CN109115167A - Three dimensional strain state testing device and method based on right-angle tetrahedron angular strain - Google Patents
Three dimensional strain state testing device and method based on right-angle tetrahedron angular strain Download PDFInfo
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- CN109115167A CN109115167A CN201811049970.5A CN201811049970A CN109115167A CN 109115167 A CN109115167 A CN 109115167A CN 201811049970 A CN201811049970 A CN 201811049970A CN 109115167 A CN109115167 A CN 109115167A
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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
Abstract
The present invention provides a kind of three dimensional strain state testing device and method based on right-angle tetrahedron angular strain, which includes right-angle tetrahedron pedestal, 6 angle measurement equipments, test lead.6 ribs of right-angle tetrahedron are respectively provided with angle measurement equipment, and angle measurement equipment is connect with test lead, form three dimensional strain state testing device.A kind of test method of three dimensional strain state testing device based on right-angle tetrahedron angular strain is provided simultaneously；According to the relationship between broad sense angular strain and conventional strain, 6 dihedral angles of right-angle tetrahedron can extrapolate the conventional strain regime under respective coordinates, and propose three dimensional strain state computation method using the space coordinates and mathematics pedestal established.The beneficial effects of the present invention are: the calculation method of new three dimensional strain state, enriches the calculating means of conventional strain regime, computational accuracy is up to the ρ of 0.6 ρ~0.8, has important references value to resistance to shear of soil strain testing and the research of this structure.
Description
Technical field
The invention belongs to soil body three dimensional strain state computation and soil deformation testing field, which can pass through two
The knots modification of plane included angle extrapolates conventional three-dimensional strain regime, thus can calculate soil body strain regime, steady to the estimation soil body
It is qualitative to be of great significance.The theory and calculation method can be used for the test and theoretical research of soil deformation.
Technical background
Strain is the reaction of stress, and size is closely related with stress, understanding and test material strain be carry out intensity,
The basis of deformation and constitutive relation research.It is different from the test of stress, the measurement of strain from theoretical basis to technological means all more
It is difficult and limited.Especially under three-dimensional condition, it is very difficult for obtaining complete strain regime by test.
Shearing strain is otherwise known as shear strain, angular strain, shear strain etc..In routine test, shearing strain is difficult to measure, still
In Continuum Mechanics, shearing strain is defined as the knots modification that right angle dihedral angle is indicated with radian, i.e., two orthogonal
The angle knots modification that face is indicated after stress deformation with radian.It is indicated relative to right angle dihedral angle, the expression of on-right angle dihedral angle is cut
Strain is with more generality.And dihedral angle shearing strain is strained with conventional with quantitatively contacting, this strains shape to calculate conventional three-dimensional
State based theoretical, and realize the possibility of strain regime test.
Current conventional three-dimensional strain regime test method is also seldom, and theoretical basis and technological means are still also short of.And by
The factors such as means of testing influence, and also will appear the not high phenomenon of measuring accuracy.Patent 201621144337.0 and patent
201610917550.9 provide a kind of device and test method for testing soil body three dimensional strain, and patent 201710191411.7 mentions
A kind of unidirectional strain detection testing device of soil body and its test method out.Different from the theoretical basis and calculation method of above-mentioned patent, originally
Patent proposes the method for calculating conventional three-dimensional strain regime using broad sense angular strain, and theoretical basis and calculation method all have can
Row and novelty.The computational theory and calculation method have wide range of applications, and theoretical test error is small, to raising conventional three-dimensional
Strain regime test possibility and measuring accuracy, which have, uses significance.
Summary of the invention
It is an object of the present invention to provide a kind of three dimensional strain state testing device and method based on right-angle tetrahedron angular strain,
Make it possible to calculate conventional three-dimensional strain by broad sense angular strain, has widened the means for calculating strain regime.
