Coupled thermal and mechanical analysis of composite cross sections using mathematical optimization strategies

In the present article an alternative approach for the coupled thermal and mechanical analysis of composite cross sections under temperature effects is introduced, which uses the mathematical optimization as a consistent methodical base. By applying the principle of the virtual source energy for the thermal and the principle of the minimum of the total potential energy for the mechanical analysis, an accurate determination of temperature fields as well as residual strain and stress distributions is possible. The coupling is enabled by the thermal strains, which are determined based on the temperature field and passed to the nonlinear mechanical analysis as tension free pre-strains. The energy functional of the heat conduction problem is derived and implemented. The resulting optimization task is strictly convex and represents an implicit formulation, which does not impose any stability criteria. The performance of the introduced method is demonstrated on a principle example and an outlook is given on possible further extensions and applications.