形状と厚さの同時最適化法の構造位相決定問題への応用自由曲面シェル構造の構造形態創生手法の提案（その2）

摘要

数ある建築構造の一つであるアーチやドームといった大空間建築rnでは建築形態と力学的構造が一体となり，形と力学の関連性は強いrn意味を持つ。力学的に根拠を持った空間構造は本来持つべき機能でrnある構造安全性を獲得し，空間に緊張感や躍動感を与え，見るものrnに感動をもたらす美しい建築を実現可能とする。%The scheme of computational morphogenesis for the shell structures with free curved surface is proposed, where shape, rrndistribution of thickness and topology can be simultaneously optimized. In the proposed scheme, distribution of thickness is rdiscretized based on those values at each node, and Non Uniform Rational B-Spline (NURBS) is utilized by which the number of runknowns can be controlled while the high degree of freedom for expression of the shape of the curved surface and rdistribution of thickness are maintained. Moreover, the contour lines with respect to shell thickness over the shell surface rare utilized by which topology of shell structures can be not only scraped but also grown up. By using this method, shell rstructure optimized with respect to not only shape and shell thickness but also topology can be obtained. The problem in rquestion has been mathematically formulated as strain energy minimization problem of which coordinate of NURBS control point rwith respect to the shape of the curved surface and distribution of thickness are adopted as the design variables and rnumerical examples are presented where the effectiveness of the proposed scheme is investigated.