Research on Automatic Layout and Optimization of Reinforced Crossed Cable Nets in Inflatable Membrane Structures
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摘要: 充气膜作为典型的柔性结构,需要索网加劲来保证结构的刚度与稳定性,然而在索网加劲膜结构的设计过程中通常将加劲索网与膜面简化为直接连接,忽略了索膜之间不能紧密贴合的问题,这种简化处理方式为膜结构的设计安全带来了一定的隐患。研究充气膜索网生成及优化方法对于解决索膜滑移问题、提高膜结构刚度与承载能力至关重要。为此,提出了基于热应力有限元的索段生成方法与索网自动布置优化方法。其中索段生成方法利用热应力有限元法在膜曲面上生成测地线,沿测地线布置的索段可以与膜面贴合更加紧密,从而解决索膜滑移问题,保证了结构的安全性与可靠性。在索段生成方法的基础上,以斜交形式布置膜面索网,对膜结构案例进行荷载分析,针对其局部间距需要调整、索网整体受力分布不均匀等问题,分别提出局部索网优化布置与均匀化布置2种优化布置方法。以矩形平面大跨充气膜结构为例详细阐述了索网布置与优化方法,并对不同优化方案进行了对比: 1)对分别采用索网布置方法得到的充气膜结构(布置方案1)与传统索网膜结构进行受力性能分析,包括两者的索网轴力分布和膜面应力分布情况。2)对方案1分别采用局部索网优化布置与均匀化布置得到方案2与方案3,分析两种方案与方案1在受力性能上的差异与优势。3)综合2种优化布置方法的优点,在方案2、3的基础上,提出稀疏中间索网、加密边缘索网的组合优化方案得到方案4,统计了4种方案索网与膜面的各项受力指标。
研究结果表明:1)两种索网的最大索轴力均集中于索网的对角点位置处,但传统斜向索网在此处的索段轴力远大于方案1索段轴力,即所提出的索网布置方法与传统方法相比有一定的优化与改善。2)局部优化布置方法可以有效改善索网局部受力过大的情况,但对膜面应力与膜面变形影响不明显;均匀化布置方法可以改善索网整体受力情况,但会使局部索段与膜面受力增大,对膜面变形影响不明显;3)新的优化布置方案可以同时达到减少索网用钢量和改善索网受力情况的优化目标,证明了该优化方案的可行性。Abstract: As a typical flexible structure, inflatable membranes require cable net reinforcement to ensure the stiffness and stability of the structure. However, in the design process of cable net reinforced membrane structures, the stiffening cable nets and membrane surface are usually simplified as direct connections, ignoring the problem of tight adhesion between cables and membranes. This simplified approach brings certain hidden dangers to the design safety of membrane structures. Studying the generation and optimization methods of inflatable membrane cable nets is crucial for solving the problem of cable slip and improving the stiffness and bearing capacity of membrane structures. Therefore, this paper proposes a cable segment generation method based on thermal stress finite element and an automatic cable net layout optimization method. The cable segment generation method utilizes the thermal stress finite element method to generate geodesic lines on the membrane surface. The cable segments arranged along the geodesic lines can fit more tightly with the membrane surface, thereby solving the cable-membrane slip problem and ensuring the safety and reliability of the structure. On the basis of the cable segment generation method, the membrane surface cable nets are arranged in an oblique form for load analysis of membrane structure cases. Two optimization layout methods, namely local cable net optimization layout and uniform layout, are proposed to address issues such as the need to adjust local spacing and uneven overall force distribution of the cable nets. Taking the rectangular plane long-span inflatable membrane structure as an example, the cable net layout and optimization methods were elaborated in detail, and different optimization schemes were compared.1) A stress performance analysis was conducted on the inflatable membrane structure (Scheme I) obtained by using the cable mesh arrangement method and the traditional cable net membrane structure, including the axial force distribution of the cable nets and the stress distribution on the membrane surface of both. 2) For Scheme I, local cable net optimization and a uniform layout were used to obtain Schemes Ⅱ and Ⅲ, and the differences and advantages in stress performance between the two schemes and Scheme I were analyzed. 3) Based on the advantages of two optimization layout methods, a combined optimization scheme featuring sparse intermediate cable nets and densely arranged edge cable nets was proposed on the basis of Schemes Ⅱ and Ⅲ to obtain Scheme Ⅳ. The various force indicators of the cable nets and membrane surfaces of the four schemes were statistically analyzed.
The research results indicated that:1) the maximum axial forces of the two cable nets were concentrated at the diagonal position of the cable nets, and the axial force of the cable segment in the traditional diagonal cable net was much greater than that in Scheme I, indicating that the proposed cable net layout method has made certain optimization and improvement compared to the traditional method; 2) the local optimization layout method effectively improved the situation of excessive local stress on the cable net, but its effects on the membrane surface stress and deformation were not significant; the uniform arrangement method improved the overall stress situation of the cable net, but it would increase the stress on local cable segments and membrane surfaces, and the effects on the membrane surface deformation were not significant; 3) the new optimized layout scheme simultaneously achieved the dual objectives of reducing the amount of steel used in the cable net and improving its stress situation, proving the feasibility of this optimization scheme. -
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