On some properties of optimal thermoelastic designs in the case of fixed stress and deformation fields (Q1084903)

The equilibrium theory of linear thermoelasticity for inhomogeneous and isotropic bodies is considered. In this case, according to the body force analogy [see, for example, \textit{D. E. Carlson}, Linear thermoelasticity, pp. 297-346 of Flüge's Enzyclopaedia of physics. Vol. VIa/2 (1972; Zbl 0277.73001)], for every result in linear elastostatics there is an associated result in the linear theory of thermoelastostatics. The authors consider the problem of the optimal distribution of elastic moduli. First, the sets of distributions of elastic moduli ensuring, for a given loading, the same stress field are studied; then, the problem of determining the optimal distribution of Young's modulus over the length of a beam from the condition of the lowest maximum value of the stress modulus for the given distribution of the deflection.