JP6464815B2 - Distortion measuring method and apparatus, program and recording medium - Google Patents

Description

  The present invention relates to a distortion measuring method and apparatus, a program, and a recording medium.

  Generally, in order to measure the stress-strain relationship of a metal material in an arbitrary stress state, it can be obtained by applying stress to a test piece and measuring the strain generated at that time. In order to measure the strain, an extensometer or a strain gauge is used.

JP 2013-53888 A Japanese Patent No. 5416082 Japanese Patent No. 5378340

Matrix finite element method I [revised edition], co-authored by O.C.Zienkiewicz / R.I.Taylor, representative of translator Motoki Yagawa, Kyadotech / Science Publishing Co., Ltd.

  In strain measurement using an extensometer, the change in the distance between a pair of contacts is converted and measured into the elastic strain of a strained body made of a copper alloy or the like, and the elastic strain of the strained body previously determined. Is multiplied by the elastic strain of the strain generating body. Thereby, the deformation amount (strain) of the test piece is measured. However, in this case, the direction of strain to be measured is limited by the mounting direction of the extensometer. Moreover, since the coefficient mentioned above changes with time, it is necessary to obtain again every fixed period, and man-hours are required.

  In strain measurement using a strain gauge, the resistance change of the resistance foil of the gauge affixed to the surface of the test piece is measured and converted into strain using the property that changes when the electrical resistance of the metal is deformed. However, in this case, the direction of strain to be measured is limited by the attaching direction of the gauge (in the case of a rosetta gauge, any direction can be measured). The measurable strain range is small. The measured value may vary depending on the application method and the deformation state of the test piece. Strictly speaking, the strain conversion factor differs for each gauge.

  Moreover, in the technique of Patent Document 1, each of these areas is regularly divided into a plurality of areas, and each area is color-coded with a different color from other adjacent areas whose outlines are in line contact with each other, The boundary portion of each area can be regarded as a line having a width of zero. For this reason, it is possible to stably perform highly accurate distortion measurement without distorting the reference. However, in this case, in the technique of Patent Document 1, the direction of distortion to be measured is limited by the direction of the pattern. Moreover, since the boundary part of each area becomes a line segment, it is difficult to recognize it as a reference point for measuring the distance with a camera or the like, and it cannot be continuously measured.

  Further, in the techniques of Patent Documents 2 and 3, it is possible to continuously measure distortion by recognizing two or more marks as reference points for measuring distances. However, in this case, the direction of distortion to be measured is limited by the arrangement of the marks. Further, when measuring the distance, there is a problem as to which position of the mark having a certain area is used as a reference, and if the position is shifted, an error may occur. In addition, it is necessary to match the direction of distortion and the direction of marking. If these directions are deviated, the measurement accuracy may be reduced. In addition, when a plurality of cameras are used, it is necessary to calibrate the cameras, which takes time.

  The present invention has been made in view of the above-described problems, and in a planar surface portion having a uniform strain distribution of an object to be measured, vertical strain and shear strain in an arbitrary direction within the plane can be accurately and An object of the present invention is to provide a highly reliable strain measuring method and apparatus, and a program, which can reliably measure continuously without contact.

The distortion measuring method of the present invention is an image obtained by imaging an n-gonal element (n is 3 or 4) applied to the surface of an object to be measured using an imaging unit. Calculating the displacement of each vertex coordinate of the n-gonal element based on the difference from the state, and using the calculated displacement of each vertex coordinate, the displacement-distortion matrix of the n-square element by a finite element method create and said saw including a step of calculating the two directions of vertical distortion and shear strain perpendicular in the measurement object, the step of calculating the displacement of the vertex coordinates of the n-gon element of the n triangular elements In the pre-deformation state, the coordinates of two arbitrary points on each side of the n-gonal element are measured, the coordinates of the intersection of the straight lines passing through the two points are calculated, and the created first virtual n-square element The first vertex coordinate In the post-deformation state of the n-gonal element, the coordinates of any two points on each side of the n-gonal element were measured, and the coordinates of the intersection of the straight lines passing through the two points were calculated. Setting a second vertex coordinate of the second virtual n-gon element, and calculating a difference value between the second vertex coordinate and the first vertex coordinate as a displacement of each vertex of the n-gon element; including.
The distortion measuring method of the present invention is an image obtained by imaging an n-gonal element (n is 3 or 4) applied to the surface of an object to be measured using an imaging unit. Calculating the displacement of each vertex coordinate of the n-gonal element based on the difference from the state, and using the calculated displacement of each vertex coordinate, the displacement-distortion matrix of the n-square element by a finite element method And calculating a vertical strain and a shear strain in two orthogonal directions in the object to be measured, and the length of one side of one pixel of the imaged image is defined as a reference length.

