CN115659690A - Curved surface near-zero stress acquisition method and device, computer and storage medium - Google Patents

Abstract

A curved surface near-zero stress acquisition method, a curved surface near-zero stress acquisition device, a computer and a storage medium relate to the field of flexible electronic mechanical design. The problems that the design of the micro-nano structure of the flexible electronic substrate depends on the experience of a designer, the period is long, the substrate processing cost is high, and the universality is poor are solved. The method comprises the following steps: acquiring a target substrate and a target curved surface which cover the flexible electronic skin; acquiring a first basic form of a curved surface and a normal vector of the curved surface according to the target substrate and the target curved surface; judging the type of the curved surface according to the first basic form of the curved surface; the method comprises the following steps of dividing a curved surface according to the type of the curved surface, and performing zero-stress expansion on the divided curved surface by adopting space mapping to obtain near-zero stress of the curved surface, wherein the method comprises the following steps: constructing a developable curved surface of the non-developable curved surface, and acquiring the near-zero stress of the curved surface; and dividing the cylindrical surface, the conical surface and the independent variable definition tangent line curved surface according to the developable curved surface to obtain the near-zero stress of the cylindrical surface, the conical surface and the independent variable definition tangent line curved surface. The method is applied to the field of flexible electronic skin.

Description

A method, device, computer and storage medium for obtaining near-zero stress on a curved surface

technical field

The invention relates to the field of flexible electronic design, in particular to a method for obtaining near-zero stress on a curved surface.

Background technique

In recent years, with the continuous development of flexible electronic technology, flexible electronic technology has shown good application prospects in human physiological signal detection, minimally invasive treatment, robotic electronic skin, flexible display and flexible energy. Many high-performance flexible electronic devices have been verified in the laboratory, but there are still many technical bottlenecks in their large-scale application. Among them, the mechanical problems of flexible electronic devices are particularly prominent. An insurmountable bottleneck. The outer surface of the target object of electronic skin, such as the body surface of the human body and the outer surface of the robot, is usually a curved surface in space, which cannot be unfolded into a plane; and the current manufacturing substrate of the electronic skin is usually a plane. This makes it impossible for the flexible electronic skin manufactured by plane to achieve seamless fit when it is pasted on the outer surface of the above-mentioned objects. Under the action of external force, the response is different; thus, the electronic skin cannot detect the external force normally and accurately. In order to solve the above problems, the current mainstream method is to improve the deformation capabilities of flexible electronic devices such as stretching, torsion, and shearing through the design of micro-nano structures on flexible substrates. However, this design method relies heavily on the designer's experience, long cycle time, high substrate processing cost, and poor versatility.

Contents of the invention

The invention solves the problems that the design of the micro-nano structure of the flexible electronic substrate with a well-attached space curved surface depends on the designer's experience, the cycle is long, the substrate processing cost is high, and the versatility is poor.

A method for obtaining near-zero stress on a curved surface according to the present invention, the method comprising:

Obtain the target substrate and the target surface covered with the flexible electronic skin;

Obtaining the first basic form of the curved surface and the normal vector of the curved surface according to the target base and the target curved surface;

Determine the surface type according to the first basic form of the surface;

The surface is divided according to the surface type, and the zero-stress expansion of the divided surface is completed by using space mapping to obtain the near-zero stress of the surface.

Further, a preferred embodiment is also provided, the first basic form of the curved surface and the normal vector of the curved surface are obtained according to the target base and the target curved surface, and the normal vector of the curved surface includes:

Among them, n(t,w,0) is the normal vector of the surface, r(t,w,0) is the target surface, t is a variable of the target surface, and w is a variable of the target surface.

Further, a preferred embodiment is also provided, wherein the judging the type of the curved surface according to the first basic form of the curved surface includes: judging whether the curved surface is a developable curved surface or a non-developable curved surface;

The criteria for determining the developable curved surface include:

r(u,v,0)=r(u)+vl(u),

(r(u),l(u),l'(u))=0,

Among them, u is a variable in the parametric equation of the surface, v is a variable in the parametric equation of the surface, r(u,v,0) is the parametric equation of the surface, r(u) is a target curve on the surface, l(u) is Another target curve on the surface, l'(u) is the derivative curve of another target curve on the surface.

