CN111707208A - Cylindrical shell structure cross section deformation monitoring method based on distributed macro strain sensing - Google Patents
Cylindrical shell structure cross section deformation monitoring method based on distributed macro strain sensing Download PDFInfo
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- CN111707208A CN111707208A CN202010588255.XA CN202010588255A CN111707208A CN 111707208 A CN111707208 A CN 111707208A CN 202010588255 A CN202010588255 A CN 202010588255A CN 111707208 A CN111707208 A CN 111707208A
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- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/16—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge
- G01B11/165—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge by means of a grating deformed by the object
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Abstract
The monitoring method for the deformation of the cross section of the cylindrical shell structure based on distributed macro-strain sensing comprises the following steps: (1) obtaining a geometric differential equation of the circumferential strain and the radial displacement by a finite differential method on the basis of a geometric differential equation of the cylindrical shell; (2) measuring the circumferential macro-strain on the surface of the cylindrical shell structure by using a distributed long-gauge-length fiber grating sensor; (3) and calculating the radial displacement of the surface of the cylindrical shell according to a geometric difference equation of the annular strain and the radial displacement, wherein the radial displacement is the radial displacement relative to the center of the circle. The algorithm has strong applicability and reliable calculation structure precision, can avoid sensor failure caused by local factors, and is easier to understand.
Description
Technical Field
The invention belongs to the field of deformation monitoring of cylindrical shell structures, and relates to a technology for monitoring deformation of a cross section of a thin-wall structure, in particular to a method for monitoring deformation of the cross section of the cylindrical shell structure based on a distributed long-gauge-length Bragg fiber grating sensor.
Background
The structures of a shield subway tunnel, a shield comprehensive pipe gallery, a silo and the like in civil engineering are all cylindrical shell structures, and the cylindrical shell structures are thin-wall structures with circular cross sections. Cross-sectional deformation is an important indicator for assessing stability and safety during normal use of a cylindrical shell structure. At present, the cross section deformation monitoring technology of the cylindrical shell structure mainly comprises three types: an automatic total station observation technology, an automatic close-range photography technology and a point type direct measurement technology. The automatic total station has long observation distance and high measurement precision, but the monitoring equipment is expensive and needs to be attended for a long time. The close-range photography technology has low requirements on observation equipment, but the measurement distance is short (only dozens of meters), and an additional light source is needed during observation, so that the requirements on the quality of the light source are high. The point measurement technology has high precision, but is expensive and not suitable for large-scale arrangement.
The distributed optical fiber sensing technology is a novel monitoring technology developed in recent years, and is also a hotspot of research in the field of domestic and foreign engineering at present. The technology provides an indirect monitoring means, so in recent years, researchers try to explore the relation between strain and deformation so as to realize indirect measurement of cross-section deformation. The learner deduces a geometric equation of the circumferential strain and the radial displacement of the curved beam structure by using a conjugate beam method, and realizes the deformation monitoring of the cross section of the tunnel on the basis of a distributed sensing technology. However, the algorithm is complex, and the finally obtained cross section is deformed into radial deflection relative to the right end point of the circumference instead of the circle center, which is not beneficial to understanding.
In the optical fiber sensing technology, the bragg fiber grating is widely used because of its advantages in measurement accuracy, spatial positioning accuracy, long-term stability and structural compatibility. Conventional fiber bragg grating sensors have a gauge length of up to 100mm and are generally considered to be point sensors. The monitoring result is greatly influenced by local cracks, damages and the like, and the integral stress condition of the structure is difficult to reflect. Moreover, in the case of civil structures, such sensors are easily deteriorated by cracks in concrete structures, welds in steel structures, and the like. The long-gauge-length fiber bragg grating sensor is a macro-strain sensor, and can measure structural strain in a large range due to the long gauge length, so that large measurement errors caused by local factors can be avoided, and even the sensor fails.
