CN104748716B - The method for observing the change of three dimensional strain tensor - Google Patents
The method for observing the change of three dimensional strain tensor Download PDFInfo
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- CN104748716B CN104748716B CN201510163382.4A CN201510163382A CN104748716B CN 104748716 B CN104748716 B CN 104748716B CN 201510163382 A CN201510163382 A CN 201510163382A CN 104748716 B CN104748716 B CN 104748716B
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- 238000000034 method Methods 0.000 title claims abstract description 21
- 238000007689 inspection Methods 0.000 claims abstract description 6
- 238000006243 chemical reaction Methods 0.000 claims description 4
- 239000000463 material Substances 0.000 description 4
- 230000005483 Hooke's law Effects 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 239000000835 fiber Substances 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 239000013307 optical fiber Substances 0.000 description 1
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- 239000007787 solid Substances 0.000 description 1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/32—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring the deformation in a solid
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Abstract
The invention discloses a kind of method for observing the change of three dimensional strain tensor, multiple line strain sensors are arranged in mutually perpendicular three planes, the line strain change in 4 directions is observed in each plane, adjacent 45 ° of observed direction interval, pass through the observation to all these direction line strain variations, convert the change of three dimensional strain tensor, and by being in harmony the inspection of relation certainly, judging the reliability of observation.Can be converted all three dimensional strain component of tensors, and can easily carry out self-inspection.
Description
Technical Field
The invention relates to a three-dimensional strain tensor detection technology, in particular to a method for observing three-dimensional strain tensor change.
Background
The strain tensor is:
in classical elastic mechanics, strain is a second order symmetric tensor. The second order tensor has nine elements in total. In a symmetric second order tensor, there are only 6 independent variables. From the strain, the stress acting on the object can be calculated by hooke's law.
In rectangular XYZ coordinate system, the strain tensor for a point can be expressed as:
wherein,x、yandzpositive strain (line strain) in the directions of X, Y and the Z-axis, respectively, andxy、yzandxzshear strains in the XY, YZ and XZ planes, respectively.
Various sensors:
conventional observations of strain are based on observations of length changes. The sensor for observing length changes is referred to herein as a linear strain sensor. Currently, there are various precision linear strain sensors, including laser ranging sensors, capacitive sensors, resistive sensors, electromagnetic sensors, vibrating wire sensors, and the like. In particular capacitive sensors, with a resolution of up to 10-10The device can be used for observing the change of the solid tide and is widely applied internationally.
The optical fiber sensor developed in recent years breaks through the limitation of the traditional strain observation method, does not need to measure length, can directly measure strain, realizes the miniaturization of the sensor, and has the resolution ratio of 10-9Provides conditions for developing a novel strain gauge.
Various strain gauges:
at present, a mature linear strain sensor is used for actual strain measurement, and various instruments are available for observing one-dimensional linear strain change and two-dimensional strain state change. The former is, for example, a pantograph for observation in a cave, and the latter is representative of, for example, a component borehole strain gauge. Recently, observation techniques for a strain component perpendicular to the ground have been successfully developed in both japan and china.
However, how to observe the three-dimensional strain tensor change is still an unsolved problem.
Disclosure of Invention
The invention provides a method for observing three-dimensional strain tensor change, which can convert all three-dimensional strain tensor components and can carry out self-inspection conveniently.
The purpose of the invention is realized by the following technical scheme:
the method for observing the change of the three-dimensional strain tensor is characterized in that a plurality of linear strain sensors are respectively arranged in three planes which are perpendicular to each other, linear strain changes in 4 directions are observed in each plane, the interval between adjacent observation directions is 45 degrees, the change of the three-dimensional strain tensor is converted through the observation of the linear strain changes in all the directions, and the observation reliability is judged through the inspection of self-consistent relations.
It can be seen from the above technical solutions provided by the present invention that, in the method for observing changes in a three-dimensional strain tensor according to the embodiments of the present invention, a plurality of linear strain sensors are respectively arranged in three planes perpendicular to each other, linear strain changes in 4 directions are observed in each plane, an interval between adjacent observation directions is 45 °, three-dimensional strain tensor changes are converted by observing strain changes in all the directions, and the reliability of observation is determined by checking a self-consistent relationship. All three-dimensional strain tensor components can be scaled and self-checking can be conveniently performed.