The distortion measuring apparatus according to the present invention includes an imaging unit and an image obtained by imaging an n-gonal element (n is 3 or 4) applied to the surface of the object to be measured using the imaging unit. Based on the difference between the previous state and the post-deformation state, the first calculation means for calculating the displacement of each vertex coordinate of the n-gonal element and the calculated displacement of each vertex coordinate by the finite element method displacement of the n triangular elements - creates a distortion matrix, seen including a second calculating means for calculating the two directions of vertical distortion and shear strain perpendicular in the object to be measured, said first calculation means, In the state before the deformation of the n-gonal element, the coordinates of any two points on each side of the n-gonal element are measured, the coordinates of the intersection of the straight lines passing through the two points are calculated, The first vertex coordinate of the virtual n-gon element is used as the n-corner In the post-deformation state of the element, the coordinates of two arbitrary points on each side of the n-gonal element are measured, the coordinates of the intersection of straight lines passing through the two points are calculated, and the created second virtual n-gon A second vertex coordinate of the element is used, and a difference value between the second vertex coordinate and the first vertex coordinate is calculated as a displacement of each vertex of the n-gonal element.
The distortion measuring apparatus according to the present invention includes an imaging unit and an image obtained by imaging an n-gonal element (n is 3 or 4) applied to the surface of the object to be measured using the imaging unit. Based on the difference between the previous state and the post-deformation state, the first calculation means for calculating the displacement of each vertex coordinate of the n-gonal element and the calculated displacement of each vertex coordinate by the finite element method And a second calculating unit that generates a displacement-strain matrix of the n-gonal element and calculates a perpendicular strain and a shear strain in two orthogonal directions in the measurement target object, the first calculating unit including imaging A length of one side of one pixel of the image is defined as a reference length.

The program according to the present invention provides an image obtained by imaging an n-gonal element (n is 3 or 4) applied to the surface of an object to be measured using an imaging unit, and a state before deformation and a state after deformation of the n-square element. Based on the difference, the procedure for calculating the displacement of each vertex coordinate of the n-gonal element and the calculated displacement of each vertex coordinate are used to create a displacement-distortion matrix of the n-square element by the finite element method. And calculating a displacement of each vertex coordinate of the n-gonal element by causing a computer to execute a normal strain and a shear strain in two orthogonal directions in the object to be measured . In the pre-deformation state, the coordinates of two arbitrary points on each side of the n-gonal element are measured, the coordinates of the intersection of the straight lines passing through the two points are calculated, and the created first virtual n-square element The first vertex coordinate In order and in the post-deformation state of the n-square element, the coordinates of two arbitrary points on each side of the n-square element were measured, and the coordinates of the intersection of straight lines passing through the two points were calculated and created A procedure for setting the second vertex coordinate of the second virtual n-gon element, and a procedure for calculating a difference value between the second vertex coordinate and the first vertex coordinate as a displacement of each vertex of the n-square element; including.
The program according to the present invention provides an image obtained by imaging an n-gonal element (n is 3 or 4) applied to the surface of an object to be measured using an imaging unit, and a state before deformation and a state after deformation of the n-square element. Based on the difference, the procedure for calculating the displacement of each vertex coordinate of the n-gonal element and the calculated displacement of each vertex coordinate are used to create a displacement-distortion matrix of the n-square element by the finite element method. Then, the computer is caused to execute a procedure for calculating vertical strain and shear strain in two orthogonal directions in the object to be measured, and the length of one side of one pixel of the captured image is defined as a reference length.

  According to the present invention, in a planar surface portion having a uniform strain distribution of an object to be measured, vertical strain and shear strain in an arbitrary direction within the surface can be continuously measured accurately and reliably without contact. Can do.

It is a mimetic diagram showing a schematic structure of a distortion measuring device by a 1st embodiment. It is a flowchart which shows the distortion measuring method by 1st Embodiment in order of a step. It is a schematic diagram which shows a mode that a virtual square element is produced. It is a top view which shows the cross-shaped test piece used in 1st Embodiment. It is a characteristic view which shows the result of having measured the stress-strain relationship using the cross-shaped test piece of FIG. It is a schematic diagram which shows the internal structure of a personal user terminal device.

