WO2018126465A1 - 一种用于消除薄膜结构拉伸褶皱的优化设计方法 - Google Patents

一种用于消除薄膜结构拉伸褶皱的优化设计方法 Download PDF

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WO2018126465A1
WO2018126465A1 PCT/CN2017/070594 CN2017070594W WO2018126465A1 WO 2018126465 A1 WO2018126465 A1 WO 2018126465A1 CN 2017070594 W CN2017070594 W CN 2017070594W WO 2018126465 A1 WO2018126465 A1 WO 2018126465A1
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film structure
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film
wrinkles
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罗阳军
亢战
李明
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Dalian University of Technology
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  • the invention belongs to the technical field of aerospace thin film structure design and graphene nano material structure design, and proposes an optimized design method of film structure for the purpose of eliminating wrinkles.
  • the invention adopts a new optimization model and method for cutting the boundary of the film and designing the hole inside to realize the regulation of the main stress distribution of the film structure under the tensile load, thereby effectively eliminating the wrinkles which may occur in the stretched state of the film. Completely achieve wrinkle-free film structure.
  • space film structures are increasingly used in aerospace structures, such as solar sails, inflatable antennas, and film mirrors.
  • aerospace structures such as solar sails, inflatable antennas, and film mirrors.
  • These structures make full use of the advantages of easy folding, easy development, light weight and small size of the film, which can solve the contradiction between the limitation of the volume and quality of the rocket carrier and the increasing requirements of large size and large diameter.
  • Human application prospects since the bending rigidity is very small, the film is prone to out-of-plane buckling, that is, wrinkles, even in a tensioned state. In aerospace applications, it is often required that such films must maintain a smooth surface.
  • graphene is called “the king of new materials” that scientists may "completely change the 21st century". It has great potential in the fields of mobile devices, aerospace and new energy batteries.
  • Graphene is a quasi-two-dimensional material structure with only one atomic layer thickness and a thickness of approximately 0.335nm, which has very similar mechanical properties to planar films, will also produce out-of-plane wrinkles under tensile load, which will affect its excellent electrical and mechanical properties. Therefore, in many applications it is necessary to eliminate wrinkles in the graphene structure.
  • Film wrinkles are a highly geometrically nonlinear post-buckling phenomenon that can often be eliminated by introducing biaxial stresses by changing external loads or constraining boundary conditions.
  • the above methods are almost impossible to achieve in aerospace thin film structures and graphene structures due to space expansion, light weight, and nanofabrication techniques. Therefore, how to eliminate wrinkles by changing the topology and shape of the structure itself without changing the external load and the constraint boundary conditions is undoubtedly a very important but challenging problem.
  • some simple film structures are designed by experience or test methods, which cannot be promoted and applied.
  • it is urgent to develop a universal optimization design method for the complete elimination of wrinkles to find innovative topological forms automatically, accurately and efficiently, and to realize wrinkle-free film structure. .
  • the invention mainly solves the problem that the film structure is prone to wrinkle under the tensile load, and proposes an optimized design method of the film structure for completely eliminating wrinkles.
  • an optimized design method of the film structure for completely eliminating wrinkles.
  • the stress state of the film is adjusted, and the topology distribution technique is used to design the distribution of the film material, thereby obtaining a structural form with curved boundaries or holes.
  • This method ensures the complete elimination of the wrinkles, the precise positioning of the shape and the hole, the high degree of automation of the optimized design, and the research and development efficiency of the wrinkle-free design of the film structure.
  • An optimized design method for eliminating stretch wrinkles of a film structure comprising the following steps:
  • the first step is to optimize the wrinkle-free topology of the film structure.
  • Constraint 1 The minimum principal stress of each finite element is greater than zero, ie Where e is the finite element number, ⁇ 1 is the maximum principal stress, and ⁇ 2 is the minimum principal stress;
  • Constraint 2 Determine the area of the film area as the upper limit of the area constraint; the film area is 60%-90% of the design area.
  • Design variables the relative density ⁇ e of the finite element elements in the design domain, ⁇ e between ⁇ and 1, representing the distribution of the film material at the cell; where ⁇ is a positive number much less than 1;
  • the second step is to optimize the shape of the film structure.
  • the specific geometric parameters of the film structure boundary and the hole are optimized, and the minimum principal stress constraint is considered to obtain more detailed and accurate structural shape parameters.
  • the obtained structural form satisfies the requirement of minimum principal stress and maximizes the overall stiffness.
  • the configuration is relatively simple, easy to manufacture, and has a nonlinear post-buckling limit element analysis and experimental verification to achieve true wrinkle-free.
  • FIG. 1 is a design field of a four-corner tensile structure according to an embodiment of the present invention.
  • Fig. 2(a) is an optimum design of the four-corner tensile structure when the film area ratio is 70%.
  • Fig. 2(b) is an optimum design of the four-corner tensile structure when the film area ratio is 80%.
  • FIG. 3 is a design field of a two-end tensile structure with a hard block in the middle according to an embodiment of the present invention.
  • Fig. 4 is an optimum design drawing of the tensile structure at both ends with a hard block in the middle of the film area ratio of 80%.
  • the first step is to optimize the wrinkle-free topology of the film structure.
  • Constraint 1 The minimum principal stress of each finite element is required to be greater than zero, ie Where e is the finite element number, ⁇ 1 is the maximum principal stress, and ⁇ 2 is the minimum principal stress.
  • Constraint 2 The amount of film area is given as the upper limit of the area constraint. The film area is used in an amount of 70% and 80% of the entire design area.
  • Constraint relaxation processing is adopted for the constraint after the step (3) transformation to avoid the stress singular solution phenomenon.
  • the second step is to optimize the shape and shape of the film structure.
  • the specific geometric parameters of the film structure boundary and the hole are optimized, and the minimum principal stress constraint is considered to obtain more detailed and accurate structural shape parameters.
  • the obtained configuration is relatively simple, easy to process and manufacture. After non-linear post-buckling limit element analysis and full-scale test verification, the entire film structure has no wrinkles, which verifies the effectiveness of the proposed method.
  • the essence of the invention is to obtain a configuration with a curved boundary or a hole by using a topology optimization method to control and optimize the minimum principal stress of the entire film to achieve the purpose of wrinkle-free. It modifies the optimization model, method, and scheme described in the foregoing embodiments, or performs equivalent replacement on some or all of the method features (for example, using a horizontal set or an explicit curve to describe structural boundaries and holes, and adopting other topology optimizations.
  • the method, the change of the objective function or the specific form of the constraint, etc. does not depart from the scope of the method and the embodiments of the embodiments of the present invention.

