Method for calculating the degree of damage of cracked plate unit

Abstract

This invention discloses a method for calculating the damage degree of a cracked plate element. The steps are as follows: Set an appropriate number of measuring points for the cracked plate; calculate the relative width of the crack based on the plate width and crack length; calculate the crack stress diffusion angle, and extrapolate the damage degree of the equivalent element using the rectangular plate and deflection curvature theory; calculate the height-to-width ratio of the plate based on its height and width; calculate the coefficients a2, a1, and a0 of the crack stress diffusion angle calculation formula based on the plate's height-to-width ratio; calculate the moment of inertia of the undamaged plate section based on the crack stress diffusion angle; calculate the moment of inertia of the plate section in the stress diffusion portion; calculate the damage degree of the plate element using the stress diffusion angle method; and calculate the damage degree of the plate element with the corrected stress diffusion angle using the corrected parameters after normalization and weighted averaging. This invention proposes a method for calculating the damage degree of a cracked plate element, providing a theoretical basis for the design and calculation of the actual damage degree when conducting quantitative damage degree tests.

Description

Technical Field

[0001] This invention belongs to the field of structural health monitoring and relates to a method for calculating the theoretical damage degree of plate structures, specifically a method for calculating the damage degree of a cracked plate unit. Background Technology

[0002] In recent years, the number of old bridges in my country has been increasing, and the problems they present have become increasingly prominent. Among various forms of bridge damage, cracking is a relatively common one, which has a significant impact on the load-bearing capacity and subsequent lifespan of bridges. Although there has been considerable research on damage identification methods for beam structures based on static indices, theoretical damage calculation methods for transverse cracks are still limited. Furthermore, the spacing between measuring points is usually fixed during damage identification. When damage is detected in the structure, it is likely that localized damage has occurred between two measuring points. In this case, what is the equivalent damage level between the two measuring points? This question is crucial for the reasonable interpretation of quantitative damage index results. Due to the difficulty in quantifying the degree of damage, there are currently few reports in the literature on experimental verification.

[0003] This method transforms the effects of crack generation into the presence of a stress-free zone at the crack location and its surroundings. Based on linear stiffness theory, it utilizes the deflection curvature damage identification theory for cracked plate structures and, according to the equivalent damage degree of each element, calculates the crack stress diffusion angle, analyzes the relationship between the diffusion angle and the model dimensions, establishes a calculation formula for the damage degree of cracked plate elements, and calculates the theoretical damage degree of each element, providing a theoretical basis for structural damage identification experiments. Summary of the Invention

[0004] To address the problem of calculating the theoretical value of the damage degree of plate elements in plate crack damage, this invention proposes a method for calculating the damage degree of cracked plate elements.

[0005] The method for calculating the damage degree of a cracked plate unit according to the present invention comprises the following steps:

[0006] (1) Set an appropriate number of measuring points for the cracked plate. The plate segment between adjacent measuring points is recorded as one unit, and the length of the measuring point unit is... This causes the crack to open in the middle of the measuring point unit;

[0007] (2) Based on the length of the crack on one side of the plate and plate model width Calculate the relative width of the crack ;

[0008] (3) Based on the width of the plate model and plate model thickness Calculate the aspect ratio of the cracked plate model. ;

[0009] (4) Calculate the crack stress diffusion angle based on the damage degree of the equivalent cracked plate element. The crack stress propagation mode is linear, and the calculation method is as follows:

[0010] ;

[0011] when hour:

[0012] ;

[0013] ;

[0014] ;

[0015] when hour:

[0016] ;

[0017] ;

[0018] ;

[0019] when hour:

[0020] ;

[0021] ;

[0022] ;

[0023] in and These are the quadratic coefficient, the linear coefficient, and the constant term in the formula for calculating the crack stress diffusion angle.

