構造物の形状決定のための逆問題有限要素法

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In the inverse variational problem, an optimal shape of a structure is determined rationally by considering a system potential energy as a function not only of variables which represent the shape of the structure but also of the variables which represent the behaviours of the body. The present method to solve the problem is : i) the object is divided into finite elements and ii) according to the magnitudes of certain variables which are corresponding to the strain energy density at the surface nodal points, the shape is reformed successively into the optimal one. We call the procedure as Finite Element Method in the Inverse Problem. This paper discusses the nature and the applicability of the method through several numerical examples. In the two-dimensional problem, besides the usefulness of the present procedure as a shape determination method, its possibility to seek optimal loading conditions for the given structure is shown. The Saint-Venant's principle in the shape determination process is also discussed. It is shown for the three-dimensional models that the present method can yield a nearly optiml shape from an initial shape which is assumed without a priori mechanical knowledge. But a redesign may be needed considering the characteristic in the discretization such as symmetry and topology to FEM mesh to obtain the exact one. In the sense, the method is more suitable for obtaining nearly optimal shapes rather than the absolute ones and the method is especially effective for the proto-design of a structure and a machine element.
日本シミュレーション学会の論文
1985-11-15

構造物の形状決定のための逆問題有限要素法

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