A method, sensor and application for measuring the bidirectional strain gradient field of a structure

Abstract

The present invention relates to the field of engineering mechanics, and discloses a method, a sensor and an application for measuring a two-way strain gradient field of a structure. The sensor includes a flexible matrix and two sets of optical fiber pairs embedded in the flexible matrix and perpendicular to each other; each set of optical fibers includes a plurality of optical fiber pairs; the optical fiber pairs within the set are parallel to each other, and an optical fiber pair includes a pair of parallel first optical fiber and second optical fiber, and the plane where the optical fiber pair is located is perpendicular to the plane formed by the two sets of optical fiber pairs; when measuring the strain gradient of a component, the flexible matrix is attached to the component, and the plane where the optical fiber pair is located is perpendicular to the neutral layer of the component. The present invention utilizes the distributed optical fiber sensing technology, which can improve the measurement ability of strain data and reduce the measurement cost of strain data.

Description

Technical Field

[0001] The present invention relates to the field of engineering mechanics, and in particular, to a method, a sensor and an application for measuring a two-way strain gradient field of a structure. Background Art

[0002] Traditional methods for measuring strain gradients usually use strain gauges, double-layer bending strain gauges, fiber Bragg gratings, etc. For example, multiple strain gauges are pasted at different positions of a component (such as the upper and lower surfaces of a plate and shell component) to measure strain data at different positions. However, this measurement method has several disadvantages. First, this measurement method is not applicable to the measurement of strain gradients in the thickness direction of closed structures (such as box girders, silos, fuel tanks, etc.) and three-dimensional solid structures (such as concrete blocks, engines, etc.). This is because it is often impossible for measurement personnel to enter the interior of closed structures and three-dimensional solid structures to paste strain gauges. Second, the number of test points is small and relatively scattered, and it is impossible to calculate the axial strain gradient and displacement of a component in a certain direction. Third, for large components, a large number of measurement points need to be arranged, and a large number of strain gauges and corresponding strain data acquisition instruments are required, resulting in high measurement costs and data processing costs. Fourth, it is impossible to measure data with concentrated strain (stress). Summary of the Invention

[0003] Based on this, in view of the above technical problems, it is necessary to provide a method, a sensor and an application for measuring a two-way strain gradient field of a structure, using distributed optical fiber sensing technology to improve the measurement ability of strain gradients and reduce the measurement cost of strain gradients.

[0004] In a first aspect of the present invention, a two-way strain sensor is provided, including a flexible matrix, and two sets of optical fiber pairs perpendicular to each other embedded in the flexible matrix. Each set of optical fiber pairs includes two first optical fibers and second optical fibers parallel to each other. The plane where the first set of optical fiber pairs is located is perpendicular to the plane where the second set of optical fiber pairs is located;

[0005] When measuring the strain gradient of a component, the flexible matrix is attached to the component, and the plane where the optical fiber pairs are located is perpendicular to the neutral layer of the component.

[0006] In a second aspect of the present invention, a method for measuring a strain gradient field is provided, including:

[0007] Arranging the optical fiber pairs as described above on a plate and shell structure;

[0008] Measuring first strain data through the first optical fiber and second strain data through the second optical fiber;

[0009] Determining the strain gradient of a certain strain pair according to the first strain data and the second strain data.

[0010] A third aspect of the present invention provides a method for measuring a strain gradient field, including:

[0011] Arranging a plurality of the above-mentioned strain sensors on a thin plate member or a thin shell member, wherein the strain sensors include a first set of parallel strain sensors arranged along the x direction and a second set of parallel strain sensors arranged along the y direction, and the x direction is perpendicular to the y direction;

[0012] Measuring x-direction strain data through the first set of parallel strain sensors, and measuring y-direction strain data through the second set of parallel strain sensors;

[0013] Determining the strain gradient field of the thin plate member or the thin shell member in the thickness direction according to the x-direction strain data and the y-direction strain data.

[0014] A fourth aspect of the present invention provides an application of the above-mentioned strain sensor in measuring local strain data of a member.

[0015] A fifth aspect of the present invention provides one or more readable storage media storing computer-readable instructions, which, when executed by one or more processors, cause the one or more processors to execute the strain gradient field measurement method as described above.

