Topographic optimization with variable boundary conditions: Enabling optimal design of interacting components

Topographic optimization provides a valuable opportunity for the design of optimal structures. A significant limitation in the current generation of topographic optimization algorithms is the non-inclusion of boundary conditions as optimization variables. This limitation significantly constrains the domain of design problems compatible with topographic optimization. For example, unique
components can be optimized for a given set of boundary conditions only. There is no opportunity to assess whether these boundary conditions are themselves optimal. This work reports on the authors novel contributions to allow boundary conditions to be included as optimization variables, thereby dramatically expanding the domain of design problems that are compatible with topographic optimization. This method is demonstrated by the optimal topographic optimization of interacting components: a previously intractable design problem.