Topology and detail geometry optimization for beam structures using homotopy modeling Original Research Article

This paper describes a novel design concept and an algorithm for topology and detail geometry design of a beam structure. Topology, layout, cross-sectional shape and size of each element are treated as a design variable. Homotopy theory is used to classify a topological type of a beam structure. In the design concept, not topology itself of a structure but a detail geometry design space defined by topology is transformed. By introducing the novel concept of an algebraic topology expression and the topology metamorphosis algorithm, active topology transformation becomes possible. A numerical example of topology, layout and cross-sectional optimization of reinforcement for a beam structure is illustrated.