Analysis of non-stationary temperature ®elds in laminated strips and plates B.Ya. Kantor * , N.V. Smetankina, A.N. Shupikov Institute for Problems in Machinery, National Academy of Sciences of Ukraine, 2/10 Pozharsky Street, Kharkov 61046, Ukraine Received 4 December 2000; in revised form 20 April 2001 Abstract A method for determination of thermal condition of laminated elements of structures is oered. The method is based on a presentation of temperature distribution through the thickness of each layer by means of orthonormal Legendre polynomials. As a numerical example, a solution of the non-stationary heat conduction problem for laminated strips and plates is obtained. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Laminated strips and plates; Non-stationary heat conduction; Temperature distribution 1. Introduction Changes of temperature are often the cause of failure of structures, especially multilayer ones, when temperature dierence between internal and external surfaces is signi®cant. The majority of publications, devoted to thermoelasticity of laminated structures, deal with deformation of such structures under conditions of steady temperature ®elds Wu and Tauchert, 1980; Reddy and Hsu, 1980; Khdeir, 1997; Verijenko et al., 1999) or dynamic temperature ®elds with prescribed distribution through the thickness Shuji and Masataka, 1991; Heuer et al., 1992). The hypothesis about a piecewise- linear temperature distribution through the thickness of a laminated package is often applied. However, the non-stationary character of a problem requires a more exact description of the temperature ®eld obtained directly from solution of a heat conduction equation. Savoia and Reddy 1995) used the quasi-static theory of thermoelasticity to examine stresses in multi- layer rectangular simply supported plates aected by thermal and mechanical loads. The authors applied polynomial and exponential temperature distributions through the thickness of each layer which allow to consider steady-state and transient thermal conditions. The temperature distribution over top and bottom surfaces of plates is given. Reddy and Chin 1998) have numerically analysed thermomechanical behaviour of functionally graded cylinders and plates under transient thermal loading conditions. Temperature and stress ®elds are International Journal of Solids and Structures 38 2001) 8673±8684 www.elsevier.com/locate/ijsolstr * Corresponding author. Fax: +380-0572-944-635. E-mail address: kantor@ipmach.kharkov.ua B.Ya. Kantor). 0020-7683/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII:S0020-768301)00099-3