A surface that does not satisfy the criteria for developing a surface is a non-developable surface.

Further, a preferred implementation is also provided, the surface is divided according to the type of the surface, and the near-zero stress of the surface is obtained, specifically including:

Construct a developable tangent surface of a non-developable surface to obtain near-zero stress on the surface;

According to the developable surface, the cylindrical surface, the conical surface and the independent variable defined tangent line surface are divided, and the near zero stress of the cylindrical surface, the conical surface and the independent variable defined tangent line surface is obtained.

Further, a preferred embodiment is also provided, the construction of the developable tangent curved surface of the non-developable curved surface includes:

For a non-developable surface r(u ₁ ,v ₁ ,0), choose a target curve:

r=r(u ₁ (t),v ₁ (t))=r(t),

Among them, u ₁ (t) is the tangent family equation of single parameter t on the target curve, v ₁ (t) is the tangent family equation of single parameter t on the target curve, r(t) is a target curve on the non-expandable surface;

Construct a developable tangent surface r(t,w) from the curve:

r(t,w)=r(t)+wl(t),

Among them, r(t) is a target curve on the non-expandable surface, and w is a variable of the target surface;

The mapping constructed by the developable tangent surface is:

Among them, u ₁ is a variable on the non-expandable surface, v ₁ is a variable on the non-expandable surface, t is a variable on the mapping surface;

The curves before and after the mapping have the same first basic form of the surface, and the normal vector direction at each point has the same length before and after the mapping:

And also need to meet:

h=k,

Among them, h is a variable on the mapping surface, and k is a variable on the non-expandable surface.

Based on the same inventive concept, the present invention also provides a curved surface near-zero stress acquisition device, which includes:

A target substrate and a target curved surface acquisition unit, configured to obtain a target substrate and a target curved surface covering the flexible electronic skin;

The first basic form of the curved surface and the normal vector acquisition unit for the curved surface are used to obtain the first basic form of the curved surface and the normal vector of the curved surface according to the target base and the target curved surface;

A surface type judging unit, configured to judge the surface type according to the first basic form of the surface;

The near-zero stress acquisition unit of the surface is used to divide the surface according to the type of the surface, and use space mapping to complete the zero-stress expansion of the surface after the division, and obtain the near-zero stress of the surface.

Further, a preferred embodiment is also provided, the first basic form of the curved surface and the normal vector acquisition unit of the curved surface include:

Among them, n(t,w,0) is the normal vector of the surface, r(t,w,0) is the target surface, t is a variable of the target surface, and w is a variable of the target surface.

Further, a preferred embodiment is also provided, the surface type judging unit includes: judging whether the curved surface is a developable curved surface or a non-developable curved surface;

The criteria for determining the developable curved surface include:

r(u,v,0)=r(u)+vl(u),

(r(u),l(u),l'(u))=0,

Among them, u is a variable in the parametric equation of the surface, v is a variable in the parametric equation of the surface, r(u,v,0) is the parametric equation of the surface, r(u) is a target curve on the surface, l(u) is Another target curve on the surface, l'(u) is the derivative curve of another target curve on the surface.

A surface that does not satisfy the criteria for developing a surface is a non-developable surface.

Based on the same inventive concept, the present invention also provides a computer-readable storage medium, which is used to store a computer program, and the computer program executes the method for obtaining near-zero stress on a curved surface described in any one of the above .

Based on the same inventive concept, the present invention also provides a computer device, including a memory and a processor, the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the A method for obtaining near-zero stress on a curved surface described in any one of the above.

The benefits of the present invention are:

The invention solves the problems that the design of the micro-nano structure of the flexible electronic substrate with a well-attached space curved surface depends on the designer's experience, the cycle is long, the substrate processing cost is high, and the versatility is poor.

A method for obtaining near-zero stress of a curved surface according to the present invention obtains the first basic form of the curved surface by obtaining the target curved surface, judges the type of the curved surface according to the form of the curved surface, and divides the curved surface, and uses space mapping to divide the divided The surface completes the zero stress unfolding of the surface. In this way, the planar substrate required for the manufacture of flexible electronic skin that is attached to the target curved surface is obtained. According to the planar substrate obtained by this method, according to the designed mapping, the stress of the flexible electronic skin on the target curved surface can be guaranteed to be approximately zero after being reversely pasted. The method for obtaining near-zero stress on a curved surface according to the present invention does not rely on the experience of the designer, and the plane stress can be developed for different types of curved surfaces according to the above method, saving time and effort. This prevents the designer from increasing the processing cost of the substrate due to operational errors. It can realize nearly zero stress inside the flat base of the flexible electronic skin, realize the seamless pasting of the flexible electronic skin on the outer surface of the object, and has good versatility and wide application range.

