WO2019120239A1 - 一种抑制褶皱的空间薄膜结构夹具形状优化设计方法 - Google Patents

一种抑制褶皱的空间薄膜结构夹具形状优化设计方法 Download PDF

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WO2019120239A1
WO2019120239A1 PCT/CN2018/122264 CN2018122264W WO2019120239A1 WO 2019120239 A1 WO2019120239 A1 WO 2019120239A1 CN 2018122264 W CN2018122264 W CN 2018122264W WO 2019120239 A1 WO2019120239 A1 WO 2019120239A1
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film
fixture
shape
film structure
design
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罗阳军
邢健
亢战
李明
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Dalian University of Technology
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    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design

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  • the invention belongs to the field of aerospace film structure design, and relates to a shape optimization design method of a space film structure.
  • the flexible film has the advantages of light weight, ability to withstand large deformation, easy folding/unfolding, and the like, and is widely used in aerospace space structures.
  • the film and the unwinding mechanism are connected by a rigid jig, and when unfolded in space, tensile stress is generated in the film surface to achieve its specific function.
  • the film can hardly withstand the in-plane compressive stress, it is prone to out-of-plane buckling, that is, wrinkling, under external load.
  • the physical test and finite element analysis of the structural form given by the traditional design show that the space film structure is prone to generate a large number of wrinkles after unfolding, which will seriously affect the shape accuracy and performance of the space structure.
  • the invention provides a shape optimization design method for a support fixture, which can improve the minimum principal stress of the film and prepare the wrinkles in the film, and can simultaneously produce a high-precision shape requirement of the space film and a large-area working film surface requirement. Ensure that the film has a large enough working area.
  • the invention is suitable for the fixture design of the space film structure such as the space antenna and the solar sail, and is advantageous for formulating the film wrinkles, ensuring the structural working performance, and not increasing any manufacturing, launching and running costs.
  • the utility model relates to a shape optimization design method for a film structure fixture for suppressing wrinkles, which mainly comprises two parts: shape optimization of a clamp component and numerical verification of a space film structure, and the specific steps are as follows:
  • the first step is to optimize the shape of the fixture components.
  • the traditional design of the film jig edge is generally a straight line. After the displacement tensile load is applied by the clamp, the minimum principal stress of the film is zero or negative, so that wrinkles occur and the shape requirements are not satisfied.
  • the present invention redesigns the jig form by means of shape optimization, so that the minimum principal stress of the film is positive, and the wrinkles are generated.
  • the rigid fixture component is simulated by a material having a sufficiently large elastic modulus; a plurality of design points are selected on the connection line between the film and the fixture, and a B-spline function is used to interpolate to generate a fixture and a film boundary;
  • the elastic modulus of the clamp material is not less than 1000 times that of the film.
  • Constraint Determine the amount of film area used as the lower limit of the constraint. The amount of the area used is not less than 95% of the initial film area.
  • Design Variable The coordinates of the design point on the fixture edge.
  • the minimum and maximum optimization targets are condensed and transformed to obtain an equivalent optimization objective function.
  • the condensing transformation includes a p-norm method, wherein the expression of the p-norm condensing function is Where S * is the minimum principal stress expected to be achieved, taking 0.1-1.0, and p is the coagulation parameter, taken as 20-50.
  • the global optimization algorithm is used to solve the problem, and the global optimal solution of the fixture shape optimization problem is obtained.
  • the optimization algorithm is a proxy model algorithm, a genetic algorithm or a gradient-based optimization algorithm.
  • the second step is to verify the spatial film structure numerically.
  • the nonlinear post-buckling analysis was carried out by introducing random defects of the film to verify the effect of the optimized space film structure.
  • the beneficial effects of the invention are: before the optimization, the clamp is in a straight line form, and the film region has a minimum principal stress of zero or a negative value under the tensile load, thereby generating wrinkles and failing to meet the requirements of high-precision profile. After the clamp of the "curved edge" form obtained by the method of the invention, the film no longer wrinkles under the load, and the minimum principal stress is positive, and the film area can be ensured.
  • the fixture has a relatively simple configuration, is easy to manufacture and manufacture, and is advantageous for assembly and space deployment.
  • the structure satisfies the performance requirements by finite element analysis and ground static test.
  • FIG. 1 is a structural design field of a space thin film antenna according to an embodiment of the present invention. In the picture: Indicates the displacement load applied to the fixture.
  • Figure 2(a) is an optimal design of a single fixture for a space film antenna structure.
  • Fig. 2(b) is a structural view showing the structure of a space film antenna designed by the method of the present invention.
  • FIG. 3 is a solar sail structure design field according to an embodiment of the present invention.
  • Figure 4(a) is an optimal design of a single fixture for a solar sail structure.
  • Fig. 4(b) is a view showing the effect of the solar sail structure designed by the method of the present invention.
  • the first step is to optimize the shape of the fixture components.
  • Constraint Determine the amount of film area used as the lower limit of the constraint. The amount of the area used is 95% of the initial film area.
  • Design Variable The coordinates of the design point on the fixture edge.
  • step 1.4 according to the shape optimization model established in step 1.3), the condensed transformation is performed on the minimum maximal optimization target, and the condensed transformation is Where S * is the minimum principal stress expected to be achieved, taking 0.5, and p is the condensing parameter, taken as 20.
  • the global optimization algorithm (such as Kriging proxy model method) is used to solve the problem, and the global optimal solution of the fixture shape optimization problem is obtained, and finally the "bow” and "convex” are obtained.
  • the shape of the space film antenna and the solar sail fixture are shown in Figures 2(a) and 4(a), respectively.
  • the second step is to verify the spatial film structure numerically.