[0016] Each solution involved in the present invention can improve the measurement ability of the strain gradient and reduce the measurement cost of the strain gradient. Description of the Drawings

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments of the present invention will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts.

[0018] Figure 1 is a schematic structural diagram of a strain sensor in an embodiment of the present invention;

[0019] Figure 2 is a schematic diagram of a strain sensor in an embodiment of the present invention measuring the strain gradient of a plate and shell member;

[0020] Figure 3 is a cross-sectional stress distribution diagram of a plate and shell member in different conditions in an embodiment of the present invention;

[0021] Figure 4 is a schematic diagram of a plate and shell member undergoing bending deformation in an embodiment of the present invention;

[0022] Figure 5Schematic diagram of the bidirectional strain gradient field sensor when it is arranged on a thin plate member;

[0023] Figure 5 Schematic side view of the strain sensor when it is arranged on a thin plate member. Specific implementation manner

[0024] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0025] Embodiment 1

[0026] As Figure 1 shown, a bidirectional strain sensor is provided, which includes a flexible matrix 03 and two sets of optical fiber pairs perpendicular to each other embedded in the flexible matrix 03; each set of optical fibers includes a plurality of optical fiber pairs; the optical fiber pairs within the set are parallel to each other, and the optical fiber pair includes a pair of first optical fibers 01 and second optical fibers 02 parallel to each other, and the plane where the optical fiber pair is located is perpendicular to the plane formed by the two sets of optical fiber pairs;

[0027] When measuring the strain gradient of the member, the flexible matrix 03 is attached to the member, and the plane where the optical fiber pair is located is perpendicular to the neutral layer of the member.

[0028] The bidirectional strain sensor provided in this embodiment can replace the existing strain gauges and be used to measure the bidirectional strain data of components. Specifically, the bidirectional strain sensor includes a flexible matrix 03 and two sets of optical fiber pairs arranged perpendicular to each other and embedded in the flexible matrix 03. Among them, the optical fiber pairs are the first optical fiber 01 and the second optical fiber 02 arranged in parallel. The flexible matrix 03 can be made of flexible materials. Schematically, the materials selected for the flexible matrix 03 can be PVC (polyvinyl chloride), epoxy resin, etc. The first optical fiber 01 and the second optical fiber 02 can be optical fibers with the same core diameter and material. Here, taking the first optical fiber 01 as an example, the first optical fiber 01 can be a multi-layer coaxial optical fiber. This optical fiber has structures such as a core, a cladding layer, a coating layer, and a protective sleeve. This type of optical fiber uses the principle of total internal reflection of light to ensure that light waves only propagate within the core and achieve the axial conduction of light waves along the optical fiber. When parameters such as the temperature and pressure outside the optical fiber change, characteristic parameters such as the amplitude, phase, polarization state, and wavelength of the light waves transmitted in the optical fiber will change accordingly, that is, the phenomenon of scattered radio frequency shift occurs, and ordinary light waves are converted into modulated signal light. That is to say, when the first optical fiber 01 is subjected to force, the optical signal in the optical fiber will change to form signal light containing information about the force on the optical fiber. The signal light is transmitted to the signal processing module through the transmission optical fiber (the optical fiber connected to the first optical fiber 01), and the first strain data of multiple detection points on the entire first optical fiber 01 can be obtained after analysis. Here, the signal processing module can use OFDR (optical frequency domain reflectometry) technology. Similarly, second strain data different from that of the first optical fiber 01 can also be detected through the second optical fiber 02. Multiple measurement points with very small spacings can be formed along the extension direction of the first optical fiber 01 of the bidirectional strain sensor. The spacing between adjacent measurement points can be as low as the millimeter level. In one example, if the bidirectional strain sensor is placed in a three-dimensional Cartesian coordinate system, in the three-dimensional Cartesian coordinate system, O is the origin, and the x, y, and z axes are perpendicular to each other in pairs. If the plane formed by the two sets of optical fiber pairs is the xOy plane (such as Figure 5 the cross-section shown in a), the plane where the optical fiber pair is located can be the xOz plane or the yOz plane (such as Figure 5 the cross-section shown in b).

