CN106777768B - Optimal design method for eliminating tensile wrinkles of film structure - Google Patents

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

An Optimal Design Method for Eliminating Tensile Wrinkles in Film Structures

technical field

The invention belongs to the technical field of aerospace thin film structure design and graphene nanomaterial structure design, and proposes a thin film structure optimization design method aiming at eliminating wrinkle phenomenon. The invention adopts a new optimization model and method to cut the boundary of the film and design the holes in the interior, so as to realize the regulation of the principal stress distribution of the film structure under the tensile load, so as to effectively eliminate the possible wrinkles of the film in the stretched state. Completely achieve wrinkle-free film-like structures.

Background technique

With the development of science and technology and the progress of human civilization, as a typical structural type, space thin-film structures are increasingly used in aerospace structures, such as solar sails, inflatable antennas, and thin-film mirrors. These structures make full use of the advantages of easy folding and unfolding of films, light weight and small size, which can solve the contradiction between the limitation of rocket carrying on volume and quality and the increasing requirements for large size and large caliber use, so they are very attractive. human application prospects. However, due to the very small bending stiffness, the film is prone to out-of-plane buckling, or wrinkling, even in tension. In aerospace applications, such films are often required to maintain a smooth surface. For example, thin-film mirrors, fixed boundary conditions can easily lead to wrinkles in the thin film, which in turn affects the reflection of surface light and reduces the accuracy of imaging. The four corners of the solar sail are also prone to wrinkles due to the concentrated force, which affects the photon reflection angle and the direction of the solar photon pressure. In addition, large wrinkles may also lead to local concentration of photon energy and cause local high temperature, and the creep phenomenon will affect the life of the film. Therefore, how to effectively eliminate the phenomenon of film wrinkles is particularly important in the aerospace field.

In addition, in the field of nanomaterials, as a new type of nanomaterial with the thinnest, the strongest, and the strongest electrical and thermal conductivity found so far, graphene is called by scientists as the "king of new materials" that may "completely change the 21st century". It has great potential for development in the fields of mobile devices, aerospace, and new energy batteries. Graphene is a quasi-two-dimensional material structure with a thickness of only one atomic layer, with a thickness of about 0.335 nm. It will affect its excellent electrical and mechanical properties. Therefore, it is necessary to eliminate the wrinkling phenomenon in the graphene structure in many applications.

Membrane wrinkling is a highly geometrically nonlinear post-buckling phenomenon that can usually be eliminated in the architectural field by introducing biaxial stresses by changing external loads or restraining boundary conditions. However, in aerospace structures or nanomaterial structures, due to the limitations of space expansion, light weight, and nanofabrication technology, the above methods are almost impossible to achieve in aerospace thin film structures and graphene structures. Therefore, how to eliminate wrinkles only by changing the topology and shape of the structure itself without changing the external loads and constraint boundary conditions is undoubtedly a very important but challenging problem. In some existing research and engineering applications, experience or experimental methods are mostly used to design the shape of some simple thin-film structures, which cannot be popularized and applied. For membrane structures with complex loads or constrained boundaries, it is urgent to develop a universal optimization design method for the purpose of completely eliminating wrinkles, to automatically, accurately and efficiently find innovative topological forms, and to achieve wrinkle-free membrane structures. .

SUMMARY OF THE INVENTION

The invention mainly solves the problem that the film structure is prone to wrinkles under the action of tensile load, and proposes an optimal design method for the film structure for the purpose of completely eliminating wrinkles. On the basis of plane finite element analysis, by controlling the minimum principal stress of each element to be a positive value, the stress state of the film is adjusted, and topology optimization technology is used to design the film material distribution, and then the structural form with curved boundaries or holes is obtained, In order to achieve the purpose of completely eliminating wrinkles. This method ensures the complete elimination of wrinkles, can achieve precise positioning of shapes and holes, and has a high degree of automation in the optimized design, which will ensure the research and development efficiency of the wrinkle-free design of the film structure.

