極小曲面法による膜構造の形状決定に関する研究 : 非線形解法の検討と収束性に関する考察

Abstract

Membrane structures keep their shapes only by in-plane stresses and, therefore, when the shapes of membrane structures are determined, minimal surfaces are often adopted as the original surfaces in the design process of membrane structures, because the shapes of the minimal surfaces completely coincide with those of the equally tensioned surfaces which are supposed to be the ideal original surfaces for this kind of structures. In the practical analysis of the minimal surfaces, Newton-Raphson method is generally adopted as the nonlinear numerical calculation method. However, the converged solutions can not be always obtained by using Newton-Raphson method, especially in the case where each nodal point has three degrees-of-freedom. In the present paper, in order to enable us to analyze the minimal surfaces even any conditions, SQP(Sequential Quadratic Programming) method is newly adopted as the nonlinear calculation method and the characteristic of the convergence of this problem is discussed.