[0029] The first optical fiber 01 and the second optical fiber 02 are connected through the flexible matrix 03, which can mean that there is a flexible matrix 03 between the first optical fiber 01 and the second optical fiber 02. This can keep a certain distance between the first optical fiber 01 and the second optical fiber 02. At the same time, when the component is stressed, part of the force can be transmitted to the second optical fiber 02 through the flexible matrix 03 (here, it is default that the first optical fiber 01 is closer to the component, even in direct contact with the component, while the second optical fiber 02 is on the side far from the component). The distance between the first optical fiber 01 and the second optical fiber 02 can be set according to actual needs (that is, different models of strain sensors are produced with corresponding different spacings).

[0030] The first optical fiber 01 and the second optical fiber 02 arranged in parallel mean that, without being affected by an external force, the first optical fiber 01 and the second optical fiber 02 are substantially parallel (i.e., in a parallel state). When there is an external force, the degrees of force on the first optical fiber 01 and the second optical fiber 02 may be different, and the deformations may also be different. At this time, the first optical fiber 01 and the second optical fiber 02 deviate from the parallel state to a certain extent.

[0031] When measuring the strain data of a component, the plane where the optical fiber pair is located is perpendicular to the neutral layer of the component. Here, the neutral layer refers to the transition layer that is neither stretched nor compressed on its cross-section during the bending process of the component, where the outer layer is stretched and the inner layer is compressed. The stress of the neutral layer is almost zero. In this embodiment, when measuring the force gradient of the cross-section of the component, the measurement data of the first optical fiber 01 and the second optical fiber 02 (referring to the signal light or the force data analyzed based on the signal light) need to be used simultaneously. At this time, the plane where the optical fiber pair is located needs to be kept perpendicular to the neutral layer to ensure the accuracy of the measured strain data.

[0032] Optionally, the elastic modulus of the flexible matrix 03 is less than or equal to one-twentieth of the elastic modulus of the component, which does not affect the deformation of the component, ensures that the bidirectional strain sensor is fully attached to the object to be measured, and basically does not affect the stiffness of the object to be measured.

[0033] In this embodiment, the elastic modulus of the flexible matrix 03 needs to be much smaller than the elastic modulus of the component. Usually, the material of the second optical fiber 02 is the same as that of the first optical fiber 01. The elastic moduli of the first optical fiber 01 and the second optical fiber 02 are equal.

[0034] Embodiment Two

[0035] As Figure 2 shown, the present invention also provides a method for measuring a strain gradient field, including:

[0036] Setting the strain sensor as described above on the plate and shell component 10;

[0037] Measuring first strain data through the first optical fiber 01 of the strain sensor, and measuring second strain data through the second optical fiber 02 of the strain sensor;

[0038] Determining the strain gradient of a certain strain pair according to the first strain data and the second strain data.

[0039] Here, the strain sensor can be attached to one side of the plate and shell component 10, and the first strain data and the second strain data are measured respectively through the first optical fiber 01 and the second optical fiber 02, and the strain gradient of the plate and shell component 10 is calculated according to the first strain data and the second strain data.

[0040] For example, asFigure 3 As shown in the screenshot of the leftmost plate and shell member, let x be the distance from the neutral axis of the plate and shell member to the second surface 102 (lower surface), and a 1 be the distance from the lower surface of the beam to the first optical fiber 01, and a 2 be the distance from the first optical fiber 01 to the second optical fiber 02. ε 1 and ε 2 are the strains at the same cross-section of the first optical fiber 01 and the second optical fiber 02 respectively (generated by transforming the first strain data and the second strain data). Here, a certain strain pair refers to one of the optical fiber pairs in any one of the two sets of optical fiber pairs.

[0041] The first optical fiber 01 and the second optical fiber 02 satisfy the following deformation condition 1: Based on deformation condition 1, the value of x can be calculated. That is: The strain gradient along the height direction of the beam (i.e., from the first surface 101 to the second surface 102) is: The measurement data of the plate and shell member 10 includes the above-mentioned strain gradient along the height direction of the beam, and also includes the strain gradient along the length direction of the first optical fiber 01. When calculating the strain gradient along the length direction of the first optical fiber 01, the strain difference between two adjacent test points can be calculated first, and then divided by the corresponding spacing (the spacing between these two adjacent test points), that is, the strain gradient along the length direction of the first optical fiber 01 is obtained.