[0024] (5) Calculate the element line stiffness of the undamaged plate. The calculation method is as follows:

[0025] ;

[0026] in The elastic modulus of the material, The moment of inertia of the undamaged plate section, ;

[0027] (6) Calculate the linear stiffness of the undamaged segment of the cracked plate damaged element. The calculation method is as follows:

[0028] ;

[0029] in The length of the undamaged side of the cracked plate damage unit is given by the length of the damaged side. , Let be the length of the plate segment on one side of the stress diffusion portion of the cracked plate damage element, where ;

[0030] (7) Calculate the linear stiffness of the stress diffusion section of the cracked plate damage element. :

[0031] The length of the plate segment on one side of the stress diffusion portion of the cracked plate damage element is... Equivalent to long of It is made up of a series of small segments. The stress diffusion section is divided into segments, each segment being a rectangular cross-section. The width of the stress-free zone in a small segment :

[0032] ;

[0033] Stress diffusion section The width of the plate section is :

[0034] ;

[0035] Stress diffusion section The moment of inertia of the plate section is :

[0036] ;

[0037] Length The Small segment linear stiffness :

[0038] ;

[0039] The linear stiffness of the stress-propagating plate segment of the cracked plate damage element was calculated using a series method. :

[0040] ;

[0041] (8) Calculate the linear stiffness of the cracked plate damage element using the series method. :

[0042] ;

[0043] (9) Calculate the damage degree of the cracked plate unit :

[0044] ;

[0045] (10) Damage degree of crack plate element with normalized regression correction of crack stress propagation angle

[0046] Diffusion angle growth rate

[0047] To verify whether the length of the cracked plate model has a significant impact on the magnitude of the crack stress propagation angle, an aspect ratio was chosen. Same, height-to-span ratio Different crack plate models were used to calculate the crack stress propagation angle growth ratio; the height-to-span ratio was taken. Using a diffusion angle of 0.001 as the baseline, the growth rate of the crack stress diffusion angle under the influence of high span ratio can be obtained. ;

[0048] Normalization

[0049] To ensure consistent correction factors, the aspect ratio is used. Using crack stress diffusion angle data as the objective function and minimizing the variance, MATLAB was used to optimize crack stress diffusion angle data with other aspect ratios, yielding optimization coefficients and the optimized diffusion angle growth rate. ;

[0050] Optimized diffusion angle growth rate data with the same average height-to-span ratio Finally, normalization is performed to normalize the diffusion angle growth rate. The formula is as follows:

[0051]

[0052] Correction of the formula for calculating the damage degree of plate crack elements

[0053] Fitting different aspect ratios Final value of crack stress diffusion angle growth rate Then, based on the normalized diffusion angle growth rate Return to true growth rate The calculation formula is as follows:

[0054]

[0055]

[0056] The original diffusion angle is corrected to obtain the corrected crack stress diffusion angle. Substituting into the original formula, the calculation formula is as follows:

[0057]

[0058]

[0059] Convert the computational model to , The rate of increase of crack stress diffusion angle in high span ratio models.

[0060] Damage level of the corrected plate crack element The calculation formula is:

[0061]

[0062] In the above formula, the subscript This indicates optimization, applicable to... .

[0063] Specifically, in step (1), the length of the measuring point unit... Not less than the width of the board model And the number of measuring points is no less than 4.

[0064] Specifically, in steps (4), (7), and (9), the number of plate segments divided on one side of the stress diffusion section... Not less than 100.

[0065] Specifically, the length of the single-sided crack in steps (2), (4), (7) to (10) is... Less than half the width of the board .

[0066] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention is based on the theory of beam structure deflection curvature damage identification, and derives the crack stress diffusion angle based on the damage degree of equivalent elements. The damage degree of the element of the cracked plate is calculated by the stress diffusion angle. The method of correcting the crack stress diffusion angle by normalization regression further improves the calculation accuracy and applicability of the damage degree of the element of the cracked plate. The applicability of the method has been verified by a large number of calculation examples, providing a theoretical basis for plate structure damage identification experiments. Attached Figure Description

[0067] Figure 1 is a flowchart of the calculation of damage degree of the cracked plate unit of the present invention.

[0068] Figure 2 is a schematic diagram of the calculation of the damage degree of the cracked plate unit of the present invention.

[0069] Figure 3 is a model of the overall damaged plate unit of the present invention.

[0070] Figure 4 is a model of the cracked plate damage unit of the present invention.

[0071] Figure 5 is a cross-sectional view of the cracked plate model of the present invention.