In order to achieve the above object, the present invention proposes a kind of three dimensional strain state verification based on right-angle tetrahedron angular strain
Device, particular technique method are as follows: device include right-angle tetrahedron pedestal, angle measurement equipment, test lead, conducting wire hole,
Total wire guide；Test lead is connect with angle measurement equipment, and the test lead of angle measurement equipment will be connected from conducting wire hole
It penetrates and is pierced by by total wire guide, will be fixed on the crest line of right-angle tetrahedron pedestal.Soil body certain point can be measured by the device
6 angular strains the three dimensional strain state of the soil body can be calculated by the relationship between shearing strain and conventional strain.
The right-angle tetrahedron pedestal of the invention is gathered around there are three right angle dihedral angle, three on-right angle dihedral angles, wherein right angle two
Face angle is the generally acknowledged dihedral angle for indicating shearing strain, and according to defined formula (1), broad sense is calculated using six right angle dihedral angles
Three dimensional strain state is infeasible, therefore replaces right angle dihedral angle, i.e. right-angle tetrahedron pedestal with three acute angle dihedral angles.The arrangement
Form can calculate three-dimensional stress constraint by 6 dihedral angles, also there is the accuracy better than other arrangement forms.
The invention provides a kind of tests of three dimensional strain state testing device based on right-angle tetrahedron angular strain simultaneously
Method.
The present invention provides a kind of three dimensional strain state testing device and method based on right-angle tetrahedron angular strain, beneficial
Effect is to construct contacting between broad sense angular strain and conventional three-dimensional strain regime, has widened three dimensional strain state computation reason
By enriching the calculating means of conventional strain regime, improve computational accuracy 0.6 ρ~0.8 ρ, building calculates conventional three-dimensional and strains shape
The new channel of state.Change in the past can only test surfaces strain and test position inaccuracy limitation, more accurately, intuitive quilt
The deformation state of interior of articles is surveyed, and the device may be reused, composite green environmental protection concept, and improve engineering construction
Safety stock provides new thinking and approach for strain testing technical field correlative study.
Detailed description of the invention
Fig. 1 is right-angle tetrahedron space vector of the present invention and component of a vector；
Fig. 2 is right-angle tetrahedron pedestal of the present invention；
Fig. 3 is right-angle tetrahedron pedestal of the present invention production figure；
Fig. 4 is test device of the present invention.
In figure: the total conducting wire in 1. right-angle tetrahedron pedestal, 2. angle measurement equipment, 3. test lead, 11. conducting wire hole 12.
6. direction vector of hole, 7. dihedral angle
Specific implementation method
In conjunction with attached drawing and table to the three dimensional strain state testing device of the invention based on right-angle tetrahedron angular strain and
Method is illustrated.
As shown in Figure 1, three right-angled edges with right-angle tetrahedron pedestal establish space coordinates, with any two contact surface
The upper vector vertical with intersecting lens defines the dihedral angle in two faces.
As shown in figs 2-4, the present invention is based on the three dimensional strain state testing device of right-angle tetrahedron angular strain, the devices
It is connected with data collection system, which includes right-angle tetrahedron pedestal 1, angle measurement equipment 2, test lead 3, conducting wire
Hole 11, total wire guide 12；Right-angle tetrahedron pedestal 1 is cut by square, and conducting wire hole 11 is distributed with thereon and always leads
String holes 12, conducting wire hole 11 are located on 1 rib of right-angle tetrahedron pedestal, and total wire guide 12 is located at the centroid in one face of pedestal,
As shown in Figure 3；Angle measurement equipment 2 is equipment on sale existing for market；Test lead 3 is connect with angle measurement equipment 2, and will be even
The test lead 3 for connecing angle measurement equipment 2 is penetrated from conducting wire hole 11 to be pierced by by total wire guide 12, will be fixed on right-angle tetrahedron
On the crest line of pedestal 1.
