CN107576302A - A kind of spherical shell type three dimensional strain observation procedure - Google Patents
A kind of spherical shell type three dimensional strain observation procedure Download PDFInfo
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Abstract
The invention discloses a kind of spherical shell type three dimensional strain observation procedure, in XYZ rectangular coordinate systems, arranges following observed direction：Tetra- observed directions of z1, z2, z3 and z4 are equidistantly spaced from 45 ° in X/Y plane, wherein z1 and z3 overlap with X-axis and Y-axis respectively；Tetra- observed directions of x1, x2, x3 and x4 are equidistantly spaced from 45 ° in YZ planes, wherein x1 and x3 overlap with Y-axis and Z axis respectively；Tetra- observed directions of y1, y2, y3 and y4 are equidistantly spaced from 45 ° in ZX planes, wherein y1 and y3 are overlapped with Z axis and X-axis respectively, and observation element is set respectively in this 9 observed directions.Measuring probe is designed as spherical, spheric probe is placed in media as well, together with medium couples, the change of 9 orient diameters of ball can be measured, for the deformation of inverting medium, make three-dimensional tensor strain observation closer to can implement.
Description
Technical field
The present invention relates to a kind of method for observing the change of three dimensional strain tensor, more particularly to a kind of spherical shell type three dimensional strain to see
Survey method.
Background technology
Before the application, applicant has proposed the model of an observation three dimensional strain tensor change
(ZL201510163382.4), referred to as Q- models.The theoretical model is only this observation and provides a basic ideas, be in reality
Implement this observation and some particular problems also be present in border.By taking Q- models as an example, actual observation is carried out fully according to the model, just
9 sensors for meaning to measure all directions line strain will firmly be coupled with medium, could so experience the change of medium
Shape.But actually this coupling is difficult to realize.
Therefore, also the method actually implemented is designed to along the thinking of theoretical model.
The content of the invention
It is an object of the invention to provide a kind of spherical shell type three dimensional strain observation procedure.
The purpose of the present invention is achieved through the following technical solutions：
The spherical shell type three dimensional strain observation procedure of the present invention, including：
In XYZ rectangular coordinate systems, following observed direction is arranged：
Be equidistantly spaced from tetra- observed directions of z1, z2, z3 and z4 in X/Y plane with 45 °, wherein z1 and z3 respectively with X-axis
Overlapped with Y-axis, with Sz1、Sz2、Sz3And Sz4Represent the observation in 4 directions；
Be equidistantly spaced from tetra- observed directions of x1, x2, x3 and x4 in YZ planes with 45 °, wherein x1 and x3 respectively with Y-axis
Overlapped with Z axis, with Sx1、Sx2、Sx3And Sx4Represent the observation in 4 directions；
Be equidistantly spaced from tetra- observed directions of y1, y2, y3 and y4 in ZX planes with 45 °, wherein y1 and y3 respectively with Z axis
Overlapped with X-axis, with Sy1、Sy2、Sy3And Sy4Represent the observation in 4 directions；
It is above-mentioned respectively to have 4 observed directions respectively on three coordinate planes, wherein relation be present：X1=z3, y1=x3 and
Z1=y3, therefore, actually only 9 observed directions set observation element respectively in this 9 observed directions；
The line strain observed on this 9 directions and the relation of three dimensional strain tensor, i.e., described spherical shell type three dimensional strain are seen
The strain reduction formula of survey method is as follows：
Z1=y3：SZ1=y3=A (εx+εy+εz)+B(εx-εy-εz)
z2：Sz2=A (εx+εy+εz)+B(-εz+2εxy)
z4：Sz4=A (εx+εy+εz)+B(-εz-2εxy)
Y1=x3：SZ1=y3=A (εx+εy+εz)+B(-εx-εy+εz)
y2：Sy2=A (εx+εy+εz)+B(-εy+2εzx)
y4：Sy2=A (εx+εy+εz)+B(-εy-2εzx)
X1=z3：SZ1=y3=A (εx+εy+εz)+B(-εx+εy-εz)
x2：Sy2=A (εx+εy+εz)+B(-εx+2εyz)
x4：Sy2=A (εx+εy+εz)+B(-εx-2εyz)；
In above formula, A replaces the coefficient of face dependent variable, and B replaces the coefficient of shearing strain item.
