Establishment method of time-varying random constitutive model of corrosion cold-formed steel based on random field

Abstract

This invention relates to a method for establishing a time-varying stochastic constitutive model of rusted cold-formed steel based on random fields. Based on corrosion degree parameters and a two-dimensional power spectral density equation, this invention can not only characterize the degree of uniform corrosion but also evaluate the degree of non-uniform corrosion. Furthermore, it can generate a large number of rusted surface morphologies of cold-formed steel that satisfy a certain statistical distribution through computer simulation. Based on the generated rusted surface morphology data, the mechanical properties of the cold-formed steel are numerically calculated using a finite element model. This method imports the large-scale generated rusted surface data into the finite element model of the cold-formed steel through a program, taking into account the discreteness and uncertainty caused by corrosion. The finite element numerical calculation results are highly consistent with the experimental results. Furthermore, this invention proposes a time-varying stochastic constitutive model of rusted cold-formed steel based on random fields, solving the problem that the constitutive model of rusted cold-formed steel is still based on deterministic experiments, and realizing the prediction of the time-varying stochastic constitutive model of cold-formed steel.

Description

Technical Field

[0001] This invention belongs to the technical field of durability and safety evaluation of steel structures in corrosive environments, and specifically relates to a method for establishing a time-varying stochastic constitutive model of corrosive cold-formed steel based on random fields. Background Technology

[0002] Cold-formed steel, as an engineering structural material with flexible cross-sectional shapes, high material utilization, light weight, and easy processing, has been widely used in lightweight roofs of industrial plants, logistics and warehousing frames, lightweight residential walls, and support frames. While the thinness and large area of ​​cold-formed steel meet the design requirements of material conservation and light weight, they also make them more susceptible to corrosion from atmospheric moisture, chloride salts, and industrial waste gases during long-term service, leading to severe corrosion problems. Corrosion creates irregular surface morphology and crack initiation areas on the surface of cold-formed steel, causing a sharp decrease in effective cross-section and localized stress concentration, significantly reducing the load-bearing capacity of the cold-formed steel structure. Accurately establishing the time-varying stochastic constitutive model of corroded cold-formed steel to prevent engineering accidents is a major challenge for engineering technicians.

[0003] Currently, existing research can only provide qualitative conclusions, lacking quantitative analysis of the impact of corrosion on the tensile mechanical properties of cold-formed steel. Furthermore, the complexity of the surface morphology of corroded cold-formed steel leads to increased randomness in the degradation of its mechanical properties. Therefore, there is an urgent need to provide a method for establishing a time-varying stochastic constitutive model for corroded cold-formed steel based on random fields. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for establishing a time-varying stochastic constitutive model of rusted cold-formed steel based on random fields, in order to solve the technical problems of insufficient accuracy of existing methods and inability to consider the influence of rust morphology on cold-formed steel.

[0005] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0006] Step 1: Based on the surface morphology of the rusted cold-formed steel and the variation law of rust characteristic parameters, the surface morphology of the rusted cold-formed steel is reconstructed, and a random field model of rust depth is established.

[0007] Step 2: Based on the established random field model of corrosion depth, establish a finite element model of cold-formed steel considering random corrosion surface.

[0008] Step 3: Numerical simulation is performed using the finite element model to conduct large-scale parametric analysis on cold-formed steel considering random rust surfaces, and the mechanical properties of cold-formed steel considering random rust surfaces are obtained. Combined with the rust degree parameters of cold-formed steel, the degradation law of the mechanical property parameters of rusted cold-formed steel is analyzed.

[0009] Step 4: Based on the degradation law of mechanical properties of cold-formed steel with randomly corroded surfaces and the corrosion degree parameters, determine its probability distribution characteristics and the relationship between its parameters and the corrosion degree parameters.

[0010] Step 5: Based on the relationship between the corrosion degree parameter and time, and combined with the probability distribution characteristic parameters of the mechanical properties of cold-formed steel, establish a time-varying stochastic constitutive model of rusted cold-formed steel based on random fields.