The three dimensional strain state testing device based on right-angle tetrahedron angular strain proposed according to the present invention proposes a kind of be somebody's turn to do
The test method of device, the specific steps are as follows:
1) measure traverse line 3 is passed through into conducting wire hole 11 in 1 shape of right-angle tetrahedron pedestal from each angle measurement equipment 2 first
It is drawn after converging at the heart by total wire guide 12 and six angle measurement equipments 2 is separately fixed on 6 ribs of right-angle tetrahedron, then will
Total wire guide 12 is filled in foam gap filler indentation, to fill the gap between measure traverse line and wire guide, is formed and is based on angle
The three dimensional strain state testing device of measuring appliance 2 and right-angle tetrahedron, as shown in figure 4, and the device is placed in the tested soil body.
2) space vector coordinates computed system is established according to right-angle tetrahedron pedestal, with three right angles of right-angle tetrahedron pedestal
Rib defines x, y, z axis respectively.The vertical vector and direction vector of the intersection of any two plane in right-angle tetrahedron, as shown in Figure 1
Angle indicate dihedral angle, vector projects to reference axis x, y, z, can score solution vector a1、b1、c1, a2、b2、c2, 1 data of table；
The direction vector value of equal right-angle tetrahedrons dihedral angle is shown in Table 1: face 1-4 describes base plane spatial position pass
System, rather than the hardness of space plane is defined.
The direction vector of the right-angle tetrahedrons dihedral angles such as table 1
3) relationship between dihedral angle knots modification Δ ω and conventional strain is established according to formula (1) and formula (2)；
Or
△ωi=λjtεab (2)
In formula, t=1,2,3,4,5,6；J=1,2,3,4,5,6；A=x, y, z；B=x, y, z；Matrix λ need to meet order
6, i.e. R (λ)=6, then λ-1In the presence of just can guarantee that the feasibility Matrix Computation Formulas for calculating conventional strain regime is formula in this way
(3)；
λ1=2a1a2 (3a)
λ2=2b1b2 (3b)
λ3=2c1c2 (3c)
λ4=a1b2+a2b1 (3d)
λ5=b1c2+b2c1 (3e)
λ6=c1a2+c2a1 (3f)
4) space coordinates established according to step 2), calculate matrix λ and inverse matrix λ using formula (3) and table 1-1；
And
5) in step 3) formula or so respectively multiplied by inverse matrix λ-1, obtain using angular strain as the conventional strain regime of variable
Solution；
In formula, t=1,2,3,4,5,6；J=1,2,3,4,5,6；A=x, y, z；B=x, y, z；
6) accidental error of six dihedral angles is Δ ω0(Δω0>=0), formula 7 is the error of the conventional strain stress calculated；
{△εj}T=△ ω0×{2.237 2.237 2.237 1 1 1}T (7)
In formula, j=1,2,3,4,5,6.
Three dimensional strain state testing device and method based on right-angle tetrahedron angular strain of the invention, can be more accurately
True strain regime inside soil body certain point to be measured is obtained, to reinforce the stability monitoring to the strain regime of inside soil body.
The present invention provides a kind of new three dimensional strain state verification means, change in the past can only test surfaces strain and test position not
Accurately limitation, measuring accuracy improve the ρ of 0.6 ρ~0.8, more accurately, the intuitive deformation state inside testee, and should
Device may be reused, composite green environmental protection concept, and improve the safety stock of engineering construction, lead for strain testing technology
Domain correlative study provides new thinking and approach.
Claims (2)
1. a kind of three dimensional strain state testing device based on right-angle tetrahedron angular strain, the device are connected with data collection system
It connects, it is characterized in that: the device includes right-angle tetrahedron pedestal (1), angle measurement equipment (2), test lead (3), conducting wire hole
(11), total wire guide (12)；Right-angle tetrahedron pedestal (1) is cut by square, and conducting wire hole (11) and total is distributed with
Wire guide (12), conducting wire hole (11) are located on right-angle tetrahedron pedestal (1) rib, and total wire guide (12) is located at one face of pedestal
Centroid at, conducting wire hole (11) penetrate through total wire guide in right-angle tetrahedron pedestal (1) the right-angle tetrahedron pedestal (1) respectively
(12)；It angle measurement equipment (2) connecting test conducting wire (3) and is fixed on the crest line of right-angle tetrahedron pedestal (1).
