Topological derivatives and generalized shape design

In this project we have developed a fictitious domain method for topology optimization in which the boundary of the optimal design is identified by a level
set of the topological derivative field of the objective function
that satisfies a given resource constraint. The response analysis
employs a smooth and consistent projection of the geometry onto the
fictitious analysis domain. We use a simple fixed-point iteration
algorithm to solve the optimization problem. The geometry
projection delivers smooth and accurate representations of the
variable structural boundary. This enhances convergence of the
optimization algorithm and supports the reintroduction of solid
material in void regions, a critical requirement for robust topology
optimization. Several examples for compliance
minimization subject to a volume resource constraint have been solved.