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Abstract

一种用于消除薄膜结构拉伸褶皱的优化设计方法，解决了宏观薄膜结构和石墨烯结构在拉伸荷载作用下容易产生褶皱现象的问题。在平面有限元分析基础上，通过约束每个单元的最小主应力为正值，调控薄膜结构的主应力分布，采用拓扑优化技术对薄膜材料分布进行设计，进而获得带有曲线边界或孔洞的结构形式，以达到完全消除褶皱的目的。这种方式保证了对褶皱的完全消除，可实现复杂薄膜结构外形和孔洞的精确定位，优化设计的自动化程度高，将保证薄膜结构无皱化创新设计的研发效率。

Description

一种用于消除薄膜结构拉伸褶皱的优化设计方法 技术领域
本发明属于航空航天薄膜结构设计和石墨烯纳米材料结构设计技术领域，提出了一种以消除褶皱现象为目的的薄膜结构优化设计方法。本发明采用一种新的优化模型及方法对薄膜边界进行裁剪和对内部进行孔洞设计，实现拉伸载荷下薄膜结构主应力分布的调控，从而有效消除薄膜在拉伸状态下可能产生的褶皱，完全实现薄膜类结构的无皱化。
背景技术
随着科技的发展和人类文明的进步，作为一种典型的结构型式，空间薄膜结构越来越多地被用于航空航天结构，如太阳帆、充气天线、薄膜反射镜等。这些结构充分利用了薄膜易折叠\易展开、重量轻、体积小等优势，可以解决火箭运载对体积、质量的限制与不断增加的大尺寸、大口径使用要求之间的矛盾，因此极具诱人的应用前景。但是，由于弯曲刚度非常小，薄膜即使在张拉状态下也很容易发生面外屈曲现象，即褶皱。在航空航天应用中，经常要求这类薄膜必须保持表面光滑。例如薄膜反射镜，固定边界条件容易导致薄膜产生褶皱，进而影响表面光的反射从而降低成像的精确性。太阳帆的四个角受到集中力也易产生褶皱，从而影响光子反射角度及太阳光子压力方向。并且，大的褶皱还可能导致光子能量的局部集中引起局部高温，发生蠕变现象影响薄膜寿命。因此，如何有效消除薄膜褶皱现象在航空航天领域显得尤其重要。
另外，在纳米材料领域，作为目前发现的最薄、强度最大、导电导热性能最强的一种新型纳米材料，石墨烯被科学家称为可能“彻底改变21世纪”的“新材料之王”，在移动设备、航空航天、新能源电池领域极具发展潜力。石墨烯(Graphene)是一种只有一个原子层厚度的准二维材料结构，厚度大约为 0.335nm，具有非常类似于平面薄膜的力学特性，在拉伸荷载作用下也会产生面外褶皱现象，将影响其优良的电学、力学等性能。因此，在很多应用中有必要消除石墨烯结构中的褶皱现象。
薄膜褶皱是一个高度几何非线性的后屈曲现象，在建筑领域通常可以通过改变外荷载或约束边界条件来引入双轴应力加以消除。然而，在航天结构或者纳米材料结构中，由于空间展开、轻质量、纳米制造技术等方面的限制，上述的方法在航天薄膜结构和石墨烯结构中几乎不可能实现。因此，如何在不改变外荷载和约束边界条件的情况下，只通过改变结构自身的拓扑和形状达到消除褶皱的目的，无疑是一个非常重要但具有挑战性的问题。在一些已有研究和工程应用中，多采取经验或者试验方法对部分简单薄膜结构进行外形设计，无法进行推广和应用。对于具有复杂荷载或约束边界的薄膜结构，亟需开展一种以完全消除褶皱为目的的普适性优化设计方法，自动、准确、高效地寻找创新性拓扑形式，实现薄膜类结构的无皱化。
发明内容
本发明主要解决薄膜结构在拉伸荷载作用下容易产生褶皱现象的问题，提出一种以完全消除褶皱为目的的薄膜结构优化设计方法。在平面有限元分析基础上，通过控制每个单元的最小主应力为正值，调节薄膜的应力状态，采用拓扑优化技术对薄膜材料分布进行设计，进而获得带有曲线边界或孔洞的结构形式，以达到完全消除褶皱的目的。这种方式保证了对褶皱的完全消除，可实现外形和孔洞的精确定位，优化设计的自动化程度高，将保证薄膜结构无皱设计的研发效率。
为了达到上述目的，本发明的技术方案为：
一种用于消除薄膜结构拉伸褶皱的优化设计方法，具体包括以下步骤：
第一步，对薄膜结构进行无皱化拓扑优化
(1)根据结构的尺寸要求和实际加载情况确定设计域，建立薄膜结构拓扑优化初始设计；在设计域中施加荷载和约束边界，划分有限元单元网格；
(2)建立薄膜结构无皱化拓扑优化模型，使薄膜结构的整体刚度最大化或者整体柔顺性最小化
a)约束一：每个有限元单元最小主应力大于零，即
Figure PCTCN2017070594-appb-000001
其中，e为有限元单元编号，σ1为最大主应力，σ2为最小主应力；
