In the process of topology optimization, topology of a structure is, in general, changed in succession. In this paper, a method of inferring the change of topology is proposed. This method makes it possible to impose constraint conditions upon topology of the structure. Topological constraint conditions can be expressed by homology groups. As a numerical example, topology of a plate is optimized using an artificial model (the density approach) under topological constraint conditions that (I) the structure is not divided into pieces during the optimization process, and (II) the number of holes is less than or equal to the prescribed number. As a result, it was found that (1) topological constraints were correctly satisfied by the proposed method, (2) the least useful members tend to be removed by topological constraints, and other ones are reinforced, and (3) the strain energy of structures obtained under certain topological constraints is somewhat higher than that of ones without topological constraint
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