The invention is applied to the field of flexible electronic skin.

Description of drawings

Fig. 1 is a flow chart of a method for obtaining near-zero stress on a curved surface described in Embodiment 1;

Fig. 2 is a schematic diagram of the original curved surface of the hyperbolic paraboloid described in Embodiment 11;

Fig. 3 is a schematic diagram of the developable tangent surface constructed along the y=0 surface of the hyperbolic paraboloid described in Embodiment 11;

Fig. 4 is a comparison diagram in the same coordinate system between the original hyperbolic paraboloid and the developable tangent surface described in Embodiment 11;

Fig. 5 is a plane development view of the developable curved surface described in the eleventh embodiment;

Fig. 6 is a comparison diagram in the same coordinate system between the developable curved surface and the unfolded plane described in the eleventh embodiment.

Detailed ways

In order to express the technical solutions and advantages of the present invention more clearly, several embodiments of the present invention are now described in further detail in conjunction with the accompanying drawings, but the various embodiments described below are only a few preferred embodiments of the present invention. , and are not intended to limit the invention.

Embodiment 1. This embodiment will be described with reference to FIG. 1 . A method for obtaining near-zero stress on a curved surface described in this embodiment, the method includes:

Obtain the target substrate and the target surface covered with the flexible electronic skin;

Obtaining the first basic form of the curved surface and the normal vector of the curved surface according to the target base and the target curved surface;

Determine the surface type according to the first basic form of the surface;

The surface is divided according to the surface type, and the zero-stress expansion of the divided surface is completed by using space mapping to obtain the near-zero stress of the surface.

A method for obtaining near-zero stress on a curved surface described in this embodiment, obtains the first basic form of the curved surface by obtaining the target curved surface, judges the type of the curved surface according to the form of the curved surface, and divides the curved surface, and uses space mapping to divide the surface The surface of the surface completes the zero stress expansion of the surface. In this way, the planar substrate required for the manufacture of flexible electronic skin that is attached to the target curved surface is obtained. According to the planar substrate obtained by this method, according to the designed mapping, the stress of the flexible electronic skin on the target curved surface can be guaranteed to be approximately zero after being reversely pasted. The method for obtaining near-zero stress on a curved surface described in this embodiment does not rely on the designer's experience, saving time and effort. This prevents designers from increasing the processing cost of the substrate due to operational errors. Realize nearly zero stress inside the plane substrate of flexible electronic skin, and have good versatility.

Embodiment 2. This embodiment is a further definition of the method for obtaining near-zero stress on a curved surface described in Embodiment 1. According to the target base and the target curved surface, the first basic form of the curved surface and the normal vector of the curved surface are obtained. The normal vectors of the surface include:

Among them, n(t,w,0) is the normal vector of the surface, r(t,w,0) is the target surface, t is a variable of the target surface, and w is a variable of the target surface.

Specifically, in this embodiment, the target curved surface to be pasted by the flexible electronic skin is selected, and the target base to be pasted by the flexible electronic skin is determined according to the target curved surface. Obtain the first basic form of the curved surface and the normal vector of the curved surface according to the target base and the target curved surface, and the normal vector n (t, w, 0) of each point on the curved surface is:

Among them, n(t,w,0) is the normal vector of the surface, r(t,w,0) is the target surface, t is a variable of the target surface, and w is a variable of the target surface.

Embodiment 3. This embodiment is a further limitation of the method for obtaining near-zero stress on a curved surface described in Embodiment 1. The determination of the surface type according to the first basic form of the curved surface includes: judging whether the curved surface is a developable surface or a non-developable surface surface;

The criteria for determining the developable curved surface include:

r(u,v,0)=r(u)+vl(u),

(r(u),l(u),l'(u))=0,

Among them, u is a variable in the parametric equation of the surface, v is a variable in the parametric equation of the surface, r(u,v,0) is the parametric equation of the surface, r(u) is a target curve on the surface, l(u) is Another target curve on the surface, l'(u) is the derivative curve of another target curve on the surface;

A surface that does not satisfy the criteria for developing a surface is a non-developable surface.

