CN106897491A - It is a kind of to suppress the construction design method that rectangular membrane tension produces fold - Google Patents

Abstract

It is a kind of to suppress the construction design method that rectangular membrane tension produces fold, belong to electronic applications and aerospace field.Based on topological optimization technology, optimization aim is turned to rigidity of structure maximum, with the minimum of minimum principal stress in rectangle face more than zero for optimizing stress is constrained, with rectangular membrane optimization structural area less than area allowable as optimization area, with film unit density value as design variable, the preferred configuration of tension corrugationless is proposed.Based on optimum results, the wrinkle-free geometry designs scheme of film tension is proposed, provide the tolerance zone of geometry designs scheme key parameter, be conducive to digitlization CAD to realize.Film optimal design proposed by the present invention, can effectively suppress and eliminate the fold that film is produced in tension, the purpose wrinkle-free so as to reach film tension.The present invention only modifies to membrane structure shape, it is easy to accomplish, without supplementary structure and extra control, input cost is low and workable.Structural design scheme proposed by the present invention, can meet the film surface smoothness requirements of harshness.

Description

A Structural Design Method for Restraining Wrinkling of Rectangular Membrane under Tension

technical field

The invention belongs to the fields of electronics and aerospace, and in particular relates to a design method for a rectangular membrane structure that requires suppression of wrinkles caused by tension, and is applied to aspects requiring higher surface precision of certain membrane structures.

Background technique

The thin film structure (width-to-thickness ratio ≥ 500) has a small out-of-plane stiffness, which is prone to external instability and wrinkles under stretching, which affects the surface smoothness, electrical properties, and mechanical properties of the thin film structure. In order to improve the performance of thin film structures, a method and scheme to suppress or eliminate wrinkles is urgently needed.

Current technologies use auxiliary structures such as rods and beams or impose additional physical, chemical, and electrical controls to suppress the derivation and development of wrinkles, but this will bring additional problems such as additional weight, application limitations, and the generation of new wrinkles. The present invention proposes a film structure optimization method and optimization scheme, by changing the free edge and loading edge curve shape of the film structure to better suppress or eliminate wrinkles and the effect of wrinkle-free tensile film, to ensure that the film structure has a high Excellent surface precision and good electrical and mechanical properties can be used in the fields of electronics and aerospace.

Contents of the invention

The problem to be solved by the present invention is: aiming at the deficiencies in the prior art, propose a structural optimization design method and optimization scheme for suppressing tensile wrinkling of a rectangular film that is fast, effective, independent of auxiliary structure weight gain, and highly operable.

Technical scheme of the present invention:

A structural design method for suppressing the wrinkling of a rectangular membrane under tension, the steps are as follows:

Step S01: Establish a rectangular membrane finite element model with a slenderness ratio greater than 1, define the two sides in the length direction as free sides, and define the two sides in the width direction as loading sides; Stress state at % tensile strain, extracting the minimum value of the minimum in-plane principal stress of the rectangular membrane;

Step S02: Establish a rectangular membrane topology optimization model, define the overall membrane as the design domain Ω _des , the design domain Ω _des includes the material domain Ω _m and the non-material domain Ω _void , and satisfies Ω _m ∪Ω _void = Ω _des and relationship; the optimization goal is to maximize the stiffness of the rectangular membrane, and simultaneously satisfy the stress constraint (the minimum value of the minimum in-plane principal stress of the rectangular membrane extracted in step S01 is greater than zero) and the area constraint (the optimized structure area is smaller than the allowable area) , the optimization variable is the density of each unit;

