We present a new model for the determination of temperature distributions in thin plates consisting of many different layers. The method uses both continuous and discrete approaches. The derived set of equations is based on a continuous representation of heat transfer phenomena at the midplane of each layer, whereas it facilitates a discrete process for introducing ply to ply, through thickness, heat transfer. For the steady state case, the resulting equations are of the Helmholtz type. Methods of solutions for the resulting system are discussed, and comparisons with the first order lamination theory are presented in a benchmark example.

1.
Niu
,
M.
, 1992,
Composite Airframe Structures
,
Conmilit
,
Hong Kong
.
2.
Mazumbar
,
S. K.
, 2002,
Composites Manufacturing
,
CRC
,
Washington, D.C.
.
3.
Potter
,
K.
, 1997,
Resin Transfer Molding
,
Chapman and Hall
,
London
.
4.
Baker
,
A. A.
, and
Jones
,
R.
, eds., 1988,
Bonded Repair of Aircraft Structures
,
Martinus Nijhoff
,
Dordrecht
.
5.
Jones
,
R.
, and
Pitt
,
S.
, 2006, “
Crack Patching Revisited
,”
Compos. Struct.
0263-8223,
76
, pp.
218
223
.
6.
Caliskan
,
M.
, 2006, “
Evaluation of Bonded and Bolted Repair Techniques With the Finite Element Method
,”
Mater. Des.
0264-1275,
27
, pp.
811
820
.
7.
Marioli-Riga
,
Z. P.
,
Tsamasphyros
,
G. J.
, and
Kanderakis
,
G. N.
, 2001, “
Design of Emergency Aircraft Repairs Using Composite Patches
,”
Mech. Compos. Mater. Struct.
1075-9417,
8
, pp.
199
204
.
8.
Kovalenko
,
A. D.
, 1969,
Thermoelasticity
,
Wolters-Noordhoff
,
Groningen
, translated from Russian.
9.
Kern
,
D. Q.
, and
Kraus
A. D.
, 1972,
Extended Surface Heat Transfer
,
McGraw-Hill
,
New York
.
10.
Noor
,
A. K.
, and
Tenek
,
L. H.
, 1992, “
Steady-State Nonlinear Heat Transfer in Multilayered Composite Panels
,”
J. Eng. Mech.
0733-9399,
118
(
8
), pp.
1661
1678
.
11.
Rolfes
,
R.
, 1991, “
Higher Order Theory and Finite Element for Heat Conduction in Composites
,”
Numerical Methods in Thermal Problems, Proceedings of the Seventh International Conference
,
R. W.
Lewis
,
et al.
, eds.,
Pineridge
,
Swansea, UK
, pp.
880
889
.
12.
Surana
,
K. S.
, and
Abusaleh
,
G.
, 1990, “
Curved Shell Elements for Heat Conduction With p-Approximation in the Shell Thickness Direction
,”
Comput. Struct.
0045-7949,
34
(
6
), pp.
861
880
.
13.
Argyris
,
J.
,
Tenek
,
L.
, and
Oberg
,
F.
, 1995, “
A Multilayer Composite Triangular Element for Steady-State Conduction/Convection/Radiation Heat Transfer in Complex Shells
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
120
, pp.
271
301
.
14.
Fourier
,
J. B. J.
, 1822,
Theorie Analytique de la Claleur
,
Gauthier-Villars
,
Paris
.
15.
Onsager
,
L.
, 1931, “
Reciprocal Relations in Irreversible Processes I
,”
Phys. Rev.
0031-899X,
37
(
4
), pp.
405
426
.
16.
Onsager
,
L.
, 1931, “
Reciprocal Relations in Irreversible Processes I
,”
Phys. Rev.
0031-899X,
38
(
12
), pp.
2265
2279
.
17.
Machlup
,
S.
, and
Onsager
,
L.
, 1953, “
Fluctuations and Irreversible Processes II
,”
Phys. Rev.
0031-899X,
91
(
6
), pp.
1512
1515
.
18.
Incropera
,
F. P.
, and
De Witt
,
D. P.
, 1990,
Fundamentals of Heat and Mass Transfer
,
Wiley
,
New York
.
19.
Mikhailov
,
M. D.
, and
Özişik
,
M. N.
, 1984,
Unified Analysis and Solutions of Heat and Mass Diffusion
,
Dover
,
New York
.
20.
Horn
,
P.
, and
Johnson
,
C.
, 1985,
Matrix Analysis
,
Cambridge University Press
,
Cambridge, UK
.
21.
Horn
,
P.
, and
Johnson
,
C.
, 1991,
Topics in Matrix Analysis
,
Cambridge University Press
,
Cambridge, UK
.
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