索膜结构初始形状确定的综合设计法

本文针对膜结构找形中的最小曲面和考虑重力后的索膜结构的形状确定问题提出了一种新的综合设计法。对膜结构的最小曲面的确定问题,本文首先采用非线性有限元格式求得初始近似曲面,然后在此曲面上采用动力松弛格式得到最小曲面。此种方法比非线性有限元格式的精度有所提高,收敛速度也比动力松弛格式快得多。对考虑重力作用的索膜结构的初始形状确定问题,本文先采用非线性有限元格式得到初始近似曲面,然后在此曲面上考虑索膜的重力,仍采用非线性有限元格式得到最终需要的平衡曲面。此种方法收敛速度比一开始考虑索膜重力快,并且收敛性更好,可以得到更为精确的初始形状。

The synthetical method for form finding of cable reinforced membrane structures

The synthetical method for form finding of cable reinforced membrane structures are proposed. In order to find the minimum curve surface of membrane structures, the nonlinear finite element method was adopted to get approximate surface, then the dynamic relaxation method was used on the approximate surface to get an accuracy surface. For cable reinforced membrane structures, gravity was taken into account to find the equilibrium surface. Similarly, the approximate surface was obtained without gravity by the nonlinear element method,then the equilibrium surface was obtained considering gravity still by use of the nonlinear element method.Numerical studies showed that the synthetical method proposed in this paper could solve successfully the form finding problems of cable reinforced membrane structures. Its accuracy is better than that got simply by the nonlinear finite element method and its speed of convergence is much better than using only the dynamic relaxation method.