[0011] Furthermore, in step 1, the random characterization model of the rusted surface morphology of the cold-formed steel is a random field model of the rust depth of the cold-formed steel with full rust; the reconstruction of the rusted surface of the cold-formed steel is the result of the full rust morphology reconstruction.

[0012] Furthermore, the process of establishing the overall corrosion morphology reconstruction results is as follows:

[0013] A random field model of corrosion depth for comprehensive corrosion of cold-formed steel was established using a pre-defined corrosion characteristic parameter model.

[0014] The corrosion degree parameters of the cold-formed steel are input into the random field model of the corrosion depth of the cold-formed steel with full corrosion, and the surface morphology data of the cold-formed steel with full corrosion is calculated to obtain the reconstruction result of the full corrosion morphology. The specific process of calculating the surface morphology data of the cold-formed steel with full corrosion is as follows:

[0015] Multi-size corrosion depth field:

[0016] (1)

[0017] in, K represents the coordinate position; K represents the number of rust pits. For the first k The depth coefficient of each rust pit; , No. k The center coordinates of the rust pits; , It is the first k pit x, y directional expansion radius; It is the amplitude of the micro-component; It is a wavenumber function; It is a random phase angle; P 、Q They are x, y Number of directional harmonic components.

[0018] 2) The adaptive anisotropic power spectral density is calculated by the following formula.

[0019] (2)

[0020] (3)

[0021] in, It is the corrosion depth proportionality coefficient; w is the isotropic weighting factor; It is the average spatial correlation length; , They are x, y Direction-dependent length; It is the directional modulation coefficient; yes x, y Directional wave number.

[0022] 3) The directional modulation wavenumber function is calculated by the following formula:

[0023] (4)

[0024] (5)

[0025] in, , They are x, y Directional discrete wavenumber; It is the frequency coupling coefficient; It is the zero-frequency stability factor

[0026] 4) Calculation of micro-component amplitude

[0027] (6)

[0028] (7)

[0029] (8)

[0030] in, surface x Orientation dimensions; surface y Orientation dimensions; Anisotropic adaptive factor; yes x Directional wavenumber resolution coefficient; yes y Directional wavenumber resolution coefficient.

[0031] 5) The cutoff wave number is calculated as follows:

[0032] (9)

[0033] The radial power spectrum is calculated as follows:

[0034] (10)

[0035] in, It is the power spectrum cutoff wavenumber; It is the standard deviation of corrosion depth; It is the energy cutoff threshold; It is the cutoff wavenumber.

[0036] 6) The step size and minimum harmonic component number are calculated as follows:

[0037]

[0038] in, , They are x, y Directional sampling interval; M, N They are x, y Number of directional sampling points; P, Q They are x, y Directional harmonic components; yes x Wavenumber resolution in the direction; yes y Wavenumber resolution in the direction.

[0039] S1-1, Standard deviation of rust depth Power spectral density parameters include Substituting into formula (2), the power spectral density of the fully corroded surface is determined. , cut off the power spectrum to wavenumber and standard deviation of corrosion depth Substitute into formula (9) to determine the cutoff wave number.

[0040] S1-2, Determine the harmonic component parameters and the surface dimensions. Cutoff wavenumber and related length Substituting into formulas (11) and (13), determine: sampling interval Number of sampling points M, N Harmonic component number P, Q .

[0041] S1-3, Generate micro-roughness, including the determined parameters. Substituting into formulas (3)-(6) generates: random phase angle Evenly distributed in Directional modulation function wavenumber function ;amplitude .

[0042] S1-4. Generate macroscopic corrosion pits, including microscopic roughness and corrosion pit parameters. Substituting into formula (1), we generate the morphology of multi-scale corrosion pits.

[0043] Furthermore, in step 2, the process of establishing a finite element model of the cold-formed steel that considers the rust surface morphology based on the reconstructed surface morphology of the cold-formed steel is as follows:

[0044] S2-1. The reconstructed surface morphology of the cold-formed steel is converted from relative values ​​to absolute coordinates to obtain the surface morphology data of the rusted cold-formed steel:

[0045] 1) Treat the upper and lower surfaces symmetrically:

[0046] (14)

[0047] in, It is the total length of the model in the x-direction; It is the original lower surface node. coordinate; It is the original lower surface coordinate; It is the original lower surface coordinate; It is the node on the upper surface after symmetry coordinate; It is the node on the upper surface after symmetry coordinate; It is the node on the upper surface after symmetry coordinate.

