膜结构找力分析的无矩理论和优化的复位平衡法

膜结构工程的实践和形状确定理论要求对膜结构进行找力分析。本文结合无矩理论推导了膜结构自平衡预应力确定的解析方程,研究表明膜结构自平衡预应力由膜曲面的特性和边界条件决定。根据相似原理提出了索膜结构找力分析的数值方法——复位平衡法,并且依据曲面上单元之间的关联对这种方法进行了优化。与无矩理论的计算结果比较显示优化的复位平衡法有很高的计算精度,能够应用到实际工程的精确分析中。

Bending-free theory and optimized reposition balance method, used to find the self-balance prestress of tensility structures

Tensility structures engineering and form-finding theory require to find the self-balance prestress of the structures.Used the bending-free theory,analytic formulae about the self-balance prestress were deduced.And the analytic formulae indicate that the self-balance prestress is mostly determined by character of the membrane curved face and the boundary condition.Based on the similarity principle,the numerical method:reposition balance method was put forward to find the prestress.This method was optimized by means of the relationship of element on the membrane curved face.Comparison between the analytic method and the numerical one indicates that the optimized reposition balance method has very high precision and can accurately analyze actual engineering.