Specifically, this embodiment provides the determination condition of the surface type, which is beneficial to further divide the surface and ensure the accuracy of the near-zero stress expansion of the surface.

Embodiment 4. This embodiment is a further limitation of the method for obtaining near-zero stress on a curved surface described in Embodiment 3. The method for obtaining the near-zero stress of the curved surface is divided according to the type of the curved surface, which specifically includes:

Construct a developable tangent surface of a non-developable surface to obtain near-zero stress on the surface;

According to the developable surface, the cylindrical surface, the conical surface and the independent variable defined tangent line surface are divided, and the near zero stress of the cylindrical surface, the conical surface and the independent variable defined tangent line surface is obtained.

Specifically, the developable tangent surface of the non-developable surface is constructed, and the zero-stress expansion along the given curve is guaranteed, so as to realize the near-zero stress expansion.

Embodiment 5. This embodiment is a further limitation of the method for obtaining near-zero stress on a curved surface described in Embodiment 4. The developable tangent curved surface of the constructed non-developable curved surface includes:

For a non-developable surface r(u ₁ ,v ₁ ,0), choose a target curve:

r=r(u ₁ (t),v ₁ (t))=r(t),

Among them, u ₁ (t) is the tangent family equation of single parameter t on the target curve, v ₁ (t) is the tangent family equation of single parameter t on the target curve, r(t) is a target curve on the non-expandable surface,

Construct a developable tangent surface r(t,w) from the curve:

r(t,w)=r(t)+wl(t),

Among them, r(t) is a target curve on the non-expandable surface, and w is a variable of the target surface.;

The mapping constructed by the developable tangent surface is:

Among them, u ₁ is a variable on the non-expandable surface, v ₁ is a variable on the non-expandable surface, t is a variable on the mapping surface;

The curves before and after the mapping have the same first basic form of the surface, and the normal vector direction at each point has the same length before and after the mapping:

And also need to meet:

h=k,

Among them, h is a variable on the mapping surface, and k is a variable on the non-expandable surface.

Specifically, the two entities r(t,w,h) and r(u ₁ ,v ₁ ,k) before and after mapping, and the positions of each point of the nearby geometric entities can be expressed by dr(t,w,h)=dr( t,w,0)+n(t,w,0)dh and dr(u,v,k)=dr(u,v,0)+n(u,v,0)dk to represent.

Embodiment 6. A curved surface near-zero stress acquisition device described in this embodiment, the acquisition device includes:

A target substrate and a target curved surface acquisition unit, configured to obtain a target substrate and a target curved surface covering the flexible electronic skin;

The first basic form of the curved surface and the normal vector acquisition unit for the curved surface are used to obtain the first basic form of the curved surface and the normal vector of the curved surface according to the target base and the target curved surface;

A surface type judging unit, configured to judge the surface type according to the first basic form of the surface;

The near-zero stress acquisition unit of the surface is used to divide the surface according to the type of the surface, and use space mapping to complete the zero-stress expansion of the surface after the division, and obtain the near-zero stress of the surface.

Embodiment 7. This embodiment is a further limitation of the near-zero stress acquisition device for a curved surface described in Embodiment 6. The first basic form of the curved surface and the normal vector acquisition unit of the curved surface include:

Among them, n(t,w,0) is the normal vector of the surface, r(t,w,0) is the target surface, t is a variable of the target surface, and w is a variable of the target surface.

Embodiment 8. This embodiment is a further limitation of the near-zero stress acquisition device for curved surfaces described in Embodiment 6. The curved surface type judging unit includes: judging whether the curved surface is a developable curved surface or a non-developable curved surface;

The criteria for determining the developable curved surface include:

r(u,v,0)=r(u)+vl(u),

(r(u),l(u),l'(u))=0,

Among them, u is a variable in the parametric equation of the surface, v is a variable in the parametric equation of the surface, r(u,v,0) is the parametric equation of the surface, r(u) is a target curve on the surface, l(u) is Another target curve on the surface, l'(u) is the derivative curve of another target curve on the surface.

