An instability simulation system for an elongated member based on double-constrained mechanical metamaterial beam electrically driven post-buckling

Abstract

The application discloses an elongated component instability simulation calculation system based on double-constraint mechanical metamaterial beam electrically-driven post-buckling, which comprises an electric driving device, a double-constraint mechanical metamaterial beam structure and a deformation monitoring system. The electric driving device is composed of a programmable direct current power supply, one mobile comb electrode, two fixed comb electrodes and three wires. The double-constraint metamaterial beam structure is connected with the mobile electrode, and the mechanical metamaterial beam generates post-buckling behavior under the action of the electric driving device. The deformation monitoring system comprises a planar rectangular coordinate system grid plate and a high-speed camera, which are used for monitoring and recording the post-buckling deformation of the mechanical metamaterial beam under a certain electric potential difference. The system can quantitatively predict the actual phenomenon of buckling instability of the elongated component of a structure in the field of civil engineering, realizes the solution of differential equations through post-buckling mechanical behavior, is not limited by computer technology, and is a more efficient, convenient and intuitive differential equation solution system.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of analog computation, and particularly relates to a buckling instability simulation system for civil engineering structure slender member based on an electrically driven post-buckling response of a double-constrained mechanical metamaterial beam. BACKGROUND

[0002] The buckling instability problem of the structure slender member in the field of civil engineering can be mathematically modeled by a differential equation, and the solution of the equation can be used to quantitatively predict the actual phenomenon. However, it is still challenging to understand the solution of the differential equation and its application in describing the physical process in some cases. In addition, with the development of technology, although many numerical and analytical methods for solving specific differential equations have emerged, they are based on computers and gradually reach the physical limit with the development of computer technology, making it difficult to meet the challenging demands of more computing resources, more model storage capacity and lower power consumption. However, the buckling instability of the structure slender member often occurs suddenly and is highly dangerous. Using numerical simulation software for simulation requires a large amount of computation and time, causing great difficulties and costs for early warning, rescue and reconstruction. Therefore, it is necessary to design a more efficient, convenient and intuitive solution system for solving differential equations. Analog computation is an innovative solution that can achieve higher performance with smaller form factor, power consumption and cost.

[0003] The structural instability of the slender element, i.e. the post-buckling behavior, provides technical support for the present application. The post-buckling behavior of the double-constrained beam structure, as an advanced multi-stable structure, has been applied in many fields such as structural health monitoring and energy harvesting. Based on the small deformation assumption, the control equation of the post-buckling behavior of the double-constrained beam structure is: “where M x is the curvature of the beam at a distance x from the fixed end, which is defined as the second derivative of the transverse displacement of the beam at a distance x from the fixed end, i.e. E is the Young's modulus of the beam; I is the sectional moment of inertia of the beam; F is the axial force applied at the force end of the beam”. In order to better control the post-buckling response of the double-constrained beam, researchers have proposed two strategies of material and geometry to regulate the stiffness EI of the beam. The material strategy of changing the material to obtain the required stiffness is limited by the types of natural materials, therefore, the geometry regulation is a better control strategy. The mechanical metamaterial has programmable microstructure, and the double-constrained beam designed by using the mechanical metamaterial can regulate the stiffness of the beam from the macro-geometric size and microstructure. SUMMARY

[0004] In view of the limitation of traditional numerical calculation on the development of computer technology, the present application provides a buckling instability simulation system for civil engineering structure slender member based on an electrically driven post-buckling response of a double-constrained mechanical metamaterial beam.

[0005] The purpose of the application is realized by the following technical scheme: an elongated member instability simulation calculation system based on double-constrained mechanical metamaterial beam electrically driven post-buckling, which comprises an electric driving device, a double-constrained mechanical metamaterial beam structure and a deformation monitoring system.

[0006] The electric driving device comprises a moving comb-shaped electrode and a fixed comb-shaped electrode, and an electric driving force is generated between the electrodes to trigger the post-buckling response of the double-constrained mechanical metamaterial beam structure.

[0007] The double-constrained mechanical metamaterial beam structure comprises a mechanical metamaterial beam, a telescopic double-wall left beam, a telescopic double-wall right beam and a base; one end of the mechanical metamaterial beam is rigidly connected with the moving comb-shaped electrode, and the other end is fixed on the base; the telescopic double-wall left beam and the telescopic double-wall right beam are respectively arranged on the two sides of the mechanical metamaterial beam and are installed between the moving comb-shaped electrode and the base.

