CN114417726A - Method and device for constructing curved surface negative Poisson's ratio design based on approximate function - Google Patents
Method and device for constructing curved surface negative Poisson's ratio design based on approximate function Download PDFInfo
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Abstract
The embodiment of the specification provides a method and a device for constructing curved surface negative Poisson's ratio design based on an approximation function, wherein the method comprises the following steps: acquiring a function curve structure of an approximate function, constructing a negative Poisson ratio structure based on the function curve structure, constructing an optimization target and a design variable based on the approximate function, and constructing an optimization function based on the optimization target and the design variable; and calculating the optimization function through a genetic algorithm to obtain an optimal optimization target and an optimal input variable, and optimizing the negative Poisson ratio structure based on the optimal optimization target and the optimal input variable. According to the invention, a curved surface which is smoother than the traditional negative Poisson ratio is constructed by the approximate function curved surface, and the optimal structure required by the negative Poisson ratio approximate function curved surface in different occasions is intelligently optimized and designed by a genetic algorithm.
Description
Technical Field
The present invention relates to the technical field of negative poisson ratio structure design, and in particular, to a method and an apparatus for constructing a curved surface negative poisson ratio design based on an approximation function.
Background
The concept of poisson ratio was first discovered and proposed by french scientists, and negative poisson ratio was discovered accidentally by Poderick Lakes during experiments, and a negative poisson ratio structure or material is also called a auxetic structure or material, which means that when the material is in unidirectional tension (compression), the material is elongated (or shortened) along the load direction and is elongated (or shortened) in the direction perpendicular to the load direction.
Compared with a positive poisson ratio material or structure, the negative poisson ratio material or structure has better impact resistance and energy absorption performance, and the safety performance of the automobile in an accident can be greatly improved by applying the negative poisson ratio material or the honeycomb structure to the automobile energy absorption box. The invention provides a design method of a negative Poisson ratio structure, in particular to a design method for intelligently constructing a curved surface negative Poisson ratio based on an approximate function, and the design method is characterized in that the current classic three-dimensional negative Poisson ratio structure has a hand-shaped structure, a star-shaped structure, a concave hexagonal structure, an arrow-shaped structure and the like, so that the design of an innovative three-dimensional negative Poisson ratio structure is difficult
At present, the traditional negative Poisson ratio structure comprises a concave structure, an arrow structure and a star structure, wherein the structures are all formed by single straight lines or curves and cannot be formed by a unified curve; secondly, indexes such as mechanical structures and energy absorption required in different occasions are different, and the same structure type cannot be intelligently constructed according to the required indexes, so that the structure cannot be optimally utilized. Therefore, the negative Poisson ratio structure design method with general significance is provided, and particularly, the negative Poisson ratio structure which is intelligently constructed by designing indexes required by different occasions on the basis of the approximate function curved surface has important theoretical and practical application significance.
Disclosure of Invention
One or more embodiments of the present specification provide a method for constructing a curved surface negative poisson's ratio design based on an approximation function, including:
acquiring a function curve structure of an approximation function, and constructing a negative Poisson ratio structure based on the function curve structure, wherein the approximation function is a function approximately representing any curve;
constructing an optimization target and a design variable based on the approximate function, and constructing an optimization function based on the optimization target and the design variable;
and calculating the optimization function through a genetic algorithm to obtain an optimal optimization target and an optimal input variable, and optimizing the negative Poisson ratio structure based on the optimal optimization target and the optimal input variable.
One or more embodiments of the present specification provide an apparatus for constructing a curved surface negative poisson's ratio design based on an approximation function, including:
constructing a negative Poisson ratio structure module, acquiring a curve structure of an approximation function, and constructing the negative Poisson ratio structure based on the curve structure, wherein the approximation function is a function approximately representing any curve;
an optimization function module is constructed, an optimization target and design variables are constructed, and an optimization function is constructed based on the optimization target and the design variables;
and the structure optimization module calculates the optimization function through a genetic algorithm to obtain an optimal optimization target and an optimal input variable, and optimizes the negative Poisson ratio structure based on the optimal optimization target and the optimal input variable.
One or more embodiments of the present specification provide an electronic device including: the system comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the computer program realizes the steps of the construction curved surface negative Poisson's ratio design method based on the approximate function when being executed by the processor.