[0072] Figure 6 shows the crack stress diffusion model of the present invention.

[0073] Figure 7 is the equivalent part of the stress diffusion mode of the present invention.

[0074] Figure 8 shows the cross-section of the m-th segment of the crack stress diffusion plate segment of the present invention.

[0075] Figure 9 shows the aspect ratio of the cracked plate of the present invention. Relationship between the coefficients for calculating the crack stress diffusion angle and the crack stress diffusion angle.

[0076] Figure 10 shows the height-to-span ratio of the cracked plate of the present invention. and the rate of increase of crack stress diffusion angle Relationship diagram.

[0077] Figure 11 shows the crack stress propagation angle growth rate optimized according to the present invention. with high span ratio Relationship diagram.

[0078] Figure 12 is a normalized fitting diagram of the crack stress diffusion angle growth rate of the present invention.

[0079] Figure 13 shows the final value of the crack stress diffusion angle growth rate and aspect ratio of the present invention. The fitting relationship diagram.

[0080] Figure 14 shows the unit numbering of the cracked plate model in Embodiment 1 of the present invention. ).

[0081] Figure 15 shows the unit numbering of the cracked plate model in Embodiment 1 of the present invention. ).

[0082] Figure 16 is a cracked plate model of Embodiment 1 of the present invention. ).

[0083] Figure 17 is a cracked plate model of Embodiment 1 of the present invention. ).

[0084] Figure 18 is a finite element model of the cracked plate according to Embodiment 1 of the present invention.

[0085] Figure 19 is a comparison of the relative error of the damage degree of the cracked plate unit before and after the correction in Embodiment 1 of the present invention (sample group 1-sample group 7).

[0086] Figure 20 is a comparison of the relative error of the damage degree of the cracked plate unit before and after the correction in Embodiment 1 of the present invention (sample group 8-sample group 13).

[0087] Figure 21 is a comparison of the relative error of the damage degree of the cracked plate unit before and after the correction in Embodiment 1 of the present invention (sample group 14-sample group 19).

[0088] Figure 22 is a comparison of the relative error of the damage degree of the cracked plate unit before and after the correction in Embodiment 1 of the present invention (sample group 20-sample group 26).

[0089] Figure 23 is a comparison of the relative error of the damage degree of the cracked plate unit before and after the correction in Embodiment 1 of the present invention (sample group 27-sample group 34).

[0090] Figure 24 is a comparison of the relative error of the damage degree of the cracked plate unit before and after the correction in Embodiment 1 of the present invention (sample group 35-sample group 41). Detailed Implementation

[0091] The present invention will be further described below with reference to the accompanying drawings and embodiments. When the following description refers to the drawings, the same or similar elements are represented unless otherwise indicated by the same numbers in different drawings.

[0092] Figure 1 is a flowchart of the analysis and calculation process of the present invention, and Figure 2 is a schematic diagram of the damage degree calculation of the cracked plate unit of the present invention. Let b, h, and b be the lengths of the measuring point unit. cr These represent the plate model width, plate model height, and single-sided crack length, respectively, EI, EI d EI eq D represents the stiffness of the undamaged plate segment, the stiffness of the damaged plate segment, and the equivalent stiffness of the damaged plate segment, respectively. e denoted as the degree of damage to the element, and denoted as the quantity to be determined.

[0093] The method for calculating the damage degree of a cracked plate unit according to the present invention comprises the following specific steps:

[0094] Step 1: Theoretical damage degree of the cracked plate unit Calculation method:

[0095] 1) Theory of Beam Structure Deflection and Curvature Damage Identification

[0096] Theoretical damage degree D of cracked plate unit e0 A quantitative method for identifying beam structure deflection curvature damage is employed. This method is based on the difference in deflection curvature before and after damage at each node of the beam structure, enabling damage localization and quantification. The deflection curvatures of node n before and after damage are as follows:

[0097] (1)

[0098] (2)

[0099] In the formula This represents the deflection at node n. The curvature of node n is represented by the subscripts 'u' and 'd', which represent the undamaged state and the damaged state, respectively.