[0048] 2) Transformation of relative z-coordinate values:

[0049] (15)

[0050] in, The z-coordinate of the upper surface after processing; The z-coordinate of the lower surface after processing; It is the highest point on the surface; It is an overall offset of the upper surface.

[0051] 3) Mesh sparsification:

[0052] (16)

[0053] in, It is the height value of the new mesh after sparsening; These are interpolation weighting coefficients; It is the height of the original dense grid; It is the x-coordinate to be interpolated; It is the y-coordinate to be interpolated; These are the x-coordinates of the corner points in the i-th and k-th columns of the original grid; These are the y-coordinates of the corner points in the j-th and m-th rows of the original grid;

[0054] S2-2. Import the surface morphology data of the corroded cold-formed steel into the node coordinates of the cold-formed steel finite element model to obtain the cold-formed steel finite element model considering the random corroded surface:

[0055] 1) Node coordinate calculation:

[0056] (17)

[0057] in, It is column j, row i, and layer k. coordinate vector; It represents the layer number; k is the layer number where the node is located; It is the vertical height increment between floors.

[0058] 2) Hexahedral element node index:

[0059] (18)

[0060] in, It is the first The global numbering vector of the 8 nodes of the unit; From three-dimensional position Mapped to a global node number.

[0061] 6) Node tolerance merging:

[0062] (19)

[0063] in, Let be the three-dimensional coordinates of the i-th node in the finite element method; Let j be the three-dimensional coordinates of the j-th node; To consolidate tolerances.

[0064] S2-3. For the finite element model of cold-formed steel considering random rust surface morphology, set material properties, set analysis steps, and apply boundary conditions and loads.

[0065] Furthermore, in step 3, the finite element method is used to perform numerical calculations on the finite element model of the cold-formed steel considering the random rust surface morphology, thereby obtaining the mechanical properties of the cold-formed steel considering the random rust surface morphology. Combined with the rust degree parameters of the cold-formed steel, the degradation law of the mechanical property parameters of the rusted cold-formed steel is analyzed, as follows:

[0066] S3-1. Perform finite element numerical calculations on a large batch of cold-formed steel sections considering random rust surface morphology to obtain their load-displacement curves.

[0067] S3-2. Perform engineering stress-strain transformation on the load-displacement curve of the large batch of rusted cold-formed steel to obtain the stress-strain curve of the large batch of rusted cold-formed steel.

[0068] S3-3. The stress-strain curves of the large batch of corroded cold-formed steel sections are processed to obtain the mechanical properties of each corroded cold-formed steel section, including elastic modulus, yield plateau slope, yield plateau length, ultimate strength, and ultimate strain.

[0069] (20)

[0070] Where E is the elastic modulus; It refers to the strain and stress at the end of the linear region;

[0071] (twenty one)

[0072] in, It is the slope of the yield plateau; These are the stress and strain at the end of the yield plateau; It refers to the stress and strain at the starting point of the yield plateau.

[0073] (twenty two)

[0074] in, The length of the yield plateau;

[0075] (twenty three)

[0076] in, It is the ultimate strength; It is an engineering stress-strain curve function.

[0077] (twenty four)

[0078] in, It is the ultimate strain.

[0079] S3-4. Based on the mechanical properties of the aforementioned rusted cold-formed steel and the rust degree parameters of the aforementioned rusted cold-formed steel, analyze its degradation law.

[0080] Furthermore, in step 4, the mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology are analyzed to clarify the probability distribution characteristics of the mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology, and the relationship between the probability distribution characteristics of the mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology and the rust degree parameters is established, as follows:

[0081] S4-1. The mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology, including elastic modulus, yield plateau slope, yield plateau length, ultimate strength, and ultimate strain, are analyzed to obtain their probability distribution histogram and perform KS test.

