CN111177848A - Method and device for acquiring strain theoretical value based on finite element model - Google Patents
Method and device for acquiring strain theoretical value based on finite element model Download PDFInfo
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Abstract
The invention provides a method and a device for acquiring a strain theoretical value based on a finite element model, wherein the method comprises the following steps: step one, determining a first finite element unit grid in a finite element model of a structural test piece, wherein the first finite element unit grid is a grid adhered with a strain gauge; step two, determining a 2x2 finite element mesh corresponding to the first finite element mesh in a finite element model of the structural test piece, wherein the 2x2 finite element mesh comprises the first finite element mesh; step three, acquiring central point strain values and central point coordinates of the 4 finite element unit grids; and step four, obtaining theoretical values corresponding to the strain gauges by adopting an interpolation algorithm according to the central point strain values and the central point coordinates of the 4 finite element unit grids. The invention solves the problem that the theoretical calculation value of the strain measurement point is difficult to obtain due to the inconsistency between the strain measurement point of the test piece and the calculation point of the finite element grid.
Description
Technical Field
The invention belongs to the field of aviation structure strength tests, and particularly relates to a method and a device for acquiring a strain theoretical value based on a finite element model.
Background
In the structural strength test of the airplane, a mechanical finite element model is generally established and stress preliminary analysis is carried out according to the structure and stress characteristics of a structural test piece. According to the stress analysis result and the test purpose, appropriate strain gauges are arranged and adhered on the structure surface of the structure test piece in advance, and the stress rationality of the structure test piece is verified by comparing the measured values of the strain gauges with the strain theoretical value of the central point of the finite element grid in the test process.
However, in general, the actual pasting position of the strain gauge is not exactly consistent with the center point of the finite element mesh due to inaccurate pasting position of the strain gauge or the fact that the pasting position is not at the center point of the finite element mesh. Therefore, the authenticity of the measured value of the strain gauge is identified, and the comparison between the measured value of the strain and the theoretical value of the strain is difficult.
Disclosure of Invention
The invention provides a method and a device for acquiring a strain theoretical value based on a finite element model, which solve the problem that the strain measurement point theoretical calculation value is difficult to acquire due to inconsistency of a test piece strain measurement point and a finite element grid calculation point.
The invention provides a method for acquiring a strain theoretical value based on a finite element model, which comprises the following steps:
step one, determining a first finite element unit grid in a finite element model of a structural test piece, wherein the first finite element unit grid is a grid adhered with a strain gauge;
step two, determining a 2x2 finite element mesh corresponding to the first finite element mesh in a finite element model of the structural test piece, wherein the 2x2 finite element mesh comprises the first finite element mesh;
step three, acquiring central point strain values and central point coordinates of the 4 finite element unit grids;
and step four, acquiring theoretical values corresponding to the strain gauges by adopting an interpolation algorithm according to the central point strain values and the central point coordinates of the 4 finite element unit grids.
Optionally, in the finite element model of the structural test piece, determining a 2x2 finite element mesh corresponding to the first finite element mesh includes:
uniformly dividing the first finite element mesh into 4 quadrants, and when the strain gauge is located at a first quadrant in the first finite element mesh, determining a 2x2 finite element mesh corresponding to the first finite element mesh as a 2x2 finite element mesh taking the first finite element mesh as a lower left corner azimuth mesh;
when the strain gauge is located in a second quadrant of the first finite element mesh, determining a 2x2 finite element mesh corresponding to the first finite element mesh as a 2x2 finite element mesh with the first finite element mesh as a lower right corner orientation mesh;
when the strain gauge is located in a third quadrant of the first finite element mesh, determining a 2x2 finite element mesh corresponding to the first finite element mesh as a 2x2 finite element mesh with the first finite element mesh as an upper right-corner azimuth mesh;
and when the strain gauge is positioned in a fourth quadrant in the first finite element mesh, determining that the 2x2 finite element mesh corresponding to the first finite element mesh is a 2x2 finite element mesh which takes the first finite element mesh as an upper left corner azimuth mesh.
Optionally, obtaining the theoretical value corresponding to the strain gauge by using an interpolation algorithm according to the central point strain value and the central point coordinate of each of the 4 finite element unit grids includes:
dividing the 4 finite element meshes into two groups of interpolation sets, wherein each group of interpolation set comprises two finite element meshes;
determining the coordinates and the strain values of the first virtual point and the second virtual point by adopting a linear interpolation algorithm according to the central point strain value and the central point coordinate of each finite element grid in the two groups of interpolation sets;
and acquiring a theoretical value corresponding to the strain gauge by adopting a linear interpolation algorithm according to the coordinates and the strain values of the first virtual point and the second virtual point.