[0100] The quantitative formula for the theoretical damage degree of a cracked plate element is:

[0101] (3)

[0102] To verify the applicability of the beam deflection-curvature damage identification theory to plate structures, ANSYS software was used. The model was a simply supported plate with a rectangular cross-section. The plate model had a width of 100mm, a height of 5mm, and a span of 1000mm. Each 100mm element was divided into sections. The model consists of 10 elements and 11 nodes, as shown in Figure 3. Nodal loads are applied to the model. The damage is located to the right of element 3 and to the left of element 7. The damage method is to reduce the elastic modulus of the damaged element. The damaged element is element 5. Shell181 plate element is used for modeling. The damage is quantified by equation (3), thereby verifying the applicability of the beam structure deflection damage identification theory to plate structures. The model diagram is shown in Figure 3, and the damage conditions are shown in Table 1.

[0103] Table 1 Damage Conditions of Simply Supported Plates

[0104]

[0105] The damage level of the model was quantified using equation (3), and the comparison with the actual damage level is shown in Table 2 below:

[0106] Table 2 Identification of Deflection and Curvature Damage Degree

[0107]

[0108] Table 2 shows that the relative error between the damage degree of the plate structure calculated by the beam structure deflection curvature damage identification theory and the actual damage degree is within 2.5%, indicating that the beam structure deflection curvature damage identification theory is applicable to plate structures.

[0109] Step 2: Damage degree of cracked plate element using stress diffusion angle method:

[0110] 1) Simplified diagram of damage to cracked plate unit

[0111] The theoretical derivation uses a cracked plate model as an example. The plate crack is a bilateral vertical crack. Taking the damage element as an example, the schematic diagrams are shown in Figures 4 and 5. In Figure 4, X n X n+1 Here are the measurement point location numbers, h is the height of the plate model, and b is the width of the plate model. The length of a single-sided crack in the plate. The measurement point unit length is shown; the shaded area in Figure 5 represents the crack-damaged portion. Only crack lengths less than half the width of the plate are considered. .

[0112] 2) Degree of damage from bilateral cracks

[0113] The derivation of the damage degree calculation method for a double-sided cracked plate damage element takes a double-sided cracked element as an example, and the schematic diagram of the model is shown in Figure 6. Only the crack length being less than half the width of the plate is considered. . Figure X n X n+1 Here are the measurement point location numbers, h is the height of the plate model, and b is the width of the plate model. The length of a single-sided crack in the plate. The length of the measuring point unit; The crack stress propagation angle, The length of the undamaged side of the damaged unit in the cracked plate is [length missing]. The length of the plate segment on one side of the stress diffusion portion of the cracked plate damage element; where ; , and The existing formulaic relationship is as follows: .

[0114] Length Undamaged plate element linear stiffness :

[0115] (4)

[0116] Now, position the crack in the middle of the measuring point element, and measure the linear stiffness of the undamaged segment of the cracked plate. :

[0117] (5)

[0118] Next, the linear stiffness of the plate segment in the stress diffusion part of the cracked plate damage element is calculated. According to the stress diffusion model, one side of the stress diffusion portion of the damaged element can be equivalent to a length of... of It is composed of several small segments connected in series, as shown in Figure 7. Each small segment in Figure 7 is a rectangular plate cross-section, and the width of the small segment is taken as the width of the plate at the middle position of the small segment. A small diagram is shown, for example, the first... The width of the stress-free zone in a small segment :

[0119] (6)

[0120] Stress diffusion section The width of the plate section is :

[0121] (7)

[0122] Stress diffusion section The moment of inertia of the plate section is :

[0123] (8)

[0124] Length is The Segment stiffness :

[0125] (9)

[0126] The linear stiffness of the stress-propagating plate segment of the cracked plate damage element was calculated using a series method. :

[0127] (10)

[0128] Using the concatenation method, two lengths are... The undamaged segment and two segments of length are The stress diffusion sections are connected in series to calculate and derive the linear stiffness of the cracked plate damage element. :

[0129] (11)

[0130] Degree of damage to cracked plate unit :

[0131] (12)

[0132] 3) Crack propagation angle and coefficient

[0133] Using the method of equivalent damage degree, i.e. The crack stress propagation angle can be calculated. , which is calculated as follows:

