Seminar by Prof. Dr. Philipp Junker

On April 20, 2023, the lecture from Prof. Dr. Philipp Junker talks place in the meeting room 5th floor of the Library

Prof. Dr. Junker presents research entitled ""Variational principles and topology optimization: a holistic approach".

Abstract:

Variational principles offer a particular elegance for modeling physical phenomena: only scalar-valued energies need to be defined to obtain the resultant governing equations by stationarity analysis. A well-known example are the Lagrange equations of second kind. In this talk, we present a generalization which is valid also for deformable continua, based on an extended Hamilton functional. Then, not only the balance of linear momentum in its weak form
result but, interestingly, also an equivalent form to the heat conduction equation as well as a generalized evolution equation for internal variables that describe the microstructure. As an application example, we consider the case of topology optimization. Since the optimization is embedded into the very same method as can be used for material modeling, this optimization is referred to as thermodynamic topology optimization. We present the general procedure as well as examples for optimizing non-linear materials, such as multi-component materials, hyperelastic materials, and hardening materials.