Strength optimized designs of thermoelastic structures

For thermoelastic structures the same optimal design does not simultaneously lead to minimum compliance and maximum strength. Compliance may be a questionable objective and focus for the present paper is on the important aspect of strength, quantified as minimization of the maximum von Mises stress. With compliance defined as the product of resulting displacements and their corresponding total loads, then for thermoelastic problems compliance is different from total elastic energy. An explicit formula for this difference is derived and numerically illustrated in the optimized examples. As an alternative to mathematical programming, which with a large number of both design variables and strength constraints, is found non-practical, we choose simple recursive iterations to obtain uniform energy density and find by examples that the obtained designs are close to fulfilling also strength maximization. In compliance minimization it may be advantageous to decrease the total volume, but for strength maximization it is argued that it is advantageous to keep the total permissible volume. With the thermoelastic analysis presented directly in a finite element formulation, simple explicit formulas for equivalent thermoelastic loads are appended.