The column formula of the rectangular membrane topology optimization model is

Among them, W(u) is the stiffness of the rectangular membrane structure, t, u and v are the surface force, displacement field and allowable virtual displacement acting on the loading boundary Γ _T , respectively; U _ad is the allowable virtual displacement space; a(u ,v) and l(v) are energy bilinear form and load linear form; min(σ _min,x )>0 is the stress constraint, where min(σ _min,x ) is the minimum value of the minimum in-plane principal stress of each unit x in the design domain Ω _m , when the minimum value is greater than zero, no wrinkles will occur; is the area constraint, A is the area of the material domain Ω _des in the design domain Ω _m , A ^* the allowable area of the material domain Ω _des in the design domain Ω _m ; χ(x)∈{0,1}x∈Ω _des is the representation The relationship between the material domain Ω _m and the non-material domain Ω _void in the design domain Ω _m , when χ(x)=1 means that the current unit is the material domain Ω _m , otherwise when χ(x)=0 means the current unit is the non-material domain Ω _void ;

Step S03: Topology optimization obtains the optimal configuration corresponding to the film being stretched without wrinkles, extracts the geometric features of the material domain in the optimized configuration, and uses finite element simulation to calculate the criticality of each geometric feature that makes the film stretch without wrinkles. value.

The shape of the free side is an overall symmetrical concave curve.

The shape of the bearing side is a locally symmetrical concave curve.

The shape of the free side is a semi-elliptical overall symmetrical concave curve, the ratio of the minor axis length b ₁ to the half-width w of the rectangular membrane is greater than 3.7%, and the rectangular membrane does not produce wrinkles when it is stretched.

The shape of the free side is a semi-cosine overall symmetrical concave curve, the ratio of the amplitude b2 to the half _- width w of the rectangular membrane is greater than 2.05%, and the rectangular membrane does not produce wrinkles when it is stretched.

The shape of the free side is a semi-hyperbolic cosine overall symmetrical concave curve, the ratio of the amplitude b ₃ to the half-width w of the rectangular membrane is greater than 2.2%, and the rectangular membrane does not produce wrinkles when it is stretched.

The shape of the free side is a spline overall symmetrical concave curve, the ratio of the amplitude b ₄ to the width of the rectangular membrane structure is greater than 1.93%, and the rectangular membrane will not produce wrinkles when it is stretched.

The shape of the free side is an overall concave symmetrical curve with local disturbances, and the disturbances can be in the form of outward protrusions or inward pits.

The shape of the free side is an overall symmetrical concave curve (it can be a semi-elliptic line, a semi-cosine curve, a semi-hyperbolic cosine curve, a spline curve or an overall concave local disturbance), and the length of the loading side is reduced.

The shape of the free side is an overall symmetrical concave curve (it can be a semi-elliptic line, a semi-cosine curve, a semi-hyperbolic cosine curve, a spline shape or an overall concave local disturbance), and the loading side adopts a symmetrical concave curve shape (It can be semi-elliptic, semi-cosine, semi-hyperbolic cosine, spline shape or overall concave local disturbance)

Based on the topology optimization model in step 2, the optimal configuration of the rectangular membrane under tension without wrinkles is obtained. Based on step 3, the geometric characteristics of the material domain in the optimized configuration are extracted and summarized as an overall symmetrical concave curve on the free side, reducing the loading side Features such as length and locally concave curves on the loaded side. Based on the wrinkle criterion, the minimum principal stress distribution of the thin film adopting the structural optimization design scheme is analyzed, and the parameter threshold value of the wrinkle-free thin film produced by the structural optimization scheme is determined.

The principal stress-based wrinkle criterion can be expressed as:

Among them, σ _min and σ _max are the minimum principal stress and maximum principal stress in the plane generated by the two-dimensional plane stress unit when the film is under tension.

Beneficial effects of the present invention:

1. The rectangular film structure optimization method and optimized design scheme for suppressing and eliminating tension wrinkles provided by the present invention can obtain smaller wrinkle amplitude or no wrinkle effect only by changing the shape of the film structure, which reduces the impact of wrinkles on the film physics. , chemical, electrical and surface accuracy, the design method is simple and effective.

2. The present invention achieves the effect of suppressing and eliminating stretching wrinkles while ensuring a large continuous working area. Compared with existing auxiliary structural solutions such as adding rods and beams, the invention is relatively simple to operate, has no additional cost, and does not cause weight increase.