Optionally, before obtaining the theoretical value corresponding to the strain gauge by using an interpolation algorithm according to the central point strain value and the central point coordinate of each of the 4 finite element unit grids, the method further includes:
unifying the directions of the central point strain values of the 4 finite element unit grids.
The invention also provides a device for acquiring the strain theoretical value based on the finite element model, which comprises:
the first grid determining module is used for determining a first finite element unit grid in a finite element model of the structural test piece, wherein the first finite element unit grid is a grid adhered with a strain gauge;
a second mesh determination module for determining a 2x2 finite element mesh corresponding to the first finite element mesh in a structural test piece finite element model, the 2x2 finite element mesh including the first finite element mesh;
the information acquisition module is used for acquiring the central point strain value and the central point coordinate of each of the 4 finite element unit grids;
and the theoretical value acquisition module is used for acquiring the theoretical value corresponding to the strain gauge by adopting an interpolation algorithm according to the central point strain value and the central point coordinate of each of the 4 finite element unit grids.
Optionally, the second grid determination module is specifically configured to,
uniformly dividing the first finite element mesh into 4 quadrants, and when the strain gauge is located at a first quadrant in the first finite element mesh, determining a 2x2 finite element mesh corresponding to the first finite element mesh as a 2x2 finite element mesh taking the first finite element mesh as a lower left corner azimuth mesh;
when the strain gauge is located in a second quadrant of the first finite element mesh, determining a 2x2 finite element mesh corresponding to the first finite element mesh as a 2x2 finite element mesh with the first finite element mesh as a lower right corner orientation mesh;
when the strain gauge is located in a third quadrant of the first finite element mesh, determining a 2x2 finite element mesh corresponding to the first finite element mesh as a 2x2 finite element mesh with the first finite element mesh as an upper right-corner azimuth mesh;
and when the strain gauge is positioned in a fourth quadrant in the first finite element mesh, determining that the 2x2 finite element mesh corresponding to the first finite element mesh is a 2x2 finite element mesh which takes the first finite element mesh as an upper left corner azimuth mesh.
Optionally, the theoretical value obtaining module is specifically configured to,
dividing the 4 finite element meshes into two groups of interpolation sets, wherein each group of interpolation set comprises two finite element meshes;
determining the coordinates and the strain values of the first virtual point and the second virtual point by adopting a linear interpolation algorithm according to the central point strain value and the central point coordinate of each finite element grid in the two groups of interpolation sets;
and acquiring a theoretical value corresponding to the strain gauge by adopting a linear interpolation algorithm according to the coordinates and the strain values of the first virtual point and the second virtual point.
Optionally, the apparatus for obtaining a theoretical value of strain based on a finite element model further includes:
and the direction unifying module is used for unifying the directions of the central point strain values of the 4 finite element unit grids.
The invention provides a method and a device for acquiring a strain theoretical value based on a finite element model, and aims at the problem of determining the strain theoretical value at any position in an airplane structure test piece. The invention provides a method for calculating the strain theoretical value of any position in the structural strength test by a linear interpolation method based on the existing finite element model and the calculation result, and solves the problem that the theoretical calculated value of the strain measurement point is difficult to obtain due to the fact that the strain measurement point of the test piece is inconsistent with the finite element grid point of the test piece in the airplane structural strength test, the theoretical value of the strain measurement point is difficult to accurately obtain due to the fact that the strain measurement point of the test piece is inconsistent with the calculation point of the finite element grid. The method has the advantages of correct theoretical basis, clear and simple implementation steps and clear engineering concept. The invention solves the problem that the strain value at any position in the aircraft structural strength test is difficult to accurately obtain from the existing finite element model and the calculation result.
Drawings
FIG. 1 is a schematic flow chart of a method for obtaining a theoretical strain value based on a finite element model according to the present invention;
FIG. 2 is a schematic diagram of a theoretical acquisition method of a strain value of a test piece at any position based on a finite element model;
fig. 3 is a schematic diagram of a strain calculation process.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
Fig. 1 is a schematic flow chart of a method for obtaining a strain theoretical value based on a finite element model according to the present invention, fig. 2 is a schematic diagram of a method for theoretically obtaining a strain value at any position of a test piece based on a finite element model, and fig. 3 is a schematic diagram of a strain calculation process referring to fig. 2 to 3.
As shown in fig. 2, the minimum finite element mesh required for applying the finite element model-based strain theory value acquisition method is composed of 1 2 by 2 finite element meshes, wherein the G point of the true adhesion position of the strain gauge in the test piece must be included in the 2 by 2 finite element meshes. The 4 finite element mesh elements are element 1, element 2, element 3 and element 4, respectively, and the central points of element 1, element 2, element 3 and element 4 are point a, point B, point C and point D, respectively, where point G is included in element 4.