As seen from the above technical solution provided by the invention, a kind of spherical shell type provided in an embodiment of the present invention is three-dimensional should
Become observation procedure, measuring probe is designed as spherical, spheric probe is placed in media as well, can be with together with medium couples
The change of 9 orient diameters of ball is measured, for the deformation of inverting medium, makes three-dimensional tensor strain observation is closer can be real
Apply.
Brief description of the drawings
Fig. 1 a and Fig. 1 b are respectively Two-dimensional strain theory observation model and three dimensional strain theory observation model schematic diagram.
Fig. 2 is the 4 observed direction schematic diagrames arranged in the embodiment of the present invention in X/Y plane.
Fig. 3 is the 4 observed direction schematic diagrames arranged in the embodiment of the present invention in YZ planes.
Fig. 4 is the 4 observed direction schematic diagrames arranged in the embodiment of the present invention in ZX planes.
Fig. 5 is that 9 diameter change observed directions that spherical shell is popped one's head in the embodiment of the present invention arrange schematic diagram.
Embodiment
The embodiment of the present invention is described in further detail below in conjunction with accompanying drawing.Do not make in the embodiment of the present invention in detail
The content of description belongs to prior art known to professional and technical personnel in the field.
The spherical shell type three dimensional strain observation procedure of the present invention, its preferable embodiment are：
Including：
In XYZ rectangular coordinate systems, following observed direction is arranged：
Be equidistantly spaced from tetra- observed directions of z1, z2, z3 and z4 in X/Y plane with 45 °, wherein z1 and z3 respectively with X-axis
Overlapped with Y-axis, with Sz1、Sz2、Sz3And Sz4Represent the observation in 4 directions；
Be equidistantly spaced from tetra- observed directions of x1, x2, x3 and x4 in YZ planes with 45 °, wherein x1 and x3 respectively with Y-axis
Overlapped with Z axis, with Sx1、Sx2、Sx3And Sx4Represent the observation in 4 directions；
Be equidistantly spaced from tetra- observed directions of y1, y2, y3 and y4 in ZX planes with 45 °, wherein y1 and y3 respectively with Z axis
Overlapped with X-axis, with Sy1、Sy2、Sy3And Sy4Represent the observation in 4 directions；
It is above-mentioned respectively to have 4 observed directions respectively on three coordinate planes, wherein relation be present：X1=z3, y1=x3 and
Z1=y3, therefore, actually only 9 observed directions set observation element respectively in this 9 observed directions；
The line strain observed on this 9 directions and the relation of three dimensional strain tensor, i.e., described spherical shell type three dimensional strain are seen
The strain reduction formula of survey method is as follows：
Z1=y3：SZ1=y3=A (εx+εy+εz)+B(εx-εy-εz)
z2：Sz2=A (εx+εy+εz)+B(-εz+2εxy)
z4：Sz4=A (εx+εy+εz)+B(-εz-2εxy)
Y1=x3：SZ1=y3=A (εx+εy+εz)+B(-εx-εy+εz)
y2：Sy2=A (εx+εy+εz)+B(-εy+2εzx)
y4：Sy2=A (εx+εy+εz)+B(-εy-2εzx)
X1=z3：SZ1=y3=A (εx+εy+εz)+B(-εx+εy-εz)
x2：Sy2=A (εx+εy+εz)+B(-εx+2εyz)
x4：Sy2=A (εx+εy+εz)+B(-εx-2εyz)；
In above formula, A replaces the coefficient of face dependent variable, and B replaces the coefficient of shearing strain item.
In XY, YZ and ZX plane, the change of the bulb diameter of four direction, the strain of spherical shell type three-dimensional tensor are observed respectively
Following observation data be present from relation of being in harmony in observation procedure：
It is in harmony relation certainly using above formula to carry out self-test to the observation for observing element：When observation data have this of above formula
From be in harmony relation when, be considered as observation be it is reliable, it is otherwise unreliable.
The strain reduction formula of the spherical shell type three dimensional strain observation procedure is simplified as：
The observation element is symmetrically installed by ball, and determines two parameters of A and B using the symmetrical formula of following synthesis：
The spherical shell type three-dimensional tensor strain observation method of the present invention, is carried using Q- models as according to proposition, this method
Three-dimensional tensor of sening as an envoy to strain observation is closer to be implemented.