[0042] Optionally, this measurement method is applicable to the measurement of the strain gradient along the height direction of plate and shell members in pure bending deformation, tension-bending deformation, and compression-bending deformation.

[0043] Here, it is necessary to analyze in combination with different situations. Such as Figure 3 shown, when x = h / 2, the plate and shell member 10 is in a pure bending deformation state; if x > h / 2, the plate and shell member 10 is in a tension-bending deformation state; if x < h / 2, the plate and shell member 10 is in a compression-bending deformation state. Given the Young's modulus E of the material used for the plate and shell member 10, the corresponding bending stress, tensile stress, and compressive stress of the plate and shell member 10 can be calculated.

[0044] Optionally, the first strain data includes the strain of the first optical fiber 01 at a specified position; the second strain data includes the strain of the second optical fiber 02 at the specified position;

[0045] The determining of the strain gradient of the plate and shell member 10 according to the first strain data and the second strain data includes:

[0046] Processing the first strain data and the second strain data through a second surface 102 strain calculation formula to determine the strain of the second surface 102 of the plate and shell member 10 at a specified position, where the second surface 102 strain calculation formula is:

[0047]

[0048] where ε d2 is the strain of the second surface 102 of the plate and shell member 10 at the specified position; ε 1 is the strain of the first optical fiber 01 at the specified position; ε 2 is the strain of the second optical fiber 02 at the specified position; a 1 is the distance between the second surface 102 of the plate and shell member 10 at the specified position and the first optical fiber 01, and the second surface 102 refers to the side that fits the strain sensor; a 2 is the distance between the first optical fiber 01 and the second optical fiber 02;

[0049] Processing the first strain data and the second strain data through a first surface 101 strain calculation formula to determine the strain of the first surface 101 of the plate and shell member 10 at a specified position, where the first surface 101 strain calculation formula is:

[0050]

[0051] where ε d1 is the strain of the first surface 101 of the plate and shell member 10 at the specified position, and h is the distance between the first surface 101 and the second surface 102 of the plate and shell member 10 (i.e., the height of the plate and shell member 10).

[0052] In this embodiment, the strain of the first surface 101 of the plate and shell member 10 at the specified position can be calculated through the first surface 101 strain calculation formula, and the strain of the second surface 102 of the plate and shell member 10 at the specified position can be calculated through the second surface 102 strain calculation formula. That is to say, since a 1 and a 2 are known quantities, when ε 1 and ε 2 at the specified position are measured, the corresponding ε d1 and ε d2 can be calculated. Here, the specified position refers to any measurement point of the strain sensor on the plate and shell member 10.

[0053] Optionally, determining the deflection of the plate and shell member 10 according to the first strain data and the second strain data includes:

[0054] Processing the first strain data and the second strain data through a deflection calculation formula to determine the deflection of the plate-shell member 10 at a specified position, the deflection calculation formula being:

[0055]

[0056] where ε x is the curvature of the deflection curve of the first surface 101 of the plate-shell member 10 at the specified position; x is the distance between the neutral axis of the plate-shell member 10 and the second surface 102, Δx is a preset distance change amount, and w(x) is the deflection of the plate-shell member 10 at the specified position.

[0057] In this embodiment, as Figure 4 shown, the specific derivation process of the deflection includes the following steps.

[0058] First, calculate the curvature of the deflection curve of the first surface 101 of the plate-shell member 10, specifically:

[0059]

[0060] where α x is the cross-sectional rotation angle along the x direction (the extension method of the first optical fiber 01), and r x is the radius of curvature along the x direction.

[0061] Furthermore, calculate the bending curvature of the plate-shell member 10, specifically: The left side of the equation is the bending curvature of the plate-shell member 10.

