送水管の内部流れの臨界流速最大化による形状設計とそのロバスト性の改善

概要

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A simple model of a pipe conveying fluid is studied in the context of a shape determination problem. The dynamics of such a pipe is a typical example of a non-conservative system. The equilibrium equations with boundary and initial conditions are transformed into the adjoint variational principle by using Lagrangian multiplier method. The stability is discussed in the critical velocity of flow, and then, the shape determination is formulated in order to maximize it. The gradient projection method is used to search the optimal solution. It is demonstrated through examples under several boundary conditions including cantilever that the proposed procedure is effective, and the obtained optimal shape is not necessarily robust with respect to a small fluctuation of the shape. A procedure is also proposed to improve the robustness of the optimal shape which is studied in the cantilever pipe.
一般社団法人日本機械学会の論文
1990-10-25