The basic consideration of spherical shell type three-dimensional tensor strain observation method, be measuring probe is designed as it is spherical.Spherical spy
Head is placed in media as well, together with medium couples.This is easier than getting up directly many line strain sensors with medium couples
Much.Contemplate a ball in media as well, ball also and then deforms when deformation of media., can be ball for small deformation
Deformation, which is regarded as from ball, becomes ellipsoid., can be with the deformation of inverse medium according to spheroid-like.
In spherical shell type three-dimensional tensor strain observation method, the sensor cloth of the shape can Q- models of ellipsoid is determined
If scheme.According to the principle, the change of 9 orient diameters of ball can be measured, for the deformation of inverting medium.
Specific embodiment：
Including theoretical foundation, observation element, observation self-test, on the spot demarcation and strain several partial contents such as conversion.
1st, basic assumption
Decisive successful four components drilling tensor strain observation is had been achieved with, is a sight to Two-dimensional strain tensor
Survey.As starting point, we are contemplated that the observation procedure of three dimensional strain tensor.Q- models are so caused, spherical shell types
Three-dimensional tensor strain observation method is also so caused.
Recall the theoretical model of two-dimensional observation, be a circular hole extended from the surface of the semi-infinite half-space toward depths, when half
When infinite space is under homogeneous state of stress field action, circular hole becomes elliptical aperture (Fig. 1 a)., can be to strain according to elliptical shape
(stress) field carries out inverse.The theoretical model of three-dimensional observation, it is to have a match play in a full infinite space under contrast,
When full infinite space is under homogeneous state of stress field action, match play becomes ellipsoid hole (Fig. 1 b).According to spheroid-like, can correspond to
Become (stress) field and carry out inverse.
In two-dimensional problems, any direction θ normal strain εθWith the strain (ε represented with geographic coordinate systemN,εE,εNE) pass
It is to be
To introduce three-dimensional observation formula, we conscientiously have a look the composition of this formula.In formula (1), equation is right
Side can regard only two as：Section 1 is relevant with face strain, and Section 2 is relevant with shearing strain.
In geographic coordinate system, the formula of two-dimentional tensor strain observation is
Sθ=A (εN+εE)+B[(εN-εE)cos2θ+2εNEsin2θ] (2)
Formula (2) can be regarded as to be developed by formula (1)：To solve Hole Stress concentration problem, it instead of face with A and strain
The coefficient of item, the coefficient of shearing strain item is instead of with B.In fact, in the case of having other media in circular hole, even for circle
There is the situation of the n collar hole periphery, and formula (2) all sets up (Savin, 1951).
In three-dimensional problem, the normal strain ε (α, beta, gamma) in certain direction (α, beta, gamma) can be expressed as
ε (α, β, γ)=εxcos2α+εycos2β+εzcos2γ
+2εxycosαcosβ+2εyzcosβcosγ+2εzxcosγcosα (3)
Wherein, (α, beta, gamma) is angle of certain direction respectively with three rectangular axes (x, y, z), cos α, cos β and cos
γ is referred to as direction cosines, is defined as：
Wherein, r is some distance of (x, y, z) to coordinate origin on certain direction.
Using the double angle formula of cosine, formula (3) can be rewritten as
Two-dimensional case is compareed, according to formula (5), it will be assumed that three-dimensional observation formula also has two parameters A and B, provides
S (α, β, γ)=A (εx+εy+εz)+B(εxcos2α+εycos2β+εzcos2γ
+4εxycosαcosβ+4εyzcosβcosγ+4εzxcosγcosα)
(6)
Wherein, it is that S (α, beta, gamma) is the relative change of diameter of the match play along certain direction, is the direct sight in three dimensional strain observation
Measurement.
Formula (6) is exactly the three dimensional strain observation formula that we actually use.We assume that：The formula is applicable not only to sky ball
The situation in hole, apply also for the situation of n-layer shell.
2 observation elements
The key element of spherical shell type three-dimensional tensor strain observation method is exactly its unique probe designs.And the probe designs
Then derive from the Q- models of three-dimensional tensor strain observation.According to Q- models, the feasibility for actual observation considers, just carries
Spherical shell type three-dimensional tensor strain observation method is gone out.All line strain sensors are placed in spheroid, implementing will be easy
Much.