One or more embodiments of the present specification provide a computer-readable storage medium, on which an implementation program for information transfer is stored, and when the program is executed by a processor, the program implements the steps of the method for constructing a curved surface negative poisson's ratio design based on an approximation function as described above.
By adopting the embodiment of the invention, any negative Poisson's ratio boundary surface is constructed by the approximate function surface, and the intelligent construction optimization design of the approximate function surface is carried out by the required indexes. The invention adopts MATLAB genetic algorithm to carry out intelligent optimization design to obtain the optimal structure of the negative Poisson ratio approximate function curved surface required in different occasions by the index requirement, the negative Poisson ratio curved surface constructed by the approximate function is smoother than the traditional negative Poisson ratio curved surface, the traditional negative Poisson ratio boundary curved surface is a multi-cell honeycomb structure formed by arranging and combining single-cell curved surfaces, and the boundary curved surface constructed by the approximate function can be the negative Poisson ratio boundary curved surface of the whole honeycomb.
Drawings
In order to more clearly illustrate one or more embodiments or prior art solutions of the present specification, the drawings that are needed in the description of the embodiments or prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present specification, and that other drawings can be obtained by those skilled in the art without inventive exercise.
FIG. 1 is a flow chart of a method for constructing a curved surface negative Poisson's ratio design based on an approximation function according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the boundary of the whole negative Poisson's ratio honeycomb structure intelligently constructed by approximating a trigonometric function curved surface according to the embodiment of the invention;
FIG. 3 is a three-dimensional negative Poisson's ratio honeycomb structure constructed by approximating a trigonometric function curved surface according to an embodiment of the present invention;
FIG. 4 is a displacement cloud diagram of a negative Poisson ratio multi-cell structure designed by approximating a cosine function curved surface according to an embodiment of the present invention;
FIG. 5 is a displacement cloud diagram of a three-dimensional negative Poisson's ratio multi-cell structure designed by an approximate quadratic function curved surface in the invention;
FIG. 6 is a schematic diagram of a negative Poisson ratio unit cell structure designed using an approximate quadratic function curve according to an embodiment of the present invention;
FIG. 7 is a schematic diagram of a negative Poisson ratio multi-cell structure designed using an approximate quadratic function surface according to an embodiment of the present invention;
FIG. 8 is a schematic diagram of a negative Poisson ratio cell structure designed using an approximate circular curve according to an embodiment of the present invention;
FIG. 9 is a schematic diagram of a negative Poisson ratio multi-cell structure using an approximate circular arc surface design in an embodiment of the present invention;
FIG. 10 is a displacement cloud diagram of a negative Poisson ratio multi-cell structure designed to approximate a circular arc curved surface in an embodiment of the present invention;
FIG. 11 illustrates an embodiment of the present invention using the approximate y ═ x999A negative Poisson ratio unit cell structure schematic diagram designed by a function surface;
FIG. 12 is a drawing showingIn the embodiment of the invention, the approximate y ═ x is used99A negative Poisson ratio unit cell structure schematic diagram designed by a function surface;
fig. 13 is a schematic diagram of a device for constructing a curved surface negative poisson's ratio design based on an approximation function according to an embodiment of the present invention.
Detailed Description
In order to make those skilled in the art better understand the technical solutions in one or more embodiments of the present disclosure, the technical solutions in one or more embodiments of the present disclosure will be clearly and completely described below with reference to the drawings in one or more embodiments of the present disclosure, and it is obvious that the described embodiments are only a part of the embodiments of the present disclosure, and not all embodiments. All other embodiments that can be derived by a person skilled in the art from one or more of the embodiments described herein without making any inventive step shall fall within the scope of protection of this document.
Method embodiment
According to an embodiment of the present invention, a method for designing a constructed curved surface negative poisson ratio based on an approximation function is provided, fig. 1 is a flowchart of the method for designing the constructed curved surface negative poisson ratio based on the approximation function according to the embodiment of the present invention, and as shown in fig. 1, the method for designing the constructed curved surface negative poisson ratio based on the approximation function according to the embodiment of the present invention specifically includes:
step S101, acquiring a function curve structure of an approximation function, and constructing a negative Poisson ratio structure based on the function curve structure, wherein the approximation function is a function approximately representing any curve; the approximate function curve can construct both the whole honeycomb negative poisson ratio structure interface and the single-cell negative poisson ratio structure curved surface.