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Abstract

一种抑制褶皱的空间薄膜结构夹具形状优化设计方法，解决空间薄膜结构在传统夹具拉伸作用下容易产生褶皱现象的问题。在非线性有限元分析基础上，通过优化夹具的形状改变加载边界条件，最大化薄膜区域内单元的最小主应力，调控薄膜的主应力分布，采用全局优化算法寻找全局最优设计，进而获得"弓形"和"凸形"边界的新型夹具形式，以达到完全拟制褶皱的目的。该方法不仅拟制薄膜中褶皱的产生，而且不对薄膜进行裁剪，能够保证薄膜具有足够大的工作面积；适合于空间天线、太阳帆等空间薄膜结构的夹具设计，有利于拟制薄膜褶皱，保证结构工作性能，并且不增加任何制造、发射及运行成本。

Description

一种抑制褶皱的空间薄膜结构夹具形状优化设计方法 技术领域
本发明属于航天薄膜结构设计领域，涉及一种空间薄膜结构的夹具形状优化设计方法。
背景技术
柔性薄膜具备重量轻、能承受大变形、易于折叠/展开等优点，广泛用于航天空间结构。薄膜和展开机构之间通过刚性夹具连接，在太空中展开后使得膜面内产生张拉应力，用以实现其特定功能。然而，由于薄膜几乎不能承受面内压缩应力，在外荷载作用下容易出现面外屈曲，即褶皱现象。对传统设计给出的结构形式进行物理试验及有限元分析表明：空间薄膜结构在展开后容易产生大量褶皱，会严重影响空间结构的形面精度和使用性能。针对此问题，通过在薄膜内部或边缘进行挖孔，虽然能够抑制褶皱，但必然会减少薄膜面积。为得到既能保证高精度形面要求，又具有足够大薄膜工作面积的有效结构形式，一个非常有效的方法是采用优化设计的手段重新设计夹具结构形式，通过改变薄膜的位移加载边界条件来调整薄膜内部区域的应力分布情况，使整个薄膜区域的最小主应力增大为正值，达到预期的完全张拉状态。
发明内容
针对空间薄膜的高精度形面要求及大面积工作膜面要求，本发明提供一种支撑夹具的形状优化设计方法，该方法能够提高薄膜的最小主应力，拟制薄膜中褶皱的产生，同时能够保证薄膜具有足够大的工作面积。本发明适合于空间天线、太阳帆等空间薄膜结构的夹具设计，有利于拟制薄膜褶皱，保证结构工作性能，并且不增加任何制造、发射及运行成本。
为了达到上述目的，本发明的技术方案为：
一种抑制褶皱的薄膜结构夹具形状优化设计方法，主要包括夹具部件形状优 化和空间薄膜结构数值验证两部分，具体步骤如下：
第一步，对夹具部件进行形状优化
传统设计给出的薄膜夹具边线一般为直线，在通过夹具施加位移拉伸载荷作用后，薄膜局部的最小主应力为零或负值，从而发生褶皱现象，不满足形面要求。为得到满足膜面精度设计要求和面积要求的空间薄膜结构，本发明通过形状优化的手段重新设计夹具形式，使得薄膜最小主应力为正值，拟制褶皱产生。
1.1)根据结构的尺寸要求和实际加载情况确定设计域，划分有限元单元网格，建立带夹具的薄膜结构有限元模型。所述的薄膜结构有限元模型中，刚性夹具部件用弹性模量足够大的材料进行模拟；在薄膜与夹具的连接线上选取若干设计点，用B样条函数插值生成夹具和薄膜边界；所述夹具材料的弹性模量不小于薄膜的1000倍。
1.2)对刚性夹具施加位移荷载，采用非线性有限元分析方法对所述薄膜结构有限元模型进行分析。
1.3)以薄膜区域内最小主应力最大化为最终设计目标，对夹具的边线进行设计，构造形状优化模型：
(a)目标：使薄膜区域的最小主应力最大化，即
Figure PCTCN2018122264-appb-000001
其中，e为有限元单元编号，S 2为最小主应力，Ω m为薄膜区域。
(b)约束：确定薄膜面积用量，作为约束下限。所述的面积用量不小于初始薄膜面积的95％。
(c)设计变量：夹具边线上设计点的坐标。
1.4)根据步骤1.3)建立的形状优化模型，对极小极大优化目标进行凝聚变换，得到等效的优化目标函数。所述凝聚变换包括p-norm方法，其中p-norm凝 聚函数的表达式为