As shown in fig. 3, the strain calculation process diagram is composed of 4 points (point a, point B, point C, and point D), 2 virtual points (point E and point F), and 1 point G of the true pasting position of the strain gauge. Point E is the first virtual point and point F is the second virtual point.
As shown in fig. 1, a method for obtaining a strain theoretical value based on a finite element model includes the following steps:
step one, searching a finite element unit grid where a true pasting position of a strain gauge is located in a finite element model of a test piece;
step two, determining a 2-by-2 finite element mesh in the finite element model of the test piece, wherein the 2-by-2 finite element mesh comprises the finite element mesh in the step one;
step three, acquiring the central point coordinate A (x) of 4 finite element unit grids of the 2-by-2 finite element grids in the step two according to the finite element model of the test piece1,y1)、B(x2,y1)、C(x2,y2)、D(x1,y2) (ii) a Acquiring strain values epsilon of central points of 4 finite element units according to stress calculation results of finite element models of test piecesA、εB、εC、εD;
Illustratively, 4 finite element units capable of forming a rectangle are taken as an example in the embodiment of the present invention.
And step four, acquiring theoretical values corresponding to the strain gauges by adopting an interpolation algorithm according to the central point strain values and the central point coordinates of the 4 finite element unit grids.
The present invention will be described in further detail with reference to a specific example.
A strain theoretical value obtaining method based on a finite element model comprises the following steps:
it is known that:
in the finite element model of the test piece, the position coordinate of the strain gauge is G (20,25), and the 2-by-2 finite element grid containing the point GThe coordinates of the central points of the 4 finite element grids are respectively A (10,15), B (30,15), C (30,40) and D (10,40), and the strain value epsilon of the central points of the 4 finite element grids in a certain determined direction, such as the X directionA=1200με、εB=1500με、εC=2200με、εD=2500με。
A strain theoretical value obtaining method based on a finite element model comprises the following steps:
step one, the real pasting position of a strain gauge in a finite element model of a test piece is a point G, and a finite element unit grid where the point G is located is a unit 4;
step two, determining a 2-by-2 finite element grid in the finite element model of the test piece, wherein the 2-by-2 finite element grid comprises the finite element unit grid in the step one, namely a unit 4, and the 4 finite element grid units are respectively a unit 1, a unit 2, a unit 3 and a unit 4;
step three, according to a finite element model of a test piece, the coordinates of the central points of 4 finite element unit grids (unit 1, unit 2, unit 3 and unit 4) of the 2-by-2 finite element grids in the step two can be respectively obtained through simple processing and are respectively A (10,15), B (30,15), C (30,40) and D (10, 40); respectively obtaining strain values epsilon of the central points of the 4 finite element units in a certain determined direction such as an X direction according to the stress calculation result of the finite element model of the test pieceA=1200με、εB=1500με、εC=2200με、εD=2500με。
And step four, acquiring theoretical values corresponding to the strain gauges by adopting an interpolation algorithm according to the central point strain values and the central point coordinates of the 4 finite element unit grids.
Calculating a strain value epsilon of the first virtual pointE,
Calculating a strain value epsilon of the second virtual pointF,
Calculating strain value epsilon of any position of structural test pieceG,
Namely, the theoretical calculation value of the strain at the point G of the strain gauge attachment position was 1310. mu. epsilon.
The invention provides a method and a device for acquiring a strain theoretical value based on a finite element model, and aims at the problem of determining the strain theoretical value at any position in an airplane structure test piece. The invention provides a method for calculating the strain theoretical value of any position in the structural strength test by a linear interpolation method based on the existing finite element model and the calculation result, and solves the problem that the theoretical calculated value of the strain measurement point is difficult to obtain due to the fact that the strain measurement point of the test piece is inconsistent with the finite element grid point of the test piece in the airplane structural strength test, the theoretical value of the strain measurement point is difficult to accurately obtain due to the fact that the strain measurement point of the test piece is inconsistent with the calculation point of the finite element grid. The method has the advantages of correct theoretical basis, clear and simple implementation steps and clear engineering concept. The invention solves the problem that the strain value at any position in the aircraft structural strength test is difficult to accurately obtain from the existing finite element model and the calculation result.
Claims (8)
1. A method for acquiring a strain theoretical value based on a finite element model is characterized by comprising the following steps:
step one, determining a first finite element unit grid in a finite element model of a structural test piece, wherein the first finite element unit grid is a grid adhered with a strain gauge;
step two, determining a 2x2 finite element mesh corresponding to the first finite element mesh in a finite element model of the structural test piece, wherein the 2x2 finite element mesh comprises the first finite element mesh;
step three, acquiring central point strain values and central point coordinates of the 4 finite element unit grids;
and step four, acquiring theoretical values corresponding to the strain gauges by adopting an interpolation algorithm according to the central point strain values and the central point coordinates of the 4 finite element unit grids.