Even if can optically measure the deformation of spheroid in the future, also also need to be represented with some parameters, then basis
Observation formula previously discussed strains (change) to convert, now there is still a need for utilizing Q- models.
In the Q- models of observation three dimensional strain tensor, we will measure the line strain in 9 directions, then utilize the model
The strain tensor of the algorithm conversion reality of offer.In spherical shell type three-dimensional tensor strain observation method, we will still observe 9
" line strain " in direction.Need to distinguish, the diameter of " line strain " actually probe spherical shell here is relative to be changed, i.e., straight
The change in footpath and diameter ratio.In Q- models, the arrangement in this 9 directions is crucial.The strain of spherical shell type three-dimensional tensor is seen
Survey method has continued to use this arrangement.
In rectangular coordinate system (x, y, z), this 9 direction arrangements are as follows：
Be equidistantly spaced from tetra- observed directions of z1, z2, z3 and z4 in X/Y plane with 45 °, wherein z1 and z3 respectively with X-axis
(Fig. 2) is overlapped with Y-axis, in Fig. 2, Sz1、Sz2、Sz3And Sz4Represent the observation in 4 directions；
Be equidistantly spaced from tetra- observed directions of x1, x2, x3 and x4 in YZ planes with 45 °, wherein x1 and x3 respectively with Y-axis
(Fig. 3) is overlapped with Z axis, in Fig. 3, Sx1、Sx2、Sx3And Sx4Represent the observation in 4 directions；
Be equidistantly spaced from tetra- observed directions of y1, y2, y3 and y4 in ZX planes with 45 °, wherein y1 and y3 respectively with Z axis
(Fig. 4) is overlapped with X-axis, in Fig. 4, Sy1、Sy2、Sy3And Sy4Represent the observation in 4 directions.
Respectively there are 4 observed directions respectively on three coordinate planes, wherein relation be present：X1=z3, y1=x3 and z1=
y3.Therefore, actually only 9 observed directions.
" line strain " observed on this 9 directions and relation all meeting formulas (6) of three dimensional strain tensor, specifically give respectively
Go out as follows：
Z1=y3：SZ1=y3=A (εx+εy+εz)+B(εx-εy-εz)
z2：Sz2=A (εx+εy+εz)+B(-εz+2εxy)
z4：Sz4=A (εx+εy+εz)+B(-εz-2εxy)
Y1=x3：SZ1=y3=A (εx+εy+εz)+B(-εx-εy+εz)
y2：Sy2=A (εx+εy+εz)+B(-εy+2εzx)
y4：Sy2=A (εx+εy+εz)+B(-εy-2εzx)
X1=z3：SZ1=y3=A (εx+εy+εz)+B(-εx+εy-εz)
x2：Sy2=A (εx+εy+εz)+B(-εx+2εyz)
x4：Sy2=A (εx+εy+εz)+B(-εx-2εyz)
(7)
3 observation self-tests
Because strain observation needs to pop one's head in and surrounding medium is coupled together and could implemented, general to be difficult to as Other Instruments
Probe is checked like that.For this observation, the self-test to data yielding condition is always highly important.
Spherical shell type three-dimensional tensor strain observation method, put down just as the observation data of Q- models are present from relation of being in harmony, each coordinate
Observation change in face, there is also be in harmony relation certainly in theory.Come below by taking the observation change of the four direction in X/Y plane as an example
Illustrate this relation.
As it was previously stated, in X/Y plane, we will observe the change of the bulb diameter of four direction, respectively Sz1、Sz2、Sz3
And Sz4.On the one hand, mutually perpendicular Sz1With Sz3Sum is
Sz1+Sz3=A (εx+εy+εz)+B(εx-εy-εz)
+A(εx+εy+εz)+B(-εx+εy-εz)
=2A (εx+εy+εz)-2Bεz (8)
On the other hand, mutually perpendicular Sz2With Sz4Sum is
Sz2+Sz4=A (εx+εy+εz)+B(-εz+2εxy)
+A(εx+εy+εz)+B(-εz-2εxy)
=2A (εx+εy+εz)-2Bεz (9)
It can be seen that two groups of mutually perpendicular observation data sums are equal.
