CN106777768B - Optimal design method for eliminating tensile wrinkles of film structure - Google Patents
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Abstract
The invention discloses an optimization design method for eliminating tensile wrinkles of a film structure, and solves the problem that a macroscopic film structure and a graphene structure are easy to wrinkle under the action of tensile load. On the basis of plane finite element analysis, the minimum principal stress of each unit is restrained to be a positive value, the principal stress distribution of the film structure is regulated, the film material distribution is designed by adopting a topological optimization technology, and then the structural form with a curve boundary or a hole is obtained, so that the aim of completely eliminating wrinkles is fulfilled. The mode ensures that wrinkles are completely eliminated, the accurate positioning of the appearance and the holes of the complex film structure can be realized, the automation degree of the optimized design is high, and the research and development efficiency of the wrinkle-free innovative design of the film structure can be ensured.
Description
Technical Field
The invention belongs to the technical field of aerospace film structure design and graphene nano material structure design, and provides a film structure optimization design method aiming at eliminating a wrinkle phenomenon. The invention adopts a new optimization model and a new optimization method to cut the film boundary and design the inner holes, and realizes the regulation and control of the main stress distribution of the film structure under the tensile load, thereby effectively eliminating the wrinkles possibly generated by the film in the tensile state and completely realizing the wrinkle-free of the film structure.
Background
With the development of science and technology and the advancement of human civilization, as a typical structure type, a space film structure is increasingly used for aerospace structures such as a solar sail, a gas-filled antenna, a film mirror and the like. The structures fully utilize the advantages of easy folding/unfolding, light weight, small volume and the like of the film, and can solve the contradiction between the limitation of rocket carrying on the volume and the mass and the continuously increased use requirements of large size and large caliber, thereby having attractive application prospect. However, since the bending stiffness is very small, the film is prone to out-of-plane buckling, i.e., wrinkling, even in the stretched state. In aerospace applications, it is often desirable that such films must maintain a smooth surface. For example, a thin film mirror, the fixed boundary condition may easily cause the thin film to wrinkle, thereby affecting the reflection of surface light and reducing the imaging accuracy. Four corners of the solar sail are easily wrinkled due to concentrated force, so that the photon reflection angle and the solar photon pressure direction are influenced. Moreover, large wrinkles may cause local concentration of photon energy to cause local high temperature, and creep phenomenon may affect the life of the film. Therefore, how to effectively eliminate the film wrinkling phenomenon is particularly important in the field of aerospace.
In addition, in the field of nano materials, as a novel nano material which is the thinnest, the largest in strength and the strongest in electric conduction and heat conduction performance and is discovered at present, graphene is called as the king of new materials which can be completely changed in the 21 st century by scientists, and has great development potential in the fields of mobile equipment, aerospace and new energy batteries. Graphene (Graphene) is a quasi-two-dimensional material structure with the thickness of only one atomic layer, the thickness of the Graphene is about 0.335nm, the Graphene has mechanical characteristics very similar to those of a planar film, an out-of-plane wrinkle phenomenon can be generated under the action of tensile load, and excellent electrical and mechanical properties of the Graphene can be affected. Therefore, it is necessary to eliminate the phenomenon of wrinkling in the graphene structure in many applications.
Film wrinkling is a highly geometrically nonlinear post-buckling phenomenon that can be eliminated in the construction field by introducing biaxial stresses, usually by varying external loads or constraint boundary conditions. However, in the aerospace structure or the nanomaterial structure, the above-described method is hardly implemented in the aerospace thin film structure and the graphene structure due to limitations in space expansion, light weight, nano fabrication technology, and the like. Therefore, how to eliminate the wrinkles by only changing the topology and shape of the structure without changing the external load and constraint boundary conditions is undoubtedly a very important but challenging problem. In some existing research and engineering applications, the appearance design of a part of simple film structures is mostly carried out by adopting experience or test methods, and the popularization and the application cannot be carried out. For a thin film structure with a complex load or a constraint boundary, a universal optimization design method aiming at completely eliminating wrinkles needs to be developed, an innovative topological form is automatically, accurately and efficiently searched, and wrinkle-free of the thin film structure is realized.
Disclosure of Invention
The invention mainly solves the problem that the film structure is easy to wrinkle under the action of tensile load, and provides a film structure optimization design method for completely eliminating wrinkles. On the basis of plane finite element analysis, the stress state of the film is adjusted by controlling the minimum principal stress of each unit to be a positive value, and the distribution of the film material is designed by adopting a topology optimization technology, so that a structural form with a curve boundary or a hole is obtained, and the aim of completely eliminating wrinkles is fulfilled. The mode ensures that wrinkles are completely eliminated, the accurate positioning of the appearance and the holes can be realized, the automation degree of the optimized design is high, and the research and development efficiency of the wrinkle-free design of the film structure can be ensured.