Figure PCTCN2018122264-appb-000002
其中S *为期望达到的最小主应力，取0.1-1.0，p为凝聚参数，取为20-50。
1.5)根据步骤1.3)和1.4)建立的形状优化模型，采用全局优化算法进行求解，得到夹具形状优化问题的全局最优解。所述优化算法为代理模型算法、遗传算法或基于梯度的优化算法。
第二步，对空间薄膜结构进行数值验证
在第一步1.5)得到的优化后夹具形式的基础上，通过引入薄膜随机缺陷，进行非线性后屈曲分析，对优化后的空间薄膜结构进行效果验证。
本发明的有益效果为：在优化前，夹具为直线形式，薄膜区域在拉伸载荷作用下存在最小主应力为零或负值的情况，从而产生褶皱，不满足高精度形面要求。采用本发明方法得到的“曲边”形式的夹具后，薄膜在荷载作用下不再产生褶皱，最小主应力为正值，也能够保证薄膜面积。该夹具构型比较简单，易于加工制造，且有利于装配以及空间展开，经有限元分析和地面静力试验验证，该结构满足性能要求。
附图说明
图1为本发明实施例提供的一种空间薄膜天线结构设计域。图中：
Figure PCTCN2018122264-appb-000003
表示施加在夹具上的位移荷载。
图2(a)为空间薄膜天线结构的单个夹具最优设计图。
图2(b)为采用本发明方法设计得到的空间薄膜天线结构效果图。
图3为本发明实施例提供的一种太阳帆结构设计域。
图4(a)为太阳帆结构的单个夹具最优设计图。
图4(b)为采用本发明方法设计得到的太阳帆结构效果图。
具体实施方式
以下结合技术方案和附图详细叙述本发明的具体实施例。
第一步，对夹具部件进行形状优化
1.1)根据结构的尺寸要求和实际加载情况确定设计域，并划分有限元单元网格，建立带夹具的薄膜结构有限元模型。刚性夹具部件用1000倍薄膜的弹性模量进行模拟。在薄膜与夹具的连接线上选取若干设计点，用B样条函数插值生成夹具和薄膜边界。图1为空间薄膜天线结构的设计域，根据结构上下对称性，每个夹具选取11个设计点，图3为太阳帆结构设计域，根据其对称性，每个夹具选取9个设计点。两种初始结构在拉伸荷载作用下均存在明显的褶皱行为。
1.2)对刚性夹具施加位移荷载，采用非线性有限元分析方法对薄膜结构有限元模型进行分析，获得每个单元的最小主应力。
1.3)以薄膜区域内最小主应力最大化为最终设计目标，对夹具的边线进行设计，构造形状优化模型：
(a)目标：使薄膜区域的最小主应力最大化，即
Figure PCTCN2018122264-appb-000004
其中，e为有限元单元编号，S 2为最小主应力，Ω m为薄膜区域；
(b)约束：确定薄膜面积用量，作为约束下限。所述的面积用量为初始薄膜面积的95％。
(c)设计变量：夹具边线上设计点的坐标。
1.4)根据步骤1.3)建立的形状优化模型，对极小极大优化目标进行凝聚变换，所述凝聚变换为
Figure PCTCN2018122264-appb-000005
其中S *为期望达到的最小主应力，取0.5，p为凝聚参数，取为20。
1.5)根据步骤1.3)和1.4)建立的形状优化问题，采用全局优化算法(如 Kriging代理模型方法)进行求解，得到夹具形状优化问题的全局最优解，最终得到“弓形”、“凸形”边界的夹具形式。空间薄膜天线和太阳帆的夹具形状分别见图2(a)和图4(a)所示。
第二步，对空间薄膜结构进行数值验证
在第一步1.5)得到的优化后夹具形式的基础上，通过引入薄膜随机缺陷，进行非线性后屈曲分析，对优化后的空间薄膜结构进行效果验证。结果表明优化得到的“弓形”夹具(如图2(b)所示，薄膜面外位移接近于0，没有局部褶皱现象，图中两侧颜色较深的为夹具，浅灰色区域表示为薄膜)和“凸形”夹具(如图4(b)所示，薄膜面外位移接近于0，没有局部褶皱现象，图中四个角黑色区域表示为夹具，浅灰色区域表示为薄膜)分别有利于提高两种结构的薄膜最小主应力，在不裁剪薄膜、不增加运行成本的情况下避免了局部褶皱现象，满足高精度形面要求。