Similarly, we can also be derived on two other coordinate plane YZ and ZX, and there is also similar relation.Conclude
To together, we have the observation data of spherical shell type three-dimensional tensor strain observation method from relation of being in harmony：
Relation can be in harmony certainly to carry out self-test to Instrument observation using formula (10)：When observation data have this pass of being in harmony certainly
When being, it is possible to think observation be it is reliable, it is otherwise unreliable.
4 strain conversions
Three-dimensional symmetric strained tensor only has 6 mutual independent variables.In spherical shell type three-dimensional tensor strain observation method
There are 9 observed quantities (Fig. 5), provided by formula (7).But wherein have 3 from relation of being in harmony, thus also there was only 6 independent variables.Go out
In the consideration of symmetrical balance, 6 mutual independent replacement observed quantities can be produced according to following equation with 9 observed quantities：
Using formula (7), we obtain substituting observed quantity and the relation of three dimensional strain tensor is as follows
In fact, we with greater need for be according to observation convert strain value formula.This formula is exported, can be incited somebody to action
Normal strain separately considers with shearing strain.
For shearing strain, we can directly write out
For normal strain, Wo Menyou
We first try by formula (14), and ε is sought with replacement observation using elimination exportxFormula.The first step, by formula
(14) obtain
Second step, the first formula in formula (15) are multiplied by A, and the second formula is multiplied by B, obtained
3rd step, two formulas in formula (16) are added, obtained
A(2sx-sy-sz)+B(sy+sz)=[4AB+2 (A-B) B] εx (17)
I.e.
2Asx+(B-A)(sy+sz)=[6AB-2B2]εx (18)
Thus solve
According to symmetry, we can also write out
Three normal strain formula are concluded to together, we just have
Formula (13) is merged with formula (21), finally given
Formula (22) is exactly the strain reduction formula of spherical shell type three-dimensional tensor strain observation method.As A=B=1/2, the public affairs
Formula is changed into the strain reduction formula of Q- models.
5 demarcate on the spot
, it is necessary to carry out some staking-out works during instrument development, production.But strain observation element need with
Surrounding medium is coupled together and can be just observed, thus demarcate on the spot it is always essential.So-called demarcation, can be with known
Amount carrys out check observation amount.Here demarcation on the spot, it is to obtain A and B when observation and all known strain value.
The formula of solution A and B a series of can be exported according to formula (6) and formula (7).If probe has preferable ball symmetrical
Shape, probe installation can also reach preferable ball symmetrical structure, then what is selected for a post and come from formula derived from formula (6) and formula (7)
Correct result should all be provided by solving A and B.But actual conditions would generally have error.Only most comprehensive symmetrical conversion is public
Error could be influenceed to be minimized by formula.
Here so-called " comprehensive symmetrical " is symmetrical from ball, mean none of direction be it is especially important,
Pursue the effect of equilibrium.To determine two parameters of A and B, it would be desirable to two symmetrical formula of synthesis.
One simplest symmetrical formula of synthesis, can be by by the observed quantity phase Calais shape of three change in coordinate axis direction
Into：
SZ1=y3+SY1=x3+SX1=z3=A (εx+εy+εz)+B(εx-εy-εz)
+A(εx+εy+εz)+B(εy-εz-εx)
+A(εx+εy+εz)+B(εz-εx-εy)
=(3A-B) (εx+εy+εz) (23)
Formula (23) is actually corresponding with body strain.Thus can it is preferable should be corresponding with shearing strain to another formula.With cutting
Formula corresponding to strain has two groups.One group of formula is
It is derived there
Another group of formula be
It is derived there
The result of two groups of formula is averaged, and is finally given
Then, this step of demarcating on the spot, is：B is first tried to achieve according to formula (28), obtained further according to formula (23)
In actual applications, it may still have to what is observed with theoretical strain tide come calibration strain on the spot.Now,
What rectangular coordinate system was chosen so that：X-axis energized south (colatitude), y-axis point to eastern (longitude), and z-axis is upward.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited thereto,
Any one skilled in the art is in the technical scope of present disclosure, the change or replacement that can readily occur in,
It should all be included within the scope of the present invention.Therefore, protection scope of the present invention should be with the protection model of claims
Enclose and be defined.