3. The present invention obtains the effect of suppressing and eliminating tension wrinkles by modifying the shape of the rectangular film structure. Compared with the existing control schemes that impose additional mechanics, chemistry, and electricity, the invention is simple in operation, convenient in implementation, and strong in versatility.

4. The present invention uses different curve expressions to describe the optimization scheme of the rectangular film structure, which can be directly used in digital CAD processing to realize batch processing.

Description of drawings

Figure 1 is a schematic diagram of the structural optimization design scheme for the rectangular membrane structure to suppress and eliminate tension wrinkles. (a) The initial rectangular membrane structure that is prone to wrinkles under tension. The center of the rectangular membrane is taken as the origin, the length direction is the x-axis, and the half-length and half-width of the rectangular membrane are l and w, respectively. (b) The optimized rectangular membrane structure that is less prone to wrinkles under tension, with the center of the rectangular membrane as the origin, the length direction as the x-axis, and the half-length and half-width of the optimized rectangular membrane structure are l, w'(w'≤w). Rectangular membrane optimization structure restrains and eliminates tensile wrinkles of rectangular membrane structure by setting overall concave free side, local concave loading side, reducing the length of loading side, etc. The amplitude of the overall concave free edge is b _i (i=1,2,3,4), when i=1, the overall concave free edge is described by a semi-elliptical line; when i=2, the overall concave free edge The semi-cosine curve is used to describe; when i=3, the overall concave free edge is described by a semi-hyperbolic cosine line; when i=4, the overall concave free edge is described by a passing point spline curve.

Fig. 2 is graphene (300nm in length, 150nm in width, 0.335nm in thickness) using the present invention to set the free side as a semi-elliptical overall concave curve optimization scheme to suppress and eliminate wrinkles. (a) Rectangular graphene is wrinkled when it is stretched, and the maximum wrinkle is 0.55nm; (b) Rectangular graphene is wrinkled when it uses a semi-ellipse free edge (b ₁ /w=2%), and the wrinkle is the largest The value is 0.16nm; (c) Rectangular graphene adopts semi-ellipse line free edge (b ₁ /w=5%) and does not produce wrinkles under tension; (d) Rectangular graphene adopts semi-ellipse line free edge (b ₁ /w = 20%), no wrinkle will be produced under tension; (e) rectangular graphene will not produce wrinkle under tension when the free edge of the semi-ellipse line (b ₁ /w = 90%) is used.

Fig. 3 is a rectangular kapton film (length 40mm, width 20mm, thickness 12.5 μm) using the present invention to set the free side as a semi-elliptical overall concave curve optimization scheme to suppress and eliminate wrinkles. (a) Rectangular Kapton membrane wrinkles when stretched, and the maximum wrinkle size is 210.5 μm; (b) Rectangular Kapton membrane does not wrinkle when the semi-elliptical free edge (b ₁ /w=10%) is stretched; (c ) Rectangular Kapton membrane with semi-ellipse free edge (b ₁ /w=30%) is stretched without wrinkling; (d) Rectangular Kapton membrane with semi-ellipse free edge (b ₁ /w=50%) under tension No wrinkles; (e) Rectangular Kapton membrane adopts semi-ellipse line free edge (b ₁ /w=70%) without wrinkle; (f) Rectangular Kapton membrane adopts semi-ellipse line free edge (b ₁ /w=70%) 90%) without wrinkling under tension.

detailed description

The specific implementation manner of the present invention will be further described in detail below in conjunction with the accompanying drawings and technical solutions.

It should be noted that in the following specific embodiments, when describing the embodiments of the present invention in detail, in order to clearly show the structure of the present invention for the convenience of description, the structures in the drawings are not drawn according to the general scale, and are drawn Partial magnification, deformation and simplification are included, therefore, it should be avoided to be interpreted as a limitation of the present invention.

