Goal oriented DWR error estimation for the Virtual Elements Method for the space-time thermodynamic topology optimization

The idea of the project is to exploit the property of Topology Optimisation (TTO) derived from the Hamiltonian principle. This innovative approach views the optimisation process as the temporal evolution of material density, providing a more holistic and physically consistent framework for structural design. For example, when considering viscoelastic material behaviour, the rate-dependent material properties can be addressed on the same time scale. This approach allows the evolution of the material to be calculated simultaneously with the material density, eliminating the need for recalculation at each optimisation step and significantly reducing computational complexity and time.

To further improve computational efficiency, mesh adaptivity through space and time must be employed. This strategy allows a coarse mesh to be used for regions of the design space filled with void material where high resolution is not required. Conversely, areas of interest, such as material interfaces or regions of high stress, can be more finely discretised. In addition, larger optimisation steps can be taken as the process approaches convergence, speeding up the overall process without compromising accuracy.

Doctoral Researcher: Christian Sellmann

Scientific Advisors: Phillip Junker, Thomas Wick, David Neron