Continuous boundary condition propagation model for topology optimization

This work presents a continuous boundary propagation model defined by a PDE that can be used as an auxiliary model to propagate boundary conditions in topology optimization problems. This is especially useful for problems where the solid domain needs to assume multiple behaviors resulting from the application of different Dirichlet boundary conditions. The propagation model is elaborated in such a way that the new material (defined by the optimization) assumes the behavior of the boundary it touches. If the new material does not touch any boundary, a predefined behavior can be imposed. The model is also relevant for 3D problems, where search procedures for finding the connections between solid and the walls can become costly. In this work, three classes of problems are provided. The first considers a fluid problem modeled via 2D-swirl Navier-Stokes with multi-velocity walls, the second deals with a thermal-flow problem with multi-temperature walls, and the third evaluates the application for structural optimization. Equilibrium equations are solved by using the finite element method. The pyadjoint libraries are used to perform the automatic sensitivity derivation and an internal point optimizer is used to update the design variable. The results show different optimization cases for 2D-swirl fluidic diodes, thermal-flow channels, and structural compliance minimization.