Claims (4)
- A kind of 1. spherical shell type three dimensional strain observation procedure, it is characterised in that including：In XYZ rectangular coordinate systems, following observed direction is arranged：Be equidistantly spaced from tetra- observed directions of z1, z2, z3 and z4 in X/Y plane with 45 °, wherein z1 and z3 respectively with X-axis and Y Overlapping of axles, with Sz1、Sz2、Sz3And Sz4Represent the observation in 4 directions；Be equidistantly spaced from tetra- observed directions of x1, x2, x3 and x4 in YZ planes with 45 °, wherein x1 and x3 respectively with Y-axis and Z Overlapping of axles, with Sx1、Sx2、Sx3And Sx4Represent the observation in 4 directions；Be equidistantly spaced from tetra- observed directions of y1, y2, y3 and y4 in ZX planes with 45 °, wherein y1 and y3 respectively with Z axis and X Overlapping of axles, with Sy1、Sy2、Sy3And Sy4Represent the observation in 4 directions；It is above-mentioned respectively to have 4 observed directions respectively on three coordinate planes, wherein relation be present：X1=z3, y1=x3 and z1= Y3, therefore, actually only 9 observed directions set observation element respectively in this 9 observed directions；The line strain observed on this 9 directions and the relation of three dimensional strain tensor, i.e., described spherical shell type three dimensional strain observation side The strain reduction formula of method is as follows：Z1=y3：α=0,SZ1=y3=A (εx+εy+εz)+B(εx-εy-εz)z2：Sz2=A (εx+εy+εz)+B(-εz+2εxy)z4：Sz4=A (εx+εy+εz)+B(-εz-2εxy)Y1=x3：γ=0, SZ1=y3=A (εx+εy+εz)+B(-εx-εy+εz)y2：Sy2=A (εx+εy+εz)+B(-εy+2εzx)y4：Sy2=A (εx+εy+εz)+B(-εy-2εzx)X1=z3：β=0,SZ1=y3=A (εx+εy+εz)+B(-εx+εy-εz)x2：Sy2=A (εx+εy+εz)+B(-εx+2εyz)x4：Sy2=A (εx+εy+εz)+B(-εx-2εyz)；In above formula, A replaces the coefficient of face dependent variable, and B replaces the coefficient of shearing strain item.
- 2. spherical shell type three dimensional strain observation procedure according to claim 1, it is characterised in that in XY, YZ and ZX plane, The change of the bulb diameter of four direction is observed respectively, and spherical shell type three-dimensional tensor strain observation method has following observation data certainly It is in harmony relation：<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>S</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow> <mi>x</mi> <mn>3</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow> <mi>x</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow> <mi>x</mi> <mn>4</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>S</mi> <mrow> <mi>y</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow> <mi>y</mi> <mn>3</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow> <mi>y</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow> <mi>y</mi> <mn>4</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>S</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow> <mi>z</mi> <mn>3</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow> <mi>z</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow> <mi>z</mi> <mn>4</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>It is in harmony relation certainly using above formula to carry out self-test to the observation for observing element：It is in harmony certainly when observation data have this of above formula During relation, be considered as observation be it is reliable, it is otherwise unreliable.