Disclosure of Invention
Aiming at the problems, the invention provides a cylindrical shell structure cross section deformation monitoring method based on distributed macro-strain sensing, which converts the circumferential strain measured by a distributed sensor into radial displacement through a conversion algorithm of circumferential deformation and radial displacement, thereby realizing the monitoring of the cross section deformation. Moreover, the long-gauge-length fiber bragg grating sensor is adopted, macro strain in a large range can be measured, and large measurement errors caused by local factors can be avoided, even the sensor fails. The algorithm has strong applicability, the calculation structure has reliable precision and is easier to understand, and in order to achieve the purpose, the invention provides a distributed macro-strain-sensing-based cylindrical shell structure cross section deformation monitoring method which is characterized by comprising the following steps:
(1) obtaining the geometric difference between the circumferential strain and the radial displacement by a finite difference method on the basis of the geometric differential equation of the cylindrical shell;
the step (1) is specifically as follows:
according to the geometric differential equation of the cylindrical shell, the radial displacement w and the circumferential strain of the middle surface can be known
Circumferential displacement v and circumferential angle
The relation of (A) is as follows:
the radius-thickness ratio R/t of the shell structure is larger, the distance z from the shell surface to the middle plane is t/2, the z/R is smaller, the z/R is ignored, the surface z of the cylindrical shell is +/-t/2, and the hoop strain is
Median circumferential strain
Radial displacement w, circumferential displacement v and circumferential rotation angle of the middle plane
The relation of (A) is as follows:
the circumferential strain of the surface of the cylindrical shell can be obtained from the formulas (a) and (b)
Radial displacement w, circumferential displacement v and circumferential rotation angle of the middle plane
The relation of (A) is as follows:
for a cylindrical shell structure which is closed in the circumferential direction and is subjected to the action of approximately uniform normal load, the movement of points on the surface of the shell along the circumferential direction of the shell is approximately ignored, namely
The surface annular response of the cylindrical shell can be obtained by the formula (c)
The relationship with the median plane radial displacement w is:
using finite difference method to obtain the i-th point annular strain on the surface of the cylindrical shell from the formula (d)
Radial displacement w of the (i-1, i + 1) th point of the middle plane, and rotation angleThe differences are
Comprises the following steps:
the equation (e) is the differential equation of the circumferential strain and the radial displacement of the cylindrical shell structure;
(2) measuring the circumferential macro-strain on the surface of the cylindrical shell structure by using a distributed long-gauge-length fiber grating sensor;
the step (2) is specifically as follows:
n long-gauge-length fiber bragg grating sensors are uniformly arranged on the surface of the structure to obtain annular macro-strain at N measuring points on the surface
Wherein i is 1, 2, 3, …, N;
(3) calculating the radial displacement of the surface of the cylindrical shell according to a geometric difference equation of the circumferential strain and the radial displacement, wherein the radial displacement is the radial displacement relative to the center of a circle;
the step (3) is specifically as follows:
circumferential macro strain at N measuring points
Radial displacement from the median plane [ w ]1,w2,L,wi,L,wN]TWherein i is 1, 2, 3, …, and N is:
(f) the matrix form of formula (la) is:
wherein the content of the first and second substances,
mean radial displacement
As a further improvement of the present invention, the monitoring method has six assumed conditions: 1) the shell material is isotropic; 2) the shell material is linear elastic; 3) the shell deforms into small deformation; 4) the shell satisfies the straight normal assumption; 5) removing the influence of the temperature on the original strain data during calculation; 6) the casing hoop displacement v being negligible, i.e.
The invention discloses a method for monitoring the deformation of a cross section of a cylindrical shell structure based on distributed macro-strain sensing, which is characterized in that compared with the prior art, the technology adopted by the invention is a distributed optical fiber sensing technology, and compared with an automatic total station observation technology, an automatic close-range photography technology and a point type direct measurement technology, the technology has the following main advantages: 1) real-time monitoring can be realized; 2) long-distance and large-range measurement can be realized; 3) the sensing optical fiber has good electromagnetic interference resistance; 4) the optical fiber structure is light and convenient to embed. Compared with a tunnel cross section deformation monitoring method based on a curved beam geometric differential equation and based on a distributed sensing technology, the method has the main advantages that: the radial displacement is relative to the center of a circle, so that the method is more visual and intuitive and is beneficial to understanding. Compared with the traditional fiber bragg grating sensor, the long-gauge-length fiber bragg grating sensor is adopted in the technology, so that the sensor failure caused by local factors such as cracks, welding seams and the like can be avoided.
Drawings
FIG. 1 is a cross-sectional view of a cylindrical shell sensor arrangement;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 is a flow chart of the present invention.
Detailed Description
The invention is described in further detail below with reference to the following detailed description and accompanying drawings:
the invention provides a method for monitoring the deformation of a cross section of a cylindrical shell structure based on distributed macro-strain sensing, which converts the circumferential strain measured by a distributed sensor into radial displacement through a conversion algorithm of circumferential deformation and radial displacement, thereby realizing the monitoring of the deformation of the cross section. Moreover, the long-gauge-length fiber bragg grating sensor is adopted, the structural strain in a large range can be measured, and large measurement errors caused by local factors and even sensor failure can be avoided. The algorithm has strong applicability, reliable calculation structure precision and is easier to understand.
