索膜结构非线性有限元分析

1、索膜结构非线性有限元分析        【中文摘要】索膜结构的突出特点之一就是外形的多样性,曲面存在着无穷的可能性,其设计也迥异于传统结构。由于索膜结构属于柔性结构,变形后位移很大,所以在计算中必须考虑其几何非线性。我国在这方面的研究近几年才开始,尚不够成熟,相关书籍也未几。本文首先扼要先容了索膜结构的国内外现状和薄膜结构的分类及特点,在薄膜结构分类中,张拉索膜结构是应用最为广泛和灵活的一种膜结构类型,这是本文研究的重点。索膜结构的分析是由初始形态确定、受荷分析和薄膜裁剪这三部分构成,这三部分相互联系、相互制约。柔

2、性的索膜材仅当加以适当的预应力时才具有确定的外形和抵抗外荷载的能力,才能真正成为“结构”,因此初始形态分析在膜结构设计中具有非常重要的意义。对于初始形态分析,现有的研究方法主要有三种,分别是力密度法、动力松弛法和非线性有限元法。这三种方法各有利弊,由于非线性有限元法具有较好的计算精度,所以本文选用了这种方法。其次,现在几乎所有索膜软件和理论都是基于空间三角形平面膜单元与空间两节点直线杆单元的组合。且该类软件也为数未几,有些软件功能还不完善。重庆大学研究生苏文章(2005)、李仁佩(2006)提出了一种精度较高且计算工作量较小的四节点等参索单元理论,并成功运用于单索结构和索网结构分析中。本文在此

3、基础上提出了一种新型的单元组合形式,即四节点等参索单元与空间三角形平面膜单元组合,其目的是将四节点等参索单元理论推广到索膜结构研究分析中。在扼要先容了钢索和膜材的物理力学性能后,本文基于空间三角形平面膜单元和四节点等参索单元的有限元理论,推导了其有限元平衡方程,并组合成索膜结构有限元平衡方程。为了验证该理论的正确性,本文使用了MATLAB语言,分别编制了两节点直线索单元与三角形平面膜单元组合的找形程序(C2M3)和四节点等参索单元与三角形平面膜单元组合的找形和荷载分析程序(C4M3)。并使用若干算例,进行了两个程序找形的对比。同时又运用CAFA、3D3S和ANSYS等软件进行计算与所编程序进行

4、对比,发现此类单元组合,不仅满足计算精度,而且还可以降低迭代次数,可以应用于工程结构设计。最后,本文利用C4M3程序研究了索膜结构膜材参数对结构找形和荷载分析的影响,比如两个方向预应力比、索的预拉力与薄膜预张力之比等因素,得到了关于索膜形态和荷载分析的一些结论和建议。');【Abstract】 One of the outstanding trait of the cable-membrane structure is the diversity of shape, curved su*ce existing infinite possibilities,and the design

5、is quite dissimilar to traditional structure. The structure of cable-membrane is belonging to flexible structure, and have a great displacement after deforming, so we must take geometrical non-linear problem into account when calculating. The relevant researches of this aspect has just begun in thes

6、e years in our country, so it's not fully mature, and we don't have much relevant literatures.This * introduces briefly the domestic and overseas Status quo, and the category as well as traits of the cable-membrane structure at first. Tensile structure is the most widely and freely used styl

7、e of the cable-membrane structure, and it's the keystone of the article. Analysis of the structure is made up of determining initial form, the analysis of bearing load,cutting out of the membrane, and the three parts are correlative and restrict to each other.Only when bringing prestress to bear

8、 on the flexible material of cable-membrane, can it have the definite shape and the capability of bearing external load, can it be the real "structure", so the analysis of initial form have a very important significance in designing the cable-membrane structure. There are three methods of

9、research ,such as force density method, dynamic relaxation method and the nonlinear finite element method to analyze initial form. These three methods each have their own advantages and disadvantages, The nonlinear finite element method have a better precision in calculation, so this article chose i

10、t.Secondly,almost all the software and theory of cable-membrane are based on the combination of the spatial * plane membrane element and the spatial two-node straight-line element. There are not a good many of the quantity of this kind of software, and the function of some software is not perfect. P

11、ostgraduate.Su Wenzhan(g2005) and Li Renpe(i2006) in Chongqing University propose a theory of four-node isoparametric cable element which has a better precision in calculation, at the same time a lower workload ,and succeeds in the analysis of single cable structure and cable net structure. In this

12、* ,a new form of combinatorial element, namely a mixed finite element model combining the four-node isoparametric cable element and the spatial * plane membrane element is presented. The purpose of this * is promoting the four-node isoparametric cable element theory to the research of cable-membrane

13、 structure.After introducing physical and mechanical capability of cable and membrane briefly, this * introduce the finite element theory of the spatial * plane membrane element and the four-node isoparametric cable element, derivate finite element equation, and become the finite element equation of

14、 cable-membrane structure.To validate the validity of this theory, the * uses MATLAB language, respectively establish the program of form-finding and load analysis which is combined two-node straight-line element with * plane membrane element (C2M3), and a similar program which is combined four-node

15、 isoparametric cable element and * plane membrane element (C4M3). This * compares the two programs via certain examples . At the same time the * compares the results which come form CAFA、3D3S and ANSYS with the program which was established by ourselves, finding that this kind of combination not only meet the precision in calculation, but also reduce the number of iterations,and can be used in engineering design.Finally, the * uses C4M3 to research the influence of the membrane's parameter in form-finding and load analysis, such the ratio of pre