- 3. spherical shell type three dimensional strain observation procedure according to claim 2, it is characterised in that the spherical shell type three dimensional strain is seen The strain reduction formula of survey method is simplified as：<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mrow> <mi>x</mi> <mi>z</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mi>y</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mrow> <mi>y</mi> <mi>z</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mi>z</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>B</mi> </mrow> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mfrac> <mrow> <mn>2</mn> <mi>A</mi> </mrow> <mrow> <mn>3</mn> <mi>A</mi> <mo>-</mo> <mi>B</mi> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mrow> <mi>B</mi> <mo>-</mo> <mi>A</mi> </mrow> <mrow> <mn>3</mn> <mi>A</mi> <mo>-</mo> <mi>B</mi> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mrow> <mi>B</mi> <mo>-</mo> <mi>A</mi> </mrow> <mrow> <mn>3</mn> <mi>A</mi> <mo>-</mo> <mi>B</mi> </mrow> </mfrac> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mi>B</mi> <mo>-</mo> <mi>A</mi> </mrow> <mrow> <mn>3</mn> <mi>A</mi> <mo>-</mo> <mi>B</mi> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mrow> <mn>2</mn> <mi>A</mi> </mrow> <mrow> <mn>3</mn> <mi>A</mi> <mo>-</mo> <mi>B</mi> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mrow> <mi>B</mi> <mo>-</mo> <mi>A</mi> </mrow> <mrow> <mn>3</mn> <mi>A</mi> <mo>-</mo> <mi>B</mi> </mrow> </mfrac> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mi>B</mi> <mo>-</mo> <mi>A</mi> </mrow> <mrow> <mn>3</mn> <mi>A</mi> <mo>-</mo> <mi>B</mi> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mrow> <mi>B</mi> <mo>-</mo> <mi>A</mi> </mrow> <mrow> <mn>3</mn> <mi>A</mi> <mo>-</mo> <mi>B</mi> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mrow> <mn>2</mn> <mi>A</mi> </mrow> <mrow> <mn>3</mn> <mi>A</mi> <mo>-</mo> <mi>B</mi> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>s</mi> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>s</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>s</mi> <mrow> <mi>x</mi> <mi>z</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>s</mi> <mi>y</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>s</mi> <mrow> <mi>y</mi> <mi>z</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>s</mi> <mi>z</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow>
- 4. spherical shell type three dimensional strain observation procedure according to claim 3, it is characterised in that the observation element presses ball pair Claim installation, and two parameters of A and B are determined using the symmetrical formula of following synthesis：<mrow> <mtable> <mtr> <mtd> <mrow> <mi>B</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mo>(</mo> <mfrac> <mrow> <msub> <mi>S</mi> <mrow> <mi>z</mi> <mn>1</mn> <mo>=</mo> <mi>y</mi> <mn>3</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>S</mi> <mrow> <mi>z</mi> <mn>3</mn> <mo>=</mo> <mi>x</mi> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>&epsiv;</mi> <mi>x</mi> </msub> <mo>-</mo> <msub> <mi>&epsiv;</mi> <mi>y</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>S</mi> <mrow> <mi>x</mi> <mn>1</mn> <mo>=</mo> <mi>z</mi> <mn>3</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>S</mi> <mrow> <mi>x</mi> <mn>3</mn> <mo>=</mo> <mi>y</mi> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>&epsiv;</mi> <mi>y</mi> </msub> <mo>-</mo> <msub> <mi>&epsiv;</mi> <mi>z</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>S</mi> <mrow> <mi>y</mi> <mn>1</mn> <mo>=</mo> <mi>x</mi> <mn>3</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>S</mi> <mrow> <mi>y</mi> <mn>3</mn> <mo>=</mo> <mi>z</mi> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>&epsiv;</mi> <mi>z</mi> </msub> <mo>-</mo> <msub> <mi>&epsiv;</mi> <mi>x</mi> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mfrac> <mrow> <msub> <mi>S</mi> <mrow> <mi>z</mi> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>S</mi> <mrow> <mi>z</mi> <mn>4</mn> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <msub> <mi>&epsiv;</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>S</mi> <mrow> <mi>y</mi> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>S</mi> <mrow> <mi>y</mi> <mn>4</mn> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <msub> <mi>&epsiv;</mi> <mrow> <mi>z</mi> <mi>x</mi> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>S</mi> <mrow> <mi>x</mi> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>S</mi> <mrow> <mi>x</mi> <mn>4</mn> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <msub> <mi>&epsiv;</mi> <mrow> <mi>y</mi> <mi>z</mi> </mrow> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow><mrow> <mi>A</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>S</mi> <mrow> <mi>z</mi> <mn>1</mn> <mo>=</mo> <mi>y</mi> <mn>3</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow> <mi>y</mi> <mn>1</mn> <mo>=</mo> <mi>x</mi> <mn>3</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow> <mi>x</mi> <mn>1</mn> <mo>=</mo> <mi>z</mi> <mn>3</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>&epsiv;</mi> <mi>x</mi> </msub> <mo>+</mo> <msub> <mi>&epsiv;</mi> <mi>y</mi> </msub> <mo>+</mo> <msub> <mi>&epsiv;</mi> <mi>z</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mi>B</mi> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
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