2. a kind of test method of the three dimensional strain state testing device based on right-angle tetrahedron angular strain according to claim 1,
Specific step is as follows:
1) measure traverse line (3) is passed through into conducting wire hole (11) in right-angle tetrahedron pedestal from each angle measurement equipment (2) first
(1) it is drawn after converging at centroid by total wire guide (12) and six angle measurement equipments (2) is separately fixed at 6 ribs of right-angle tetrahedron
On, total wire guide (12) then is filled into foam gap filler indentation, to fill the gap between measure traverse line and wire guide, shape
At the three dimensional strain state testing device based on angle measurement equipment (2) and right-angle tetrahedron, and the device is placed in the tested soil body
In.
2) space vector coordinates computed system is established according to right-angle tetrahedron pedestal, with three right-angled edges of right-angle tetrahedron pedestal point
X, y, z axis is not defined；
3) relationship between dihedral angle knots modification Δ ω and conventional strain is established according to formula (1) and formula (2)；
Or
△ωi=λjtεab (2)
In formula, t=1,2,3,4,5,6；J=1,2,3,4,5,6；A=x, y, z；B=x, y, z；It is 6 that matrix λ, which need to meet order, i.e. R
(λ)=6, then λ-1In the presence of just can guarantee the feasibility for calculating conventional strain regime in this way, Matrix Computation Formulas is following formula
(3)；
λ1=2a1a2 (3a)
λ2=2b1b2 (3b)
λ3=2c1c2 (3c)
λ4=a1b2+a2b1 (3d)
λ5=b1c2+b2c1 (3e)
λ6=c1a2+c2a1 (3f) (3)
4) space coordinates established according to step 2), calculate matrix λ and inverse matrix λ using formula (3)-1；
And
5) in step 3) formula or so respectively multiplied by inverse matrix λ-1, obtain using angular strain as the solution of the conventional strain regime of variable；
In formula, t=1,2,3,4,5,6；J=1,2,3,4,5,6；A=x, y, z；B=x, y, z.
6) accidental error of six dihedral angles is Δ ω0(Δω0>=0), formula 7 is the error of the conventional strain stress calculated；
{△εj}T=△ ω0×{2.237 2.237 2.237 1 1 1}T (7)
In formula, j=1,2,3,4,5,6.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811049970.5A CN109115167A (en) | 2018-09-11 | 2018-09-11 | Three dimensional strain state testing device and method based on right-angle tetrahedron angular strain |
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| CN201811049970.5A CN109115167A (en) | 2018-09-11 | 2018-09-11 | Three dimensional strain state testing device and method based on right-angle tetrahedron angular strain |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110411804A (en) * | 2019-09-02 | 2019-11-05 | 上海交通大学 | A kind of contact face mechanical property test sample, preparation method and the test method of the soil body and structure |
| CN113155612A (en) * | 2021-04-16 | 2021-07-23 | 浙江科技学院 | Deformation prediction method for microfiber mixed silica sol solidified calcareous sand |
-
2018
- 2018-09-11 CN CN201811049970.5A patent/CN109115167A/en not_active Withdrawn
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110411804A (en) * | 2019-09-02 | 2019-11-05 | 上海交通大学 | A kind of contact face mechanical property test sample, preparation method and the test method of the soil body and structure |
| CN110411804B (en) * | 2019-09-02 | 2024-04-16 | 上海交通大学 | Test sample for mechanical properties of contact surface of soil body and structure, preparation method and test method |
| CN113155612A (en) * | 2021-04-16 | 2021-07-23 | 浙江科技学院 | Deformation prediction method for microfiber mixed silica sol solidified calcareous sand |
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Application publication date: 20190101 |