境界輪体によるトラスの位相最適化　不適切な構造を回避する設計変数の導出

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  • Optimization of Truss Topology Using Boundary Cycle. Derivation of Design Variables to Avoid Inexpedient Structure.
  • キョウカイ リンタイ ニ ヨル トラス ノ イソウ サイテキカ フ テキセツ

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This paper deals with optimization of truss topology using boundary cycle in algebraic topology. Elimination of unnecessary members from the ground structure, one of the popular means to optimize truss topology, is employed. The elimination has a disadvantage that unstable structures possibly appear in the process of optimization. Boundary homomorphism, which makes the boundary cycle from chain, is equipped with an important feature to represent equilibrium of internal forces in members. Design variables derived by the boundary cycle can always satisfy this equilibrium and avoid a category of unstable structures without imposing any constraint. Dimensions of members are dependent on each other and related mutually through the design variables. Numerical examples of minimizing the total weight of a plane truss are attempted under the condition that the distribution of strain energy density is uniform and equal to a certain value. The truss is fixed to a rigid wall and supports a vertical load acting at a point distant from the wall. The validity of this formulation is verified by the numerical examples.

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