal effects in solid mechanics
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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[1] Aboudi, J, Mechanics of composite materials – a unified micromechanical approach, (1991), Elsevier Science Publishing Amsterdam, The Netherlands · Zbl 0837.73003
[2] Bahar, L.Y, State space approach to elasticity, J. franklin inst., 229, 33-41, (1975) · Zbl 0316.73012
[3] Benveniste, Y, A new approach to the application of mori – tanaka’s theory in composite materials, Mech. mater., 6, 147-157, (1987)
[4] Cheng, Z.Q; Batra, R.C, Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates, J. sound vib., 229, 879-895, (2000) · Zbl 1235.74209
[5] Cheng, Z.Q; Batra, R.C, Three-dimensional thermoelastic deformations of a functionally graded elliptic plate, Compos. part B: eng., 31, 97-106, (2000)
[6] Cheng, Z.Q; Batra, R.C, Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories, Archives mech., 52, 143-158, (2000) · Zbl 0972.74042
[7] Cheng, Z.Q; Kitipornchai, S, Membrane analogy of buckling and vibration of inhomogeneous plates, J. eng. mech., 125, 1293-1297, (1999)
[8] Cheng, Z.Q; Kitipornchai, S, Exact bending solution of inhomogeneous plates from homogeneous thin-plate deflection, Aiaa j., 38, 1289-1291, (2000)
[9] Cribb, J.L, Shrinkage and thermal expansion of a two phase material, Nature, 220, 576-577, (1968)
[10] Fukui, Y, Fundamental investigation of functionally gradient material manufacturing system using centrifugal force, Int. J. jpn soc. mech. engineers, ser. III, 34, 144-148, (1991)
[11] Gol’denveizer, A.L, Boundary layer and its interaction with the interior state of stress of an elastic thin shell, J. appl. math. mech., 33, 971-1001, (1969) · Zbl 0223.73054
[12] Gong, S.W; Lam, K.Y; Reddy, J.N, The elastic response of functionally graded cylindrical shells to low velocity impact, Int. J. impact eng., 22, 397-417, (1999)
[13] Hashin, Z; Shtrikman, S, A variational approach to the theory of the elastic behavior of multiphase materials, J. mech. phys. solids, 13, 213-222, (1963) · Zbl 0108.36902
[14] Hatta, H; Taya, M, Effective thermal conductivity of a misoriented short fiber composite, J. appl. phys., 58, 2478-2486, (1985)
[15] Iyengar, K.T.S.R; Pandya, S.K, Analysis of orthotropic rectangular thick plates, Fibre sci. tech., 18, 19-36, (1983)
[16] Koizumi, M, The concept of FGM, Ceramic trans., functionally gradient mater., 34, 3-10, (1993)
[17] Levin, V.M, Thermal expansion coefficients of heterogeneous materials, Mekh. tverd. tela, 2, 88-94, (1967)
[18] Loy, C.T; Lam, K.Y; Reddy, J.N, Vibration of functionally graded cylindrical shells, Int. J. mech. sci., 41, 309-324, (1999) · Zbl 0968.74033
[19] Mori, T; Tanaka, K, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta metall., 21, 571-574, (1973)
[20] Murphy, G, Properties of engineering materials, (1957), International Textbook Company Scranton, Pennsylvania
[21] Pagano, N.J, Exact solutions for composite laminates in cylindrical bending, J. compos. mater., 3, 398-411, (1969)
[22] Pagano, N.J, Exact solutions for rectangular bi-directional composites and sandwich plates, J. compos. mater., 4, 20-34, (1970)
[23] Pindera, M.J; Aboudi, J; Arnold, S.M, Limitations of the uncoupled, RVE-based micromechanical approaches in the analysis of functionally graded composites, Mech. mater., 20, 77-94, (1995)
[24] Praveen, G.N; Chin, C.D; Reddy, J.N, Thermoelastic analysis of functionally graded ceramic-metal cylinder, J. eng. mech., 125, 1259-1267, (1999)
[25] Praveen, G.N; Reddy, J.N, Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, Int. J. solids struct., 35, 4457-4476, (1998) · Zbl 0930.74037
[26] Reddy, J.N, Mechanics of laminated composite plates: theory and analysis, (1997), CRC Press Boca Raton, Florida · Zbl 0899.73002
[27] Reddy, J.N, Analysis of functionally graded plates, Int. J. numer. methods eng., 47, 663-684, (2000) · Zbl 0970.74041
[28] Reddy, J.N; Chin, C.D, Thermomechanical analysis of functionally graded cylinders and plates, J. thermal stresses, 21, 593-626, (1998)
[29] Reddy, J.N; Wang, C.M; Kitipornchai, S, Axisymmetric bending of functionally graded circular and annular plates, European J. mech., A/solids, 18, 185-199, (1999) · Zbl 0942.74044
[30] Reiter, T; Dvorak, G.J; Tvergaard, V, Micromechanical models for graded composite materials, J. mech. phys. solids, 45, 1281-1302, (1997)
[31] Rosen, B.W; Hashin, Z, Effective thermal expansion coefficients and specific heats of composite materials, Int. J. eng. sci., 8, 157-173, (1970)
[32] Schapery, R.A, Thermal expansion coefficients of composite materials based on energy principles, J. compos. mater., 2, 380-404, (1968)
[33] Tanaka, K; Tanaka, Y; Enomoto, K; Poterasu, V.F; Sugano, Y, Design of thermoelastic materials using direct sensitivity and optimization methods: reduction of thermal stresses in functionally gradient materials, Comput. methods appl. mech. eng., 106, 271-284, (1993) · Zbl 0783.73043
[34] Tanaka, K; Tanaka, Y; Watanabe, H; Poterasu, V.F; Sugano, Y, An improved solution to thermoelastic materials designed in functionally gradient materials: scheme to reduce thermal stresses, Comput. methods appl. mech. eng., 106, 377-389, (1993) · Zbl 0845.73006
[35] Tanigawa, Y, Some basic thermoelastic problems for nonhomogeneous structural materials, Appl. mech. rev., 48, 377-389, (1995)
[36] Tarn, J.Q; Wang, Y.M, Asymptotic thermoelastic analysis of anisotropic inhomogeneous and laminated plates, J. thermal stresses, 18, 35-58, (1995)
[37] Van Vlack, L.H, Elements of materials science and engineering, (1985), Addison-Wesley Publishing Company Reading, Massachusetts
[38] Wang, Y.M; Tarn, J.Q, A three-dimensional analysis of anisotropic inhomogeneous and laminated plates, Int. J. solids struct., 31, 497-515, (1994) · Zbl 0828.73040
[39] ()
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