  Hereinafter, embodiments of a distortion measuring method and apparatus, a program, and a recording medium will be described in detail with reference to the drawings.

(First embodiment)
FIG. 1 is a schematic diagram illustrating a schematic configuration of a strain measurement apparatus according to the first embodiment. FIG. 2 is a flowchart showing the distortion measuring method according to the first embodiment in order of steps.
As shown in FIG. 1, the distortion measuring apparatus according to the present embodiment includes, for example, a CCD camera 1, a first calculation unit 2, a second calculation unit 3, a third calculation unit 4, and a display unit 5 that are imaging units. It is prepared for. The display unit 5 appropriately displays an image captured by the CCD camera 1, a calculation result by the second calculation unit 3, a calculation result by the third calculation unit 4, and the like.

  The non-measurement object 10 is made of metal, and a predetermined n-gonal element is provided (drawn) as a strain measurement mark on a planar surface portion (at least a part of the entire surface) having a uniform strain distribution. Or formed). Here, n is 3 or 4, that is, a triangle or a quadrangle, and in the present embodiment, the case of the quadrilateral element 10a is illustrated. The square element 10a is formed on the surface portion by drawing using a lacquer or the like, or by predetermined etching. The quadrilateral elements are color-coded with a color different from the background surface portion in order to improve the detection accuracy.

  In order to measure the strain of the non-measurement object 10, as shown in FIG. 2, the non-measurement object 10 is not yet subjected to a load in the biaxial tensile testing machine in which the non-measurement object 10 is installed (pre-deformation state). Then, imaging of the square element 10a by the CCD camera 1 is started (step S1).

  The first calculation means 2 calculates the coordinates of any two points on each side of the quadrilateral element 10a in the pre-deformation state in the image obtained by capturing the quadrilateral element 10a by the CCD camera 1 (step S2). At this time, in order to improve the processing speed of the calculation, the detection means provided in the CCD camera 1 for detecting the contrast pattern of the image in one direction is used to contrast at the boundary portion between the quadrilateral element 10a and the surface portion of the background. The positions in the image of the pixels whose pattern has greatly changed are defined as two arbitrary points. In addition, the length of one side of one pixel in the image is set as a reference length so that the distance conversion process is unnecessary. Since distortion is a dimensionless quantity, it is used that there is no need for metric conversion. The state at this time is illustrated in FIG. Arbitrary two points on each side in the image are a1 to a8.

  Subsequently, the first calculation means 2 calculates the coordinates of the intersection of the straight lines passing through the two points on each side of the quadrangular element 10a, and the first vertex coordinates of the created first virtual quadrangular element 10b. (Step S3). In FIG. 3A, the first vertices are b1 to b4.

Subsequently, a predetermined load is applied to the non-measuring object 10 in the biaxial tensile tester to set the non-measuring object 10 in a deformed state (post-deformation state) (step S4).
Subsequently, in the post-deformation state of the quadrangular element 10a, the first calculating means 2 measures the coordinates of two arbitrary points on each side of the quadrangular element 10a, and straight lines passing through the two points, as in step S2. The coordinates of the intersections are calculated (step S5). The state at this time is illustrated in FIG. Arbitrary two points on each side in the image are A1 to A8. In the present embodiment, any two points on each side need not coincide before and after the deformation of the rectangular element 10a. That is, a1 and A1, a2 and A2,..., A8 and A8 do not need to match and may be arbitrary. Thus, since the position on each side may change before and after the deformation of the rectangular element 10a, tracking observation is unnecessary (fixed point observation may be sufficient).

Subsequently, the first calculation means 2 calculates the coordinates of the intersection of the straight lines passing through the two points on each side of the quadrilateral element 10a, and the second vertex coordinates of the created second virtual quadrilateral element 10c. (Step S6). In FIG.3 (b), let the 2nd vertex be B1-B4.
Subsequently, the first calculation means 2 uses the difference values (B1-b1,..., B4-b4) between the second vertex coordinates and the first vertex coordinates as the first and second virtual square elements 10b. , 10c is calculated as the displacement of each vertex (step S7).

Subsequently, the second calculation means 3 uses the calculated displacement of each vertex coordinate to calculate the first and second virtual quadrilateral elements 10b and 10c (that is, the quadrilateral element 10a) by the finite element method (FEM). A so-called displacement-strain matrix (B matrix) is created (step S8).
Subsequently, the second calculation means 3 calculates a perpendicular strain and a shear strain in two orthogonal directions on the surface portion of the measurement object 10 (step S9). In the present embodiment, the concept of the B matrix used for general FEM analysis is applied (for example, see Non-Patent Document 1). The distortion {ε} can be obtained from the displacement {u _d } of the vertex coordinates using the B matrix [B] as follows.