In order to achieve the purpose, the technical scheme of the invention is as follows:
an optimized design method for eliminating the stretching wrinkles of a film structure specifically comprises the following steps:
firstly, carrying out wrinkle-free topological optimization on the thin film structure
(1) Determining a design domain according to the size requirement and the actual loading condition of the structure, and establishing a topological optimization initial design of the thin film structure; applying load and constraint boundaries in a design domain, and dividing finite element unit grids;
(2) establishing a wrinkle-free topological optimization model of the film structure to maximize the overall rigidity or minimize the overall flexibility of the film structure
a) Restraining one: the minimum principal stress of each finite-element being greater than zero, i.e.
Wherein e is a finite element sheetElement number, σ 1 Is the maximum principal stress, σ 2 Is the minimum principal stress;
b) and (2) constraining: determining the area consumption of the film as an upper limit of area constraint; the area usage of the thin film is 60% -90% of the area of the design domain.
c) Designing variables: relative density rho of finite element elements in design domain e ，ρ e The value is between alpha and 1, and represents the distribution of the thin film material at the unit; wherein α is a positive number much less than 1;
(3) according to the topological optimization model established in the step (2), the constraint equivalence transformation is carried out
In which I 1 And J 2 A first and a second invariant of stress of the finite element unit respectively;
(4) constraint relaxation treatment is adopted for the constraint transformed in the step (3), so that the stress singular solution phenomenon is avoided; carrying out iterative solution by adopting an SIMP punishment strategy and an optimization algorithm to obtain the optimal material distribution of the thin film structure;
second, the shape of the film structure is optimally designed
And (5) optimizing specific geometric parameters of the boundaries and holes of the film structure on the basis of the topological form of the film structure obtained in the first step (4), and obtaining more detailed and accurate structural shape parameters by considering the minimum principal stress constraint. The obtained structural form meets the requirement that the minimum principal stress is positive and the maximum integral rigidity, the configuration is simple, the processing and the manufacturing are easy, and the real wrinkle-free performance is realized through nonlinear post-buckling element-limiting analysis and experimental verification.
The invention has the beneficial effects that:
before the structure of the film is optimized, the structure has obvious large-area wrinkling phenomenon under the action of tensile load. After the film in the wrinkle-free structural form is adopted, the minimum principal stress of the whole film is ensured to be a positive value larger than zero through numerical simulation and test examination, and wrinkles are not observed completely. The structure is easy to process and manufacture, and only simple cutting and hole forming are needed. Meanwhile, the wrinkle-free optimization method avoids complex post-buckling calculation in the optimization process, consumes extremely small workload, obviously improves the design efficiency, and is expected to become an effective method for innovative design of film structures in the aerospace field and the micro-nano field.
Drawings
Fig. 1 is a design domain of a four-corner stretching structure according to an embodiment of the present invention.
FIG. 2(a) is an optimum design diagram of a four-corner stretching structure when the area ratio of the film is 70%.
FIG. 2(b) is an optimal design diagram of a four-corner stretching structure when the area ratio of the film is 80%.
FIG. 3 is a schematic diagram of a design domain with a hard block in the middle of the design domain for a two-end tensile structure according to an embodiment of the present invention.
FIG. 4 is an optimal design diagram of a two-end stretching structure with a hard block in the middle when the area ratio of the film is 80%.
Detailed Description
The following detailed description of the embodiments of the invention refers to the accompanying drawings.
Firstly, carrying out wrinkle-free topological optimization on the thin film structure
(1) Determining a design domain according to the size requirement and the actual loading condition of the structure, and establishing a topological optimization initial design of the thin film structure; and applying load and constraint boundaries in a design domain and dividing a finite element mesh. Fig. 1 is a design domain of a four-corner stretching structure, where the number of divided finite element grids N is 6400, fig. 3 is a design domain of a two-end stretching structure with a rigid hard block in the middle, and the number of divided finite element grids N is 5000. The two initial structures have obvious folding behavior under the action of tensile load.
(2) Establishing a wrinkle-free topological optimization model of the film structure:
(a) the target is as follows: the overall stiffness of the thin-film structure is maximized or the overall compliance is minimized.
(b) Restraining one: requiring the minimum principal stress of each finite-element to be greater than zero, i.e.
Wherein e is the finite element number, σ 1 Is the maximum principal stress, σ 2 Is the minimum principal stress.
(c) And (2) constraining: the film area dose is given as the upper limit of the area constraint. The film area dosage is 70% and 80% of the whole design domain area.
(d) Designing variables: relative density ρ of cells in design domain e The value α, between 0.001 and 1, represents the distribution of the film material at the unit.