[0008] The deformation monitoring system is used for monitoring and recording the post-buckling deformation of the mechanical metamaterial beam under the action of the electric driving force, and the second-order derivative of the transverse deformation curve D x of the mechanical metamaterial beam is The second-order derivative is the solution of the differential equation obtained by the simulation calculation system, wherein x is the distance from the cross section of the mechanical metamaterial beam to the fixed end of the beam, and the actual phenomenon of buckling instability of the structure elongated member with different stiffness can be predicted according to the result of the solution.

[0009] Further, the electric driving device is provided with a programmable direct current power supply, a moving comb-shaped electrode, a fixed comb-shaped electrode and a wire;

[0010] The programmable direct current power supply is connected with the moving comb-shaped electrode and the fixed comb-shaped electrode through the wire respectively, and provides a potential difference to generate an attractive force between the moving comb-shaped electrode and the fixed comb-shaped electrode; for a comb-shaped electrode group with specific comb-shaped electrode thickness, long-tooth quantity and double-tooth gap parameters, the attractive force between the electrodes depends on the potential difference between the electrodes.

[0011] Further, the attractive force between the moving comb-shaped electrode and the fixed comb-shaped electrode is converted into an axial pressure of the moving comb-shaped electrode acting on the mechanical metamaterial beam, and the axial pressure drives the mechanical metamaterial beam to have a post-buckling behavior; the mechanical metamaterial beam has a programmable microstructure, and specific beam stiffness is obtained by adjusting and controlling the macro-geometric size and the microstructure; the mechanical metamaterial beam has the characteristic of elastic deformation and can restore its original shape when the potential difference is released.

[0012] Further, the telescopic double-wall left beam and the telescopic double-wall right beam each comprise an upper beam and a lower beam, the lower beam is designed as a hollow beam, and the upper beam can be embedded in the lower beam; the telescopic property of the telescopic double-wall left beam and the telescopic double-wall right beam is realized by sliding of the upper beam in the web of the lower beam; the telescopic double-wall left beam is provided with a semicircular convex at both ends, so that the telescopic double-wall left beam can be moved horizontally through the groove of the moving comb electrode and the base, thereby realizing regulation and control of the net gap between the double walls in the horizontal direction.

[0013] Further, the telescopic double-wall left beam is installed on the base through a clamp.

[0014] Further, the deformation monitoring system is provided with a planar rectangular coordinate system grid plate and a high-speed camera, which are used for monitoring and recording the post-buckling deformation of the mechanical metamaterial beam under a certain potential difference; the post-buckling deformation curve D of the mechanical metamaterial beam is quantitatively determined through the coordinate values of multiple points on the deformation curve obtained by the planar rectangular coordinate system grid plate, and is monitored and recorded through the high-speed camera.

[0015] Further, by connecting multiple mechanical metamaterial beams with different stiffnesses in series, multiple differential equations can be solved at the same time, i.e., the actual phenomenon of buckling instability of a structure slender member with different stiffnesses can be predicted.

[0016] The beneficial effects of the present application are as follows: the present application proposes a civil engineering structure slender member buckling instability simulation calculation system based on the post-buckling response of the double-constrained mechanical metamaterial beam driven by electricity, considering that the traditional numerical calculation is limited by the development of computer technology. The simulation calculation system of the present application is not limited by the development of computer technology, and is a more efficient, convenient and intuitive differential equation solving system. The present application realizes intuitive solving of differential equations through post-buckling mechanical behavior, realizes large-range regulation and control of beam stiffness through structural innovation, and applies controllable axial force to the mechanical metamaterial beam through an electric driving mode. The simulation calculation system provided by the present application can quantitatively predict the actual phenomenon of buckling instability of a structure slender member in the field of civil engineering through the post-buckling response of the double-constrained mechanical metamaterial beam structure. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is a schematic view of connection between the electric driving device and the double-constrained mechanical metamaterial beam structure;

[0018] Figure 2 is a schematic view of the double-constrained mechanical metamaterial beam structure;

[0019] Figure 3 is a schematic view of the structure of the telescopic double-wall left beam;

[0020] Figure 4 is a schematic view of the post-buckling deformation of the double-constrained mechanical metamaterial beam;

[0021] Figure 5is a structural schematic diagram of the simulation system provided by the application;

[0022] In the figure: electric drive device 1; double-constraint mechanical metamaterial beam structure 2; deformation monitoring system 3; programmable direct current power supply 101; mobile comb-shaped electrode 102; fixed comb-shaped electrode 103; wire 104; mechanical metamaterial beam 201; telescopic double-wall left beam 202; telescopic double-wall right beam 203; upper beam 204 and lower beam 205 of telescopic double-wall left beam 202; base 206; clamp 207; planar rectangular coordinate system grid plate 301; high-speed camera 302. DETAILED DESCRIPTION

[0023] The specific embodiments of the application are further described in detail below with reference to the accompanying drawings.

