CN108413861B - A kind of method of real-time of opening section thin walled beam constrained twisting deformability - Google Patents
A kind of method of real-time of opening section thin walled beam constrained twisting deformability Download PDFInfo
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- CN108413861B CN108413861B CN201810090103.XA CN201810090103A CN108413861B CN 108413861 B CN108413861 B CN 108413861B CN 201810090103 A CN201810090103 A CN 201810090103A CN 108413861 B CN108413861 B CN 108413861B
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- 238000000034 method Methods 0.000 title claims abstract description 22
- 238000005259 measurement Methods 0.000 claims abstract description 35
- 238000006073 displacement reaction Methods 0.000 claims abstract description 26
- 238000012544 monitoring process Methods 0.000 claims abstract description 15
- 239000000835 fiber Substances 0.000 description 3
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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
- G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
- G01B7/16—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring the deformation in a solid, e.g. by resistance strain gauge
- G01B7/18—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring the deformation in a solid, e.g. by resistance strain gauge using change in resistance
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Abstract
The invention discloses a kind of method of real-time of opening section thin walled beam constrained twisting deformability, by using the axial strain of strain transducer measurement beam, the warp displacement and windup-degree of beam arbitrary section can be obtained using theoretical method, realize the real-time monitoring of structural constraint torsional deflection.This method facilitates the Accurate Reconstruction of structural stress strain state, and further work provides shape monitoring data for planform control etc..The present invention proposes the specific embodiment based on limited element calculation model to verify accuracy of the invention.The present invention has many advantages, such as precision height, saves time and cost, is high-efficient compared with the method for other measurement beam constrained twisting deformabilities at present.
Description
Technical Field
The invention relates to the technical field of real-time monitoring of constrained torsional deformation of open-section thin-walled beams in the fields of aerospace, civil engineering, bridges and the like, in particular to a real-time monitoring method of constrained torsional deformation of open-section thin-walled beams.
Background
In the engineering field, the torsion of the open thin-wall beam is easy to bring catastrophic results such as structural instability and damage. The structural constraint torsional deformation comprises complex behaviors such as section warping and the like, and is difficult to predict accurately. Conventional resistive strain gauge sensors and advanced fiber sensors (e.g., Fiber Bragg Gratings (FBGs), distributed fibers) can measure the surface strain of a structure, and then reconstruct the structure shape according to the surface strain. At present, a method for calculating the torsional deformation by directly utilizing the quantitative relation between the surface strain and the torsional deformation of the structure is lacked. The main torsional deformation comprises a section torsional angle and a section buckling displacement, the conventional measuring method has complicated steps and complicated equipment when measuring the torsional angle, and cannot complete online monitoring, and on the other hand, a method capable of accurately monitoring the section buckling displacement is lacked.
Disclosure of Invention
According to the problems in the prior art, the invention discloses a real-time monitoring method for restrained torsional deformation of an open-section thin-wall beam, which comprises the following specific steps: the method comprises the steps of selecting a strain measurement point on the surface of the open-section thin-wall beam along the axial direction, pasting a strain sensor on the strain measurement point, measuring axial strain in real time, calculating the sector area of the section of the open-section thin-wall beam, and deducing the torsion angle and the warping displacement of each cross section through the strain measurement value and the sector area, thereby monitoring the torsion deformation of the open-section thin-wall beam in real time.
The cross section torsion angle and the buckling displacement of the open-section thin-wall beam are calculated in the following mode:
s1: calculating the distribution of the section sector area omega(s) of the thin-wall beam:
wherein s is the curve coordinate of the measuring point on the section outline, and h(s) is the distance from the rotating center to the tangent line of the s point;
s2: dividing the beam into a plurality of measuring sections along the axial direction, wherein the length of each measuring section is equal;
s3: at the end point of each measuring section, the measuring point of the strain sensor is arranged on the surface of the beam, and the position of the measuring point is x0，x1，x2，…xnWhere n +1 is the number of measurement points, x0At one end of the beam, xnAt the other end of the beam, with the other measurement point at x0And xnAre arranged in sequence; x is the number of1To xnArranged on a straight line parallel to the beam axis; on the beam section, the coordinate of the outline corresponding to the measuring point is sm；
In the measuring section [ x ]i-1,xi]Above, the strain expression is:
wherein epsiloni-1And εiIs xi-1And xiThe strain measurement at (a), the x-direction being the beam axis direction;
s4: the relationship between the surface strain and the torsion angle is obtained as follows:
wherein,is the torsion angle, ω(s)m) Is the cross-sectional sector area at the measurement point;
s5: obtaining a relation between the section warping displacement and the strain as follows:
u(x)＝∫ε(x)dx (5)
s6: and (3) deducing a warping displacement calculation formula of any section and any position on the section by combining the formulas (1), (3) and (5):
wherein u isiIs xiIs the warp displacement,. DELTA.l is the distance between the measuring points,. epsilonj-1And εjIs xj-1And xjMeasured value of strain of (u)0Is x0Warp displacement of (c) for a clamped beam at one end, u0＝0；
S7: based on equation (4), in the measurement section [ x ]i-1,xi]Above, there are
S8: combining equations (1), (3) and (7) to obtain xiThe twist angle of (d) is:
where Δ l is the distance between the measurement points, ω(s)m) Is the area of the sector at the point of measurement,ε0，εiand εjIs x0，xiAnd xjThe measured value of the strain at (a),and u0Is x0Torsion angle and warp displacement of the beam, for a clamped beam at one end
The thin-wall beam is a cantilever beam with an equal section, wherein the section of the cantilever beam is an open section and comprises a T shape, an L shape, an I shape and a cap shape.
