CN115659690A - Curved surface near-zero stress acquisition method and device, computer and storage medium - Google Patents
Curved surface near-zero stress acquisition method and device, computer and storage medium Download PDFInfo
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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
Technical Field
The invention relates to the field of flexible electronic design, in particular to a method for acquiring near-zero stress of a curved surface.
Background
In recent years, with the continuous development of flexible electronic technology, the flexible electronic technology has shown good application prospects in the aspects of human body physiological signal detection, minimally invasive treatment, robot electronic skin, flexible display, flexible energy and the like. Many high-performance flexible electronic devices have been verified in laboratories, but they are going to be applied in large scale, and there are many technical bottlenecks, among which, the mechanical problem of the flexible electronic devices is more prominent, and the bottleneck which is difficult to overcome is exposed when the external surface of the target object is covered. The outer surfaces of electronic skin attaching target objects such as the body surface of a human body, the outer surface of a robot and the like are usually space curved surfaces and cannot be unfolded into planes; the substrates for current electronic skin fabrication are generally planar. Therefore, seamless attachment can not be realized when the flexible electronic skin manufactured on the plane is attached to the outer surface of the object, and the initial stress states borne by the flexible electronic skin at all positions are different, so that the flexible electronic skin can generate different responses to the same external force in the working process; thereby causing the electronic skin to fail to accurately detect external force effects. In order to solve the problems, the current mainstream method is to improve the deformation capabilities of the flexible electronic device such as stretching, twisting, shearing and the like through the micro-nano structure design of the flexible substrate. However, this design approach is heavily dependent on the designer's experience, long cycle times, high substrate processing costs, and poor versatility.
Disclosure of Invention
The invention solves the problems that the design of the micro-nano structure of the flexible electronic substrate with a well-pasted space curved surface depends on the experience of a designer, the period is long, the processing cost of the substrate is high, and the universality is poor.
The invention relates to a curved surface near-zero stress acquisition method, which 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;
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 the near-zero stress of the curved surface.
Further, there is provided in a preferred embodiment that the obtaining of 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 includes:
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.
Further, there is provided a preferred embodiment, wherein the determining the type of the curved surface according to the first basic form of the curved surface includes: 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 parameter equation of the curved surface, v is a variable in the parameter equation of the curved surface, r (u, v, 0) is the parameter equation of the curved surface, r (u) is a target curve on the curved surface, l (u) is another target curve on the curved surface, and l' (u) is a derivative curve of another target curve on the curved surface.
And if the judgment condition of the developable surface is not met, the developable surface is an undevelopable surface.
Further, a preferred embodiment is provided, where the curved surface division is performed according to the type of the curved surface to obtain the near-zero stress of the curved surface, specifically including:
constructing an extensible cutting curved surface of the inextensible curved surface to obtain 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.
Further, there is provided a preferred embodiment, wherein the method for constructing the developable curved surface of the non-developable curved surface includes:
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-expandable curved surface.
Based on the same inventive concept, the invention also provides a curved surface near-zero stress acquisition device, which comprises:
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.
Further, there is provided a preferred embodiment, wherein the first basic form of the curved surface and the normal vector acquiring unit of the curved surface include:
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.
Further, there is provided a preferred embodiment, wherein the curved surface type determining unit includes: 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.
Based on the same inventive concept, the present invention further provides a computer-readable storage medium, where the computer-readable storage medium is used for storing a computer program, and the computer program executes any one of the above methods for obtaining near-zero stress of a curved surface.
Based on the same inventive concept, the invention further provides a computer device, which comprises 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 the curved surface near-zero stress acquisition method according to any one of the above.
The invention has the advantages that:
the invention solves the problems that the design of the micro-nano structure of the flexible electronic substrate with a well-pasted space curved surface depends on the experience of a designer, the period is long, the processing cost of the substrate is high, and the universality is poor.
The method for obtaining the near-zero stress of the curved surface obtains a first basic form of the curved surface by obtaining a target curved surface, judges the type of the curved surface according to the form of the curved surface, divides the curved surface, and adopts space mapping to perform zero stress expansion on the divided curved surface. Thereby obtaining the plane substrate needed by manufacturing the flexible electronic skin attached on the target curved surface. According to the planar substrate obtained by the method, after the planar substrate is reversely pasted according to the designed mapping, the stress of the flexible electronic skin on the target curved surface can be ensured to be approximately zero. The method for acquiring the near-zero stress of the curved surface does not depend on the experience of designers, and can be used for unfolding the plane stress of different types of curved surfaces according to the method, so that the time and the labor are saved. The increase of the processing cost of the substrate caused by misoperation of a designer is avoided. The method can realize the nearly zero stress in the manufacturing plane substrate of the flexible electronic skin, realize the seamless pasting of the flexible electronic skin on the surface curved surface of the object, and has good universality and good application range.