Drawings
FIG. 1 shows the manner in which the linear strain sensors are arranged in the XY plane, sz1、sz2、sz3And sz4A 4-direction linear strain sensor is shown.
FIG. 2 shows the way in which the linear strain sensors are arranged in the YZ plane, sx1、sx2、sx3And sx4A 4-direction linear strain sensor is shown.
FIG. 3 shows the way in which the linear strain sensors are arranged in the ZX plane, sy1、sy2、sy3And sy4A 4-direction linear strain sensor is shown.
FIG. 4 is a three-dimensional sensor layout of an embodiment of the present invention, wherein sy1And sx3，sz1And sy3，sx1And sz3The two quantities each represent a sensor in the same direction.
Detailed Description
The following describes embodiments of the present invention in further detail.
The preferred embodiment of the method for observing the change of the three-dimensional strain tensor is as follows:
the method comprises the steps of respectively arranging a plurality of linear strain sensors in three planes which are perpendicular to each other, observing linear strain changes in 4 directions in each plane, enabling the adjacent observation directions to be separated by 45 degrees, converting three-dimensional strain tensor changes through observation of the linear strain changes in all the directions, and judging the reliability of observation through inspection of self-consistent relations.
With 9 wire strain sensors, arranged in the following manner:
firstly, establishing a rectangular coordinate system XYZ;
arranging linear strain sensors in XY plane, and observing linear strain s in 4 directions at equal intervals of 45 °z1、sz2、sz3And sz4Wherein s isz1And sz3Respectively coinciding with the X-axis and the Y-axis;
arranging linear strain sensors in YZ plane, and observing linear strain s in 4 directions at 45 ° intervalsx1、sx2、sx3And sx4Wherein s isx1And sx3Respectively coinciding with the Y axis and the Z axis;
arranging linear strain sensors in ZX plane, respectively observing linear strain s in 4 directions at equal intervals of 45 DEGy1、sy2、sy3And sy4Wherein s isy1And sy3Respectively coinciding with the Z axis and the X axis;
actually, only line strain observation in 9 directions exists, and the following equivalent relationship exists in the 12 nominal observation quantities:
sx3＝sy1
sy3＝sz1
sz3＝sx1
then, the three-dimensional strain tensor change is obtained through the following equation conversion:
and self-checking by the following equation:
sx2+sx4＝sx1+sx3
sy2+sy4＝sy1+sy3
sz2+sz4＝sz1+sz3。
the specific embodiment is as follows:
with 9 wire strain sensors, arranged in the following manner:
establishing a rectangular coordinate system XYZ;
4 linear strain sensors are arranged in the XY plane, and linear strains s in 4 directions are respectively observed at equal intervals of 45 DEGz1、sz2、sz3And sz4Wherein s isz1And sz3Coinciding with the X and Y axes respectively (fig. 1);
arranging 4 linear strain sensors in YZ plane, respectively observing linear strain s in 4 directions at equal intervals of 45 DEGx1、sx2、sx3And sx4Wherein s isx1And sx3Coinciding with the Y-axis and the Z-axis respectively (fig. 2).
4 linear strain sensors are arranged in the ZX plane, and the linear strains s in 4 directions are respectively observed at equal intervals of 45 DEGy1、sy2、sy3And sy4Wherein s isy1And sy3Coinciding with the Z-axis and X-axis respectively (fig. 3);
there are actually only 9 line strain observations, and the following equivalence exists among 12 nominal observations (fig. 4):
sx3＝sy1
sy3＝sz1
sz3＝sx1(2)
conversion method
Self-checking equation:
sx2+sx4＝sx1+sx3
sy2+sy4＝sy1+sy3
sz2+sz4＝sz1+sz3(7)
has the advantages that:
at present, no method for observing three-dimensional strain tensor change exists. The invention provides a method for observing three-dimensional strain tensor change by using an existing linear strain sensor. The method arranges a plurality of linear strain sensors in a completely symmetrical mode, and has the characteristic of conveniently carrying out self-checking while converting all three-dimensional strain tensor components. This self-checking function is particularly important for strain observation, since all sensors of a strain gauge are fixed in an object (e.g. a formation) and cannot directly check how their operating state is as it is for other gauges.