b)约束二：确定薄膜面积用量，作为面积约束上限；所述的薄膜面积用量为设计域面积的60％-90％。
c)设计变量：设计域内有限元单元的相对密度ρe，ρe取值为α和1之间，代表单元处薄膜材料的分布；其中，α是一个远小于1的正数；
(3)根据步骤(2)建立的拓扑优化模型，对约束一等效变换为
Figure PCTCN2017070594-appb-000002
其中I1和J2分别为有限元单元的应力第一和第二不变量；
(4)对步骤(3)变换后的约束采用约束松弛处理，避免应力奇异解现象；采用SIMP惩罚策略和优化算法进行迭代求解，得到薄膜结构最优材料分布；
第二步，对薄膜结构进行形状优化设计
在第一步(4)得到的薄膜结构拓扑形式的基础上，对薄膜结构边界及孔洞的具体几何参数进行优化，考虑最小主应力约束，获得更加详细和准确的结构形状参数。得到的结构形式满足最小主应力为正的要求和最大化整体刚度，构型比较简单，易于加工制造，经有非线性后屈曲限元分析和试验验证，实现真正的无皱化。
本发明的有益效果为：
在薄膜结构优化前，该类结构在拉伸载荷作用下存在显著的大面积褶皱现 象。采用本发明的“无皱化”结构形式的薄膜后，通过数值模拟和试验考核，整个薄膜的最小主应力均保证为大于零的正值，完全观测不到褶皱产生。结构容易加工制造，只需要进行简单的裁剪和开孔。同时，本发明所建立的无皱化优化方法避免了在优化过程中进行复杂的后屈曲计算，所耗费的工作量极小，将显著提高设计效率，有望成为航空航天领域、微纳米领域中薄膜结构创新性设计的有效方法。
附图说明
图1为本发明实施例提供的一种四角拉伸结构设计域。
图2(a)为薄膜面积比为70％时四角拉伸结构最优设计图。
图2(b)为薄膜面积比为80％时四角拉伸结构最优设计图。
图3为本发明实施例提供的一种中间具有硬块的两端拉伸结构设计域。
图4为薄膜面积比为80％时中间具有硬块的两端拉伸结构最优设计图。
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，对薄膜结构进行无皱化拓扑优化
(1)根据结构的尺寸要求和实际加载情况确定设计域，建立薄膜结构拓扑优化初始设计；在设计域中施加荷载和约束边界并划分有限元网格。图1为四角拉伸结构的设计域，划分有限元网格数N＝6400个，图3为中间具有刚性硬块的两端拉伸结构设计域，划分有限元网格数N＝5000个。两种初始结构在拉伸荷载作用下均存在明显的褶皱行为。
(2)建立薄膜结构无皱化拓扑优化模型：
(a)目标：薄膜结构的整体刚度最大化或者整体柔顺性最小化。
(b)约束一：要求每个有限元单元的最小主应力大于零，即
Figure PCTCN2017070594-appb-000003
其中e为有限元单元编号，σ1为最大主应力，σ2为最小主应力。
(c)约束二：给定薄膜面积用量，作为面积约束上限。所述的薄膜面积用量为整个设计域面积的70％和80％。
(d)设计变量：设计域内单元的相对密度ρe，取值为α＝0.001和1之间，代表单元处薄膜材料的分布。
(3)根据步骤(2)建立的拓扑优化模型，对约束一等效变换为
Figure PCTCN2017070594-appb-000004
其中I1和J2分别为应力第一和第二不变量。
(4)对步骤(3)变换后的约束采用约束松弛处理，避免应力奇异解现象。采用cosine-type松弛方法，其中cosine-type松弛函数的表达式为θ＝(1-cos(ρe·π))/2。
(5)优化模型采用SIMP惩罚策略和优化算法进行迭代求解，得到薄膜结构最优材料分布，分别见图2和图4。
第二步，对薄膜结构进行细节形状优化设计
在第一步(5)得到的薄膜结构拓扑的基础上，对薄膜结构边界和孔洞的具体几何参数进行优化，考虑最小主应力约束，获得更加详细和准确的结构形状参数。得到的构型比较简单，易于加工制造，经有非线性后屈曲限元分析和全尺寸试验验证，整个薄膜结构没有褶皱发生，验证了本发明所提方法的有效性。
本发明的实质是采用拓扑优化方法得到具有曲边边界或孔洞的构型，以对整个薄膜最小主应力进行控制和优化，达到无皱化目的。其对前述各实施例所记载的优化模型、方法、方案进行修改，或者对其中部分或者全部方法特征进行等同替换(例如采用水平集或者显式曲线对结构边界与孔洞进行描述、采用其他拓扑优化方法、改变目标函数或约束具体形式等)，并不使相应方法与方案的本质脱离本发明各实施例方法与方案的范围。