2. The method of claim 1, wherein determining the 2x2 finite element mesh corresponding to the first finite element mesh in the structural test part finite element model comprises:
uniformly dividing the first finite element mesh into 4 quadrants, and when the strain gauge is located at a first quadrant in the first finite element mesh, determining a 2x2 finite element mesh corresponding to the first finite element mesh as a 2x2 finite element mesh taking the first finite element mesh as a lower left corner azimuth mesh;
when the strain gauge is located in a second quadrant of the first finite element mesh, determining a 2x2 finite element mesh corresponding to the first finite element mesh as a 2x2 finite element mesh with the first finite element mesh as a lower right corner orientation mesh;
when the strain gauge is located in a third quadrant of the first finite element mesh, determining a 2x2 finite element mesh corresponding to the first finite element mesh as a 2x2 finite element mesh with the first finite element mesh as an upper right-corner azimuth mesh;
and when the strain gauge is positioned in a fourth quadrant in the first finite element mesh, determining that the 2x2 finite element mesh corresponding to the first finite element mesh is a 2x2 finite element mesh which takes the first finite element mesh as an upper left corner azimuth mesh.
3. The method according to claim 2, wherein the obtaining the theoretical values corresponding to the strain gauges by using an interpolation algorithm according to the strain values and the central point coordinates of the central points of the 4 finite element grids comprises:
dividing the 4 finite element meshes into two groups of interpolation sets, wherein each group of interpolation set comprises two finite element meshes;
determining the coordinates and the strain values of the first virtual point and the second virtual point by adopting a linear interpolation algorithm according to the central point strain value and the central point coordinate of each finite element grid in the two groups of interpolation sets;
and acquiring a theoretical value corresponding to the strain gauge by adopting a linear interpolation algorithm according to the coordinates and the strain values of the first virtual point and the second virtual point.
4. The method according to claim 1, wherein before obtaining the theoretical values corresponding to the strain gauges by using an interpolation algorithm according to the strain values and the central point coordinates of the central points of the 4 finite element grids, the method further comprises:
unifying the directions of the central point strain values of the 4 finite element unit grids.
5. An apparatus for obtaining a theoretical strain value based on a finite element model, comprising:
the first grid determining module is used for determining a first finite element unit grid in a finite element model of the structural test piece, wherein the first finite element unit grid is a grid adhered with a strain gauge;
a second mesh determination module for determining a 2x2 finite element mesh corresponding to the first finite element mesh in a structural test piece finite element model, the 2x2 finite element mesh including the first finite element mesh;
the information acquisition module is used for acquiring the central point strain value and the central point coordinate of each of the 4 finite element unit grids;
and the theoretical value acquisition module is used for acquiring the theoretical value corresponding to the strain gauge by adopting an interpolation algorithm according to the central point strain value and the central point coordinate of each of the 4 finite element unit grids.
6. The apparatus of claim 5, wherein the second grid determination module is specifically configured to,
uniformly dividing the first finite element mesh into 4 quadrants, and when the strain gauge is located at a first quadrant in the first finite element mesh, determining a 2x2 finite element mesh corresponding to the first finite element mesh as a 2x2 finite element mesh taking the first finite element mesh as a lower left corner azimuth mesh;
when the strain gauge is located in a second quadrant of the first finite element mesh, determining a 2x2 finite element mesh corresponding to the first finite element mesh as a 2x2 finite element mesh with the first finite element mesh as a lower right corner orientation mesh;
when the strain gauge is located in a third quadrant of the first finite element mesh, determining a 2x2 finite element mesh corresponding to the first finite element mesh as a 2x2 finite element mesh with the first finite element mesh as an upper right-corner azimuth mesh;
and when the strain gauge is positioned in a fourth quadrant in the first finite element mesh, determining that the 2x2 finite element mesh corresponding to the first finite element mesh is a 2x2 finite element mesh which takes the first finite element mesh as an upper left corner azimuth mesh.
7. The apparatus of claim 6, wherein the theoretical value obtaining module is specifically configured to,
dividing the 4 finite element meshes into two groups of interpolation sets, wherein each group of interpolation set comprises two finite element meshes;
determining the coordinates and the strain values of the first virtual point and the second virtual point by adopting a linear interpolation algorithm according to the central point strain value and the central point coordinate of each finite element grid in the two groups of interpolation sets;
and acquiring a theoretical value corresponding to the strain gauge by adopting a linear interpolation algorithm according to the coordinates and the strain values of the first virtual point and the second virtual point.
8. The apparatus of claim 5, further comprising:
and the direction unifying module is used for unifying the directions of the central point strain values of the 4 finite element unit grids.
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