[0134] (13)

[0135] With model , For example, taking different model heights, the crack stress diffusion angle is fitted using a quadratic polynomial. Relative width of crack The fitting coefficients are shown in the table below (only partial values ​​are shown):

[0136] Table 3 Fit coefficients

[0137]

[0138] The relationship curve between the two was found to satisfy a quadratic polynomial with a high degree of fit, i.e., the crack stress diffusion angle. Relative width of crack satisfy:

[0139] (14)

[0140] and These are the quadratic coefficient, linear coefficient, and constant term of the crack stress diffusion angle formula, respectively.

[0141] By using models with different heights (L=1000mm, b=100mm) for calculation and analysis, a large amount of crack stress propagation angle data and fitted quadratic polynomial coefficients were obtained. Analysis shows that different model heights correspond to different crack stress propagation angles, and also to different quadratic polynomial coefficients for crack propagation angles. Since the plate model height h is dimensional data and not suitable for generalization of the formula, the aspect ratio is used here. Replace the model height h with aspect ratio The relationship between the fitting coefficients is shown in Figure 9.

[0142] As can be seen from Figure 9, when the aspect ratio exist The coefficients a2 and a1 in the formula for calculating the crack stress diffusion angle show a turning point, therefore, the coefficients a2, a1, and a0 in the formula for calculating the crack stress diffusion angle are related to the aspect ratio. Perform piecewise fitting:

[0143] when hour;

[0144] (15)

[0145] (16)

[0146] (17)

[0147] when At this stage, the irregularity of the crack stress propagation angle coefficients a2 and a1 can lead to a large fitting error. Therefore, coefficients a2 and a1 are set to constant values, and coefficient a0 is fitted.

[0148] (18)

[0149] (19)

[0150] (20)

[0151] when hour;

[0152] (twenty one)

[0153] (twenty two)

[0154] (twenty three)

[0155] The goodness of fit R of equations (15)-(23) 2 All are above 0.99, for The sample model was used for verification. The model was a rectangular cross-section plate simulating a simply supported plate with a span of 1000 mm and a material elastic modulus of [missing value]. Its density is 2.7 g / cm³. 3 The Poisson's ratio is 0.33. Nodal loads are applied to the model at locations 300mm and 700mm from the model constraints, with uniform and symmetrical loading. The relative errors between the model cross-sectional dimensions and the damage degree of the cracked plate elements and the theoretical damage degree of the cracked plate elements are shown in Tables 4-7.

[0156] Table 4 Damage Degree of Cracked Plate Units Compared with theoretical damage level Relative error (b=100mm)

[0157]

[0158] Table 5 Damage Degree of Cracked Plate Units Compared with theoretical damage level Relative error (b=50mm)

[0159]

[0160] Table 6 Damage Degree of Cracked Plate Units Compared with theoretical damage level Relative error (b=10mm)

[0161]

[0162] Table 7 Damage Degree of Cracked Plate Units Compared with theoretical damage level Relative error (b=5mm)

[0163]

[0164] Since the calculation formula is derived from sample data of L=1000mm and b=100mm, when generalized to other models, when the aspect ratio is... Similarly, the height-to-span ratio of the model will differ significantly from that of the model derived from the calculation formula. Table 4 shows the data obtained from the model derived from the calculation formula, with relative errors mostly within 1%, indicating good applicability. Tables 4 and 5 show that when the height-to-width ratio... When the height-to-span ratio of the model is similar to that of the model derived from the calculation formula, the relative error is within 3.5%, indicating that the calculation formula has good applicability. Tables 4, 6, and 7 show that when the height-to-width ratio... At the same time, as the difference between the height-to-span ratio of the model and the height-to-span ratio of the model derived from the calculation formula increases, some relative errors exceed 5%, indicating poor applicability of the calculation formula. As shown in Table 4, when extending the formula, the directly calculated damage degree of the cracked plate element... The relative error between the theoretical damage degree of the cracked plate element and the actual damage degree exceeds 5%, indicating that the calculation results are mediocre. This suggests that the damage degree of the cracked plate element... The calculation formula has poor applicability, and it is necessary to correct the crack stress diffusion angle.