[0082] S4-2. The mechanical property parameters of the cold-formed steel considering random rust surface morphology in a large batch, including elastic modulus, yield plateau slope, yield plateau length, ultimate strength, and ultimate strain, are calculated to obtain the mean and variance of the mechanical property parameters of the cold-formed steel considering random rust surface morphology in a large batch.

[0083] S4-3. By combining the mean and variance of the mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology with the rust degree parameter, the relationship between the probability distribution characteristic parameter of the mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology and the rust degree parameter is obtained.

[0084] Furthermore, in step 5, based on the relationship between the corrosion degree parameter and time, the mechanical property parameters of cold-formed steel with random rust surface morphology are considered in large batches, and the relationship between the probability distribution characteristic parameters and the corrosion degree parameter is established to form the time-varying stochastic constitutive model of the rusted cold-formed steel based on the random field.

[0085] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0086] This invention provides a method for establishing a time-varying stochastic constitutive model of rusted cold-formed steel based on a random field. By using a random field model of rust depth, a rust surface morphology characterization model that satisfies certain probability distribution characteristics is established. Based on a small amount of surface morphology data, large-scale reconstruction of the morphology of the entire rusted surface of cold-formed steel can be achieved, providing data support for subsequent numerical calculations. Numerical calculations are then performed on the large-scale reconstructed finite element model of cold-formed steel considering the rusted surface using the finite element method. This method imports the large-scale reconstructed data of the entire rusted surface into the finite element model, which can take into account the randomness and discreteness of rust in space, resulting in highly accurate mechanical performance results. By analyzing the mechanical property parameters of corroded cold-formed steel, the degradation law of these parameters was obtained, the probability distribution characteristics of the mechanical property parameters were clarified, and the relationship between the probability distribution characteristic parameters and the weight loss rate was established. Utilizing the relationship between corrosion degree and time, a time-varying stochastic constitutive model of corroded cold-formed steel based on a random field was established. The widespread application of this invention will effectively expand the performance and evaluation technology system in the field of steel structure engineering durability and safety, providing more scientific and systematic technical support for the inspection, identification, safety assessment, and reinforcement of existing engineering structures. Specifically, this research result will not only enrich the theoretical foundation of steel structure durability assessment but also provide reliable technical basis and practical guidance for professionals engaged in engineering structure inspection, identification, safety performance assessment, and reinforcement design by establishing a complete evaluation index system and standardized testing methods. Simultaneously, the implementation of this invention will help improve the full life-cycle management level of existing steel structure engineering projects, and has significant engineering application value for ensuring the safe operation of major infrastructure and extending the service life of structures. Attached Figure Description

[0087] Figure 1 This is a flowchart of the technical solution of the present invention;

[0088] Figure 2 This is a schematic diagram of the point cloud coordinate transformation and import of rusted cold-formed steel into the finite element method.

[0089] Figure 3 The stress-strain curves of randomly generated finite element models and test specimens of rusted cold-formed steel are shown.

[0090] Figure 4 It is a reconstruction of the time-varying stochastic constitutive model of rusted cold-formed steel. Detailed Implementation

[0091] To make the technical problems solved by the present invention, the technical solutions, and the beneficial effects clearer, the following specific embodiments provide a further detailed description of the present invention. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of the invention.

[0092] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0093] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0094] Example

[0095] As attached Figure 1 This embodiment provides a method for establishing a time-varying stochastic constitutive model of rusted cold-formed steel based on random fields. The method includes: establishing a stochastic characterization model of the rusted surface of the cold-formed steel using the stochastic rusted surface morphology of the cold-formed steel and pre-set rust degree parameters; obtaining a reconstructed morphology of the overall rusted surface of the cold-formed steel based on the stochastic characterization model; establishing a finite element model of the cold-formed steel considering the rusted surface morphology based on the reconstructed morphology; and obtaining the desired morphology using the finite element model calculation method. The mechanical properties of rusted cold-formed steel were analyzed. Based on these results, the degradation characteristics of the mechanical property parameters were analyzed, the probability distribution characteristics of the mechanical property indices were clarified, and the relationship between the probability distribution characteristics of the mechanical property parameters and the weight loss rate was established. Based on this relationship, and combined with the relationship between the weight loss rate and time, a method for establishing a time-varying stochastic constitutive model of rusted cold-formed steel based on a random field was developed.