A structural design method for suppressing the wrinkling of a rectangular membrane under tension, the steps are as follows:

Step S01: Establish a rectangular membrane finite element model with a slenderness ratio greater than 1, define the two sides in the length direction as free sides, and define the two sides in the width direction as loading sides; Stress state at % tensile strain, extracting the minimum value of the minimum in-plane principal stress of the rectangular membrane;

Step S02: Establish a rectangular membrane topology optimization model, define the overall membrane as the design domain Ω _des , the design domain Ω _des includes the material domain Ω _m and the non-material domain Ω _void , and satisfies Ω _m ∪Ω _void = Ω _des and relationship; the optimization goal is to maximize the stiffness of the rectangular membrane, and simultaneously satisfy the stress constraint (the minimum value of the minimum in-plane principal stress of the rectangular membrane extracted in step S01 is greater than zero) and the area constraint (the optimized structure area is smaller than the allowable area) , the optimization variable is the density of each unit;

The column formula of the rectangular membrane topology optimization model is

Among them, W(u) is the stiffness of the rectangular membrane structure, t, u and v are the surface force, displacement field and allowable virtual displacement acting on the loading boundary ΓT, respectively; U _ad is the allowable virtual displacement space; a(u, v) and l(v) are energy bilinear form and load linear form; min(σ _min,x )>0 is the stress constraint, where min(σ _min,x ) is the minimum value of the minimum in-plane principal stress of each unit x in the design domain Ω _m , when the minimum value is greater than zero, no wrinkles will occur; is the area constraint, A is the area of the material domain Ω _des in the design domain Ω _m , A ^* the allowable area of the material domain Ω _des in the design domain Ω _m ; χ(x)∈{0,1}x∈Ω _des is the representation The relationship between the material domain Ω _m and the non-material domain Ω _void in the design domain Ω _m , when χ(x)=1 means that the current unit is the material domain Ω _m , otherwise when χ(x)=0 means the current unit is the non-material domain Ω _void ;

Step S03: Topology optimization obtains the optimal configuration corresponding to the film being stretched without wrinkles, extracts the geometric features of the material domain in the optimized configuration, and uses finite element simulation to calculate the criticality of each geometric feature that makes the film stretch without wrinkles. value.

In this step, there are three different schemes for the geometric characteristics of the material domain, namely, setting the shape of the free side as an overall symmetrical concave curve, reducing the length of the loaded side, and setting the shape of the loaded side as a locally symmetrical concave curve, such as Figure 1 shows. For optimizing the boundary geometric characteristics of the membrane structure, one of the above three schemes or any combination of them can be used.

When the scheme of setting the shape of the free side as an overall symmetrical concave curve is adopted, the free side can adopt a semi-elliptical line with an overall symmetrical concave curve, the center of the rectangular membrane is the origin of the elliptic line equation, and the direction of the tensile load is the x-axis. Using the semi-elliptic line equations x ² /l ² +(yw) ² /b ₁ ² =1(wb ₁ ≤y≤w) and x ² /l ² +(y+w) ² /b ₁ ² =1(- w≤y≤-w+b ₁ ) Set the shape of the free sides at the upper and lower ends of the rectangular thin film structure. Among them, l, w, b ₁ are the half-width, half-length and the minor axis length of the semi-elliptic line respectively. When the ratio of the minor-axis length b ₁ of the semi-elliptic line to the half-width w of the rectangular film is greater than 3.7%, the rectangular film is affected by No creases when pulled.

When the scheme of setting the shape of the free side as an overall symmetrical concave curve is adopted, the free side can adopt a half-cosine overall symmetrical concave curve, the center of the rectangular membrane is the origin of the half-cosine curve equation, and the direction of the tensile load is the x-axis. Use the half-cosine equations y=-b ₂ cos(0.5πx/l)+w(-l≤x≤l,wb ₂ ≤y≤w) and y=b ₂ cos(0.5πx/l)-w(-l ≤x≤l, -w≤y≤b ₂ -w) Set the shape of the free sides at the upper and lower ends of the rectangular thin film structure. Among them, l, w, b ₂ are the half-width, half-length and half-cosine amplitude of the rectangular membrane respectively. When the ratio of the half-cosine curve amplitude b ₂ to the half-width w of the rectangular membrane is greater than 2.05%, the rectangular membrane is stretched Won't crease.