[0024] As shown in Figures 1-5 , the application provides a civil engineering structure slender member buckling instability simulation system based on double-constraint mechanical metamaterial beam electric drive post-buckling, which comprises an electric drive device 1, a double-constraint mechanical metamaterial beam structure 2 and a deformation monitoring system 3.

[0025] As shown in Figure 1 and Figure 2 , the electric drive device 1 is provided with a programmable direct current power supply 101, a mobile comb-shaped electrode 102, two fixed comb-shaped electrodes 103 and three wires 104.

[0026] The electric drive device 1 can generate an electric drive force to trigger the double-constraint mechanical metamaterial beam structure 2 to have a post-buckling response. The programmable direct current power supply 101 is connected to the mobile comb-shaped electrode 102 and the fixed comb-shaped electrode 103 through the wires 104, respectively, to provide a potential difference to generate an attractive force between the mobile comb-shaped electrode 102 and the fixed comb-shaped electrode 103. For a comb-shaped electrode group with specific structural parameters (comb-shaped electrode thickness, number of long teeth and double-tooth gap), the attractive force between the electrodes depends on the potential difference between the electrodes.

[0027] As shown in Figure 2 and Figure 4 , the double-constraint mechanical metamaterial beam structure 2 is provided with a mechanical metamaterial beam 201, a telescopic double-wall left beam 202, a telescopic double-wall right beam 203, a base 206 and a clamp 207.

[0028] The double-constrained mechanical metamaterial beam structure 2 is rigidly connected with the moving comb-shaped electrode 102, and the attraction force between the electrodes is converted into the axial pressure of the moving comb-shaped electrode 102 acting on the mechanical metamaterial beam 201, which drives the post-buckling behavior of the mechanical metamaterial beam 201. The mechanical metamaterial beam 201 has a programmable microstructure, and specific beam stiffness can be obtained by adjusting the macro-geometric size and microstructure. The mechanical metamaterial beam 201 must have the characteristics of elastic deformation and can restore its original shape when the potential difference is released.

[0029] As shown in Figure 2 and Figure 3 , the telescopic double-wall left beam 202 and the telescopic double-wall right beam 203 each include an upper beam 204 and a lower beam 205, and the lower beam 205 is designed as a hollow beam, and the upper beam 204 can be embedded in the lower beam 205. The telescopic double-wall is realized by the slippage of the upper beam 204 in the web of the lower beam 205. The telescopic double-wall left beam 202 is provided with a semicircular convex at both ends, so that the telescopic double-wall left beam 202 can be transversely moved through the recesses of the moving comb-shaped electrode 102 and the base 206, thereby realizing the regulation of the net gap between the transverse constraints (double walls). The clamp 207 is used to fix the telescopic double-wall left beam 202 on the base 206.

[0030] As shown in Figure 5 , the deformation monitoring system 3 is provided with a planar rectangular coordinate system grid plate 301 and a high-speed camera 302, which are used to monitor and record the post-buckling deformation of the mechanical metamaterial beam 201 under a certain potential difference. The post-buckling deformation curve D x of the mechanical metamaterial beam 201 is quantitatively determined by the coordinate values of multiple points on the deformation curve obtained by the planar rectangular coordinate system grid plate 301, and is monitored and recorded by the high-speed camera 302.

[0031] The simulation calculation system provided by the present application can quantitatively predict the buckling instability of the slender member of the structure in the field of civil engineering through the post-buckling response of the double-constrained mechanical metamaterial beam structure 2, that is, intuitively solve the second-order differential equation with specific coefficients and boundary conditions: , wherein A represents the stiffness of the mechanical metamaterial beam 201, B represents the applied axial force, C represents the net gap between the transverse constraints (double walls), and x represents the distance from the cross section of the mechanical metamaterial beam 201 to the fixed end of the beam. Note that A, B, and C are values reduced according to the actual working conditions. The second derivative of the post-buckling deformation curve D x of the mechanical metamaterial beam 201 monitored and recorded The solution of the differential equation obtained by the engineering simulation calculation system. The simulation calculation system provided by the application is not limited by the development of computer technology, and is a more efficient, convenient and intuitive differential equation solving strategy. The application realizes the intuitive solution of the differential equation through the post-buckling mechanical behavior; realizes the large-scale regulation and control of the beam stiffness through structural innovation; and applies the controllable axial force of the mechanical metamaterial beam through the electric driving mode. And by connecting multiple mechanical metamaterial beams with different stiffness, multiple differential equations with different A values can be solved at the same time, that is, the actual phenomenon of buckling instability of the slender member of the structure with different stiffness can be predicted.