The embodiment of the invention takes the design of a negative Poisson ratio honeycomb structure by an approximate trigonometric function curved surface, the design of a negative Poisson ratio structure by an approximate quadratic function curved surface in an even-order function curved surface, the design of a negative Poisson ratio structure by an approximate circular arc curved surface, the design of an approximate y ^ x ^999 and the design of an approximate y ^ x ^99 curved surface in an odd-order function curved surface as examples, and the embodiment of the invention can design any negative Poisson ratio structure.
Fig. 2 is a schematic diagram of the boundary of the whole negative poisson ratio honeycomb structure intelligently constructed by the approximate trigonometric function curved surface in the embodiment of the invention, and as shown in fig. 2, the boundary curved surface of the negative poisson ratio honeycomb structure constructed by the complete approximate function curved surface is smoother than the boundary curved surface of the honeycomb structure formed by single cell arrangement and combination, and has better mechanical property.
Fig. 3 shows a negative poisson's ratio honeycomb structure formed by the boundary curved surface in fig. 2, and fig. 3 shows a three-dimensional negative poisson's ratio honeycomb structure constructed by an approximate trigonometric function curved surface according to an embodiment of the present invention; by applying pressure to the negative poisson's ratio honeycomb structure in fig. 3, a displacement cloud picture can be formed, as shown in fig. 4, and fig. 4 is a displacement cloud picture of a negative poisson's ratio multi-cell structure designed by an approximate cosine function curved surface in the embodiment of the invention.
Fig. 5 is a displacement cloud diagram of a three-dimensional negative poisson ratio multi-cell structure designed by an approximate quadratic function curved surface, according to fig. 5, when a pressure in the Z direction is applied, the multi-cell structure is compressed in the Z direction and simultaneously contracts inwards perpendicular to the load direction, and the overall structure has a negative poisson ratio characteristic of more obvious compression thinning and narrowing, and is more remarkable than a classical three-dimensional structure.
Step S102, constructing an optimization target and a design variable based on the approximate function, and constructing an optimization function based on the optimization target and the design variable; the construction method comprises the following steps: by constructing an optimization target eta and a set of design variables (x)1,x2,x3,x4,x5…xn) Functional relationship between: eta ═ f (x)1,x2,x3,x4,x5…xn) An optimization function η (x) is obtained.
Step S103, calculating the optimization function through a genetic algorithm to obtain an optimal optimization target and an optimal input variable, and optimizing the negative Poisson ratio structure based on the optimal optimization target and the optimal input variable, wherein the step S103 specifically comprises the following steps: and according to different required indexes of different occasions, obtaining an optimal design variable x and an optimal target eta by the obtained optimization function eta (x) and calling genetic algorithm intelligent optimization design through MATLAB software according to the required indexes.
FIG. 6 shows an embodiment of the present inventionThe negative Poisson ratio unit cell structure diagram is designed by an approximate quadratic function curve, wherein the expression of the approximate quadratic function is recorded as y-axn+bxt+ c wherein n is>t, n ∈ 2,4, 6,8 …, by approximation y ═ x in fig. 62The curve designs a negative Poisson's ratio single-cell structure, and the degree of curvature of the single-cell curved surface is adjusted by adjusting the parameter values n, t, a, b and c of the even function and adjusting the L, R value required by the index. Designing a curved side of a negative Poisson ratio single-cell structure by approximating a quadratic function curve, designing a curved surface by approximating the curved side of the quadratic function, introducing two boundary rods to form a negative Poisson ratio approximate quadratic function curved surface single-cell structure, rotating the single-cell structure by 90 degrees along a normal direction to form a single three-dimensional structure, and further forming a negative Poisson ratio multi-cell structure by arraying in an X direction and a Z direction, wherein the formed negative Poisson ratio multi-cell structure is shown in figure 7, and figure 7 is a schematic diagram of the negative Poisson ratio multi-cell structure designed by using the approximated quadratic function curved surface in the embodiment of the invention;
FIG. 8 is a schematic diagram of a negative Poisson ratio unit cell structure designed by using an approximate circular curve, which is recorded as
Wherein, a>b>And 0, adjusting the bending degree of the single-cell curved surface by adjusting the values of the parameters a and b and controlling the value of R, L, thereby designing a negative Poisson ratio structure of any arc-edge curved surface boundary and achieving the purpose of negative Poisson ratio structure indexes required in different occasions. The negative Poisson ratio curved edge is designed through an approximate arc edge curve, so that any arc edge curved surface is designed to form a single cell structure, the single cells are sequentially overlapped in the Z direction, the X direction is connected with the arc edge concave part through a horizontal rod, the negative Poisson ratio honeycomb structure is formed through linear arrays, the formed honeycomb structure is shown in fig. 9, when the pressure in the Z direction is applied, the negative Poisson ratio characteristic that the compression of the multi-cell structure is narrowed occurs, the compression effect is obvious, and the extrusion effect is shown in fig. 10.
