TAILIEUCHUNG - Elasticity Part 12

Tham khảo tài liệu 'elasticity part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Sadd Elasticity Final Proof 6 04pm page 319 12 Thermoelasticity Many important stress analysis problems involve structures that are subjected to both mechanical and thermal loadings. Thermal effects within an elastic solid produce heat transfer by conduction and this flow of thermal energy establishes a temperature field within the material. Most solids exhibit a volumetric change with temperature variation and thus the presence of a temperature distribution generally induces stresses created from boundary or internal constraints. If the temperature variation is sufficiently high these stresses can reach levels that may lead to structural failure especially for brittle materials. Thus for many problems involving high temperature variation the knowledge of thermal stress analysis can be very important. The purpose of this chapter is to provide an introduction to thermoelasticity that is elasticity with thermal effects. We develop the basic governing equations for isotropic materials and investigate several solutions to problems of engineering interest. We have already briefly discussed the form of Hooke s law for this case in Section . More detailed information may be found in several texts devoted entirely to the subject such as Boley and Weiner 1960 Nowacki 1962 Parkus 1976 Kovalenko 1969 Nowinski 1978 and Burgreen 1971 . We start our study with some developments of heat conduction in solids and the energy equation. Heat Conduction and the Energy Equation As mentioned the flow of heat in solids is associated with temperature differences within the material. This process is governed by the Fourier law of heat conduction which is the constitutive relation between the heat flux vector q and the temperature gradient T. This theory formulates a linear relationship that is given by q -kijT J where kj is the thermal conductivity tensor. It can be shown that this tensor is symmetric that is kj kji. For the isotropic case kj k ôjj and thus qi -kT i

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