Embodiment 9. A computer-readable storage medium described in this embodiment, where the computer-readable storage medium is used to store a computer program, and the computer program executes one of the methods described in any one of Embodiments 1 to 5. A method for obtaining near-zero stress on curved surfaces.

Embodiment 10. A computer device described in this embodiment includes a memory and a processor, the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes A method for obtaining near-zero stress on a curved surface described in any one of Embodiments 1 to 5.

Embodiment 11. This embodiment will be described with reference to FIG. 2 , FIG. 3 , FIG. 4 , FIG. 5 and FIG. 6 . This embodiment is to provide a specific implementation method for a method for obtaining near-zero stress on a curved surface described in Embodiment 1, and is also used to explain Embodiments 1 to 5. Specifically:

Step 1: Select the target surface to be pasted by the flexible electronic skin, determine the target substrate to be pasted by the flexible electronic skin as r(t,w,h) according to the target surface, and determine the target surface as r(t,w,0), according to The following formula calculates the normal vector n(t,w,0) of each point on the surface:

Among them, n(t,w,0) is the normal vector of the surface, r(t,w,0) is the target surface, t is a variable of the target surface, and w is a variable of the target surface.

Step 2: Determine whether the surface is a developable surface:

If the parametric equation r(u,v,0) of the surface can be written as r(u,v,0)=r(u)+vl(u), and (r(u),l(u),l'(u ))=0, then the surface is a developable surface, and go directly to step 4; if the parameter equation r(u,v,0) of the surface cannot be written as r(u,v,0)=r(u)+vl (u), then the surface is a non-developable surface, go to step 3.

Step 3: Construct the developable tangent surface of the non-developable surface, and ensure the zero-stress development along the given curve, so as to realize the near-zero stress development.

为映射曲面上法向量。For the non-developable surface r(u ₁ ,v ₁ ,0), select a target curve r=r(u ₁ (t),v ₁ (t))=r(t), and then construct a developable surface along the curve r(t,w)=r(t)+wl(t), where:

is the normal vector on the mapping surface.

The mapping constructed by the developable tangent surface is:

Among them, u ₁ is a variable on the non-expandable surface, v ₁ is a variable on the non-expandable surface, and t is a variable on the mapping surface.

And ensure that the curve has the same first basic form of the surface before and after the selection of mapping and the length of the normal vector direction at each point remains unchanged before and after mapping, that is, satisfy the formulas (3) and (4):

The two entities r(t,w,h) and r(u ₁ ,v ₁ ,k) before and after the mapping, and the positions of the points of the nearby geometric entities can be expressed by dr(t,w,h)=dr(t,w, 0)+n(t,w,0)dh and dr(u,v,k)=dr(u,v,0)+n(u,v,0)dk to represent. And also need to meet:

h=k (5)

Among them, h is a variable on the mapping surface, and k is a variable on the non-expandable surface.

Step 4: Take the obtained developable surface (including the developable tangent surface r(u ₁ ,v ₁ ,k) obtained in step 3) and obtain r(t,w according to t=u,v=w,h=k respectively , h). Further, r(t,w,h) is classified according to the following formula:

(1) If l'(t)=0, the developable surface is a cylinder. Take the generatrix of the cylinder as the positive direction of the z-axis, and project the original directrix r(t)=(f(t), g(t), h(t)) onto the generatrix l=(0,0,1 ) plane to get a new directrix. Among them, f(t) is a function of variable t, g(t) is a function of variable t, h(t) is a function of variable t.

A form in which the cylinder can be written. Generate a region of target space from a surface and its normal vectors:

r ₁ (t,w,h)=r ₁ (t,w)+hn(t,w).

The corresponding plane area r ₀ (t ₀ ,w ₀ ,h ₀ ) is:

r ₁ (t,w)=(f ₁ (t),g ₁ (t),w),

r ₀ (t ₀ ,w ₀ ,h ₀ )=r ₀ (t ₀ ,w ₀ )+h ₀ n(t ₀ ,w ₀ )=t ₀ i+w ₀ l+h ₀ j,

Among them, r ₀ (t ₀ , w ₀ ) is the plane parametric equation, n(t ₀ , w ₀ ) is the plane parametric equation, h ₀ is the variable, t ₀ is the variable, w ₀ is the variable, i is the x-axis coordinate vector , l is the y-axis coordinate vector, j is the z-axis coordinate vector.