When the scheme of setting the shape of the free side as an overall symmetrical concave curve is adopted, the free side can adopt a semi-hyperbolic cosine overall symmetrical concave curve, the center of the rectangular membrane is the origin, and the direction of the tensile load is the x-axis. Use the semi-hyperbolic cosine equation with Set the shape of the free edges at the upper and lower ends of the rectangular membrane structure. Where l, w, b ₃ are the half-width, half-length and amplitude of the semi-hyperbolic cosine curve of the rectangular membrane, respectively, when the ratio of the semi-hyperbolic cosine curve amplitude b ₃ to the half-width w of the rectangular membrane is greater than 2.2%, the rectangular membrane is affected by No creases when pulled.

When the scheme of setting the shape of the free side as an overall symmetrical concave curve is adopted, the free side can adopt a spline overall symmetrical concave curve, the center of the rectangular membrane is the origin, and the direction of the tensile load is the x-axis. Use the spline curve design of the points (-l,w),(0,b ₄ ),(l,w) and (-l,-w),(0,-b ₄ ),(l,-w) Determine the shape of the free sides at the upper and lower ends of the rectangular film structure. Where l, w, b ₄ are the half-width, half-length and the amplitude of the spline curve of the rectangular membrane respectively, when the ratio of the spline curve amplitude b ₄ to the half-width w of the rectangular membrane is greater than 1.93%, when the rectangular membrane is stretched Won't crease.

When the scheme of setting the shape of the free side as an overall symmetrical concave curve is adopted, the free side can adopt a design scheme of local perturbation of the spline overall symmetrical concave curve. That is, the overall shape adopts a concave shape, and the local part adopts the form of outward protrusion or inward pit disturbance. The overall concave shape may be, but not limited to, the above-mentioned semi-elliptic line, semi-cosine curve, semi-hyperbolic cosine curve, and spline curve.

When the scheme of setting the shape of the free side as an overall symmetrical concave curve is adopted, the length of the loaded side can be reduced at the same time. The half-length of the loaded side is w', as shown in Figure 1(b), and its allowable range is w-b<w'<w, which can eliminate the tensile wrinkles of the rectangular membrane structure. The concave shape of the free edge may be, but not limited to, the above-mentioned semi-elliptic line, semi-cosine curve, semi-hyperbolic cosine curve, and spline curve.

When the scheme of setting the shape of the free side as an overall symmetrical concave curve is adopted, the local symmetrical concave shape of the loading side can be set at the same time. The concave shape of the loading side may be, but not limited to, the above-mentioned semi-elliptic line, semi-cosine curve, semi-hyperbolic cosine curve, and spline curve.

The rectangular thin-film structure is suitable for two-dimensional planar structures with a width-to-thickness ratio greater than 500, ranging from discrete molecular structures such as graphene at the microscopic scale to thin-film structures at the macroscopic scale. In order to further express the beneficial effect of the above scheme, the effectiveness of the optimization scheme is verified by taking the microscopic graphene rectangular film material and the macroscopic polyimide Kapton rectangular film as examples. The specific parameters and technical solutions are respectively described as follows.

Embodiment 1: the selection length is 300nm, the width is 150nm, and the thickness is a single-layer graphene film of 0.335nm. The free edge adopts a semi-ellipse concave curve. The ratios b ₁ /w are 0%, 2%, 5%, 20%, and 90%, respectively. For pristine rectangular graphene films, the maximum magnitude of wrinkles during stretching is 0.55 nm. When b ₁ /w=2%, the maximum wrinkle amplitude during stretching is 0.16nm. When b ₁ /w>3.7%, there is no obvious wrinkle in the graphene film stretching process.

Embodiment 2: select the polyimide Kapton film that size is (40mm * 20mm * 12.5 μ m), free edge adopts semi-ellipse concave curve, as shown in Figure 3, semi-ellipse minor axis long and graphene film half-width The ratio b ₁ /w is 0%, 10%, 30%, 50%, 70%, 90%, respectively. It can be observed that under the tensile strain of 7.5%, the original rectangular film has wrinkles, but after adopting the free edge of the semi-elliptical concave curve shape, the film has no obvious wrinkles.

