Criteria for assumptions on the stress state in the uncoupled linear thermoelasticity in the quasistationary displacement field approximation in the case of cylindrical symmetry

The equations of the uncoupled linear thermoelasticity in the quasistationa ry displacement field approximation in case of cylindrical symmetry are tra nsformed to the form, in which: the separated equations for sigma (rz), sig ma (zz) et sigma (z phi) coordinates of the stress tensor (in the cylindric al coordinate system r, z, phi) are obtained; the explicit formulae for dis placement coordinates u(r) and u(z) in terms of sigma (rz), sigma (zz), vol ume force coordinate F-r and temperature T are given; also an explicit form ula for displacement coordinate u(phi) in terms of sigma (z phi), volume fo rce F-phi is given. If equations for sigma (rz), sigma (zz) and sigma (z ph i), are replaced by assumptions on the stress state, then these equations r epresent criteria (necessary conditions) of validity of these assumptions. In particular, for the plane state of stress (sigma (rz) = 0 = sigma (zz) = sigma (z phi)) with no volume force the criterion for sigma (rz) reads: si gma/sigma (r) (del T-2) = 0 (del (2) stands for the Laplacean), and the cri teria for sigma (zz) and sigma (z phi) are satisfied automatically.