Topology Optimization Using Iterative Continuum-Type Optimality Criteria (COC) Methods for Discretized Systems

Abstract

Two algorithms for the iterative optimization of discretized systems are discussed in this lecture: one concerns layout optimization, the simultaneous optimization of topology, geometry and cross-sectional dimensions for grid-like structures; and the other one generalized shape optimization, the simultaneous optimization of boundary topology and boundary shape for continua. Both methods are based on new optimality criteria methods (COC, DCOC). Discretized layout optimization is illustrated with test examples involving trusses and grillages, and combinations of stress and displacement constraints. In generalized shape optimization, the emphasis is on solutions in which porous regions are suppressed and only solid and empty regions remain (SE topologies). It is demonstrated that solid isotropic microstructures with penalty (SIMP) for intermediate densities are highly efficient in locating optimal SE topologies.