The invention is applied to the field of flexible electronic skin.
Drawings
Fig. 1 is a flowchart of a curved surface near-zero stress obtaining method according to a first embodiment;
fig. 2 is a schematic view of a primary curved surface of a hyperbolic paraboloid according to an eleventh embodiment;
fig. 3 is a schematic view of a developable surface of a hyperbolic paraboloid of an embodiment eleventh, which is configured along a y =0 curved surface;
fig. 4 is a comparison diagram of the original hyperbolic paraboloid surface and the developable curved surface in the same coordinate system according to the eleventh embodiment;
FIG. 5 is a plan view of an embodiment of an eleventh embodiment of a curved stretch-cuttable surface;
fig. 6 is a comparison diagram of the developable curved surface and the development plane in the same coordinate system according to the eleventh embodiment.
Detailed Description
In order to make the technical solutions and advantages of the present invention more apparent, several embodiments of the present invention will be described in further detail with reference to the accompanying drawings, but the embodiments described below are only some preferred embodiments of the present invention, and are not intended to limit the present invention.
First embodiment this embodiment will be described with reference to fig. 1. The method for acquiring the near-zero stress of the curved surface in the embodiment 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;
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 the near-zero stress of the curved surface.
In the method for obtaining near-zero stress of a curved surface according to this embodiment, a first basic form of the curved surface is obtained by obtaining a target curved surface, a type of the curved surface is determined according to the form of the curved surface, the curved surface is divided, and zero stress expansion of the curved surface is completed on the divided curved surface by using spatial mapping. Thereby obtaining the plane substrate needed by manufacturing the flexible electronic skin attached on the target curved surface. According to the planar substrate obtained by the method, after the planar substrate is reversely pasted according to the designed mapping, the stress of the flexible electronic skin on the target curved surface can be ensured to be approximately zero. The method for acquiring the near-zero stress of the curved surface does not depend on the experience of a designer, and is time-saving and labor-saving. Avoid the increase of the processing cost of the substrate caused by the operation error of the designer. The internal approximate zero stress of the plane substrate for manufacturing the flexible electronic skin is realized, and the universality is good.
In a second aspect of the present invention, there is provided the method for obtaining a near-zero stress of a curved surface according to the first aspect, wherein the obtaining a first basic form of the curved surface and a normal vector of the curved surface based on the target substrate and the target curved surface includes:
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.
Specifically, in this embodiment, a target curved surface to which the flexible electronic skin is to be attached is selected, and a target substrate to which the flexible electronic skin is to be attached is determined according to the target curved surface. 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, wherein the normal vector n (t, w, 0) of each point on the curved surface is as follows:
wherein n (t, w, 0) is a normal vector of the curved surface, r (t, w, 0) is a target curved surface, t is a variable of the target curved surface, and w is a variable of the target curved surface.
In a third aspect of the present invention, in the method for obtaining near-zero stress of a curved surface according to the first aspect, the determining the type of the curved surface according to the first basic form of the curved surface includes: 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 a curved surface parameter equation, v is a variable in a curved surface parameter equation, r (u, v, 0) is a 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.
Specifically, the embodiment provides a condition for judging the type of the curved surface, which is beneficial to further dividing the curved surface and ensuring the accuracy of near-zero stress expansion of the curved surface.
In a fourth embodiment, the method for obtaining near-zero stress of a curved surface according to the third embodiment is further limited, where the dividing the curved surface according to the type of the curved surface to obtain the near-zero stress of the curved surface specifically includes:
constructing an extensible cutting curved surface of the inextensible curved surface to obtain 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.
Specifically, the developable and incisable curved surface of the non-developable curved surface is constructed, and zero-stress expansion along a given curve is ensured, so that near-zero stress expansion is realized.
In a fifth aspect of the present invention, the method for obtaining near-zero stress of a curved surface according to the fourth aspect further includes:
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, r (t) is a target curve on the non-developable curve,
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 non-expandable 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-expandable curved surface.
Specifically, two entities r (t, w, h) and r (u) before and after mapping 1 ,v 1 K), and the positions of the points in the vicinity of the geometric solid can be represented 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.
Sixth, a curved surface near-zero stress obtaining apparatus according to this embodiment includes:
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.
A seventh aspect of the present invention is directed to the device for acquiring a near-zero stress of a curved surface according to the sixth aspect, wherein the first basic form of the curved surface and the normal vector acquiring unit of the curved surface include:
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.
