最適化手法を用いた膜構造物の裁断図解析

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Current structural design methods for determining the initial equlibrium configuration of membrane structures are based on the assumption that the membrane stress distribution is uniform all over the surface. However, a typical method of fabricating these structures is to divide the complex curved surface into a number of plane membrane strips called 'cutting patterns', which are then assembled and finally stretched between fixed boundary members. Presently, the cutting pattern is obtained by dividing the curved surface into several approximate plane developed strips by utilizing geodestic lines, and then obtaining the cutting pattern by estimating the membrane elongation corresponding to the initial membrane stress distribution. Errors occur in developing the non-developable curved surface and also in estimating the membrane elongation. Therefore, the actual stress distribution deviates from the assumed uniform stress state and the accuracy of the cutting pattern is considered to be an important factor affecting the behavior and safety of actual membrane structures. In this paper, a new analytical method for producing a more accurate cutting pattern by utilising an optimization technique is proposed. The optimum cutting pattern is definde so that the membrane stress distribution in the actual initial equilibrium state becomes as closely as possible to the uniform stress distribution assumed in the design stage. An optimization problem is formulated and solved for determining the geometry of the optimum cutting pattern. The proposed method is applied to simple membrane structural models. As the results, it is found that the optimum cutting pattern obtained from the proposed method is able to form the close stress distribution to the uniform one assumed in the design, and the necessity of the proposed method for producing the accurate cutting pattern is confirmed. The applicabilty and validity of the proposed method are also verified through simulation analysis of an actual fabrication process for an actual membrane structure.
社団法人日本建築学会の論文
1989-01-30

最適化手法を用いた膜構造物の裁断図解析

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