[0032] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the application, and not to limit them; although the application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the application.

Claims

1. An elongated member instability simulation system based on the post-buckling of an electrically driven beam of a dual-constrained mechanical metamaterial, characterized in that, The system comprises an electric driving device (1), a double-constrained mechanical metamaterial beam structure (2) and a deformation monitoring system (3); The electric driving device (1) comprises a moving comb-shaped electrode (102) and a fixed comb-shaped electrode (103), and an electric driving force is generated between the electrodes to trigger the double-constrained mechanical metamaterial beam structure (2) to generate a post-buckling response. The double-constrained mechanical metamaterial beam structure (2) comprises a mechanical metamaterial beam (201), a telescopic double-wall left beam (202), a telescopic double-wall right beam (203) and a base (206); one end of the mechanical metamaterial beam (201) is rigidly connected to the moving comb-shaped electrode (102), and the other end is fixed on the base (206); the telescopic double-wall left beam (202) and the telescopic double-wall right beam (203) are respectively arranged on the two sides of the mechanical metamaterial beam (201) and are installed between the moving comb-shaped electrode (102) and the base (206). The deformation monitoring system (3) is used to monitor and record the post-buckling deformation of the metamaterial beam (201) under electric driving force. The deformation monitoring system (3) is equipped with a plane rectangular coordinate system grid plate (301) and a high-speed camera (302) to monitor and record the post-buckling deformation of the metamaterial beam (201) under a certain potential difference; the post-buckling deformation curve of the metamaterial beam (201) is shown. The coordinates of multiple points on the deformation curve obtained by the Cartesian coordinate system grid plate (301) are quantitatively determined, and the transverse deformation curve of the mechanical metamaterial beam (201) is monitored and recorded by the high-speed camera (302). The second derivative That is, the solution to the differential equation obtained by the simulation calculation system, where, Let be the distance from the cross section of the mechanical metamaterial beam (201) to the fixed end of the beam. By connecting multiple mechanical metamaterial beams with different stiffnesses in series, multiple differential equations can be solved simultaneously. Based on the solution results, the actual phenomenon of buckling instability of slender structural members with different stiffnesses can be predicted.

2. The system for instability simulation of an electrically post-buckled elongated member based on dual-constrained mechanical metamaterial beams of claim 1, wherein, The electric driving device (1) is provided with a programmable direct-current power supply (101), a moving comb-shaped electrode (102), a fixed comb-shaped electrode (103) and a wire (104). The programmable direct-current power supply (101) is connected to the moving comb-shaped electrode (102) and the fixed comb-shaped electrode (103) through the wire (104) to provide a potential difference to generate an attractive force between the moving comb-shaped electrode (102) and the fixed comb-shaped electrode (103); for a comb-shaped electrode group with specific comb-shaped electrode thickness, long-tooth quantity and double-tooth gap parameters, the attractive force between the electrodes depends on the potential difference between the electrodes.

3. The system for instability simulation of an electrically driven post-buckled slender member based on dual-constrained metamaterial beams of claim 1, wherein, The attractive force between the moving comb-shaped electrode (102) and the fixed comb-shaped electrode (103) is converted into an axial pressure of the moving comb-shaped electrode (102) acting on the mechanical metamaterial beam (201), and the axial pressure drives the mechanical metamaterial beam (201) to generate a post-buckling behavior; the mechanical metamaterial beam (201) has a programmable microstructure, and specific beam stiffness is obtained by adjusting the macro-geometric size and the microstructure; the mechanical metamaterial beam (201) has the characteristic of elastic deformation and can restore its original shape when the potential difference is released.

4. The system for instability simulation of an electrically driven post-buckled slender member based on dual-constrained metamaterial beams of claim 1, wherein, The telescopic double-wall left beam (202) and the telescopic double-wall right beam (203) each comprise an upper beam (204) and a lower beam (205), the lower beam (205) is designed as a hollow beam, and the upper beam (204) can be embedded in the lower beam (205); the telescopic property of the telescopic double-wall left beam (202) and the telescopic double-wall right beam (203) is realized by the slippage of the upper beam (204) in the web of the lower beam (205); the telescopic double-wall left beam (202) is provided with semicircular convexes at both ends, so that the telescopic double-wall left beam (202) can move horizontally through the grooves of the moving comb-shaped electrode (102) and the base (206), thereby realizing the regulation of the net gap between the double walls in the horizontal direction.

5. The system for instability simulation of an electrically driven post-buckled slender member based on dual-constrained mechanical metamaterial beams of claim 1, wherein, The telescopic double-wall left beam (202) is installed on the base (206) through a clamp (207).

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