[0165] Step 3: Normalize regression to correct the damage degree of the crack plate element with crack stress propagation angle:

[0166] 1) Diffusion angle growth rate

[0167] To verify whether the model length has a significant impact on the crack stress propagation angle, an aspect ratio was chosen. Same, height-to-span ratio Different crack plate models were used to calculate crack stress propagation angle data. To ensure the rationality and consistency of model dimensions and facilitate subsequent calculations, the aspect ratio was adjusted. The height-to-span ratio is calculated by taking values ​​of 0.2, 0.25, 0.4, and 0.5 within the range of 0.01-0.5. The values ​​were taken as 0.001, 0.01, 0.02, 0.03, 0.04, and 0.05 within the range of 0.001 to 0.05, as shown in Tables 8-11:

[0168] Table 8 Aspect Ratio The same crack stress diffusion angle )

[0169]

[0170] Table 9 Aspect Ratio The same crack stress diffusion angle )

[0171]

[0172] Table 10 Aspect Ratio The same crack stress diffusion angle )

[0173]

[0174] Table 11 Aspect Ratio The same crack stress diffusion angle )

[0175]

[0176] Take the height-to-span ratio Using a diffusion angle of 0.001 as the baseline, the growth rate of crack stress diffusion angle under the influence of high span ratio was calculated. The average growth rate of crack stress diffusion angle for different span ratios is shown in Tables 12-15.

[0177] Table 12 The crack stress diffusion angle growth ratio

[0178]

[0179] Table 13 The crack stress diffusion angle growth ratio

[0180]

[0181] Table 14 The crack stress diffusion angle growth ratio

[0182]

[0183] Table 15 The crack stress diffusion angle growth ratio

[0184]

[0185] Will Using the crack stress angle growth rate as the origin, the crack stress diffusion angle growth rate can be obtained. with high span ratio The relationship diagram is shown in Figure 10.

[0186] 2) Normalization processing

[0187] To ensure a consistent correction function, the aspect ratio is used. The crack stress propagation angle growth rate data with a value of 0.5 is used as the objective function, as shown in Table 16 below:

[0188] Table 16 Crack Stress Propagation Angle Growth Rate

[0189]

[0190] That is to Using the data as the target, calculate the optimization coefficients so that the optimized data for other aspect ratios are consistent with... The data variance is minimized, that is Using MATLAB, we optimized crack stress propagation angle data with other aspect ratios, and optimized the coefficients. and the optimized diffusion angle growth rate As shown in Figure 11.

[0191] Average aspect ratios Same height-to-span ratio Optimized diffusion angle growth rate Finally, normalization is performed by dividing the average crack stress propagation angle growth rate by the average height-to-span ratio. Crack stress diffusion angle growth rate, normalized diffusion angle growth rate As shown in Figure 12, the normalization formula is as follows:

[0192] (twenty four)

[0193] 3) Correction of the formula for calculating the damage degree of plate crack elements

[0194] Fitting different aspect ratios Final value of crack stress diffusion angle growth rate The fitting plot is shown in Figure 13, representing the normalized diffusion angle growth rate. Return to true growth rate The calculation formula is as follows:

[0195] (25)

[0196] (26)

[0197] Since the calculation formula is based on the dimensions of the plate model. , It was calculated that when calculating other models, the aspect ratio of the cross-section of the calculation model needs to be changed to... The aspect ratio at that time, and then the length of the calculation model is changed to This is the extrapolation model corresponding to the calculation model, and the calculation formula is as follows; then, the original diffusion angle is corrected to obtain the corrected crack stress diffusion angle. Substituting into the original formula, the crack stress diffusion angle takes the following form:

[0198] (27)

[0199] (28)

[0200] Convert the computational model to , Equation (28) is applicable to the crack stress diffusion angle growth rate of the high span ratio in the extrapolation model. .

[0201] Damage level of the corrected plate crack element The calculation formula is:

[0202] (29)

[0203] In the formula, the subscript This indicates optimization.