According to the isometric mapping formula, the zero stress expansion formula of the cylinder can be obtained as:

Wherein, f ₁ '(t) is the derivative function of f ₁ (t), and g ₁ '(t) is the derivative function of g ₁ (t).

(2) If l'≠0, r'(t)×l'(t)=0, cr'(t)=l'(t), where c is a constant, and c≠0, the curved surface is a cone noodle. The parametric equation of the cone surface is:

是球坐标系

下ρ＝1的球面上的曲线的矢函数。

is the spherical coordinate system

The vector function of the curve on the sphere with ρ=1.

的形式。Surface r(t,w)=r(g(t),h(t))w is a conical surface. The conical surface needs to satisfy the condition that l'(t)=cr'(t), c≠0. For surface r(t,w), since the cone point is used as the origin, r(t)=r(g(t),h(t)), and according to the form of developable surface, l(t)=r (g(t), h(t)), naturally satisfy the condition of the cone. Taking the cone point as the origin, it can be written as

form.

通过直角坐标系与球坐标系之间的转化关系，生成一条新的准线r₁(t)＝r(g₁(t),h₁(t))。其中：In the Cartesian coordinate system, define r(t)=(f(t),g(t),h(t)).

A new directrix r ₁ (t)=r(g ₁ (t),h ₁ (t)) is generated through the conversion relationship between the rectangular coordinate system and the spherical coordinate system. in:

e_θ＝(-sinθ,cosθ,0),

这三个单位基矢量作为随体坐标系加以描述，它们之间具有如下关系：Pick

e _θ = (-sinθ,cosθ,0),

These three unit basis vectors are described as satellite coordinate systems, and they have the following relationship:

For surfaces:

r(t,w)=r(g ₁ (t),h ₁ (t))w,

Spatial regions can be generated:

构成的空间区域Correspondingly, the xoy plane can be taken as

constituting the spatial region

Then the near-zero stress expansion formula of the conical surface is as follows:

(3) If r'(t)×l(t)=0, it can also be written as r'(t)=cl(t), where c is a constant. Then the independent variables (t,w) define the vector function of the tangent surface:

Wherein, the relationship between the parameter t and the arc length s of the curve is t=t(s).

如果以弧长s作为自变量定义r(s)＝(f(s),g(s),h(s))，那么此时|r'(s)|＝1。此时的切线曲面可以写成r(s,w)＝r(s)+wr'(s)。那可以构造一个空间区域r(s,w,h)＝r(s)+wr'(s)+hn(s,w),

and

If r(s)=(f(s), g(s), h(s)) is defined with the arc length s as an independent variable, then |r'(s)|=1 at this time. The tangent surface at this time can be written as r(s,w)=r(s)+wr'(s). That can construct a spatial region r(s,w,h)=r(s)+wr'(s)+hn(s,w),

所以展平后导线与x轴的夹角

则展平后导线a(s)的表达式

则对应的切线曲面为r₀(s,w)＝a(s)+wa'(s)。对应平面区域为：r₀(s₀,w₀,h₀)＝a(s₀)+wa'(s₀)+h₀n(s₀,w₀)。First, find the curvature of the directrix

So the angle between the wire and the x-axis after flattening

Then the expression of the wire a(s) after flattening

Then the corresponding tangent surface is r ₀ (s,w)=a(s)+wa'(s). The corresponding plane area is: r ₀ (s ₀ , w ₀ , h ₀ )=a(s ₀ )+wa'(s ₀ )+h ₀ n(s ₀ ,w ₀ ).

Then the zero stress expansion formula of the tangent surface is:

Step 5: Select an appropriate mechanical model for the target surface according to the actual surface condition and the selected material, determine the strain field according to the displacement field determined in steps 1-4, and then solve the stress field, and finally determine the stress required for deformation. A near-zero stress expansion of the target surface is accomplished.

Taking the expansion of a hyperbolic paraboloid as an example, the near-zero stress expansion process of this surface is briefly described.