In order to achieve the above object, the technical scheme of the present invention is:

An optimized design method for eliminating tensile folds of a film structure, which specifically includes the following steps:

First step, wrinkle-free topology optimization of the thin film structure

(1) Determine the design domain according to the size requirements of the structure and the actual loading situation, and establish the initial design of the topology optimization of the membrane structure; apply loads and constraint boundaries in the design domain, and divide the finite element mesh;

(2) Establish a wrinkle-free topology optimization model of the film structure to maximize the overall stiffness or minimize the overall flexibility of the film structure

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；a) Constraint 1: The minimum principal stress of each finite element element is greater than zero, namely

Among them, e is the finite element element number, σ ₁ is the maximum principal stress, σ ₂ is the minimum principal stress;

b) Constraint 2: Determine the area dosage of the film as the upper limit of the area constraint; the film area dosage is 60%-90% of the design domain area.

c) Design variables: the relative density ρ _e of the finite element element in the design domain, ρ _e is between α and 1, representing the distribution of the film material at the element; where α is a positive number far less than 1;

其中I₁和J₂分别为有限元单元的应力第一和第二不变量；(3) According to the topology optimization model established in step (2), the constraint-equivalent transformation is

where I ₁ and J ₂ are the stress first and second invariants of the finite element element, respectively;

(4) Constraint relaxation processing is adopted for the transformed constraints in step (3) to avoid the phenomenon of stress singular solution; SIMP penalty strategy and optimization algorithm are used for iterative solution to obtain the optimal material distribution of the thin film structure;

The second step is to optimize the shape of the thin film structure

On the basis of the topological form of the thin film structure obtained in the first step (4), the specific geometric parameters of the thin film structure boundary and holes are optimized, and the minimum principal stress constraints are considered to obtain more detailed and accurate structural shape parameters. The obtained structural form satisfies the requirement that the minimum principal stress is positive and maximizes the overall stiffness, the configuration is relatively simple, and it is easy to manufacture.

The beneficial effects of the present invention are:

Before the optimization of the film structure, this kind of structure has a significant large-area wrinkling phenomenon under the action of tensile load. After adopting the film of the present invention in the form of "wrinkle-free" structure, through numerical simulation and test evaluation, the minimum principal stress of the entire film is guaranteed to be a positive value greater than zero, and no wrinkles are observed at all. The structure is easy to process and manufacture, only simple cutting and opening are required. At the same time, the wrinkle-free optimization method established by the present invention avoids the complicated post-buckling calculation in the optimization process, and consumes a very small amount of work, which will significantly improve the design efficiency, and is expected to become a thin film in the aerospace field and micro-nano field. Effective methods for the innovative design of structures.

Description of drawings

FIG. 1 is a design domain of a four-corner tensile structure provided by an embodiment of the present invention.

Figure 2(a) shows the optimal design of the four-corner tensile structure when the film area ratio is 70%.

Figure 2(b) shows the optimal design of the four-corner tensile structure when the film area ratio is 80%.

FIG. 3 is a design domain of a tensile structure at both ends with a hard block in the middle according to an embodiment of the present invention.

Figure 4 is the optimal design diagram of the tensile structure at both ends with a hard block in the middle when the area ratio of the film is 80%.

Detailed ways

The specific embodiments of the present invention will be described in detail below with reference to the technical solutions and the accompanying drawings.

First step, wrinkle-free topology optimization of the thin film structure

(1) Determine the design domain according to the size requirements of the structure and the actual loading situation, and establish the initial design of the topology optimization of the membrane structure; apply loads and constraint boundaries in the design domain and divide the finite element mesh. Figure 1 shows the design domain of the four-corner tensile structure, with N=6400 finite element meshes, and Figure 3 shows the design domain of the tensile structure at both ends with rigid blocks in the middle, with N=5000 finite element meshes. Both initial structures have obvious folding behavior under tensile load.

(2) Establish a topological optimization model of thin film structure without wrinkling:

(a) Objective: Maximize the overall stiffness or minimize the overall compliance of the membrane structure.

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) Constraint 1: The minimum principal stress of each finite element element is required to be greater than zero, namely

where e is the finite element element number, σ ₁ is the maximum principal stress, and σ ₂ is the minimum principal stress.

