索网式可展开天线的形态分析与优化设计
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摘要
索网式可展开天线由于包含柔性索网结构而具有重量轻、空间收纳率高等优点，该类天线目前已被广泛应用于雷达、侦查、对地观测、深空探测等领域。本文在西安电子科技大学展开天线课题组已有研究工作的基础上，对索梁组合结构的形态计算方法、索网式可展开天线的形态优化设计以及索网式可展开天线的整体结构优化设计等方面进行了深入的研究。
为提高索梁组合结构形态计算的效率，提出了索梁组合结构的结构划分方法。该方法将索梁组合结构划分为两大部分，一是内部索网结构，二是由边界索网和与其相连的框架梁单元组成的结构。基于非线性有限元法，本文对两部分结构间的预张力平衡关系进行了理论推导，提出了划分准则和划分条件。
对自身为纯索网结构且具有指定形状和拓扑形式的内部索网结构，以索单元预张力分布均匀为目标，结合平衡矩阵分析法对其进行形态优化计算，可得到索网体系的最优预张力分布。
对边界索网—梁结构，将平衡矩阵分析法与非线性有限元法结合使用，对梁单元变形影响下的边界索网进行预张力补偿，得到能够与内部索网预张力形成平衡力系的边界索网预张力。由于边界索网—梁结构比原整体结构形式简单，故对其进行的非线性有限元迭代计算的计算规模比较小、求解复杂程度也比较低。
结合上面的索网形态计算方法，提出了一种可使索网式可展开天线索网体系具有理想形态的天线整体优化方法。该方法以结构重量最轻为优化目标，以天线节点位移精度为约束条件，并结合前面提出的索梁组合结构形态迭代计算方法来对索网式可展开天线进行结构优化计算。由于优化中加入了可以使天线索网体系满足预设形态要求的预张力迭代计算，故由优化得到的天线结构可以在具有最优结构设计参数的同时，还能够保有预设的理想索网形态。
为验证上述理论方法及所编制设计软件的正确性，实际研制了2m口径索网式可展开天线模型，并进行了相关实验研究，取得了满意的结果。此外，将理论方法与软件分别应用于某17米口径正馈可展开天线与某10m口径偏馈可展开天线原理样机的工程实践中，不仅验证了方法的正确性和有效性，且指导了样机的研制工作。
Cable-mesh deployable antenna with flexible cablenet system is utilized widely inradar, reconnaissance, earth observation and deep space exploration for its light weightand small stowed volume. Based on existing results achieved by deployable antennaresearch team of Xidian University, the problems like cable pretension design forcable-beam structure, optimum design for pretension and structure of cable-meshdeployable antenna are discussed in this paper.
A structural division method that can help to improve efficiency of pretensiondesign for cable-beam structure is proposed. In this method, a cable-beam structure isdivided into inner cablenet structure and edge cablenet-beam structure. The pretensionequilibrium conditions of these two parts are studied by non-linear finite elementmethod, and based on this, division condition and division principle of the structuraldivision method is deduced in theory.
Because inner cablenet is a pure cablenet structure with given shape and topology,balance matrix analysis method is used to help obtain the best pretension distribution ofinner cablenet with the uniformity as objective.
For edge cablenet-beam structure, with obtaining equilibrium force of innercablenet’s pretension as goal, non-linear finite element method combined with balancematrix analysis method is used for pretension compensation iterative adjustment of edgecablenet that is affected by beam’s displacement. Because edge cablenet-beam structurehas less cable elements than overall structure, its non-linear finite element iterativecalculations are easier to be implemented, and its stiffness matrix is easier to be workout also.
In order to obtain optimal antenna structure with ideal cable system shape andpreset pretension distributions, an iterative optimum structural design method based oncablenet system iterative adjustment method described above is proposed here. Themathematical model of optimization selects minimum weight of structure as objective,and antenna’s shape accuracy as constraint. By combining cablenet system iterativeadjustment method to solve above mathematical model, the shape accuracy of antennacablenet system and beam can meet the constraint requirements at the same time, andthe antenna structure with both optimal weight and ideal cablenet system shape can alsobe obtained at last.
