本文將簡支承複合積層板有限層板方法推展成適用於具厚度相關材料性質的簡支承雙曲率層殼方法。將指定之溫度條件設置在雙曲率殼的上表面和下表面，兩種依據沿著殼厚度方向組成的體積分數決定之模型 (即冪次和S形模型)作為兩相複合材料的材料性質依據，其有效材料性質則使用Mori-Tanaka模型來做評估。藉由基於Reissner混合變分原理推衍出有限雙曲率層殼方法的歸一弱形式數學方程式以及殼域中的Euler-Lagrange方程式，將其有限雙曲率層殼法的結果進行比較，而本RMVT有限雙曲率層殼方法的收斂速率及精確度則透過和已知文獻的擬三維和二維解之比較，進行驗證。

In this paper the authors extend the finite layer methods for simply-supported, laminated composite plates to those for simply-supported, doubly curved (DC) shells with thickness- material properties. The specified temperature conditions are prescribed on the top and bottom surfaces of the DC shell. A two-phase composite material is considered with two different models of the material properties (i.e., the power-law and sigmoid function models) according to the volume fractions of the constituents through the thickness direction of the shell. The effective material properties are estimated using the Mori-Tanaka model. A unified weak-form formulation of the finite doubly curve layer (FDCL) methods is derived on the basis of Reissner’s mixed variational theorem (RMVT), and the system equations in the shell domain are derived. The accuracy and convergence rate of these RMVT-based FDCL methods are validated by comparing their solutions with the quasi three-dimensional and accurate two-dimensional solutions available in the literature.

Akbari Alashti, R., Khorsand, M., “Three-dimensional nonlinear thermo-elastic analysis of functionally graded cylindrical shells with piezoelectric layers by differential quadrature method”, Acta Mech. 223, 2565-2590, 2012.
Arefi, M., “Nonlinear thermoelastic analysis of thick-walled functionally graded piezoelectric cylinder”, Acta Mech. 224, 2771-2783, 2013.
Brischetto, S., Leetsch, R., Carrera, E., Wallmersperger, T., , B., “Thermo-mechanical bending of functionally graded plates”, J. Therm. Stresses 31, 286-308, 2008.
Brischetto, S., Carrera, E., “Thermal stress analysis by refined multilayered composite shell theories”, J. Therm. Stresses 32, 165-186, 2009.
Brischetto, S., Carrera, E., “Coupled thermo-mechanical analysis of one-layered and multilayered plates”, Compos. Struct. 92, 1793-1812, 2010.
Carrera, E., “An assessment of mixed and classical theories for the thermal stress analysis of orthotropic multilayered plates”, J. Therm. Stresses 23, 797-831, 2000.
Carrera, E., “Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessments and benchmarking”, Arch. Comput. Methods Eng. 10, 215-296, 2003.
Chi, S.H., Chung, Y.L., “Mechanical behavior of functionally graded material plates under transverse load-Part I: Analysis”, Int. J. Solids Struct. 43, 3657-3674, 2006.
Carrera, E., Boscolo, M., Robaldo, A., “Hierarchic multilayered plate elements for coupled multifield problems of piezoelectric adaptive structures: formulation and numerical assessment”, Arch. Comput. Methods Eng. 14, 383-430, 2007.
Carrera, E., Brischetto, S., Robaldo, A., “Variable kinematic model for the analysis of functionally graded materials plates,” AIAA J. 46, 194-203, 2008.
Chung, Y.L., Chang, H.X., “Mechanical behavior of rectangular plates with functionally graded coefficient of thermal expansion subjected to thermal loading”, J. Therm. Stresses 31, 368-388, 2008.
Cinefra, M., Carrera, E., Brischetto, S., Belouettar, S., “Thermo-mechanical analysis of functionally graded shells”, J. Therm. Stresses 33, 942-963, 2010.
Carrera, E., Cinefra, M., Fazzolari, F.A., “Some results on thermal stress of layered plates and shells by using unified formulation”, J. Therm. Stresses 36, 589-625, 2013.
Dai, H.L., Dai, T., “Analysis of the thermoelastic bending of a functionally graded material cylindrical shell”, Meccanica 49, 1069-1081, 2014.
Hill, R., “A self-consistent mechanics of composite materials”, J. Mech. Phys. Solids 13, 213-222, 1965.
Heydarpour, Y., Malekzadeh, P., Golbahar Haghighi, M.R., “Thermoelastic analysis of rotating laminated functionally graded cylindrical shells using layerwise differential quadrature method”, Acta Mech. 223, 81-93, 2012.