[0096] The method for establishing a time-varying stochastic constitutive model for rusted cold-formed steel based on random fields, as described in this embodiment, specifically includes the following steps:

[0097] Step 1: Based on the corrosion degree parameters and the random corrosion surface morphology of the cold-formed steel, determine the corrosion characteristic parameters. The evaluation indices for these corrosion characteristic parameters are divided into macroscopic mechanical performance indicators and overall corrosion characteristic parameters, which are used to characterize the corrosion morphology of the cold-formed steel. A random characterization model for the corrosion surface is established using the preset corrosion degree parameters and random corrosion surface morphology of the cold-formed steel. This random characterization model is a comprehensive corrosion model for cold-formed steel based on a random field of corrosion depth. Based on this random field model of corrosion depth for comprehensive corrosion of the cold-formed steel, the corrosion surface morphology of the cold-formed steel is reconstructed, resulting in a large number of reconstructed comprehensive corrosion surface morphology results for the cold-formed steel.

[0098] The mechanical performance indicators include weight loss rate, non-uniform corrosion rate, uniform corrosion rate, surface roughness, rectangularity, and surface corrosion density.

[0099] The comprehensive corrosion characteristic parameters include the average corrosion depth, standard deviation of corrosion depth, skewness, maximum corrosion depth, area of ​​the corrosion region, shape factor of the corrosion region, distribution density of corrosion points, and rate of change of corrosion thickness.

[0100] The calculation process for each parameter in the corrosion characteristic parameters is as follows:

[0101] Weightlessness rate:

[0102] (1)

[0103] Where W is the weight loss rate, which represents the percentage of mass lost after corrosion relative to the initial mass; The initial mass; This refers to the quality after corrosion.

[0104] Non-uniform corrosion rate:

[0105] (2)

[0106] Wherein, NR represents the non-uniform corrosion rate, describing the difference between different regions of the corroded surface. Let be the corrosion depth at point i. Let n be the average corrosion depth across all points, and n be the number of points.

[0107] Uniform corrosion rate:

[0108] (3)

[0109] Wherein, UR represents the uniform corrosion rate, which describes the approximately uniform degree of corrosion on the rusted surface. Let be the corrosion depth at the i-th point, and n be the number of points.

[0110] Surface roughness:

[0111] (4)

[0112] Where Ra represents surface roughness, used to measure the roughness of rusted surfaces. Let be the height of the i-th point. Let n be the average height of the points on the surface, and n be the number of points.

[0113] Surface rust density:

[0114] (5)

[0115] Where SD is the surface corrosion density, which is used to calculate the distribution density of the corrosion area. It is the area of ​​the corroded region. It is the total surface area of ​​an object.

[0116] Average rust depth:

[0117] (6)

[0118] in, It represents the average depth of rust, the average depth of all rust spots on the surface. Let be the corrosion depth at the i-th point, and n be the number of points.

[0119] Standard deviation of corrosion depth:

[0120] (7)

[0121] in, The standard deviation of corrosion depth represents the dispersion of the depth of all corrosion points on the surface. Let be the corrosion depth at point i. The average corrosion depth of all points, where n is the number of points.

[0122] Skewness:

[0123] (8)

[0124] in, The skewness value is the skewness value of the corrosion depth data, reflecting the degree of data skewness.

[0125] Maximum rust depth:

[0126] (9)

[0127] in, This represents the maximum rust depth, the deepest rust spot depth on the surface. The corrosion depth at all points.

[0128] Area of ​​rusted region:

[0129] (10)

[0130] in, The area of ​​the corroded region is the projected area of ​​the corroded region. Let n be the area of ​​the i-th rusted region, and n be the number of regions.

[0131] Shape factor of rusted area:

[0132] (11)

[0133] Where SF is the shape factor of the rusted area, which describes the complexity of the shape of the rusted area, P is the perimeter of the rusted area, and A is the area of ​​the rusted area.

[0134] Distribution density of rust spots:

[0135] (12)

[0136] Where PD represents the distribution density of rust spots, used to assess the point density of rust, and n represents the number of rust spots. This represents the total surface area.