FIG. 11 illustrates an embodiment of the present invention using the approximate y ═ x999A negative Poisson ratio unit cell structure schematic diagram designed by a function surface; fig. 12 illustrates an embodiment of the present invention using the approximate y ═ x99A negative Poisson ratio unit cell structure schematic diagram designed by a function surface; two areRespectively approximating the function y ═ ax in the approximation function curved surfacen+bxt+c，(n>t, n ∈ 1,3,5,7 …), y ═ x999、y＝x99The curve design negative Poisson's ratio single-cell curved surface can adjust the bending degree of the single-cell curved surface through the values of n, t, a, b and c, and the conversion from a straight line design surface to a curve design surface is realized.
The embodiment of the invention has the following beneficial effects:
by the intelligent curved surface negative Poisson ratio construction method of the approximate function, any negative Poisson ratio structure can be designed, the whole honeycomb structure boundary curved surface can be constructed, and the single cell negative Poisson ratio structure boundary curved surface can also be constructed. The boundary surface of the honeycomb structure with the negative Poisson ratio constructed by the complete approximate function surface is smoother than the boundary surface of the honeycomb structure formed by single cell arrangement; the optimal structure of the negative Poisson ratio approximation function curved surface required in different occasions can be designed by designing a negative Poisson ratio structure and adopting a computer MATLAB genetic algorithm to carry out intelligent optimization design according to index requirements of different occasions, so that the structure can be optimally utilized, and the utilization rate of the negative Poisson ratio structure is further improved.
Device embodiment
According to an embodiment of the present invention, there is provided a device for designing a constructed curved surface negative poisson ratio based on an approximation function, fig. 13 is a schematic diagram of the device for designing a constructed curved surface negative poisson ratio based on an approximation function according to an embodiment of the present invention, and as shown in fig. 13, the device for designing a constructed curved surface negative poisson ratio based on an approximation function according to an embodiment of the present invention specifically includes:
a negative Poisson ratio structure building module 130, which is used for obtaining a curve structure of an approximation function, and building the negative Poisson ratio structure based on the curve structure, wherein the approximation function is a function approximately representing any curve; for example, the approximation function constructs a negative poisson ratio sine-cosine boundary surface, the approximation function constructs a negative poisson ratio quadratic cubic function boundary surface, the approximation function constructs a negative poisson ratio arc boundary surface, the approximation function constructs an involute surface design boundary surface and the like.
The construct optimization function module 132 constructs optimization objectives and design variables based onThe optimization target and the design variable construct an optimization function, and the construct optimization function module 132 specifically includes: by constructing an optimization target eta and a set of design variables (x)1,x2,x3,x4,x5…xn) Functional relationship between: eta ═ f (x)1,x2,x3,x4,x5…xn) An optimization function η (x) is obtained.
The structure optimization module 134 calculates the optimization function through a genetic algorithm to obtain an optimal optimization target and an optimal input variable, and optimizes the negative poisson's ratio structure based on the optimal optimization target and the optimal input variable, wherein the structure optimization module 134 specifically includes: and according to different required indexes of different occasions, obtaining an optimal design variable x and an optimal target eta by the obtained optimization function eta (x) and calling genetic algorithm intelligent optimization design through MATLAB software according to the required indexes.
The embodiment of the invention has the following beneficial effects:
by the intelligent curved surface negative Poisson ratio construction method of the approximate function, any negative Poisson ratio structure can be designed, the whole honeycomb structure boundary curved surface can be constructed, and the single cell negative Poisson ratio structure boundary curved surface can also be constructed. The boundary surface of the honeycomb structure with the negative Poisson ratio constructed by the complete approximate function surface is smoother than the boundary surface of the honeycomb structure formed by single cell arrangement; the optimal structure of the negative Poisson ratio approximation function curved surface required in different occasions can be designed by designing a negative Poisson ratio structure and adopting a computer MATLAB genetic algorithm to carry out intelligent optimization design according to index requirements of different occasions, so that the structure can be optimally utilized, and the utilization rate of the negative Poisson ratio structure is further improved.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (10)
1. A method for constructing a curved surface negative Poisson's ratio design based on an approximation function is characterized by comprising the following steps:
acquiring a function curve structure of an approximation function, and constructing a negative Poisson ratio structure based on the function curve structure, wherein the approximation function is a function approximately representing any curve;
constructing an optimization target and a design variable based on the approximate function, and constructing an optimization function based on the optimization target and the design variable;
and calculating the optimization function through a genetic algorithm to obtain an optimal optimization target and an optimal input variable, and optimizing the negative Poisson ratio structure based on the optimal optimization target and the optimal input variable.