The above are only preferred embodiments of the present invention, and the embodiments are not intended to limit the scope of patent protection of the present invention. Therefore, all equivalent structural changes made by using the description and accompanying drawings of the present invention should be included in the same way. Within the protection scope of the present invention.

Claims (10)

1. A structural design method for suppressing the tension generation of rectangular membranes, characterized in that the steps are as follows: Step S01: Establish a finite element model of a rectangular membrane with a slenderness ratio greater than 1, define the two sides in the length direction as free sides, and define the two sides in the width direction as loading sides; Stress state at % tensile strain, extracting the minimum value of the minimum in-plane principal stress of the rectangular membrane; Step S02: Establish a rectangular membrane topology optimization model, define the overall membrane as the design domain Ω _des , the design domain Ω _des includes the material domain Ω _m and the non-material domain Ω _void , and satisfies Ω _m ∪Ω _void = Ω _des and Relation; the optimization objective is to maximize the stiffness of the rectangular membrane and satisfy both the stress constraint and the area constraint. The stress constraint is that the minimum value of the minimum in-plane principal stress of the rectangular membrane extracted in step S01 is greater than zero, and the area constraint is the optimized structure area is smaller than the allowable area, the optimization variable is the density of each unit; The column formula of the rectangular membrane topology optimization model is $\begin{array}{cc}\underset{\mathrm{<span\; class="notranslate">\; \&chi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; max</span>}}& \mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}\\ \mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>& \begin{array}{cc}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; \&ForAll;</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; d</span>}}\end{array}\\ & \begin{array}{cc}\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; \&ForAll;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\end{array}\\ & \mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}}\mathrm{<span\; class="notranslate">\; \&chi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; \&Omega;</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; *</span>}\\ & \begin{array}{cc}\mathrm{<span\; class="notranslate">\; \&chi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \}</span>& \mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}\end{array}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ Among them, W(u) is the stiffness of the rectangular membrane structure, t, u and v are the surface force, displacement field and allowable virtual displacement acting on the loading boundary Γ _T , respectively; U _ad is the allowable virtual displacement space; a(u ,v) and l(v) are energy bilinear form and load linear form; min(σ _min,x )>0 is the stress constraint, where min(σ _min,x ) is the minimum value of the minimum in-plane principal stress of each unit x in the design domain Ω _m , when the minimum value is greater than zero, no wrinkles will occur; is the area constraint, A is the area of the material domain Ω _des in the design domain Ω _m , A ^* is the allowable area of the material domain Ω _des in the design domain Ω _m ; χ(x)∈{0,1}x∈Ω _des is Characterize the relationship between the material domain Ω _m and the non-material domain Ω _void in the design domain Ω _m , when χ(x)=1 means that the current unit is the material domain Ω _m , when χ(x)=0 means the current unit is the non-material domain Ω _void ; Step S03: Topology optimization obtains the optimal configuration corresponding to the film being stretched without wrinkles, extracts the geometric features of the material domain in the optimized configuration, and uses finite element simulation to calculate the criticality of each geometric feature that makes the film stretch without wrinkles. value; There are three schemes for the geometric characteristics of the material domain: set the shape of the free side as an overall symmetrical concave curve, reduce the length of the loaded side, and set the shape of the loaded side as a locally symmetrical concave curve. To optimize the boundary geometric characteristics of the membrane structure, use One of the above three schemes or any combination of them. 2. The structural design method according to claim 1, characterized in that, when the shape of the free side is set as an overall symmetrical concave curve, the free side adopts a semi-elliptical line with an overall symmetrical concave curve, with the center of the rectangular membrane as The origin of the elliptic line equation, with the tensile load direction as the x-axis; use the semi-elliptic line equation x ² /l ² +(yw) ² /b ₁ ² =1(wb ₁ ≤y≤w) and x ² /l ² +(y+w) ² /b ₁ ² ＝1(-w≤y≤-w+b ₁ ) set the shape of the upper and lower free sides of the rectangular membrane structure; where l, w, b ₁ are the half-width, Half length and minor axis length of the semi-ellipse line, when the ratio of the minor axis length b ₁ of the semi-ellipse line to the half-width w of the rectangular film is greater than 3.7%, the rectangular film will not produce wrinkles when it is stretched. 