[0137] Corrosion thickness variation rate:

[0138] (13)

[0139] Where TR represents the rate of change of corrosion thickness, the percentage change between the maximum residual thickness and the initial thickness. For the initial thickness, This represents the maximum residual thickness.

[0140] Rectangle ratio:

[0141] (14)

[0142] in, Rectangularity measures how closely the shape of a region approximates a rectangle. It is the area of ​​the outline region. It is the area of ​​the smallest bounding rectangle.

[0143] In this embodiment, the random field-based model for the overall corrosion of cold-formed steel is suitable for the random characterization of the surface morphology of overall corrosion, as shown in the attached figure. Figure 2 The process of establishing the comprehensive rust morphology reconstruction result of the cold-formed steel is as follows: A random characterization model of the rust surface is established using preset rust degree parameters and the rust surface morphology of the cold-formed steel; the rust characteristic parameters are substituted into the random field-based rust cold-formed steel model to obtain comprehensive rust morphology data of the cold-formed steel, thus obtaining the comprehensive rust morphology reconstruction result of the cold-formed steel; specifically, the process of calculating the comprehensive rust morphology data of the rusted cold-formed steel is as follows: the power spectral density equation of the rusted cold-formed steel surface is determined based on the average rust depth and standard deviation of the rust depth; based on the power spectral density equation of the rusted cold-formed steel surface, combined with a two-dimensional random harmonic function, the comprehensive rust morphology data of the cold-formed steel is obtained, thus obtaining the comprehensive rust morphology reconstruction result of the rusted cold-formed steel.

[0144] The specific process is as follows:

[0145] 1) Multi-size corrosion depth field:

[0146] (15)

[0147] in, K represents the coordinate position; K represents the number of rust pits. For the first k The depth coefficient of each rust pit; No. k The center coordinates of the rust pits; It is the first k pit x, y directional expansion radius; It is the amplitude of the micro-component; It is a wavenumber function; It is a random phase angle; P 、Q They are x, y Number of directional harmonic components.

[0148] 2) The adaptive anisotropic power spectral density is calculated by the following formula.

[0149]

[0150] in, It is the corrosion depth proportionality coefficient; w is the isotropic weighting factor; It is the average spatial correlation length; They are x, y Direction-dependent length; It is the directional modulation coefficient; yes x, y Directional wave number.

[0151] 3) The directional modulation wavenumber function is calculated by the following formula:

[0152]

[0153] in, They are x, y Directional discrete wavenumber; It is the frequency coupling coefficient; It is the zero-frequency stability factor

[0154] 4) Calculation of micro-component amplitude

[0155]

[0156] in, surface x Orientation dimensions; surface y Orientation dimensions; Anisotropic adaptive factor; yes x Directional wavenumber resolution coefficient; yes y Directional wavenumber resolution coefficient.

[0157] 5) The cutoff wave number is calculated as follows:

[0158] (twenty three)

[0159] The radial power spectrum is calculated as follows:

[0160] (twenty four)

[0161] in, It is the power spectrum cutoff function; It is the standard deviation of corrosion depth; It is the energy cutoff threshold; It is the cutoff wavenumber.

[0162] 6) The step size and minimum harmonic component number are calculated as follows:

[0163]

[0164] in, They are x, y Directional sampling interval; M, N They are x, y Number of directional sampling points; P, Q They are x, y Directional harmonic components; yes x Wavenumber resolution in the direction; yes y Wavenumber resolution in the direction.

[0165] S1-1, Standard deviation of rust depth Power spectral density parameters include Substituting into formula (16), the power spectral density of the fully corroded surface is determined. , cut off the power spectrum to wavenumber and standard deviation of corrosion depth Substitute into formula (23) to determine the cutoff wave number. The corrosion degree parameters and characteristic parameters of some cold-formed steel sections with different corrosion degrees are shown in Table 1.

[0166] Table 1 shows the corrosion degree parameters and characteristic parameters of some cold-formed steel sections with different corrosion degrees.

[0167]

[0168] S1-2, Determine the harmonic component parameters and the surface dimensions. Cutoff wavenumber and related length Substituting into formulas (25) and (27), determine: sampling interval Number of sampling points M, N Harmonic component number P, Q .

