Analytical solutions based on the two-scale asymptotic homogenization method for thermoelastic problem pertinent to general thin composite shells are obtained. The model allows the determination of both local fields and effective elastic and thermal expansion coefficients of composite sandwich shells made of generally orthotropic materials. Orthotropy in the material characteristics leads to a significantly complex set of thermoelastic local problems and is considered for the first time in the present article. First, a 3D-to-2D general asymptotic homogenization composite shell model based on a set of four unit-cell problems is derived. Secondly, the expansion of the model is continued to the further derivation of formulae for the forces, moments, displacements, strains, stresses, and effective thermoelastic coefficients that are representatives of the sandwich shell. Finally, the theory is illustrated by examples pertaining to thin composite sandwich shells with hexagonal honeycomb, hexagonal-triangular, and star-hexagonal cellular cores of orthotropic materials.
Noor, A.K., Burton, W.S. and Bert, C.W. (1996). Computational Models for Sandwich Panels and Shells , Applied Mechanics Review, 49(3): 155-199.
3.
Bolotin, V.V. (1963). Nonconservative Problems of the Theory of Elastic Stability, Pergamon Press, London .
4.
Kalam, M.A. (1981). Modified Rayleigh-Ritz Method in Nonaxisymmetric Thermoelastic Analysis of an Orthotropic Cylinder, Journal of Thermal Stresses, 4: 31-38.
5.
Jekot, T. (1986). Numerical Analysis of Thermal Stresses in a Nonlinear Thermoelastic Thick Cylindrical Shell and Tube, Journal of Thermal Stresses, 9(1): 59-68.
6.
Jianping, P. and Harik, I.E. (1991). Axisymmetric Pressures and Thermal Gradients in Conical Missile Tips, Journal of Aerospace Engineering, 4(3): 237-255.
7.
Bakhvalov, N.S. and Panasenko, G.P. (1989). Homogenization: Averaging Processes in Periodic Media, Kluwer, Dordrecht.
8.
Sanchez-Palencia, E. (1980). Non-Homogeneous Media and Vibration Theory (Springer Lecture Notes in Physics), Springer , Berlin.
9.
Saha, G.C., Kalamkarov, A.L. and Georgiades, A.V. (2007). Micromechanical Analysis of Effective Piezoelastic Properties of Smart Composite Sandwich Shells Made of Generally Orthotropic Materials, Smart Materials and Structures , 16: 866-883.
10.
Duvaut, G. (1976). Analyse Fonctionnelle et Mechanique Des Milieux Continus, In: Proceedings of the14th IUTAM Congress , Delft, pp. 119-132.
11.
Kalamkarov, A.L. (1987). On the Determination of Effective Characteristics of Cellular Plates and Shells of Periodic Structure , Mechanics of Solids, 22: 175-179.
12.
Caillerie, D. (1984). Thin Elastic and Periodic Plates, Mathematical Methods in the Applied Science, 6: 159-191.
13.
Kohn, R.V. and Vogelius, M. (1984). A New Model for Thin Plates with Rapidly Varying Thickness, International Journal of Solids and Structures , 20: 333-350.
14.
Guedes, J.M. and Kikuchi, N. (1990). Preprocessing and Postprocessing for Materials Based on the Homogenization Method with Adaptive Finite Element Methods, Computational Methods in Applied Mechanical Engineering , 83: 143-198.
15.
Kalamkarov, A.L. (1992). Composite and Reinforced Elements of Construction, Wiley, Chichester, New York.
16.
Kalamkarov, A.L. and Georgiades , A.V. (2002). Modeling of Smart Composites on Account of Actuation, Thermal Conductivity and Hygroscopic Absorption, Composites Part B: Engineering , 33: 141-152.
17.
Georgiades, A.V., Challagulla, K.S. and Kalamkarov , A.L. (2006). Modeling of the Thermopiezoelastic Behavior of Prismatic Smart Composite Structures made of Orthotropic Materials, Composites Part B: Engineering , 37: 569-582.
18.
Nowacki, W. (1966). Dynamic Problems of Thermoelasticity, Noordhoff, the Netherlands.
19.
Bensoussan, A., Lions, J.L. and Papanicolaou, G. (1978). Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam.
20.
Kalamkarov, A.L. and Kolpakov, A.G. (1997). Analysis, Design and Optimization of Composite Structures, Wiley, Chichester, New York.
21.
Nayfeh, A. (1973). Perturbation Methods, Wiley , New York.
22.
Holmes, M.H. (1995). Introduction to Perturbation Methods, Springer, New York.
23.
Kalamkarov, A.L. , Saha, G.C. and Georgiades , A.V. (2007). General Micromechanical Modeling of Smart Composite Shells with Application to Smart Honeycomb Sandwich Structures, Composite Structures , 79: 18-33.
24.
Timoshenko, S. (1940). Theory of Plates and Shells, McGraw-Hill, New York.
25.
Kalamkarov, A.L. (1989). Thermoelastic Problem for Structurally Non-uniform Shells of Regular Structure, Journal of Applied Mechanics and Technical Physics, 30(6): 981-988.
26.
Vinson, J.R. (1993). The Behavior of Shells Composed of Isotropic and Composite Materials, Kluwer, Dordrecht .
27.
Gibson, R.F. (1994). Principles of Composite Material Mechanics, McGraw-Hill, New York.
28.
Kalamkarov, A.L. and Georgiades , A.V. (2004). Asymptotic Homogenization Models for Smart Composite Plates with Rapidly Varying Thicknesses: Part I - Theory, Int. J. Multiscale Computational Engineering, 2: 133-148.
29.
Vinson, J.R. (1999). The Behavior of Sandwich Structures of Isotropic and Composite Materials, Technomic Publ., Lancaster, Pennsylvania.
30.
Gibson, L.J. and Ashby, M.F. (1997). Cellular Solids: Structure and Properties, Cambridge University Press, Cambridge, UK.
31.
Christensen, R.M. (2000). Mechanics of Cellular and Other low-Density Materials, Int. J. Solids and Structures , 37: 93-104.
32.
Tang, Y.Y., Noor, A.K. and Xu, K. (1996). Assessment of Computational Models for Thermoelectroelastic Multilayered Plates, Computer and Structures, 61: 915-933.
33.
Reddy, J.N. (1997). Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press, Boca Raton, Florida.
