ANALYTICAL METHODS FOR THE SOLUTION OF THE PLANE PROBLEM OF THE THERMOELASTIC EQUILIBRIUM

Abstract

In this paper, analytical methods for the solution of the plane problem of the thermoelastic equilibrium (PPTE) by means of complex functions are presented. Supposing that the thermal complex potential t(z, z ) and the thermoelastic displacement potential ϕ(z, z ) are determined, one can compute the displacements, the deformations and the stress state in plates (plane sections) ( ) i ij ij u ,ε ,T . Two problems are presented: the decoupled problem (P1) when the states ( ) i ij ij u ,ε ,T are generated by the thermal field T on the boundary (i.e. without mechanical loadings) and the coupled problem (P2) when the medium is subjected to thermal stress and mechanical loadings on the boundary. These studies made for the canonical domains (half-plane or circle) lead to boundary value problems with special boundary conditions for harmonic or biharmonic functions. These methods can also be applied to composite media. At the end of this paper, applications to half-plane or circle are presented. For more general domains, conformal transforms can be applied.