パラメトリック曲面として記述された極小曲面の形態創生手法

摘要

空気膜構造やサスペンション膜構造は，膜材やケーブル材などの 曲げに抵抗しない柔部材によって構成され，その力学的な安定性は 原型曲面の形状に大きく依存する。しわや弛みを起こすことのない 力学的安定性を有する膜構造を設計するためには，膜構造の設計原 型曲面として，等張力条件を満足する曲面形状である等張力曲面を 採用することが一般的である。%It is often that, to obtain a minimal surface, the surface area computed with triangular discretization is minimized by using some optimization methods. With this method, it is difficult to evaluate the error of the solution from the minimal surface, and accuracy of the solution depends on the fineness of triangulation which leads to increasing data size. In this paper, the surface is discretized by parametric surface to avoid such problems. The surface area of a B-spline surface is minimized by nonlinear programming and the error from the true minimal surface is measured by using the square of the mean curvature. The effectiveness of the proposed approach is confirmed through various examples, and the characteristics of the optimal solutions are discussed.