[0062] The relationship between the curvature of the deflection curve and the deflection can be expressed as: According to the calculation formula of the bending curvature and the relationship formula between the curvature of the deflection curve and the deflection, the deflection can be calculated by using the measured strain data. The calculation process requires 2 integrations and can be realized by the finite difference method. The finite difference method refers to a numerical solution method that uses a set of finite difference equations to replace differential equations and corresponding boundary conditions. The finite difference method can transform the boundary value problem of a differential equation that is difficult to solve into an algebraic equation system problem that is easy to solve.

[0063] According to Taylor's theorem, if the displacement w is four times continuously differentiable, then there is the following relationship:

[0064]

[0065]

[0066] Here, x - Δx < c 2 < x < c 1 < x + Δx. Adding the above two equations to eliminate the first derivative term gives:

[0067]

[0068] According to the general mean value theorem, let w be a continuous function on the interval [a, b], x 1 , …x n is a point in [a, b], and a 1 , …a n > 0, then there is a number c between a and b such that

[0069] (a 1 +…+a n )w(c)=a 1 w(x 1 )+…+a n w(x n )

[0070] Combine the error terms of the formulas for calculating w(x+Δx) and w(x-Δx) and divide both sides by Δx 2 The three-point central difference formula for the second-order derivative is obtained:

[0071]

[0072] Combining the above equations and ignoring the higher-order error terms, the relationship between deflection and strain is:

[0073]

[0074] Taking advantage of the fact that the distance between the strain sensor test points is very small, the relative deflection can be calculated by the finite difference method. If a test point does not move, the deflection of the actual structure can be measured. In the calculation process of the above formula, Δx is the preset distance change, which can be set to a very small value as needed.

[0075] Embodiment 3

[0076] The present invention also provides a strain gradient field measurement method, comprising:

[0077] A plurality of strain sensors as described above are arranged on a thin plate member or a thin shell member, wherein the strain sensors include a first strain sensor arranged along an x ​​direction and a second strain sensor arranged along a y direction, and the x direction and the y direction are orthogonal to each other;

[0078] Measure x-direction strain data through the first strain sensor and y-direction strain data through the second strain sensor;

[0079] The strain gradient field of the thin plate component or the thin shell component is determined according to the x-direction strain data and the y-direction strain data.

[0080] In this embodiment, strain sensors can be arranged on thin plate members or thin shell members to measure the strain data of multiple test points (including the strain data in the x-direction and the strain data in the y-direction), and then calculate the required strain gradient. Different from the plate and shell member 10, when measuring thin plate members, two groups of strain sensors with different directions can be used for measurement, namely, the first strain sensor arranged in the x-direction and the second strain sensor arranged in the y-direction. The x-direction and the y-direction are in an intersecting relationship. In some cases, the two directions can be perpendicular or nearly perpendicular to each other. The thin plate member can refer to thin steel plates, thin wood boards, thin cement boards, etc. The thin shell member can refer to box girders, silos, fuel tanks, pipelines, etc. As Figure 5 shown Figure 5 Figure a is a schematic diagram of the bidirectional strain gradient field sensor arranged on a thin plate member Figure 5 Figure b is a side schematic diagram of the bidirectional strain gradient field sensor arranged on a thin plate member

[0081] Embodiment 4

[0082] The present invention also provides an application of the above bidirectional strain sensor in measuring local strain data of a member

[0083] Specifically, the present invention can also be used to measure the strain gradient and stress distribution near local strain (or stress) concentration, for example, there is stress concentration near the ends of composite plates (or steel plates) reinforced beams and plates, the strain gradient at the edge of the composite cloth reinforcing columns, etc. The spacing between the measurement points of the strain sensor can reach the millimeter level or sub-millimeter level, and the measurement of local strain data can be realized

[0084] Embodiment 5

[0085] In the fifth embodiment of the present invention, one or more computer-readable storage media storing computer-readable instructions are provided. The readable storage media provided in this embodiment include non-volatile readable storage media and volatile readable storage media. Computer-readable instructions are stored on the readable storage media, and when the computer-readable instructions are executed by one or more processors, the strain gradient field measurement method as described above is implemented

[0086] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through computer-readable instructions. The computer-readable instructions can be stored in a non-volatile computer-readable storage medium. When the computer-readable instructions are executed, they can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided in the present application can include non-volatile and / or volatile memories. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0087] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the above division of each functional unit and module is used as an example. In actual applications, the above functions can be allocated to different functional units and modules according to needs, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above.