The present method and design software is applied to the development of a2m cable-mesh deployable antenna model, and the results of model experiments show thatthe present method is valid and correct. Also, the method and software is used toinstruct the development of a17m axi-symmetric reflector antenna experimentalprototype and a10m offset parabolic reflector antenna experimental prototype, and thepractical application results are satisfying as well.
为提高索梁组合结构形态计算的效率，提出了索梁组合结构的结构划分方法。该方法将索梁组合结构划分为两大部分，一是内部索网结构，二是由边界索网和与其相连的框架梁单元组成的结构。基于非线性有限元法，本文对两部分结构间的预张力平衡关系进行了理论推导，提出了划分准则和划分条件。
对自身为纯索网结构且具有指定形状和拓扑形式的内部索网结构，以索单元预张力分布均匀为目标，结合平衡矩阵分析法对其进行形态优化计算，可得到索网体系的最优预张力分布。
对边界索网—梁结构，将平衡矩阵分析法与非线性有限元法结合使用，对梁单元变形影响下的边界索网进行预张力补偿，得到能够与内部索网预张力形成平衡力系的边界索网预张力。由于边界索网—梁结构比原整体结构形式简单，故对其进行的非线性有限元迭代计算的计算规模比较小、求解复杂程度也比较低。
结合上面的索网形态计算方法，提出了一种可使索网式可展开天线索网体系具有理想形态的天线整体优化方法。该方法以结构重量最轻为优化目标，以天线节点位移精度为约束条件，并结合前面提出的索梁组合结构形态迭代计算方法来对索网式可展开天线进行结构优化计算。由于优化中加入了可以使天线索网体系满足预设形态要求的预张力迭代计算，故由优化得到的天线结构可以在具有最优结构设计参数的同时，还能够保有预设的理想索网形态。
为验证上述理论方法及所编制设计软件的正确性，实际研制了2m口径索网式可展开天线模型，并进行了相关实验研究，取得了满意的结果。此外，将理论方法与软件分别应用于某17米口径正馈可展开天线与某10m口径偏馈可展开天线原理样机的工程实践中，不仅验证了方法的正确性和有效性，且指导了样机的研制工作。
Cable-mesh deployable antenna with flexible cablenet system is utilized widely inradar, reconnaissance, earth observation and deep space exploration for its light weightand small stowed volume. Based on existing results achieved by deployable antennaresearch team of Xidian University, the problems like cable pretension design forcable-beam structure, optimum design for pretension and structure of cable-meshdeployable antenna are discussed in this paper.
A structural division method that can help to improve efficiency of pretensiondesign for cable-beam structure is proposed. In this method, a cable-beam structure isdivided into inner cablenet structure and edge cablenet-beam structure. The pretensionequilibrium conditions of these two parts are studied by non-linear finite elementmethod, and based on this, division condition and division principle of the structuraldivision method is deduced in theory.
Because inner cablenet is a pure cablenet structure with given shape and topology,balance matrix analysis method is used to help obtain the best pretension distribution ofinner cablenet with the uniformity as objective.
For edge cablenet-beam structure, with obtaining equilibrium force of innercablenet’s pretension as goal, non-linear finite element method combined with balancematrix analysis method is used for pretension compensation iterative adjustment of edgecablenet that is affected by beam’s displacement. Because edge cablenet-beam structurehas less cable elements than overall structure, its non-linear finite element iterativecalculations are easier to be implemented, and its stiffness matrix is easier to be workout also.
In order to obtain optimal antenna structure with ideal cable system shape andpreset pretension distributions, an iterative optimum structural design method based oncablenet system iterative adjustment method described above is proposed here. Themathematical model of optimization selects minimum weight of structure as objective,and antenna’s shape accuracy as constraint. By combining cablenet system iterativeadjustment method to solve above mathematical model, the shape accuracy of antennacablenet system and beam can meet the constraint requirements at the same time, andthe antenna structure with both optimal weight and ideal cablenet system shape can alsobe obtained at last.
The present method and design software is applied to the development of a2m cable-mesh deployable antenna model, and the results of model experiments show thatthe present method is valid and correct. Also, the method and software is used toinstruct the development of a17m axi-symmetric reflector antenna experimentalprototype and a10m offset parabolic reflector antenna experimental prototype, and thepractical application results are satisfying as well.
引文
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