(c) Constraint 2: The amount of film area is given as the upper limit of the area constraint. The area usage of the film is 70% and 80% of the entire design domain area.

(d) Design variable: the relative density ρ _e of the element in the design domain, which is between α=0.001 and 1, representing the distribution of the thin film material at the element.

其中I₁和J₂分别为应力第一和第二不变量。(3) According to the topology optimization model established in step (2), the constraint-equivalent transformation is

where I ₁ and J ₂ are the stress first and second invariants, respectively.

(4) Constraint relaxation is used for the transformed constraints in step (3) to avoid the phenomenon of stress singular solution. The cosine-type relaxation method is adopted, wherein the expression of the cosine-type relaxation function is θ=(1-cos(ρ _e ·π))/2.

(5) The optimization model adopts the SIMP penalty strategy and the optimization algorithm to iteratively solve, and obtains the optimal material distribution of the thin film structure, as shown in Figure 2 and Figure 4, respectively.

The second step is to carry out the detailed shape optimization design of the thin film structure

On the basis of the thin film structure topology obtained in the first step (5), the specific geometric parameters of the thin film structure boundaries and holes are optimized, and the minimum principal stress constraints are considered to obtain more detailed and accurate structural shape parameters. The obtained configuration is relatively simple, easy to manufacture, and has been verified by nonlinear post-buckling finite element analysis and full-scale test that no wrinkles occur in the entire film structure, which verifies the effectiveness of the method proposed in the present invention.

The essence of the present invention is to use the topology optimization method to obtain a configuration with curved edge boundaries or holes, so as to control and optimize the minimum principal stress of the entire film to achieve the purpose of no wrinkling. It modifies the optimization models, methods, and schemes described in the foregoing embodiments, or performs equivalent replacements on some or all of the method features (for example, using level sets or explicit curves to describe structural boundaries and holes, using other topology optimization methods) method, changing the objective function or constraining the specific form, etc.), does not make the essence of the corresponding method and scheme deviate from the scope of the method and scheme of each embodiment of the present invention.

Claims (4)

1. an optimized design method for eliminating stretch folds of film structure is characterized in that the following steps: First step, wrinkle-free topology optimization of the thin film structure (1) Determine the design domain according to the size requirements of the structure and the actual loading situation, and establish the initial design of the topology optimization of the membrane structure; apply loads and constraint boundaries in the design domain, and divide the finite element mesh; (2) Establish a wrinkle-free topology optimization model of the film structure to maximize the overall stiffness or minimize the overall flexibility of the film structure a) Constraint 1: The minimum principal stress of each finite element element is greater than zero, namely

Among them, e is the number of the finite element element, and σ ₂ is the minimum principal stress; b) Constraint 2: Determine the amount of film area as the upper limit of the area constraint; the amount of film area is 60%-90% of the design domain area; c) Design variables: the relative density ρ _e of the finite element element in the design domain, ρ _e is between α and 1, representing the distribution of the film material at the element; where α is a positive number far less than 1; (3) According to the topology optimization model established in step (2), the constraint-equivalent transformation is

where I ₁ and J ₂ are the stress first and second invariants of the finite element element, respectively; (4) Constraint relaxation processing is adopted for the transformed constraints in step (3) to avoid the phenomenon of stress singular solution; SIMP penalty strategy and optimization algorithm are used for iterative solution to obtain the optimal material distribution of the thin film structure; The second step is to optimize the shape of the thin film structure On the basis of the obtained thin film structure topology, the specific geometric parameters of the thin film structure boundary and holes are optimized, and the minimum principal stress constraints are considered to obtain more detailed and accurate structural shape parameters. 2 . The optimization design method according to claim 1 , wherein the constraint relaxation process in the first step includes an ε relaxation method or a qp relaxation method. 3 . 3. The optimization design method according to claim 1, wherein the constraint relaxation processing comprises a cosine-type relaxation method, wherein the expression of the cosine-type relaxation function is θ=(1-cos(ρ _e · π))/2. 4. The optimization design method according to claim 1, 2 or 3, wherein the optimization algorithm is a criterion method, an MMA algorithm, an ESO method or a Level set method.

Images