[0088] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention and should all be included in the protection scope of the present invention.

Claims

1. A bidirectional strain sensor, characterized in that, it includes a flexible substrate, and two sets of optical fiber pairs arranged perpendicular to each other and embedded in the flexible substrate; each set of optical fiber pairs includes several pairs of optical fibers; the optical fiber pairs within the set are parallel to each other, and the optical fiber pairs within the set include a pair of parallel first optical fiber and second optical fiber, and the plane where each set of optical fiber pairs is located is perpendicular to the plane formed by the optical fiber pairs within the set; when measuring the strain gradient of a member, the flexible substrate is attached to the member, and the plane where the optical fiber pairs are located is perpendicular to the neutral layer of the member; The bidirectional strain sensor is used in a method for measuring a bidirectional strain gradient field, including: arranging the two sets of optical fiber pairs on a plate and shell structure; measuring first strain data through the first optical fiber and second strain data through the second optical fiber; determining the strain gradient of a certain strain pair according to the first strain data and the second strain data; The first strain data includes the strain of the first optical fiber at a specified position; the second strain data includes the strain of the second optical fiber at a specified position; The determining the strains of the first surface and the second surface of the certain strain pair according to the first strain data and the second strain data includes: processing the first strain data and the second strain data through a second surface strain calculation formula to determine the strain of the second surface of the certain strain pair at the specified position, and the second surface strain calculation formula is: ； Wherein, is the strain of the second surface of the certain strain pair at the specified position; is the strain of the first optical fiber at the specified position; is the strain of the second optical fiber at the specified position; is the distance between the second surface of the certain strain pair and the first optical fiber at the specified position, where the second surface refers to the surface that is in contact with the strain sensor, and the second surface is disposed opposite to the first surface; is the distance between the first optical fiber and the second optical fiber; processing the first strain data and the second strain data through a first surface strain calculation formula to determine the strain of the first surface of the certain strain pair at the specified position, and the first surface strain calculation formula is: ； wherein, is the strain of the first surface of a certain strain pair at a specified position, h is the distance between the first surface and the second surface of a certain strain pair.

2. The bidirectional strain sensor according to claim 1, characterized in that, the elastic modulus of the flexible substrate is less than or equal to one-twentieth of the elastic modulus of the member, so that the bidirectional strain sensor is completely attached to the object to be measured.

3. The method for measuring a bidirectional strain gradient field according to claim 1, characterized in that, the strain gradient belongs to the strain gradient of bending deformation, tension-bending deformation or compression-bending deformation.

4. The method for measuring a bidirectional strain gradient field according to claim 1, characterized in that, the determining the strain gradient of the certain strain pair according to the first strain data and the second strain data includes: processing the first strain data and the second strain data through a deflection calculation formula to determine the deflection of the certain strain pair at the specified position, and the deflection calculation formula is: wherein, is the curvature of the deflection curve of the first surface at the specified position for the certain strain pair; x is the distance between the neutral axis of the certain strain pair and the second surface, is the preset distance change amount, is the deflection of the certain strain pair at the specified position.

5. A method for measuring a bidirectional strain gradient field, characterized in that, it includes: A number of the bidirectional strain sensors as described in Claim 1 or 2 are provided on a thin plate member or a thin shell member, wherein the bidirectional strain sensors include a first bidirectional strain sensor arranged along the x direction and a second bidirectional strain sensor arranged along the y direction, and the x direction intersects with the y direction; Measure through the first bidirectional strain sensor x directional strain data, and measure through the second bidirectional strain sensor y directional strain data; Based on the described x directional strain data and the described y directional strain data, determine the biaxial strain gradient field of the thin plate member or the thin shell member.

6. A method of application in measuring local strain data of a member, characterized in that, the application method uses the bidirectional strain sensor according to claim 1 or 2.

7. One or more readable storage media storing computer-readable instructions, which when executed by one or more processors, cause the one or more processors to execute the strain gradient field measurement method according to any one of claims 4 or 5.

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