Researchers: Krister Svanberg and Mathias Stolpe.
Sponsor: The Swedish Research Council for Engineering Sciences (TFR).
Structural optimization deals with optimal design of load-carrying structures. The purpose of this project is to develop mathematical models and efficient numerical methods for different types of structural optimization problems. Here follows a brief summary of our research during the year. First, we have studied the trajectories of optimal solutions to penalized or relaxed topology optimization problems as the penalization- or relaxation parameter is varied. As a result, we identified certain intrinsic difficulties with penalization- and relaxation methods in topology optimization, see [A30], [A31], [C40]. Second, we have developed a new artificial material interpolation model, defining stiffness as a certain rational function of density. The model appear to be a useful tool for obtaining zero-one solutions in topology optimization, see [R14]. Third, we have proved global convergence of a new version of our structural optimization method MMA, [R15], and later extended this convergence proof to a larger class of optimization methods based on conservative convex approximations, [R16].
Research 1999/2000
Large-scale nonlinear programming
Optimal damping of forced oscillations in discrete-time systems