椭圆鞍形单层正交索网结构解析计算方法与形态优化  

ANALYTICAL METHOD AND SHAPE OPTIMIZATION OF SADDLE SINGLE-LAYER ORTHOGONAL CABLE-NET STRUCTURE

作　　者：王博厚 孙逊 方立新[3] WANG Bo-hou;SUN Xun;FANG Li-xin(School of Civil Engineering,Southeast University,Nanjing,Jiangsu 210096,China;Architects&Engineers Co.,Ltd.of Southeast University,Nanjing,Jiangsu 210096,China;School of Architecture,Southeast University,Nanjing,Jiangsu 210096,China)

机构地区：[1]东南大学土木工程学院,江苏南京210096 [2]东南大学建筑设计研究院有限公司,江苏南京210096 [3]东南大学建筑学院,江苏南京210096

出　　处：《工程力学》2024年第1期103-113,共11页Engineering Mechanics

摘　　要：常见的单层正交索网结构由马鞍面和椭圆柱面相切而成,该类型结构在国内外的大型场馆、公共建筑中得到广泛应用。该文提出一种连续化解析计算方法,以求解椭圆鞍形单层正交索网结构的变形、内力和最优形态,求解过程中仅需解一元方程。计算方法利用平衡方程、变形协调方程,以竖向位移为未知量,推导了正交单层索网连续化计算公式,采用伽辽金法求得近似解。在此基础上,以外环梁平面内弯矩最小为优化目标,以中央承重索垂度为优化变量,以索力、竖向位移和矢跨比为约束条件,利用外环梁弯矩计算公式,通过求解方程得到结构的最优形态并给出优化流程。最后对一个简单算例分别采用有限元法与解析法计算,验证了解析法所得位移、索力、外环弯矩和形态优化结果的准确性。在结构初步设计阶段,利用该解析计算方法,可快速得到荷载态下结构的位移、受力情况和最优形态,避免了有限元法编程、反复试算的繁杂过程。The common single-layer orthogonal cable-net structure is formed by the intersection of saddle surface and elliptic cylinder.This structure is widely used in large-scale stadiums and public buildings at home and abroad.A method is proposed to obtain the deformation,internal force and optimal shape of elliptic saddle single-layer orthogonal cable-net structure by using continuous analytical method.In this process,only the one-dimensional equation needs to be solved.The continuous calculation formula of orthogonal single-layer cable-network is deduced by the balance equation and deformation coordination equation,and takes the vertical displacement as the unknown which approximate solution is obtained by Galerkin method.On this basis,it takes the minimum in-plane moment of the outer-ring beam as the optimization objective,takes the sag of the central bearing cable as the optimization variable,and takes the cable force,vertical displacement and rise span ratio as the constraints.And then,it uses the formula for calculating the outer ring bending moment to obtain the optimum structure and the optimization process is given.Finally,a simple example is calculated by the finite element method and analytical method respectively to verify the accuracy of the calculation formulas of displacement,cable force,outer-ring moment and shape optimization results obtained by the analytical method.In the preliminary design stage of the structure,the displacement,stress and optimal shape can be quickly obtained by using this method,which avoids the complicated process of finite element programming and repeated calculation.

关 键 词：单层索网结构 解析解 连续化理论 形态优化 有限元 

分 类 号：TU318.1[建筑科学—结构工程] TU393.3