[0204] Example 1:

[0205] 1) Case Implementation

[0206] The model is a rectangular cross-section plate model simulating a simply supported plate with a span of 1000mm. At that time, 100mm is used to divide the unit into two parts, that is... There are a total of 10 units and 11 nodes, as shown in Figure 14; when Divide the time into 200mm units, that is There are a total of 5 elements and 6 nodes, as shown in Figure 15. The material's elastic modulus is... Its density is 2.7 g / cm³. 3 Poisson's ratio is 0.33; when At that time, nodal loads were applied to the model, located on the right side of element 3 and the left side of node 7, with uniform and symmetrical loading; the crack was located in element 5, as shown in Figure 16. At that time, nodal loads were applied to the model, located in the middle of element 2 and the middle of node 4, with uniform and symmetrical loading. The crack was located in element 3, as shown in Figure 17.

[0207] Crack singularities were defined using the kscon command in ANSYS software and modeled using Shell181 elements, as shown in Figure 18.

[0208] 2) Sampling Analysis

[0209] The crack stress propagation angle coefficient exhibits a piecewise fit with the aspect ratio of the plate model, i.e. To fit the first stage; To fit the second stage; To fit the third stage, the high span ratio of the formula for calculating the damage degree of plate crack elements is applicable. Take a model with a length of 1000mm, and measure the aspect ratio... The values ​​are taken evenly within each stage range, with a high span ratio. The values ​​are taken uniformly within the applicable range, and the width dimensions (mm) of the sample group and plate model are shown in Table 17:

[0210] Table 17 Sample Group and Plate Model Width Values

[0211]

[0212] The width of the upper panel model is only considered. A total of forty-one sample groups were collected. Sample groups 1 and 2 were based on the relative crack width. Each group of seven samples was used for verification, with the relative crack width taken from sample groups 3 to 41. Each group consists of eight samples for verification. When verifying the sample groups, the width of the board model is taken from small to large, and the aspect ratio is taken from small to large, corresponding to forty-one sample groups. The sample group number is in the parentheses in the table above.

[0213] The theoretical damage level D of the cracked plate model e0 The theoretical formula (3) for deflection curvature damage identification is used for quantitative analysis.

[0214] Damage level of the corrected cracked plate unit Use formula (29) for calculation.

[0215] Degree of damage to cracked plate unit Equation (12) is used for calculation. During the calculation, the stress diffusion side is divided into... part, Take 200, , With D e0 The error graphs are shown in Figures 19-24.

[0216] As can be seen from Figures 19 and 20, the degree of damage to the cracked plate element is... Damage degree D according to the cracked plate model theory e0 The relative error reached a maximum of 20%, indicating the degree of damage to the cracked plate unit. The calculation results are poor; the damage degree of the corrected cracked plate element is poor. Damage degree D according to the cracked plate model theory e0 With a relative error within 3%, the calculation effect is significantly improved, demonstrating a good correction effect; as shown in Figures 21, 22, and 24, the degree of damage to the cracked plate element is... Damage degree D according to the cracked plate model theory e0 The relative error is mostly within 5%; the damage degree of the corrected crack plate element. Damage degree D according to the cracked plate model theory e0 The relative error is within 3%, and the degree of damage of the corrected crack plate element is... relative to the degree of damage of the cracked plate unit The improved calculation results have a certain corrective effect; as shown in Figure 23, the degree of damage of the corrected cracked plate element is... relative to the degree of damage of the cracked plate unit The calculation results are mostly consistent and do not have a corrective effect. Overall, it can be seen that when the height-to-span ratio of the calculated model differs significantly from the estimated model (greater than twice), directly using the crack stress diffusion method for calculation is ineffective. The relative error between the damage degree of the model sample and the actual damage degree is relatively large, reaching a maximum of 20%, resulting in poor calculation performance. Therefore, it is necessary to revise the formula. The revised formula for calculating the damage degree of the crack stress diffusion element... The relative error between the damage degree of the calculated model and the model sample is mostly below 3%, with some relative errors below 1%, indicating good computational performance. When the height-to-span ratio of the calculated model and the estimated model is not significantly different (less than twice), the damage degree of the cracked plate element is... The calculation results are good, and no correction is needed.