An eighth embodiment is the device for acquiring a curved surface near-zero stress according to the sixth embodiment, wherein the curved surface type determination unit includes: 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.
In an embodiment ninth, the computer-readable storage medium is used for storing a computer program, and the computer program executes the method for acquiring near-zero stress of a curved surface according to any one of the first to fifth embodiments.
Tenth embodiment and a computer apparatus according to this embodiment include a memory and a processor, where 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 obtaining method according to any one of the first to fifth embodiments.
The present embodiment will be described with reference to fig. 2, 3, 4, 5, and 6. The present embodiment provides a specific embodiment for the method for acquiring a near-zero stress of a curved surface in the first embodiment, and is also used to explain the first to fifth embodiments, specifically:
step 1: selecting a target curved surface to be attached to the flexible electronic skin, determining a target substrate to be attached to the flexible electronic skin as r (t, w, h) and a target curved surface as r (t, w, 0) according to the target curved surface, and solving a normal vector n (t, w, 0) of each point on the curved surface according to the following formula:
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.
Step 2: judging whether the curved surface is an expandable curved surface:
if the parametric equation r (u, v, 0) for a 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, proceed directly to step 4; if the parameter equation r (u, v, 0) of the curved surface can not be written as r (u, v, 0) = r (u) + vl (u), the curved surface is an undevelopable curved surface, and the step 3 is carried out.
And step 3: and constructing the developable and cutting curved surface of the non-developable curved surface, and ensuring zero-stress expansion along the given curve, thereby realizing near-zero-stress expansion.
For non-developable surface r (u) 1 ,v 1 0), choose a target curve r = r (u) 1 (t),v 1 (t)) = r (t), and then constructing a developable curved surface r (t, w) = r (t) + wl (t) along the curve, where:
is used for mapping the normal vector on the 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 Is a variable on the non-developable surface, and t is a variable on the mapping surface.
And ensuring that the curve has the same first basic form of the curved surface before and after the selection of the mapping and the lengths before and after the normal vector direction of each point are unchanged, namely, the following formulas (3) and (4) are satisfied:
mapping two entities r (t, w, h) and r (u) before and after 1 ,v 1 K), and the positions of the points in the vicinity of the geometric solid can be represented 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. And also needs to satisfy:
h＝k (5)
wherein h is a variable on the mapping curved surface, and k is a variable on the non-expandable curved surface.
Step 4, the obtained developable curved surface (comprising the developable cutting curved surface r (u) obtained in the step 3) 1 ,v 1 K)), r (t, w, h) is obtained as t = u, v = w, h = k, respectively. Further, r (t, w, h) is classified according to the following formula:
(1) If l' (t) =0, the developable surface is a cylindrical surface. The generatrix of the cylindrical surface is taken as the positive z-axis direction, and the original alignment line r (t) = (f (t), g (t), h (t)) is projected into a plane perpendicular to the generatrix l = (0,0,1), so as to obtain a new alignment line. Where f (t) is a function with respect to the variable t, g (t) is a function with respect to the variable t, and h (t) is a function with respect to the variable t.
The cylinder may be written in the form of. Generating a target space region according to the curved surface and the normal vector of the curved surface:
r 1 (t,w,h)＝r 1 (t,w)+hn(t,w)。
corresponding plane area r 0 (t 0 ,w 0 ,h 0 ) Comprises the following steps:
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，
wherein r is 0 (t 0 ,w 0 ) Is a planar parametric equation, n (t) 0 ,w 0 ) Is a plane parameter equation, h 0 Is a variable, t 0 Is a variable, w 0 Is a variable, i is an x-axis coordinate vector, l is a y-axis coordinate vector, and j is a z-axis coordinate vector.
According to the equidistant mapping formula, the zero-stress expansion formula of the cylindrical surface can be obtained as follows:
wherein, f 1 ' (t) is f 1 (t) derivative function, g 1 ' (t) is g 1 (t) a derivative function.
(2) If l ' ≠ 0,r ' (t) × l ' (t) =0, cr ' (t) = l ' (t), where c is constant and c ≠ 0, the curved surface is a cone. The conical surface parameter equation is:
The curved surface r (t, w) = r (g (t), h (t)) w is a conical surface. The condition that the taper needs to satisfy is l '(t) = cr' (t), c ≠ 0. Since the curved surface r (t, w) has a tapered point as an origin, r (t) = r (g (t), h (t)), and l (t) = r (g (t), h (t)) naturally satisfies the condition of the tapered surface according to the form of the developable surface. With the cone point as the origin, can be written as
In the form of (1).
In a rectangular coordinate system, r (t) = (f (t), g (t), h (t)) is defined.
