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Topology and detail geometry optimization for beam structures using homotopy modeling. (English) Zbl 1019.74032

Summary: This paper describes a 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 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 concept of algebraic topology expression and the topology metamorphosis algorithm, active topology transformation becomes possible. Finally, we give a numerical example of topology, layout and cross-sectional optimization of reinforcement for a beam structure is illustrated.

MSC:

74P15 Topological methods for optimization problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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