[0217] The above description is only one embodiment of the present invention. All equivalent changes and modifications made within the scope of the claims of the present invention are within the scope of the present invention.

Claims

1. A method for calculating the damage degree of a cracked plate unit, characterized in that... Includes the following steps: (1) Set an appropriate number of measuring points for the cracked plate. The plate segment between adjacent measuring points is recorded as one unit, and the length of the measuring point unit is... This causes the crack to open in the middle of the measuring point unit; (2) Based on the length of the crack on one side of the plate and plate model width Calculate the relative width of the crack ; (3) Based on the width of the plate model Height of the board model Calculate the aspect ratio of the cracked plate model. ; (4) Based on the relative width of the crack and aspect ratio Calculate the crack stress diffusion angle The crack stress propagation mode is linear, and the calculation method is as follows: ； when hour: ； ； ； when hour: ； ； ； when hour: ； ； ； in and These are the quadratic coefficient, the linear coefficient, and the constant term in the formula for calculating the crack stress diffusion angle. (5) Calculate the element line stiffness of the undamaged plate. The calculation method is as follows: ； in The elastic modulus of the material, The moment of inertia of the undamaged plate section, ; (6) Calculate the linear stiffness of the undamaged segment of the cracked plate damage element. The calculation method is as follows: ； in The length of the undamaged portion of the plate segment within the cracked plate damage unit is given by the following formula: , Let be the length of the plate segment on one side of the stress diffusion portion of the cracked plate damage element, where ; (7) Calculate the linear stiffness of the stress diffusion section of the cracked plate damage element. : Let the length of the plate segment on one side of the stress diffusion portion of the cracked plate damage element be considered as the length. of It is composed of a series of small segments. The stress diffusion section is divided into segments, each segment being a rectangular cross-section. The width of the stress-free zone in a small segment : ； Stress diffusion section The width of the plate section is : ； Stress diffusion section The moment of inertia of the plate section is : ； Length The Plate stiffness of segment : ； The linear stiffness of the stress-propagating plate segment of the cracked plate damage element was calculated using a series method. : ； (8) Calculate the linear stiffness of the cracked plate damage element using the series method. : ； (9) Calculate the damage degree of the cracked plate unit : ； (10) Damage degree of crack plate element with normalized regression correction of crack stress propagation angle Diffusion angle growth rate μ Take aspect ratio Same, height-to-span ratio Different crack plate models were used to calculate the crack stress propagation angle growth ratio; the height-to-span ratio was taken. Using a diffusion angle of 0.001 as the baseline, the growth rate of the crack stress diffusion angle under different height-to-span ratios was calculated. The average growth rate of the crack stress diffusion angle under different height-to-span ratios was then obtained. ; Normalization Take aspect ratio Using the crack stress propagation angle data as the objective function, the optimization coefficients for the remaining aspect ratios are calculated. and the optimized diffusion angle growth rate ; Optimized diffusion angle growth rate for the same average height-to-span ratio Finally, normalization is performed to normalize the diffusion angle growth rate. The calculation formula is as follows: ； Correction of the formula for calculating the damage degree of plate crack elements Fitting different aspect ratios Final value of crack stress diffusion angle growth rate Then, based on the normalized diffusion angle growth rate Return to true growth rate The calculation formula is as follows: ； ； The original diffusion angle is corrected to obtain the corrected crack stress diffusion angle. Substituting into the original formula, the calculation formula is as follows: ； ； Convert the computational model to , The rate of increase of crack stress diffusion angle in high span ratio models; Damage level of the corrected plate crack element The calculation formula is: ； In the above formula, the subscript This indicates optimization, applicable to... .

2. The method for calculating the damage degree of a cracked plate unit according to claim 1, characterized in that: In step (1), the length of the measuring point unit Not less than the width of the board model And the number of measuring points is no less than 4.

3. The method for calculating the damage degree of a cracked plate unit according to claim 1, characterized in that: The number of plate segments on one side of the stress diffusion section in step (7) Not less than 100.

4. The method for calculating the damage degree of a cracked plate unit according to claim 1, characterized in that: Step (2) Length of crack on one side of plate Less than half the width of the board .

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