Due to the adoption of the technical scheme, the real-time monitoring method for the restrained torsional deformation of the open-section thin-wall beam provided by the invention has the advantages that the axial strain of the beam is measured by adopting the strain sensor, the warp displacement and the torsion angle of any section of the beam can be obtained by applying a theoretical method, and the real-time monitoring of the restrained torsional deformation of the structure is realized. The method facilitates accurate reconstruction of the stress-strain state of the structure and provides shape monitoring data for further work such as structure shape control. The invention proposes a specific implementation based on finite element calculation models to verify the accuracy of the invention. Compared with other methods for measuring beam constrained torsional deformation at present, the method has the advantages of high precision, time and cost saving, high efficiency and the like.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a schematic diagram of a hat-shaped section thin-walled beam and a strain measurement position according to the present invention
FIG. 2 is a schematic cross-sectional view of a hat-section thin-walled beam according to the present invention;
FIG. 3 is a comparison of cross-sectional warp displacements and finite element results calculated by the method of the present invention;
FIG. 4 is a comparison of the cross-sectional torsion angle calculated by the method of the present invention and the finite element results.
In the figure: 1. a hat-section thin-walled beam; 2. strain measurement point positions; 3. the straight line (parallel to the axial direction) where the strain measurement point is located; 4. strain measurement point spacing; 5. a cross-sectional symmetry axis; 6. strain measurement point location
Detailed Description
In order to make the technical solutions and advantages of the present invention clearer, the following describes the technical solutions in the embodiments of the present invention clearly and completely with reference to the drawings in the embodiments of the present invention:
the method for monitoring the constrained torsional deformation of the open-section thin-wall beam comprises the steps of selecting a strain measurement point on the surface of the open-section thin-wall beam along the axial direction, pasting a strain sensor on the test point, measuring the axial strain in real time, calculating the sector area of the section of the open-section thin-wall beam, and deducing the torsional angle and the torsional displacement of each cross section through the strain measurement value and the sector area, so as to monitor the torsional deformation of the open-section thin-wall beam in real time.
The cross section torsion angle and the buckling displacement of the open-section thin-wall beam are calculated in the following mode:
s1: calculating the distribution of the sector area omega(s) of the section of the thin-wall beam:
wherein s is the curve coordinate of the measuring point on the section outline, and h(s) is the distance from the rotating center to the tangent line of the s point;
s2: dividing the beam into a plurality of measuring sections along the axial direction, wherein the length of each measuring section is equal;
s3: at the end point of each measuring section, the measuring point of the strain sensor is arranged on the surface of the beam, and the position of the measuring point is x0，x1，x2，…xnWhere n +1 is the number of measurement points, x0At one end of the beam, xnAt the other end of the beam, with the other measurement point at x0And xnAre arranged in sequence; x is the number of1To xnArranged on a straight line parallel to the beam axis; on the beam section, the coordinate of the outline corresponding to the measuring point is sm；
In the measuring section [ x ]i-1,xi]Above, the strain expression is:
wherein epsiloni-1And εiIs xi-1And xiThe strain measurement at (a), the x-direction being the beam axis direction;
s4: the relationship between the surface strain and the torsion angle is obtained as follows:
wherein,is the torsion angle, ω(s)m) Is the cross-sectional sector area at the measurement point;
s5: obtaining a relation between the section warping displacement and the strain as follows:
u(x)＝∫ε(x)dx (5)
s6: and (3) deducing a warping displacement calculation formula of any section and any position on the section by combining the formulas (1), (3) and (5):
wherein u isiIs xiIs the warp displacement,. DELTA.l is the distance between the measuring points,. epsilonj-1And εjIs xj-1And xjMeasured value of strain of (u)0Is x0Warp displacement of (c) for a clamped beam at one end, u0＝0；
S7: based on equation (4), in the measurement section [ x ]i-1,xi]Above, there are
S8: combining equations (1), (3) and (7) to obtain xiThe twist angle of (d) is:
where Δ l is the distance between the measurement points, ω(s)m) Is the sector area, epsilon, of the measuring position0，εiAnd εjIs x0，xiAnd xjThe measured value of the strain at (a),and u0Is x0Torsion angle and warp displacement of the beam, for a clamped beam at one end
Further, the material of the thin-wall beam is isotropic material.