{Ε} = [B] {u _d }
{U _d } = (u ₁ , v ₁ , u ₂ , v ₂ , u ₃ , v ₃ , u ₄ , v ₄ ) ^T
{Ε} = (ε _x , ε _y , γ _xy ) where ε _x and ε _y are vertical strains in the x direction and y direction, and γ _xy is a shear strain.

The third calculation means 4 can calculate a strain or a main strain in an arbitrary direction by coordinate transformation of strain using the calculated vertical strain and shear strain (step S10).
The distortion can be converted from the coordinate system of the CCD camera 1 to an arbitrary coordinate system (rotated by θ from the coordinates of the CCD camera 1) by the following expression.

  Further, the main strain can be obtained by the following equation.

  In the present embodiment, a cross-shaped test piece (ISO 16842: 2014) as shown in FIG. For example, a square element is drawn or added to the center portion of the cross-shaped test piece.

  In this embodiment, when measuring the distortion of the measurement object 10, (1) the n-square element always exists in the image of the CCD camera 1, and (2) the n-square element is a deformation of the measurement object 10. (3) that each side of the n-square element keeps a straight line (at least the in-plane strain distribution is uniform) Is necessary).

  FIG. 5 shows the results of actual measurement of the stress-strain relationship using the cross-shaped test piece of FIG. 4 by the strain measurement method of the present embodiment. In FIG. 5, the result of having attached the strain gauge to the cross-shaped test piece and measuring the stress-strain relationship is also shown. As described above, the stress-strain relationship according to the strain measurement method of the present embodiment was almost the same as the stress-strain relationship according to the strain measurement method using the strain gauge.

According to the present embodiment, in a planar surface portion having a uniform strain distribution of the object 10 to be measured, vertical strain and shear strain in an arbitrary direction in the plane are continuously and accurately measured without contact. can do.
Each side of the n-gonal element, the direction in which distortion is desired to be measured, and the horizontal and vertical axes of the image do not need to coincide with each other, and calibration-less is realized. Moreover, the measurement direction of distortion is not limited.

  In the present embodiment, the case of the quadrilateral element 10a is exemplified as the n-gonal element to be given to the non-measurement object 10, but a triangular element (a virtual n-gonal element becomes a virtual triangular element) is given. Also good. In this case, for each of the three sides of the triangular element, the displacement of each vertex coordinate of the triangular element is calculated based on the difference between the pre-deformation state and the post-deformation state, and the calculated displacement of each vertex coordinate is used. Then, a B matrix of triangular elements is created by FEM, and the perpendicular strain and shear strain in two orthogonal directions in the measurement object 10 are calculated.

(Second Embodiment)
The functions of the constituent elements of the strain measurement apparatus according to the first embodiment described above (the first calculation means 2, the second calculation means 3, the third calculation means 4 and the like in FIG. 1) are the functions of a computer RAM, This can be realized by operating a program stored in a ROM or the like. Similarly, each step (steps S2 to S3, S5 to S10, etc. in FIG. 2) of the distortion measurement method according to the first embodiment can be realized by operating a program stored in a RAM, a ROM, or the like of the computer. Steps S8 to S9 are realized by a calculation program of Labview biaxial strain calculation 130605.txt, for example. This program and a computer-readable recording medium on which the program is recorded are included in this embodiment.

  Specifically, the above program is recorded on a recording medium such as a CD-ROM, or provided to a computer via various transmission media. As a recording medium for recording the program, a flexible disk, a hard disk, a magnetic tape, a magneto-optical disk, a nonvolatile memory card, and the like can be used in addition to the CD-ROM. On the other hand, a communication medium in a computer network system for propagating and supplying program information as a carrier wave can be used as the program transmission medium. Here, the computer network is a WAN such as a LAN or the Internet, a wireless communication network, or the like, and the communication medium is a wired line such as an optical fiber or a wireless line.

  Further, the program included in the present embodiment is not limited to the one in which the function of the first embodiment is realized by the computer executing the supplied program. For example, when the function of the first embodiment is realized in cooperation with an OS (operating system) running on a computer or other application software, the program is included in this embodiment. . Further, when all or part of the processing of the supplied program is performed by the function expansion board or function expansion unit of the computer and the functions of the first embodiment are realized, such a program is included in this embodiment. It is.

