Integrated Analysis Theory And Software Development Of Large-scale Tensioned Membrane Structures

Membrane structure, as a kind of light weight and new type of large-scale spatial structure, is widely used in china and abroad. The theory of membrane structure has been continuously developed, however with the increasing scale and growing complexity of tensioned membrane structure, there are still many problems to be solved including integrated analysis of membrane structure with supported structure, design efficiency of integrated shape-state analysis, approaches of wrinkling analysis, modeling method of CFD and accuracy of wind load applied on the structure. This thesis focuses on these problems, and corresponding approaches are proposed. Integrated analysis and design theory of large-scale tensioned membrane structures are improved. Meanwhile, the professional software of membrane structures CAFA1.0 is updated to CAFA2.0 with the presented approaches and programming optimization techniques. Finally, all achievements are applied on complicated membrane structure projects.In view of the fact that existing beam element can not be applied directly on the finite element calculation of the membrane structure, geometrical nonlinear finite element formulations of spatial beam element (three dimensional) are derived in details, including linear stiffness matrix, nonlinear stiffness matrix, coordinate transition matrix, equivalent nodal force and nodal force increment. One auxiliary array is used to record the smallest row number of nodal degrees of freedom in the total stiffness matrix to complete element stiffness matrix integration with mixing degrees of freedom.For the key issues in large-scale tensioned membrane structure projects, four approaches are proposed which are state-fixed and shape-fixed elements method of integrated shape-state analysis, three-step design method from local part to entirety, the improved modified constitutive relationship method and facet modeling method. The detailed contents are as follows:1) Integrated calculation of large-scale tensioned membrane structures should take account of the interaction between the membrane structure and the supporting structure in the shape-state analysis. However, all exsiting integrated shape-state analysis mehods can't keep controlling points of membrane surface shape fixed. A state-fixed and shape-fixed elements method of integrated shape-state analysis is presented in the thesis. On the first step, the stress-fixed membrane element and cable element with small Young's modulus are adopted to simulate the membrane and cable (contained in membranes) respectively. The shape-fixed link element with the normal elastic modulus is used to simulate the particular cable and pole supporting structure. The beam element with the normal elastic modulus is to simulate the beam. The whole numerical model is developed to conduct the first shape-state analysis. In each calculation step, the stress-fixed elements update the configuration and keep the internal forces (stresses) constant while the shape-fixed elements update the internal forces (stresses) and keep the configuration unchanged. On the second step, basing on the shape and internal forces obtained in the former step, the shape-fixed elements are released, i.e., displacements and internal forces are updated in each iteration step. Meanwhile, other elements are the same as that of the first step. Thus, the second shape-state analysis is taken. The state-fixed and shape-fixed elements method can consider the interaction between the membrane structure and the supporting structure, keep the boundary of shape controlling points fixed and ensure the design stress state of membranes. Comparing to the results obtained from ANSYS, the proposed method is verified to be of correctness and advantages.2) In the state-fixed and shape-fixed elements method, the results of integrated shape-state analysis are usually obtained by repeating the estimation of pre-stresses and calculation constantly. It is a low efficient work for large-scale tensioned membrane structures. Thus, a three-step design method from local part to entirety is developed. Firstly, without considering the supporting structure, for typical structural unit of cable-membrane structure, the process of estimation of pre-stresses and calculation is repeated several times by means of trial calculation and revision. Then the rational results would be obtained. Secondly, according to the results obtained from the first step, the pre-stresses are applied on the cables (contained in membranes) of other structural units basing on the principle that the pre-tension linear density of cables with the same functional type is relatively equal. The special components of supporting system have a stress-fixed or shape-fixed treatment. The integrated numerical model considering supported structure is established. Finally, the two-step method of the integrated shape-state analysis is conducted. By several times of fine adjustments of pre-stress on cables (contained in membranes) of the unreasonable membrane surface shape, the results meeting the requirements can be obtained. The method breaks the conventional form-finding mode that pre-stresses of cables are estimated only with experience. Moreover, the numerical model which needs to repeat the calculation is changed from the large scale model into the small scale model. Thus, the efficiency of engineering design is improved significantly. Analysis and design of roof structure of Wuhu stadium are studied again via this method.3) The influence of wrinkling membrane on the structure mechanical characteristics can not be negligible. The appearance of wrinkling makes the stress on some regions lower or higher than others, and that can induce decrease of structure local rigidity or large strain and creep of membrane. The modified constitutive relationship method is commonly used to consider the influence of wrinkling membrane in the design. However, in the case of uniaxial wrinkling, the modified first principal stress obtained from this method may be negative. This is not true and it may cause a convergence problem. Thus an adaptive method is presented to overcome this shortcoming. Comparing the old method with the improved method, the results show that they are different. The applicability of the adaptive method is proved by practical projects.4) Wind load is one of the control loads. Basing on the discretization of finite element method, facet modeling method is proposed to simulate membrane surface rapidly and accurately by CFD and transfer wind pressure data precisely. This method is a surface modeling technique that finite element mesh is directly used to generate facet. Through compiling data interface program among AutoCAD, ANSYS, ICEM, CFX5, numerical simulation of the wind load is achieved by automatic operation of the four softwares. It makes numerical model establishment more efficient. Compared with existing analysis results and experiment results, the presented method is proved to be of high efficiency and accuracy. Meanwhile, subprograms are developed to treat with wind pressure distribution coefficient on surface and imposition of wind load, which can make wind load applied precisely in the loading analysis of tensioned membrane structure.In addition, on the basis of the techniques above and some methods including the skills of array programming, LDL factorization algorithm based on total stiffness matrix of the one-dimensional change bandwidth memory and grid node-numbering optimization (RCM), CAFA1.0 is updated to CAFA2.0. Analysis function and calculation efficiency of the software are improved dramatically. CAFA2.0 is still developed by ObjectARX and FORTRAN programming language on AutoCAD2002 platform. There are five modules in this software, which are model establishing module, shape-state forming module, natural vibration module, loading module and cutting pattern module. The integrated shape-state analysis, natural vibration analysis and loading analysis on the roof structure of Qingdao Yizhong stadium are studied by CAFA2.0, the results show that the software can adapt to the analysis and design of large-scale tensioned membrane structures.