Hyperbolic paraboloid expression: r (u, v) = (3 (u, v), 2 (uv), 2uv), first draw the original surface diagram, as shown in Figure 2. Select the intersection line between the original curved surface and the plane y=0 as the expanded curve, and obtain its parameter equation as r(t)=(6t,0.2t ² ), and calculate r(t,w)=r through the formula of the above steps 1-5 (t)+wl(t), and the mapping relationship between the two surfaces is given as:

It can be proved that the above conditions for near-zero stress expansion along a given curve are satisfied. The developable tangent surface can be calculated as (6t,-w,2t ² ). The graph of the developable tangent surface is made as shown in Figure 3. Draw the two surfaces in the same coordinate system, the result is shown in Figure 4.

After completing the construction of the developable tangent surface of the non-developable surface, the developable tangent surface is developed into a plane by isometric mapping. By calculating l'=0, it can be judged that the developable tangent surface is a cylinder, so the cylinder expansion equation is used for expansion, namely:

Through the construction of developable tangent surface, the unfolding work of hyperbolic paraboloid is transformed into the work of cylinder unfolding. Make the developed plan view 5 and the comparison view 6 together with the developable cut surface.

The above steps complete the mapping process from the non-developable surface to the plane, that is, the unfolding process of the non-developable surface. Since the unfolding process from a developable surface to a plane is an equidistant mapping, the deformation of all the surfaces during the unfolding process is caused by the first step, and the analysis shows that the deformation of the surface around the unfolding line is very small, so through the appropriate By selecting the expansion line, the expansion error can be well controlled, and the goal of nearly zero stress expansion can be achieved.

While preferred embodiments of the present disclosure have been described, additional changes and modifications to these embodiments can be made by those skilled in the art once the basic inventive concept is appreciated. Therefore, it is intended that the appended claims be construed to cover the preferred embodiment and all changes and modifications which fall within the scope of the present disclosure.

Obviously, those skilled in the art can make various changes and modifications to the present disclosure without departing from the spirit and scope of the present disclosure. Thus, if these modifications and variations of the present disclosure fall within the scope of the claims of the present disclosure and equivalent technologies thereof, the present disclosure also intends to include these modifications and variations.

Those skilled in the art should understand that the embodiments of the present disclosure may be provided as methods, systems or computer program products. Accordingly, the present disclosure can take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present disclosure may take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein. The present disclosure is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the present disclosure. It should be understood that each procedure and/or block in the flowchart and/or block diagram and a combination of procedures and/or blocks in the flowchart and/or block diagram can be realized by computer program instructions. These computer program instructions may be provided to a general purpose computer, special purpose computer, embedded processor, or processor of other programmable data processing equipment to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing equipment produce a An apparatus for realizing the functions specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram. These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to operate in a specific manner, such that the instructions stored in the computer-readable memory produce an article of manufacture comprising instruction means, the instructions The device realizes the function specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram. These computer program instructions can also be loaded onto a computer or other programmable data processing device, causing a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process, thereby The instructions provide steps for implementing the functions specified in the flow chart or blocks of the flowchart and/or the block or blocks of the block diagrams.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present disclosure rather than limit the scope of protection thereof. Although the present disclosure has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: After reading this disclosure, those skilled in the art can still make various changes, modifications or equivalent replacements to the specific embodiments of the invention, but these changes, modifications or equivalent replacements are all within the scope of protection of the pending claims.

Claims (10)

1. A curved surface near-zero stress acquisition method is characterized by comprising the following steps:

acquiring a target substrate and a target curved surface covering the flexible electronic skin;

acquiring a first basic form of a curved surface and a normal vector of the curved surface according to the target substrate and the target curved surface;

judging the type of the curved surface according to the first basic form of the curved surface;

and carrying out curved surface division according to the type of the curved surface, and adopting space mapping to carry out zero stress expansion on the divided curved surface so as to obtain a near-zero stress expansion form of the curved surface.

2. The method of claim 1, wherein the obtaining the first basic form of the curved surface and the normal vector of the curved surface according to the target substrate and the target curved surface comprises:

wherein n (t, w, 0) is a normal vector of the curved surface, r (t, w, 0) is the target curved surface, t is a variable of the target curved surface, and w is a variable of the target curved surface.