Jabbari, M., Sohrabpour, S., Eslami, M.R., “Mechanical and thermal stresses in functionally graded hollow cylinder due to radially symmetric loads”, Int. J. Pressure Vessel Piping 79, 493-497, 2002.
Jabbari, M., Sohrabpour, S., Eslami, M.R., “General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisymmetric steady-state loads”, J. Appl. Mech. 70, 111-118, 2003.
Koizumi, M., “Recent progress of functionally graded materials in Japan”, Ceram. Eng. Sci. Proc. 13, 333-347, 1992.
Koizumi, M., “FGM activities in Japan”, Compos. Part B 28B, 1-4, 1997.
Khare, R.K., Kant, T., Garg, A.K., “Closed-form thermo-mechanical solutions of higher-order theories of cross-ply laminated shallow shells”, Compos. Struct. 59, 313-340, 2003.
Kulikov G.M., Plotnikova, S.V., “3D exact thermoelastic analysis of laminated composite shells via sampling surfaces method”, Compos. Struct. 115, 120-130, 2014.
Kulikov G.M., Plotnikova, S.V., “Three-dimensional thermal stress analysis of laminated composite plates with general layups by a sampling surfaces method”, Eur. J. Mech. A/Solids 49, 214-226, 2015a.
Kulikov G.M., Plotnikova, S.V., “A sampling surfaces method and its implementation for 3D thermal stress analysis of functionally graded plates”, Compos. Struct. 120, 315-325, 2015b.
Mori, T., Tanaka, K., “Average stress in matrix and average elastic energy of materials with misfitting inclusions”, Acta Metall. 21, 571-574, 1973.
Murakami, H., “Laminated composite plates theory with improved in-plane response”, J. Appl. Mech. 53, 661-666, 1986.
Poultangari, R., Jabbari, M., Eslami, M.R., “Functionally graded hollow spheres under non-axisymmetric thermo-mechanical loads”, Int. J. Pressure Vessel Piping 85, 295-305, 2008.
Reddy, J.N., “A simple higher-order theory for laminated composite plates”, J. Appl. Mech. 51, 745-752, 1984.
Reddy, J.N., Chin, C.D., “Thermomechanical analysis of functionally graded cylinders and plates”, J. Therm. Stresses 21, 593-626, 1998.
Reddy, J.N., Cheng, Z.Q., “Three-dimensional thermomechanical deformations of functionally graded rectangular plates”, Eur. J. Mech. A/Solids 20, 841-855, 2001.
Shaw, L.L., “Thermal residual stresses in plates and coating composed of multi-layered and functionally graded materials”, Compos. Part B 29B, 199-210, 1998.
Wu, C.P., Chiu, K.H., Wang, Y.M., “A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells”, CMC-Comput. Mater. Continua 8, 93-132, 2008.
Wu, C.P., Lu, Y.C., “A modified Pagano method for the 3D dynamic responses of functionally graded magneto-electro-elastic plates”, Compos. Struct. 90, 363-372, 2009.
Wu, C.P., Li, H.Y., “The RMVT- and PVD-based finite layer methods for the three-dimensional analysis of multilayered composite and FGM plates”, Compos. Struct. 92, 2476-2496, 2010.
Wu, C.P., Chang, Y.T., “A unified formulation of RMVT-based finite cylindrical layer methods for sandwich circular hollow cylinders with an embedded FGM layer”, Compos. Part B 43, 3318-3333, 2012.
Wu, C.P., Li, H.Y., “An RMVT-based finite rectangular prism method for the 3D analysis of sandwich FGM plates with various boundary conditions”, CMC-Comput. Mater. Continua 34, 27-62, 2013a.
Wu, C.P., Li, H.Y., “RMVT-based finite cylindrical prism methods for multilayered functionally graded circular hollow cylinders with various boundary conditions”, Compos. Struct. 100, 592-608, 2013b.
Wu, C.P., Liu, Y.C., “A review of semi-analytical numerical methods for laminated composite and multilayered functionally graded elastic/piezoelectric plates and shells”, Compos. Struct. 147, 1-15, 2016.
Zenkour, A.M., Alghamdi, N.A., “Thermoelastic bending analysis of functionally graded sandwich plates”, J. Mater. Sci. 43, 2574-2589, 2008.
Zenkour, A.M., Alghamdi, N.A., “Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads”, Mech. Adv. Mater. Struct. 17, 419-432, 2010.