Generating a new alignment r through the transformation relation between the rectangular coordinate system and the spherical coordinate system 1 (t)＝r(g 1 (t),h 1 (t)). Wherein:
get
e θ ＝(-sinθ,cosθ,0),
These three unit basis vectors are described as a random coordinate system, with the following relationships between them:
for curved surfaces:
r(t,w)＝r(g 1 (t),h 1 (t))w，
the spatial region may be generated:
corresponding to this, can be taken from xoy plane
Formed space region
The near zero stress expansion equation for the cone is as follows:
(3) If r '(t) × l (t) =0, it is also possible to write r' (t) = cl (t), where c is a constant. The argument (t, w) defines the vector function of the tangent surface:
wherein, the relation between the parameter t and the curve arc length s is t = t(s).
While
If r(s) = (f(s), g(s), h (s)) is defined with the arc length s as an argument, | r'(s) | =1 at this time. The tangent curved surface at this time can be written as r (s, w) = r(s) + wr'(s). That makes it possible to construct a spatial region r (s, w, h) = r(s) + wr'(s) + hn (s, w),
first, the curvature of the alignment line is determined
So that the included angle between the flattened lead and the x axis
Expression of the flattened conductor a(s)
The corresponding tangent curved surface is r 0 (s, w) = a(s) + wa'(s). The corresponding planar areas are: r is 0 (s 0 ,w 0 ,h 0 )＝a(s 0 )+wa'(s 0 )+h 0 n(s 0 ,w 0 )。
The zero-stress expansion formula of the tangent curved surface is as follows:
and 5: selecting a proper mechanical model for the target curved surface according to the actual condition of the attached curved surface and the selected material, determining a strain field according to the displacement field determined in the step 1-4, further solving the stress field, finally determining the stress required by deformation, and completing the near-zero stress expansion of the target curved surface.
The hyperbolic paraboloid unfolding is taken as an example, and the near-zero stress unfolding process of the curved surface is briefly described.
Hyperbolic paraboloid expression: r (u, v) = (3 (u, v), 2 (u-v), 2 uv), the original surface map is drawn first, as shown in fig. 2. Selecting the intersection line of the original curved surface and the plane y =0 as an expansion curve to obtain the parameter equation of r (t) = (6 t, 0.2t) 2 ) Calculating r (t, w) = r (t) + wl (t) by the formula of the above steps 1-5, and giving a mapping relation between two curved surfaces as follows:
it can be shown that the above-mentioned condition for near-zero stress deployment along a given curve is satisfied. The calculated developable curved surface is (6 t, -w,2 t) 2 ). A graph of the stretch-cuttable curved surface is thus produced as shown in fig. 3. The two curved surfaces are plotted in the same coordinate system, and the result is shown in fig. 4.
After the deployable and incisable curved surface structure of the non-deployable curved surface is completed, the deployable and incisable curved surface is deployed into a plane through equidistant mapping. By calculating l' =0, the developable curved surface can be judged to be a cylindrical surface, so the developable curved surface is developed by adopting a cylindrical surface development equation, namely:
the unfolding work of the hyperbolic paraboloid is converted into the cylindrical surface unfolding work through the structure of the unfolding-cutting curved surface. A developed plan view 5 and a comparison with a developable curved surface together figure 6 are made separately.
The steps are carried out, and the mapping process from the non-developable surface to the plane, namely the unfolding process of the non-developable surface is completed. Because the unfolding process from the developable curved surface to the plane is equidistant mapping, the deformation of all the curved surfaces in the unfolding process is caused by the first step, and the analysis shows that the deformation of the curved surfaces around the unfolding line is very small, so that the unfolding error can be well controlled by properly selecting the unfolding line, and the aim of unfolding near zero stress is fulfilled.
While the preferred embodiments of the present disclosure have been described, additional variations and modifications of these embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including the preferred embodiment and all changes and modifications that fall within the scope of the present disclosure.
It will be apparent to those skilled in the art that various changes and modifications can be made in the present disclosure without departing from the spirit and scope of the disclosure. Thus, if such modifications and variations of the present disclosure fall within the scope of the claims of the present disclosure and their equivalents, the present disclosure is intended to include such modifications and variations as well.
As will be appreciated by one skilled in the art, embodiments of the present disclosure may be provided as a method, system, or computer program product. Accordingly, the present disclosure may 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, and so forth) 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 disclosure. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present disclosure and not for limiting the scope of protection thereof, and although the present disclosure is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: those skilled in the art who review this disclosure will readily appreciate that many alternatives, modifications, and equivalents are possible in the specific embodiments of the invention, as those variations, modifications, and equivalents are within the scope of the disclosure as defined in the appended 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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