The method of the invention is preferably carried out using a fibre optic sensor. There may be two observation modes. One is to fix the sensor arrangement according to the invention in a material that is as elastic as the observed object and then to couple it together. Alternatively, the sensor arrangement of the present invention may be fixed in a material to form a probe which is then coupled to the object to be observed. The former method requires the preparation of corresponding materials for different objects, but is simple to scale. The latter method can be installed in objects of various materials, but requires relatively complicated conversion to give the actual strain change from the observed amount.
The invention provides a method for observing the strain change of a certain position in an object (such as a stratum) by using the existing linear strain sensor, and establishes a conceptual model for observing the three-dimensional strain tensor change. According to the method, a plurality of linear strain sensors are respectively arranged in three planes which are perpendicular to each other, linear strain changes in 4 directions are observed in each plane, and the interval between every two adjacent observation directions is 45 degrees. By observing the line strain changes in these directions, the three-dimensional strain tensor changes are converted, and the reliability of the observation is judged by checking the self-consistent relationship. The invention can be applied in the fields of geotechnical engineering, geodynamics and the like.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (1)
1. A method for observing three-dimensional strain tensor change is characterized in that a plurality of linear strain sensors are respectively arranged in three planes which are perpendicular to each other, linear strain change in 4 directions is observed in each plane, the interval between adjacent observation directions is 45 degrees, three-dimensional strain tensor change is converted through observation of linear strain change in all the directions, and the observation reliability is judged through inspection of self-consistent relation;
with a plurality of wire strain sensors, arranged in the following manner:
firstly, establishing a rectangular coordinate system XYZ;
arranging linear strain sensors in XY plane, and observing linear strain s in 4 directions at equal intervals of 45 °z1、sz2、sz3And sz4Wherein s isz1And sz3Respectively coinciding with the X-axis and the Y-axis;
arranging linear strain sensors in YZ plane, and observing linear strain s in 4 directions at 45 ° intervalsx1、sx2、sx3And sx4Wherein s isx1And sx3Respectively coinciding with the Y axis and the Z axis;
arranging linear strain sensors in ZX plane, respectively observing linear strain s in 4 directions at equal intervals of 45 DEGy1、sy2、sy3And sy4Wherein s isy1And sy3Respectively coinciding with the Z axis and the X axis;
actually, only line strain observation in 9 directions exists, and the following equivalent relationship exists in the 12 nominal observation quantities:
sx3＝sy1
sy3＝sz1
sz3＝sx1；
then, the three-dimensional strain tensor change is obtained through the following equation conversion:
in the formula,x、yandzrespectively X, Y and the Z-axis,xy、yzandxzrespectively, the shear strain in XY, YZ and XZ planes;
and self-checking by the following equation:
sx2+sx4＝sx1+sx3
sy2+sy4＝sy1+sy3
sz2+sz4＝sz1+sz3。
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| CN107300362A (en) * | 2016-05-12 | 2017-10-27 | 中国计量大学 | A kind of right-angle prismatic cone optical fiber grating structure body detected for three dimensional strain |
| CN107576302A (en) * | 2017-09-08 | 2018-01-12 | 中国地震局地壳应力研究所 | A kind of spherical shell type three dimensional strain observation procedure |
| CN109374442A (en) * | 2018-11-09 | 2019-02-22 | 天津城建大学 | Strain value calculating method based on rotational right angle tetrahedron shearing strain test device |
| CN114485380B (en) * | 2022-02-24 | 2023-06-20 | 应急管理部国家自然灾害防治研究院 | Indoor simulation self-checking device of component type drilling strain gauge |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103954386A (en) * | 2014-04-15 | 2014-07-30 | 沈阳建筑大学 | Three-dimensional space stress-strain measurement method based on fiber bragg grating sensor |
| CN104482913A (en) * | 2014-12-05 | 2015-04-01 | 天津城建大学 | Test device and test method used for testing three-dimensional strained condition |
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| US20110084209A1 (en) * | 2009-10-08 | 2011-04-14 | Texas Instruments Incorporated | Reproducible lattice strain measurement method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103954386A (en) * | 2014-04-15 | 2014-07-30 | 沈阳建筑大学 | Three-dimensional space stress-strain measurement method based on fiber bragg grating sensor |
| CN104482913A (en) * | 2014-12-05 | 2015-04-01 | 天津城建大学 | Test device and test method used for testing three-dimensional strained condition |
Non-Patent Citations (1)
| Title |
|---|
| 正交曲线坐标系应变张量的普适表达;刘序俨等;《大地测量与地球动力学》;20080831;第28卷(第4期);第89-96页 * |
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