  For example, FIG. 6 is a schematic diagram illustrating an internal configuration of a personal user terminal device. In FIG. 6, reference numeral 1200 denotes a personal computer (PC) having a CPU 1201. The PC 1200 executes device control software stored in the ROM 1202 or the hard disk (HD) 1211 or supplied from the flexible disk drive (FD) 1212. The PC 1200 generally controls each device connected to the system bus 1204.

  By the program stored in the CPU 1201, the ROM 1202 or the hard disk (HD) 1211 of the PC 1200, the procedure of steps S2 to S3 and S5 to S10 in FIG. 1 of the first embodiment is realized.

  Reference numeral 1203 denotes a RAM which functions as a main memory, work area, and the like for the CPU 1201. A keyboard controller (KBC) 1205 controls instruction input from a keyboard (KB) 1209, a device (not shown), or the like.

  Reference numeral 1206 denotes a CRT controller (CRTC), which controls display on a CRT display (CRT) 1210. Reference numeral 1207 denotes a disk controller (DKC). The DKC 1207 controls access to a hard disk (HD) 1211 and a flexible disk (FD) 1212 that store a boot program, a plurality of applications, an edit file, a user file, a network management program, and the like. Here, the boot program is a startup program that starts execution (operation) of hardware and software of a personal computer.

Reference numeral 1208 denotes a network interface card (NIC) which performs bidirectional data exchange with a network printer, another network device, or another PC via the LAN 1220.
Instead of using the personal user terminal device, a predetermined computer specialized for the strain measuring device may be used.

DESCRIPTION OF SYMBOLS 1 CCD camera 2 1st calculation means 3 2nd calculation means 4 3rd calculation means 10 Non-measurement object 10a Square element 10b 1st virtual square element 10c 2nd virtual square element

Claims (16)

