【作者】 毛国栋；

【导师】 孙炳楠；

【作者基本信息】 浙江大学 ， 结构工程， 2004， 博士

【摘要】 索膜结构的设计过程可以分为三个阶段。第一阶段是找形设计阶段。即在建筑师给定预想的曲面形状的前提下，找出与此曲面相接近的初始平衡状态—初始张力的大小、分布和几何形状。第二阶段是荷载分析阶段，即找形分析获得的曲面在各种可能荷载组合的作用下，求解其变形、位移、索膜内力及判别薄膜是否有褶皱产生或索是否有松弛现象。第三阶段是裁剪设计阶段，其目的是将已经通过荷载分析的三维膜曲面转化成离散的平面膜片，在市售的薄膜卷材上进行下料分析，获得可以施工的裁剪下料图。 对于索膜找形分析，目前普遍常用的是非线形有限元法、动力松弛法和力密度法。但以上每一种方法都存在着缺陷。本文将动力松弛法和非线性有限元法合为一体，提出了全新的综合设计法。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。同时针对找形分析中的动力松弛格式，本文提出了全新的控制网格变形的动力松弛法，此方法能够有效地解决膜结构找形分析中网格的大变形问题，克服了在曲率较小处网格过于稀疏的缺陷，在曲率较小处保证了单元的密度和初始构形的精度，并且收敛性较好，为准确进行荷载分析和裁剪分析奠定了基础。 对于静力分析，本文提出了全新的考虑膜材主轴方向的非线性有限元法。对双曲形和伞形索膜结构，分别计算了索膜结构在不同参数下的结构响应，得到了各个参数对结构静力性能的影响，指出了膜材主轴方向在静力分析中不可忽视。 风荷载是设计中的控制荷载。本文针对封闭式薄膜结构和敞开式薄膜结构推导了全新的非线性流固耦合风振响应公式，其中耦合因素包括附加空气质量、气承刚度和声致阻尼以及相对运动速度，并将此理论应用于一气弹模型的计算，获得了位移、速度、加速度时程以及加速度均方根。计算值同试验结果吻合良好，证明了本方法的正确性。 膜结构的裁剪分析，主要包括裁剪线的确定、曲面的展开和张力释放。对于裁剪线的确定，本章采用了曲面的最短线—测地线。根据最小势能原理，详细推导了全新的测地线生成的非线性有限单元法。对于曲面的展开，详细推导了全新的基于弹簧—质点系统的薄膜结构曲面展开算法。同时，对曲面展开常用的非线性有限元法进行了研究，并指出了其缺点。最后针对膜片的张力释放的几何补偿问题，首次创新地探讨了膜面初始预张力方向对几何补偿的影响。更多还原

【Abstract】 The whole procedure of cable-reinforced membrane structures design is composed of three parts The first one is form-finding analysis. The aim of this part is to find an initial equilibrium state , the value and distribution of tension force and the geometry of the surface, when the location of the control points are confirmed. The second part is load analysis. Bases on the form-finding, the stress, strain and displacement etc are calculated under loads. Also the problem of membrane drape and cable relaxation should be considered during this procedure. The third part is cutting pattern finding. In this section, the whole surface of membrane structures is divided into several membrane strips. Then the strips are developed into plane to get the cutting pattern on the membrane roll.For form-finding of membrane structures, the common methods mainly indued three theory: nonliner FEM, dynamic relaxation method and force density method. But each method has disadvantages by itself. The synthetical method for form finding of cable-reinforced membrane structures are proposed in this paper. In order to find the minimum surface of membrane structures, firstly the nonlinear finite element method is adopted to get approximate surface, then the dynamic relaxation method is used on the approximate surface to get an accuracy surface. For cable-reinforced membrane structures, gravity is taken into account to find the equilibrium surface. Similarly, the approximate surface is obtained without gravity by the nonlinear element method, then the equilibrium surface is obtained considering gravity by the nonlinear element method. Numerical studies show that the synthetical method proposed in this paper can solve successfully the form finding problems of cable-reinforced membrane structures.A new technique of controlling mesh distortion is presented during the form-finding of membrane structures by dynamic relaxation method. In the course of form-finding, triangle plate element was applied . The damp which was proportion to the velocity of the edge deformation between the two nodes of element was introduced. The node force corresponding to damp was used to control the mesh distortion. Numerical studies show that the method proposed by this paper can successfully control the severe distortion of mesh and retain the density of elements during the membrane form-finding when the damp viscosity coefficient is in a limited scale. Especially this method can avoid the sparseness of mesh in the location of lower curvature and have good convergence characteristic.For loads analysis , a new method considering the effect of meterial main axia is proposed using FEM. For hyperboloid and highpoint shape membran structures, the influence of different parameter to the character of the structures under load is calculated and discussed. The main axid of material should not be neglected.The effect to membrane strucutres of the wind load is prominent. Based on the characteristics of the membrane structures, wind-induced nonlinear coupling dynamic response analysis which can be applied to closed membrane structures is developed and the added air mass the pneumatic stiffness and the acoustical damping of the closed membrane structures are deduced. Applying the method to an aeroelastic model of wind tunnel test, the displacement the velocity and the acceleration of corresponding prototype structure in time domain are obtained. The calculation values have good agreement with the results of the experiment. Numerical studies show that the method proposed in the paper can successfully solve the wind-induced nonlinear coupling dynamic response problems of the closed membrane structures. The present study solves the important problem in the analysis of membrane structures and establishes the foundation of the closed membrane structures design.Cutting pattern finding has three procedures: cutting lines obtainment, curve surface into plane and tension force release. A new method is proposed for geodesic lines generation by nonlinear element method in c更多还原