【作者】 谭锋；

【导师】 沈世钊； 杨庆山；

【作者基本信息】 北京交通大学 ， 结构工程， 2007， 博士

【摘要】 经过近十余年来的发展，薄膜结构的基本理论己为我国一些科研人员所掌握，但是仍有一些问题尚未得到解决，如薄膜结构的褶皱分析、动力特性分析以及其在风荷载作用下可能存在的流固耦合作用分析。本文着重在前两个方面开展工作。作为薄膜结构荷载分析和褶皱分析的基础，本文首先研究了初始构形和现时构形下应力的定义，根据Kirchhoff应力和Cauchy应力之间的关系，推导了三节点三角形平面膜单元和两节点直线索单元的两种应力关系有限元列式，同时给出了与应力对应的两种应变和两种构形下本构矩阵之间的关系式。本文对褶皱判别的主应力准则、主应变准则和主应力—主应变准则进行了分析，得出了主应力—主应变准则最为适用于薄膜结构褶皱判别的结论。数值分析中处理褶皱的方法有多种，如张力场理论、可变泊松比法、修正变形梯度法、修正本构矩阵法和分叉理论等，论文对其进行了讨论，在对修正本构矩阵方法做了进一步完善后，将其应用于薄膜结构的褶皱处理，推导了单元褶皱时的公式。在前面两章理论基础上，给出了薄膜结构褶皱分析的具体方法，在本课题组编制的薄膜结构分析软件中嵌入褶皱分析模块，并利用有理论解的算例对程序进行了验证。之后对典型薄膜结构在静荷载作用下的褶皱进行了分析，得出了结构在静荷载作用下的受力特性及褶皱的影响因素。本文采用子空间迭代法编写了薄膜结构自振特性分析程序，在验证了程序的正确性之后对三种典型薄膜结构进行了动力特性分析，得出了结构自振特性与其影响因素间的关系。采用Newmark法、全Newton-Raphson迭代法和修正本构矩阵法相结合的方法实现了可同时考虑几何非线性和物理非线性的薄膜结构全过程动力分析，编写了分析程序。通过算例验证了程序的正确性，并给出了一典型薄膜结构在动荷载作用下的基本形态。利用本文编写的动力分析程序，分别对预应力和结构尺寸不同的刚性边界马鞍形薄膜结构在不同简谐荷载作用下进行了分析，得到了结构反应与荷载频率、预应力以及结构尺度的关系。按照相同的崽路对另外两种典型的结构也进行了分析，并对三种结构的反应进行了对比。最后，本文采用Davenport谱生成了脉动风速时程，利用计算流体力学方法得到结构的风压系数，分别对三类典型薄膜结构进行了风振反应分析，得到了结构在风荷载作用下的反应特性以及褶皱单元对结构受力性能的影响。最后对一实际工程进行了风致动力反应分析。更多还原

【Abstract】 In the recent years, the fundamental theories of membrane structures have been understood, while there are still some problems needed to be solved, such as Wrinkling Analysis, Dynamic Analysis and Wind-Structure Interaction Analysis. The first two problems are focused in this dissertation.As the basis of the loading and wrinkling analysis, the definitions of Kirchhoff Stress in the original reference configurations and Cauchy Stress in the updated reference configurations are studied. According to the relationship between these two stresses the finite element formulas of plan membrane unit and cable unit are developed. The relationship between the Green Strain and Almansi Strain is also presented. Further more the relationship of two constitutive matrixes is developed.There are a few criteria for the wrinkling judgment, such as Principal Stress Criterion, Principal Strain Criterion and Principal Stress-Strain Criterion. After carefully studying, Principal Stress and Strain Criterion is believed to be the most appropriate one for membrane structures wrinkling judgment. A few approaches for wrinkling analysis, such as, Tension Field Theory, Variable Poisson’s Ratio Method, Modified Deformation Tensor Method, Modified Constitutive Relationship Method and Bifurcation Buckling Theory, are introduced. After the Modified Constitutive Relationship Method is improved, it is used in the Membrane Structure Wrinkling analysis.The process of the Membrane Structure Wrinkling Analysis is given and attached to self-owned Membrane Structure Analysis Software. The validated program is applied to analyze the wrinkling of membrane structures under the static loading.The dynamic characteristics analysis program of membrane structures is programmed by Subspace Iteration Method. Natural frequencies and modes of three typical kinds of saddle shaped membrane structures are analyzed.Dynamic Analysis equations are developed in which Newmark method, Newton-Raphson Iteration method and Modified Constitutive Relationship Method are applied, geometrical nonlinearity and material nonlinearity are considered at the same time. The membrane structure dynamic analysis is programmed according to the equations. And the basic performance of a membrane structure under dynamic loading is presented.Three typical kinds of membrane structure with different pretension, dimension under different harmony loading are analyzed. The relationships between the structure response and harmony load frequency, pretension force, structural dimension are given. And the results of these three kinds of structures are compared.The fluctuating wind speed with Davenport Spectrum is generated, and the pressure coefficients of structure are gotten by using Computational Fluid Dynamics method. The Membrane Structures under the wind load are analyzed. And the performance of Membrane Structures under the dynamic wind load and the influence of membrane wrinkling are discussed. The dynamic analysis of an engineering project under wind loading is also presented.更多还原