索网和膜结构的最小曲面分析  

THE MINIMAL SURFACE ANALYSIS OF CABLE-NETS AND FABRIC STRUCTURES

作　　者：易发安[1] 胡加珠[2] 岳艳芳[2] 

机构地区：[1]同济大学建筑设计研究院同远公司,上海200092 [2]东南大学土木工程学院,南京210096

出　　处：《工程力学》2004年第4期167-171,共5页Engineering Mechanics

摘　　要：数学上,最小曲面指的是(在给定边界条件下的)面积最小曲面。而在索膜结构分析中,最小曲面指的是具有某种力学特征的能量最小曲面。推导了等应力膜索网分析模型的应变、应力关系,对索膜结构的能量最小曲面进行了分析。根据曲面的能量函数,论文分析比较了对应相同能量极值的两种曲面(等力密度曲面与等拉力曲面)的力学特性以及两种曲面存在时对应的不同边界条件。Mathematic minimal surface is a surface of minimal area under prescribed boundary condition. Engineering minimal surface, however, refers to a surface of minimal energy with some mechanic attributes. In this paper, the strain and stress equations of cable net model for equivalent stress membrane analysis are developed and the minimal energy surface of cable and membrane structures is analyzed. The mechanic attributes and different boundary conditions of two available minimal surfaces, equivalent force density surface and equivalent tension surface, are compared.

关 键 词：索膜结构 最小曲面 能量方法 力密度法 边界条件 

分 类 号：TU383[建筑科学—结构工程] TU393.3