Abstract
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.
Highlights
Thermal effects lead to mechanical deformations of structures
It is based on a direct transformation of the extremum principle of heat conduction into an optimization task, which can be solved using solver-tools for nonlinear optimization, which are implemented in mathematical standard software like MS Excel or Matlab
The introduced numerical approach is a powerful method for the coupled thermal and mechanical analysis of composite cross sections subjected to combined thermal and mechanical influences, which uses the mathematical optimization as a uniform methodical base
Summary
Thermal effects lead to mechanical deformations of structures. When such deformations are restrained, they create internal stresses through the coupling of thermal and mechanical behaviour. An alternative approach for the calculation of temperature fields in composite cross sections is introduced in the present article. It is based on a direct transformation of the extremum principle of heat conduction into an optimization task, which can be solved using solver-tools for nonlinear optimization, which are implemented in mathematical standard software like MS Excel or Matlab. The resulting optimization task can be solved by standard software, too This approach for the mechanical analysis of composite cross sections under load and/or constraint influences is well investigated and published (Raue 2005, 2007; Schröter 2014). A fire exposed cross section will be taken as a principle example for illustrating the performance of the introduced method
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