Claims (4)

  1. 一种用于消除薄膜结构拉伸褶皱的优化设计方法，其特征在于以下步骤：
    第一步，对薄膜结构进行无皱化拓扑优化
    (1)根据结构的尺寸要求和实际加载情况确定设计域，建立薄膜结构拓扑优化初始设计；在设计域中施加荷载和约束边界，划分有限元单元网格；
    (2)建立薄膜结构无皱化拓扑优化模型，使薄膜结构的整体刚度最大化或者整体柔顺性最小化
    a)约束一：每个有限元单元最小主应力大于零，即
    Figure PCTCN2017070594-appb-100001
    其中，e为有限元单元编号，σ1为最大主应力，σ2为最小主应力；
    b)约束二：确定薄膜面积用量，作为面积约束上限；所述的薄膜面积用量为设计域面积的60％-90％；
    c)设计变量：设计域内有限元单元的相对密度ρe，ρe取值为α和1之间，代表单元处薄膜材料的分布；其中，α是一个远小于1的正数；
    (3)根据步骤(2)建立的拓扑优化模型，对约束一等效变换为
    Figure PCTCN2017070594-appb-100002
    其中I1和J2分别为有限元单元的应力第一和第二不变量；
    (4)对步骤(3)变换后的约束采用约束松弛处理，避免应力奇异解现象；采用SIMP惩罚策略和优化算法进行迭代求解，得到薄膜结构最优材料分布；
    第二步，对薄膜结构进行形状优化设计
    在得到的薄膜结构拓扑的基础上，对薄膜结构边界及孔洞的具体几何参数进行优化，考虑最小主应力约束，获得更加详细和准确的结构形状参数。
  2. 根据权利要求1所述的优化设计方法，其特征在于，第一步中所述的约束松弛处理包括ε松弛方法或qp松弛方法。
  3. 根据权利要求1所述的优化设计方法，其特征在于，所述的约束松弛处理包括cosine-type松弛方法，其中cosine-type松弛函数的表达式为θ＝(1-cos(ρe·π))/2。
  4. 根据权利要求1或2或3所述的优化设计方法，其特征在于，所述的优化算法为准则法、MMA算法、ESO方法或Level set方法。
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