Reference will now be made in further detail to the drawings of an embodiment of the present invention, in which FIG. 1 is a cross-sectional view of a cylindrical shell sensor arrangement; FIG. 2 is a flow chart of the method of the present invention; FIG. 3 is a flow chart of the present invention.
The steps in fig. 3 are described in detail below:
in step 1, the scheme of the current monitoring needs to be determined, a specific monitoring model is determined by the monitoring scheme, and then step 2 is executed.
In step 2, determining various parameters of the monitoring model, including total division number of the measuring sections, measuring point positions, long gauge length sensor gauge length, the radius of the middle surface of the cylindrical shell and the thickness of the shell, and then executing step 3;
in step 3, according to the method of the present invention, the deformation data, i.e., the final deformation amount of each monitoring point, is calculated from the original strain data, and then the process is ended.
It should be appreciated that the sensors may be disposed on either the outer or inner surface of the cylindrical shell. The sensors are also not limited to long gauge sensors, including any macro strain sensor that enables distributed sensing.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, but any modifications or equivalent variations made according to the technical spirit of the present invention are within the scope of the present invention as claimed.
Claims (2)
1. The method for monitoring the deformation of the cross section of the cylindrical shell structure based on distributed macro-strain sensing is characterized by comprising the following steps:
(1) obtaining the geometric difference between the circumferential strain and the radial displacement by a finite difference method on the basis of the geometric differential equation of the cylindrical shell;
the step (1) is specifically as follows:
according to the geometric differential equation of the cylindrical shell, the radial displacement w and the circumferential strain of the middle surface can be known
Circumferential displacement v and circumferential angle
The relation of (A) is as follows:
the radius-thickness ratio R/t of the shell structure is larger, the distance z from the shell surface to the middle plane is t/2, the z/R is smaller, the z/R is ignored, the surface z of the cylindrical shell is +/-t/2, and the hoop strain is
Median circumferential strain
Radial displacement w, circumferential displacement v and circumferential rotation angle of the middle plane
The relation of (A) is as follows:
the surface ring direction of the cylindrical shell can be obtained by the formulas (a) and (b)Strain of
Radial displacement w, circumferential displacement v and circumferential rotation angle of the middle plane
The relation of (A) is as follows:
for a cylindrical shell structure which is closed in the circumferential direction and is subjected to approximately uniform normal load, the movement of points on the surface of the shell along the circumferential direction of the shell is approximately ignored, namely
The circumferential strain of the surface of the cylindrical shell can be obtained from the formula (c)
The relationship with the median plane radial displacement w is:
using finite difference method to obtain the i-th point annular strain on the surface of the cylindrical shell from the formula (d)
The radial displacement w of the (i-1, i + 1) th point of the middle plane is related, and the rotation angle difference is
Comprises the following steps:
the equation (e) is the differential equation of the circumferential strain and the radial displacement of the cylindrical shell structure;
(2) measuring the circumferential macro-strain on the surface of the cylindrical shell structure by using a distributed long-gauge-length fiber grating sensor;
the step (2) is specifically as follows:
n long-gauge-length fiber bragg grating sensors are uniformly arranged on the surface of the structure to obtain annular macro-strain at N measuring points on the surface
Wherein i is 1, 2, 3, …, N;
(3) calculating the radial displacement of the surface of the cylindrical shell according to a geometric difference equation of the circumferential strain and the radial displacement, wherein the radial displacement is the radial displacement relative to the center of a circle;
the step (3) is specifically as follows:
circumferential macro strain at N measuring points
Radial displacement from the median plane [ w ]1,w2,L,wi,L,wN]TWherein i is 1, 2, 3, …, and N is:
(f) the matrix form of formula (la) is:
wherein the content of the first and second substances,
mean radial displacement
2. The method for monitoring the deformation of the cross section of the cylindrical shell structure based on the distributed macro strain sensing is characterized in that the monitoring method has six assumed conditions: 1) the shell material is isotropic; 2) the shell material is linear elastic; 3) the shell deforms into small deformation; 4) the shell satisfies the straight normal assumption; 5) removing the influence of temperature on the original strain data during calculation; 6) the casing hoop displacement v being negligible, i.e.
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