2. The method of claim 1, wherein the constructing a negative poisson's ratio structure based on the curved junction specifically comprises:
and constructing a negative Poisson ratio single cell structure through the approximate function curve, and constructing a negative Poisson ratio honeycomb structure based on the single cell structure.
3. The method of claim 1, wherein constructing a negative poisson's ratio structure based on a curve of an approximation function further comprises:
and directly constructing a negative Poisson ratio honeycomb structure through the approximate function curve.
4. The method of claim 1, wherein the constructing optimization objectives and design variables, and the constructing an optimization function based on the optimization objectives and design variables specifically comprises:
by constructing an optimization target eta and a set of design variables (x)1，x2，x3，x4，x5…xn) Functional relationship between: eta ═ f (x)1，x2，x3，x4，x5…xn) Obtaining an optimization function eta (x), wherein n is the number of variable parameters in the approximation function, x1，x2，x3，x4，x5…xnIs a variable parameter in the approximation function.
5. An approximation function-based constructed curved surface negative Poisson's ratio design device, which is based on any one of claims 1 to 4, and is characterized in that the approximation function-based constructed curved surface negative Poisson's ratio design method comprises the following steps:
constructing a negative Poisson ratio structure module, acquiring a curve structure of an approximation function, and constructing the negative Poisson ratio structure based on the curve structure, wherein the approximation function is a function approximately representing any curve;
an optimization function building module is used for building an optimization target and design variables and building an optimization function based on the optimization target and the design variables;
and the structure optimization module is used for calculating the optimization function through a genetic algorithm to obtain an optimal optimization target and an optimal input variable, and optimizing the negative Poisson ratio structure based on the optimal optimization target and the optimal input variable.
6. The apparatus of claim 5, wherein the build negative poisson's ratio structural module is specifically configured to:
and constructing a negative Poisson ratio single cell structure through the approximate function curve, and constructing a negative Poisson ratio honeycomb structure based on the single cell structure.
7. The apparatus of claim 5, wherein the build negative Poisson ratio structure module is further to:
and directly constructing a negative Poisson ratio honeycomb structure through the approximate function curve.
8. The apparatus according to claim 5, wherein the configuration optimization module specifically comprises:
by constructing the excellentNormalizing the target eta with a set of design variables (x)1，x2，x3，x4，x5…xn) Functional relationship between: eta ═ f (x)1，x2，x3，x4，x5…xn) Obtaining an optimization function eta (x), wherein n is the number of variable parameters in the approximation function, x1，x2，x3，x4，x5…xnIs a variable parameter in the approximation function.
9. An electronic device, comprising: a memory, a processor and a computer program stored on the memory and executable on the processor, the computer program when executed by the processor implementing the steps of the method of constructing a curved surface negative poisson's ratio design based on an approximation function as claimed in any one of claims 1 to 4.
10. A computer-readable storage medium, on which an implementation program for information transfer is stored, the program, when executed by a processor, implementing the steps of the method for constructing a curved surface negative poisson's ratio design based on an approximation function according to any one of claims 1 to 4.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN114838072A (en) * | 2022-05-25 | 2022-08-02 | 武汉理工大学 | Negative Poisson ratio honeycomb cell element and multi-cell structure introducing square function curved edge |
| CN115199693A (en) * | 2022-09-16 | 2022-10-18 | 南京航空航天大学 | Optimize reentrant corner constitutional unit and panel |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN114838072A (en) * | 2022-05-25 | 2022-08-02 | 武汉理工大学 | Negative Poisson ratio honeycomb cell element and multi-cell structure introducing square function curved edge |
| CN115199693A (en) * | 2022-09-16 | 2022-10-18 | 南京航空航天大学 | Optimize reentrant corner constitutional unit and panel |
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