[0169] S1-3, Generate micro-roughness, including the determined parameters. Substitute into formula (18-20) to generate: random phase angle Evenly distributed in Directional modulation function wavenumber function ;amplitude .

[0170] S1-4. Generate macroscopic rust pits, including rust pit parameters. Substituting into the macroscopic part of formula (15), the macroscopic rust pit morphology is generated.

[0171] S1-5. Repeat the above operations to generate large-scale, fully rusted surfaces of cold-formed steel sections.

[0172] Step 2: Based on the reconstructed overall rust morphology of the cold-formed steel, establish a finite element model of the cold-formed steel that considers the rust surface morphology. (See attached image.) Figure 1 The process of establishing the finite element model of cold-formed steel considering the morphology of rusted surfaces is as follows:

[0173] S2-1. The reconstructed surface morphology of the cold-formed steel is converted from relative values ​​to absolute coordinates to obtain the surface morphology data of the rusted cold-formed steel:

[0174] 1) Treat the upper and lower surfaces symmetrically:

[0175] (28)

[0176] in, y is the total length of the model in the x direction; x is the x-coordinate of the original lower surface node; y is the y-coordinate of the original lower surface; z is the z-coordinate of the original lower surface. It is the x-coordinate of the node on the upper surface after symmetry; It is the y-coordinate of the node on the upper surface after symmetry; It is the z-coordinate of the node on the upper surface after symmetry.

[0177] 2) Transformation of relative z-coordinate values:

[0178] (29)

[0179] in, The z-coordinate of the upper surface after processing; The z-coordinate of the lower surface after processing; It is the highest point on the surface; It is an overall offset of the upper surface.

[0180] 3) Mesh sparsification:

[0181] (30)

[0182] in, It is the height value of the new mesh after sparsening; These are interpolation weighting coefficients; It is the height of the original dense grid; It is the x-coordinate to be interpolated; It is the y-coordinate to be interpolated; These are the x-coordinates of the corner points in the i-th and k-th columns of the original grid; These are the y-coordinates of the corner points in the j-th and m-th rows of the original grid;

[0183] S2-2. Import the surface morphology data of the corroded cold-formed steel into the node coordinates of the cold-formed steel finite element model to obtain the cold-formed steel finite element model considering the random corroded surface:

[0184] 1) Node coordinate calculation:

[0185] (31)

[0186] in, It is column j, row i, and layer k. coordinate vector; It represents the layer number; k is the layer number where the node is located; It is the vertical height increment between floors.

[0187] 2) Hexahedral element node index:

[0188] (32)

[0189] in, It is the first The global numbering vector of the 8 nodes of the unit; From three-dimensional position Mapped to a global node number.

[0190] 6) Node tolerance merging:

[0191] (33)

[0192] in, Let be the three-dimensional coordinates of the i-th node in the finite element method; Let j be the three-dimensional coordinates of the j-th node; To consolidate tolerances.

[0193] S2-3. For the finite element model of cold-formed steel considering random rust surface morphology, set material properties, set analysis steps, and apply boundary conditions and loads.

[0194] Step 3: Using the finite element method, perform finite element numerical calculations on the finite element model of the cold-formed steel considering the rusted surface morphology to obtain the mechanical property results of the rusted cold-formed steel. Specifically, for the finite element model of the cold-formed steel considering the rusted surface morphology, set constitutive parameters, apply boundary conditions, analysis steps, and loads, and perform finite element numerical calculations to obtain the mechanical property results of the rusted cold-formed steel, as follows:

[0195] S3-1. Perform finite element numerical calculations on a large batch of cold-formed steel sections considering random rust surface morphology to obtain their load-displacement curves.

[0196] S3-2. Perform engineering stress-strain transformation on the load-displacement curve of the large batch of rusted cold-formed steel to obtain the stress-strain curve of the large batch of rusted cold-formed steel.

[0197] S3-3. The stress-strain curves of the large batch of corroded cold-formed steel sections are processed to obtain the mechanical properties of each corroded cold-formed steel section, including elastic modulus, yield plateau slope, yield plateau length, ultimate strength, and ultimate strain.

