Application of a new thermoelastic thick shell theory to solar boiler tubes

The classical thin shell theory relies on Kirchhoff's hypotheses which notably lead one to neglect normal stresses in the 'thickness direction', shearing stresses on surfaces parallel to the mean surface, warping and extension of fibers normal to the same surface. As is well known, the thermoelastic constitutive equations contradict these assumptions, which are no longer acceptable when the shell is not 'very thin' and when the thermal gradient through the thickness becomes noticeable. The thick shell theory proposed here was initially meant to describe the behavior of solar boiler tubes, but it is also applicable to piping elements encountered in most energy conversion systems, such as fossil-fired power plants, nuclear reactors, etc. For the sake of simplicity, the presentation is restricted to the study of a long tube subjected to an intense heat flux on one side; this tube carries a working fluid and the temperature distribution in the metal is not axisymmetric. By generalizing the asymptotic expansion theory of Reiss to the thermoelastic case, it is shown that higher order theory immediately following the classical thin shell approach should be based upon a displacement field whose radial component is a second order polynomial in the thickness coordinate z, whereas the tangential component is a third order polynomial in the same coordinate; the coefficients of these two polynomials are the generalized displacements of the theory. Then a 'generalized' Kirchhoff hypothesis is used, which consists in requiring the shearing stresses or deformations to vanish on the inner and outer tube surfaces only. This allows one to express two of the generalized displacements in terms of the others. The so-constructed displacement distribution is sufficiently general to account for warping and extension of fibers normal to the mean surface as well as shearing on surfaces z = constant; these effects are usually neglected. (orig.)