3. The method for obtaining near-zero stress of a curved surface according to claim 1, wherein the determining the type of the curved surface according to the first basic form of the curved surface comprises: judging whether the curved surface is an extensible curved surface or a non-extensible curved surface;

the judgment condition of the developable surface comprises the following steps:

r(u,v,0)＝r(u)+vl(u)，

(r(u),l(u),l'(u))＝0，

wherein u is a variable in the curved surface parameter equation, v is a variable in the curved surface parameter equation, r (u, v, 0) is the curved surface parameter equation, r (u) is a target curve on the curved surface, l (u) is another target curve on the curved surface, and l' (u) is another target curve derivative curve on the curved surface;

and if the judgment condition of the developable surface is not met, the developable surface is an undevelopable surface.

4. The method for obtaining the near-zero stress of the curved surface according to claim 3, wherein the step of dividing the curved surface according to the type of the curved surface to obtain the near-zero stress of the curved surface specifically comprises:

constructing a developable curved surface of the non-developable curved surface, and acquiring the near-zero stress of the curved surface;

and dividing the cylindrical surface, the conical surface and the independent variable definition tangent line curved surface according to the developable curved surface to obtain the near-zero stress of the cylindrical surface, the conical surface and the independent variable definition tangent line curved surface.

5. The method of claim 4, wherein constructing the developable surface of the inextensible surface comprises:

for inextensible surfaces r (u) ₁ ,v ₁ 0), selecting a target curve:

r＝r(u ₁ (t),v ₁ (t))＝r(t)，

wherein u is ₁ (t) is the tangent family equation of a single parameter t on the target curve, v ₁ (t) is a tangent family equation of a single parameter t on the target curve, and r (t) is a target curve on the non-developable curved surface;

constructing a developable curved surface r (t, w) according to the curve:

r(t,w)＝r(t)+wl(t)，

wherein r (t) is a target curve on the inextensible curved surface, and w is a variable of the target curved surface;

the map constructed by the developable curved surface is:

wherein u is ₁ Is a variable on the non-developable surface, v ₁ A variable on the non-expandable curved surface is represented by t, and a variable on the mapping curved surface is represented by t;

the curves before and after mapping have the same first basic form of the curved surface, and the lengths before and after mapping in the normal vector direction at each point are unchanged:

and also needs to satisfy:

h＝k，

wherein, h is a variable on the mapping curved surface, and k is a variable on the non-deployable curved surface.

6. A curved surface near-zero stress obtaining apparatus, comprising:

the target substrate and target curved surface acquisition unit is used for acquiring a target substrate and a target curved surface which cover the flexible electronic skin;

the curved surface normal vector acquisition unit is used for acquiring a first basic form of the curved surface and a normal vector of the curved surface according to the target substrate and the target curved surface;

the curved surface type judging unit is used for judging the type of the curved surface according to the first basic form of the curved surface;

and the curved surface near-zero stress acquisition unit is used for dividing the curved surface according to the type of the curved surface, and adopting space mapping to complete zero stress expansion of the curved surface on the divided curved surface so as to acquire the near-zero stress of the curved surface.

7. The curved surface near-zero stress extraction device of claim 6, wherein the curved surface first basic form and the curved surface normal vector extraction unit comprise:

wherein n (t, w, 0) is a normal vector of the curved surface, r (t, w, 0) is the target curved surface, t is a variable of the target curved surface, and w is a variable of the target curved surface.

8. The curved surface near-zero stress acquisition apparatus according to claim 6, wherein the curved surface type determination unit comprises: judging whether the curved surface is an extensible curved surface or a non-extensible curved surface;

the judgment condition of the developable surface includes:

r(u,v,0)＝r(u)+vl(u)，

(r(u),l(u),l'(u))＝0，

wherein u is a variable in the curved surface parameter equation, v is a variable in the curved surface parameter equation, r (u, v, 0) is the curved surface parameter equation, r (u) is a target curve on the curved surface, l (u) is another target curve on the curved surface, and l' (u) is another target curve derivative curve on the curved surface.

And if the judgment condition of the developable surface is not met, the developable surface is an undevelopable surface.

9. A computer-readable storage medium storing a computer program for executing a curved surface near-zero stress acquisition method according to any one of claims 1 to 5.

10. A computer device, characterized by: comprising a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes a curved surface near-zero stress acquisition method according to any one of claims 1-5.

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