(3) According to the topological optimization model established in the step (2), equivalent transformation to constraint is carried out
Wherein I 1 And J 2 The first and second invariant of stress, respectively.
(4) And (4) constraint relaxation treatment is adopted for the constraint transformed in the step (3), so that the stress singular solution phenomenon is avoided. Adopting a cosine-type relaxation method, wherein the expression of the cosine-type relaxation function is (1-cos (rho) ═ c e ·π))/2。
(5) And (3) carrying out iterative solution on the optimization model by adopting a SIMP punishment strategy and an optimization algorithm to obtain the optimal material distribution of the thin film structure, which is shown in the figure 2 and the figure 4 respectively.
Secondly, carrying out detailed shape optimization design on the thin film structure
And (4) optimizing specific geometric parameters of the boundaries and holes of the film structure on the basis of the topology of the film structure obtained in the first step (5), and obtaining more detailed and accurate structural shape parameters by considering the minimum principal stress constraint. The obtained configuration is simple, the processing and the manufacturing are easy, the nonlinear post-buckling element-limiting analysis and the full-size test verify that the whole film structure has no wrinkles, and the effectiveness of the method provided by the invention is verified.
The essence of the invention is that the configuration with the curved edge boundary or the hole is obtained by adopting a topological optimization method so as to control and optimize the minimum main stress of the whole film and achieve the purpose of wrinkle prevention. Modifications to the optimization models, methods, and schemes described in the foregoing embodiments, or equivalent substitutions of some or all of the method features (for example, describing structure boundaries and holes by level sets or explicit curves, using other topological optimization methods, changing objective functions or specific forms of constraints, etc.) are made without departing from the scope of the methods and schemes of the embodiments of the present invention.
Claims (4)
1. An optimized design method for eliminating the stretching wrinkles of a film structure is characterized by the following steps:
firstly, carrying out wrinkle-free topological optimization on the thin film structure
(1) Determining a design domain according to the size requirement and the actual loading condition of the structure, and establishing a topological optimization initial design of the thin film structure; applying load and a constraint boundary in a design domain, and dividing a finite element unit grid;
(2) establishing a wrinkle-free topological optimization model of the film structure to maximize the overall rigidity or minimize the overall flexibility of the film structure
a) Restraining one: minimum principal stress of each finite element is greater than zero, i.e.
Wherein e is the finite element number, σ 2 Is the minimum principal stress;
b) and (2) constraining: determining the area usage of the film as an upper limit of area constraint; the area usage of the film is 60% -90% of the area of the design domain;
c) designing variables: relative density rho of finite element units in design domain e ，ρ e The value is between alpha and 1, and represents the distribution of the thin film material at the unit; wherein α is a positive number much less than 1;
(3) according to the topological optimization model established in the step (2), equivalent transformation to constraint is carried out
In which I 1 And J 2 Respectively a stress first invariant and a stress second invariant of the finite element unit;
(4) constraint relaxation treatment is adopted for the constraint transformed in the step (3), so that the stress singular solution phenomenon is avoided; performing iterative solution by adopting a SIMP punishment strategy and an optimization algorithm to obtain the optimal material distribution of the thin film structure;
second, the shape of the film structure is optimally designed
On the basis of the obtained film structure topology, specific geometric parameters of the film structure boundary and the holes are optimized, and more detailed and accurate structure shape parameters are obtained by considering the minimum principal stress constraint.
2. The method of claim 1, wherein the constraint relaxation process in the first step comprises an epsilon relaxation process or a qp relaxation process.
3. The optimal design method of claim 1, wherein the constraint relaxation process comprises a cosine-type relaxation method, wherein the cosine-type relaxation function has an expression of θ (1-cos (ρ) ═ e ·π))/2。
4. The optimal design method according to claim 1, 2 or 3, wherein the optimization algorithm is a criteria method, an MMA algorithm, an ESO method or a Level set method.
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| CN108133097B (en) * | 2017-12-21 | 2021-01-19 | 大连理工大学 | Space film structure clamp shape optimization design method for inhibiting wrinkles |
| CN111285336B (en) * | 2018-12-10 | 2023-02-03 | 北京清正泰科技术有限公司 | Method for eliminating two-dimensional material wrinkles |
| CN112800642B (en) * | 2020-12-29 | 2022-07-19 | 中国人民解放军国防科技大学 | Film wrinkle strength evaluation method and system based on nonlinear finite element |
| CN112784457B (en) * | 2021-01-19 | 2022-05-20 | 中国人民解放军国防科技大学 | Thin film structure reinforcing band layout optimization method and system based on genetic algorithm |
| CN113221201B (en) * | 2021-05-12 | 2023-08-04 | 西安电子科技大学 | Folding design method of small-curvature paraboloid-of-revolution film |
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