Claims (5)

  1. 一种抑制褶皱的空间薄膜结构夹具形状优化设计方法，其特征在于以下步骤：
    第一步，对夹具部件进行形状优化
    1.1)根据结构的尺寸要求和实际加载情况确定设计域，划分有限元单元网格，建立带夹具的薄膜结构有限元模型；所述的薄膜结构有限元模型中，刚性夹具部件用弹性模量大的材料进行模拟；在薄膜与夹具的连接线上选取若干设计点，用B样条函数插值生成夹具和薄膜边界；
    1.2)对刚性夹具施加位移荷载，采用非线性有限元分析方法对所述薄膜结构有限元模型进行分析；
    1.3)以薄膜区域内最小主应力最大化为最终设计目标，对夹具的边线进行设计，构造形状优化模型：
    (a)目标：使薄膜区域的最小主应力最大化，即
    Figure PCTCN2018122264-appb-100001
    其中，e为有限元单元编号，S 2为最小主应力，Ω m为薄膜区域；
    (b)约束：确定薄膜面积用量，作为约束下限；所述的面积用量不小于初始薄膜面积的95％；
    (c)设计变量：夹具边线上设计点的坐标；
    1.4)根据步骤1.3)建立的形状优化模型，对极小极大优化目标进行凝聚变换；
    1.5)根据步骤1.3)和1.4)建立的形状优化问题，采用全局优化算法进行求解，得到夹具形状优化问题的全局最优解；
    第二步，对空间薄膜结构进行数值验证
    在第一步1.5)得到的优化后夹具形式的基础上，通过引入薄膜随机缺陷，进行非线性后屈曲分析，对优化后的空间薄膜结构进行效果验证。
  2. 根据权利要求1所述的一种抑制褶皱的空间薄膜结构夹具形状优化设计方法， 其特征在于，步骤1.1)中所述材料的弹性模量不小于薄膜的1000倍。
  3. 根据权利要求1或2所述的一种抑制褶皱的空间薄膜结构夹具形状优化设计方法，其特征在于，步骤1.4)中所述凝聚变换包括p-norm方法，其中p-norm凝聚函数的表达式为
    Figure PCTCN2018122264-appb-100002
    其中S *为期望达到的最小主应力，取0.1-1.0，p为凝聚参数，取为20-50。
  4. 根据权利要求1或2所述的一种抑制褶皱的空间薄膜结构夹具形状优化设计方法，其特征在于，步骤1.5)所述优化算法为代理模型算法、遗传算法或基于梯度的优化算法。
  5. 根据权利要求3所述的一种抑制褶皱的空间薄膜结构夹具形状优化设计方法，其特征在于，步骤1.5)所述优化算法为代理模型算法、遗传算法或基于梯度的优化算法。
PCT/CN2018/122264 2017-12-21 2018-12-20 一种抑制褶皱的空间薄膜结构夹具形状优化设计方法 Ceased WO2019120239A1 (zh)

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