Based on the difference between the pre-deformation state and the post-deformation state of the n-gonal element in the image obtained by imaging the n-square element (n is 3 or 4) applied to the surface of the object to be measured using the imaging means, Calculating a displacement of each vertex coordinate of the n-gonal element;
A step of creating a displacement-strain matrix of the n-gonal element by a finite element method using the calculated displacement of each vertex coordinate, and calculating a perpendicular strain and a shear strain in two orthogonal directions in the measurement object. viewing including the door,
Calculating the displacement of each vertex coordinate of the n-gonal element;
In the state before the deformation of the n-gonal element, the coordinates of any two points on each side of the n-gonal element are measured, the coordinates of the intersection of the straight lines passing through the two points are calculated, Setting the first vertex coordinates of the virtual n-gonal element;
In the post-deformation state of the n-gonal element, the coordinates of any two points on each side of the n-gonal element are measured, the coordinates of the intersection of straight lines passing through the two points are calculated, and the created second Setting the second vertex coordinate of the virtual n-gonal element;
And calculating a difference value between the second vertex coordinate and the first vertex coordinate as a displacement of each vertex of the n-gonal element . The distortion measurement method according to claim 1, wherein a length of one side of one pixel of the captured image is defined as a reference length. When measuring the coordinates of any two points on each side of the n-sided element, the position in the image of the pixel whose contrast pattern has greatly changed is determined using means for detecting the contrast pattern of the image in one direction. distortion measuring method according to claim 1 or 2 characterized in that the two points to. Based on the difference between the pre-deformation state and the post-deformation state of the n-gonal element in the image obtained by imaging the n-square element (n is 3 or 4) applied to the surface of the object to be measured using the imaging means, Calculating a displacement of each vertex coordinate of the n-gonal element;
A step of creating a displacement-strain matrix of the n-gonal element by a finite element method using the calculated displacement of each vertex coordinate, and calculating a perpendicular strain and a shear strain in two orthogonal directions in the measurement object. When
Including
A distortion measuring method , wherein a length of one side of one pixel of the imaged image is defined as a reference length . Using the calculated vertical strain and shear strain was, by the coordinate transformation of the strain according to any one of claims 1-4, characterized by further comprising the step of calculating the distortion or primary distortion in any direction Strain measurement method. Imaging means;
Based on the difference between the pre-deformation state and the post-deformation state of the n-square element in an image obtained by imaging the n-square element (n is 3 or 4) applied to the surface of the object to be measured using the imaging means. First calculating means for calculating a displacement of each vertex coordinate of the n-gonal element;
Using the calculated displacement of each vertex coordinate, a displacement-strain matrix of the n-gonal element is created by a finite element method, and a perpendicular strain and a shear strain in two orthogonal directions in the object to be measured are calculated. and second calculation means only including,
The first calculation means includes
In the state before the deformation of the n-gonal element, the coordinates of any two points on each side of the n-gonal element are measured, the coordinates of the intersection of the straight lines passing through the two points are calculated, Let it be the first vertex coordinate of the virtual n-square element,
In the post-deformation state of the n-gonal element, the coordinates of any two points on each side of the n-gonal element are measured, the coordinates of the intersection of straight lines passing through the two points are calculated, and the created second The second vertex coordinates of the virtual n-gon element,
A distortion measuring apparatus , wherein a difference value between the second vertex coordinate and the first vertex coordinate is calculated as a displacement of each vertex of the n-gonal element . The distortion measuring apparatus according to claim 6, wherein the first calculation unit defines a length of one side of one pixel of the captured image as a reference length. A detector for detecting a contrast pattern of an image in one direction when measuring the coordinates of any two points on each side of the n-gonal element;
The distortion measuring apparatus according to claim 6, wherein the first calculation unit sets the positions in the image of the pixels whose contrast pattern has changed significantly as the two arbitrary points. Imaging means;
Based on the difference between the pre-deformation state and the post-deformation state of the n-square element in an image obtained by imaging the n-square element (n is 3 or 4) applied to the surface of the object to be measured using the imaging means. First calculating means for calculating a displacement of each vertex coordinate of the n-gonal element;
Using the calculated displacement of each vertex coordinate, a displacement-strain matrix of the n-gonal element is created by a finite element method, and a perpendicular strain and a shear strain in two orthogonal directions in the object to be measured are calculated. 2 calculation means
Including
The first calculation means defines a length of one side of one pixel of the imaged image as a reference length, and the distortion measuring apparatus is characterized in that: Using the calculated vertical strain and shear strain was, claim 6-9, characterized by further comprising a third calculating means for calculating the distortion or primary distortion in any direction by the coordinate transformation of strain 1 The distortion measuring device according to item. Based on the difference between the pre-deformation state and the post-deformation state of the n-gonal element in the image obtained by imaging the n-square element (n is 3 or 4) applied to the surface of the object to be measured using the imaging means, Calculating a displacement of each vertex coordinate of the n-gonal element;
Using the calculated displacement of each vertex coordinate, a displacement-strain matrix of the n-gonal element is created by a finite element method, and a perpendicular strain and a shear strain in two orthogonal directions in the measurement object are calculated. Let the computer run and
The procedure for calculating the displacement of each vertex coordinate of the n-gonal element is as follows:
In the state before the deformation of the n-gonal element, the coordinates of any two points on each side of the n-gonal element are measured, the coordinates of the intersection of the straight lines passing through the two points are calculated, A procedure for setting the first vertex coordinates of the virtual n-gonal element;
In the post-deformation state of the n-gonal element, the coordinates of any two points on each side of the n-gonal element are measured, the coordinates of the intersection of straight lines passing through the two points are calculated, and the created second A procedure for setting the second vertex coordinates of the virtual n-gonal element;
Calculating a difference value between the second vertex coordinate and the first vertex coordinate as a displacement of each vertex of the n-gonal element;
The program characterized by including . The program according to claim 11, wherein the length of one side of one pixel of the captured image is defined as a reference length. When measuring the coordinates of any two points on each side of the n-gonal element, in the procedure for detecting the contrast pattern of the image in one direction, the position in the image of the pixel in which the contrast pattern has changed greatly is set to the arbitrary two points. The program according to claim 11 , wherein the program is a point. Based on the difference between the pre-deformation state and the post-deformation state of the n-gonal element in the image obtained by imaging the n-square element (n is 3 or 4) applied to the surface of the object to be measured using the imaging means, Calculating a displacement of each vertex coordinate of the n-gonal element;
Using the calculated displacement of each vertex coordinate, a displacement-strain matrix of the n-gonal element is created by a finite element method, and a perpendicular strain and a shear strain in two orthogonal directions in the measurement object are calculated. When
To the computer,
A program that defines the length of one side of one pixel of the captured image as a reference length . Calculated using said vertical strain and shear strain, according to any one of claims 11 to 14, characterized in that it further comprises the steps of calculating the distortion or primary distortion in any direction by the coordinate transformation of the strain Program.   The computer-readable recording medium which recorded the program of any one of Claims 11-15.

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