3. The structural design method according to claim 1, characterized in that, when the shape of the free side is set as an overall symmetrical concave curve, the free side adopts a half-cosine overall symmetrical concave curve, with the center of the rectangular membrane as half The origin of the cosine curve equation, with the tensile load direction as the x-axis; use the half-cosine equation y=-b ₂ cos(0.5πx/l)+w(-l≤x≤l,wb ₂ ≤y≤w) and y =b ₂ cos(0.5πx/l)-w(-l≤x≤l,-w≤y≤b ₂ -w) sets the shape of the upper and lower free sides of the rectangular thin film structure; among them, l, w, b ₂ are respectively For the half-width, half-length and half-cosine amplitude of the rectangular membrane, when the ratio of the half-cosine curve amplitude b ₂ to the half-width w of the rectangular membrane is greater than 2.05%, the rectangular membrane will not wrinkle when it is pulled. 4. The structural design method according to claim 1, characterized in that, when the shape of the free side is set as an overall symmetrical concave curve, the free side adopts a semi-hyperbolic cosine overall symmetrical concave curve, with the center of the rectangular membrane as Origin, with the direction of tensile load as the x-axis; use the semi-hyperbolic cosine equation with Set the shape of the upper and lower free sides of the rectangular membrane structure; where, l, w, b ₃ are the half-width, half-length and amplitude of the semi-hyperbolic cosine line of the rectangular membrane, respectively, when the amplitude of the semi-hyperbolic cosine curve b ₃ and the half The ratio of width w is greater than 2.2%, and the rectangular membrane will not produce wrinkles when it is stretched. 5. The structural design method according to claim 1, characterized in that, when the shape of the free side is set as an overall symmetrical concave curve, the free side adopts a spline overall symmetrical concave curve, with the center of the rectangular membrane as the origin , with the tensile load direction as the x-axis; using the points (-l,w),(0,b ₄ ),(l,w) and (-l,-w),(0,-b ₄ ),( The spline curve of l,-w) sets the shape of the upper and lower free sides of the rectangular membrane structure; among them, l, w, b ₄ are the half-width, half-length and the amplitude of the spline curve of the rectangular membrane respectively, when the spline curve amplitude The ratio of the value b ₄ to the half-width w of the rectangular membrane is greater than 1.93%, and the rectangular membrane will not wrinkle when it is stretched. 6. The structural design method according to any one of claims 2-5, characterized in that, when the shape of the free side is set as an overall symmetrical concave curve, the free side is combined with a local disturbance design method, that is, the whole adopts a symmetrical inner curve. The shape of the concave curve locally takes the form of outward protrusion or inward pit disturbance. 7. According to the structural design method described in any one of claims 2-5, it is characterized in that, when the shape of the free side is set as an overall symmetrical concave curve, the length of the loaded side is reduced at the same time; the half length of the loaded side is w ', the allowable range is w-b<w'<w, to achieve the effect of eliminating the tensile wrinkle of the rectangular membrane structure. 8. The structural design method according to any one of claims 2-5, characterized in that, when the shape of the free side is set as an overall symmetrical concave curve, the local symmetrical concave shape of the loading side is set at the same time, so as to eliminate the rectangular shape The effect of the film being stretched and wrinkled. 9. The structural design method according to claim 6, characterized in that, when the shape of the free side is set as an overall symmetrical concave curve containing local disturbances, the local symmetrical concave shape of the loading side is set at the same time, so as to eliminate the rectangular film The effect of tension wrinkles. 10. The structural design method according to claim 2, 3, 4, 5 or 8, characterized in that, the material of the rectangular membrane is microscopic material graphene, and its aspect ratio is greater than 500:1; or the The material of the rectangular film is a macro material polyimide Kapton film with an aspect ratio greater than 500:1.