Further, the sensor for measuring strain comprises a resistive strain gauge sensor.
Further, the strain measuring sensor includes a Fiber Bragg Grating (FBG) sensor. Or the sensor measuring strain comprises a distributed fibre optic sensor.
Further, the strain sensors are distributed along a line on the surface of the structure, the line being parallel to the beam axis.
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 person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.
Claims (2)
1. A real-time monitoring method for constrained torsional deformation of an open-section thin-wall beam is characterized in that a strain measurement point is selected on the surface of the open-section thin-wall beam along the axial direction, a strain sensor is pasted on the strain measurement point and measures axial strain in real time, the sectional fan area of the open-section thin-wall beam is calculated, the torsional angle and the torsional displacement of each cross section are deduced through the strain measurement value and the fan area, and the torsional deformation of the open-section thin-wall beam is monitored in real time;
the cross section torsion angle and the buckling displacement of the open-section thin-wall beam are calculated in the following mode:
s1: calculating the distribution of the section sector area omega(s) of the thin-wall beam:
wherein s is the curve coordinate of the measuring point on the section outline, and h(s) is the distance from the rotating center to the tangent line of the s point;
s2: dividing the beam into a plurality of measuring sections along the axial direction, wherein the length of each measuring section is equal;
s3: at the end point of each measuring section, the measuring point of the strain sensor is arranged on the surface of the beam, and the position of the measuring point is x0，x1，x2，…xnWhere n +1 is the number of measurement points, x0At one end of the beam, xnAt the other end of the beam, with the other measurement point at x0And xnAre arranged in sequence; x is the number of1To xnArranged on a straight line parallel to the beam axis; on the beam section, the coordinate of the outline corresponding to the measuring point is sm；
In the measuring section [ x ]i-1,xi]Above, the strain expression is:
wherein epsiloni-1And εiIs xi-1And xiThe strain measurement value is measured, the x direction is the beam axis direction, wherein i represents the serial number of the test point, and delta l represents the distance between the test points;
s4: the relationship between the surface strain and the torsion angle is obtained as follows:
wherein,is the torsion angle, ω(s)m) Is the cross-sectional sector area at the measurement point;
s5: obtaining a relation between the section warping displacement and the strain as follows:
u(x)＝∫ε(x)dx (5)
s6: and (3) deducing a warping displacement calculation formula of any section and any position on the section by combining the formulas (1), (3) and (5):
wherein u isiIs xiIs the warp displacement,. DELTA.l is the distance between the measuring points,. epsilonj-1And εjIs xj-1And xjMeasured value of strain of (u)0Is x0Warp displacement of (c) for a clamped beam at one end, u0＝0；
S7: based on equation (4), in the measurement section [ x ]i-1,xi]Above, there are
S8: combining equations (1), (3) and (7) to obtain xiThe twist angle of (d) is:
where Δ l is the distance between the measurement points, ω(s)m) Is the sector area, ε, at the measurement point0，εiAnd εjIs x0，xiAnd xjThe measured value of the strain at (a),and u0Is x0Torsion angle and warp displacement of the beam, for a clamped beam at one end
2. The real-time monitoring method for the constrained torsional deformation of the open-section thin-walled beam according to claim 1, further characterized by comprising the following steps: the thin-wall beam is a cantilever beam with an equal section, wherein the section of the cantilever beam is an open section and comprises a T shape, an L shape, an I shape and a cap shape.
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| KR20160064639A (en) * | 2014-11-28 | 2016-06-08 | 현대위아 주식회사 | Apparatus for measuring an object to be measured |
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| JP3612587B2 (en) * | 2000-04-18 | 2005-01-19 | 株式会社東京計測 | Link type displacement meter |
| EP2214960B1 (en) * | 2007-12-05 | 2012-02-01 | ONERA (Office National d'Etudes et de Recherches Aérospatiales) | Elongated, torsion-deformable aerodynamic element |
| CN102322842A (en) * | 2011-05-25 | 2012-01-18 | 吉林大学 | Simplified analysis method for bending property of box-section thin-wall beam |
| CN106524894A (en) * | 2016-09-29 | 2017-03-22 | 宇龙计算机通信科技(深圳)有限公司 | Flexible screen bending degree detection method and terminal |
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