[0198] (34)

[0199] Where E is the elastic modulus; It refers to the strain and stress at the end of the linear region;

[0200] (35)

[0201] in, It is the slope of the yield plateau; These are the stress and strain at the end of the yield plateau; It refers to the stress and strain at the starting point of the yield plateau.

[0202] (36)

[0203] in, The length of the yield plateau;

[0204] (37)

[0205] in, It is the ultimate strength; It is an engineering stress-strain curve function.

[0206] (38)

[0207] in, It is the ultimate strain.

[0208] S3-4. Based on the mechanical properties of the aforementioned rusted cold-formed steel and the rust degree parameters, the degradation law is analyzed. Table 2-5 provides relative values ​​of the mechanical properties of some cold-formed steels with different rust degrees. (See attached table.) Figure 3 As shown, the stress-strain curve of the finite element model of cold-formed steel considering the morphology of the corroded surface is almost identical to the experimental curve, indicating that the finite element model of cold-formed steel considering the morphology of the corroded surface proposed in this embodiment has high accuracy.

[0209] Table 2. Relative values ​​of elastic modulus for some cold-formed steel sections with different degrees of corrosion.

[0210]

[0211] Table 3. Relative values ​​of yield strength for some cold-formed steel sections with different degrees of corrosion.

[0212]

[0213] Table 4. Relative values ​​of ultimate strength of some cold-formed steel sections with different degrees of corrosion.

[0214]

[0215] Table 5. Relative values ​​of ultimate strain for some cold-formed steel sections with different degrees of corrosion.

[0216]

[0217] Step 4: Based on the mechanical property results of the rusted cold-formed steel, clarify the probability distribution characteristics of the mechanical property parameters of the rusted cold-formed steel, and establish the relationship between the probability distribution characteristics of the mechanical property parameters of the rusted cold-formed steel and the weight loss rate. Calculate the probability distribution characteristics of the mechanical property parameters of the rusted cold-formed steel using equation (39), and perform the KS test using equation (40).

[0218] The specific process is as follows:

[0219] S4-1. The mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology, including elastic modulus, yield plateau slope, yield plateau length, ultimate strength, and ultimate strain, are analyzed to obtain their probability distribution histogram and perform KS test.

[0220] S4-2. The mechanical property parameters of the cold-formed steel considering random rust surface morphology in a large batch, including elastic modulus, yield plateau slope, yield plateau length, ultimate strength, and ultimate strain, are calculated to obtain the mean and variance of the mechanical property parameters of the cold-formed steel considering random rust surface morphology in a large batch.

[0221] S4-3. By combining the mean and variance of the mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology with the rust degree parameter, the relationship between the probability distribution characteristic parameter of the mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology and the rust degree parameter is obtained.

[0222] 1) Calculation of probability density equation

[0223] (39)

[0224] in, It is the average value of each mechanical property parameter; It is the standard deviation of each mechanical property parameter;

[0225] 2) KS test

[0226] (40)

[0227] in, Indicates the supremacy. It is an empirical distribution function; It is the theoretical distribution function

[0228] Step 5: Based on the relationship between the corrosion degree parameter and time, and considering the relationship between the probability distribution characteristic parameters of the mechanical property parameters of cold-formed steel with randomly corroded surface morphology and the corrosion degree parameter, establish the time-varying stochastic constitutive model of the corroded cold-formed steel based on a random field. Reconstruct the stochastic constitutive models of cold-formed steel with different corrosion times to obtain the following results: Figure 4 The stress-strain curve shown.

[0229] This embodiment describes a method for establishing a time-varying stochastic constitutive model of rusted cold-formed steel based on random fields. It uses parameters of the degree of rust on the cold-formed steel and random functions to establish a stochastic characterization model of the rusted surface, and performs large-scale reconstruction of the rusted surface morphology. The mechanical properties of the cold-formed steel are then tested by importing the large-scale randomly generated rusted surface into a finite element model that considers the rusted surface morphology. Based on the mechanical property results, the degradation law of its parameters is analyzed, the probability distribution characteristics of the mechanical property indicators of the rusted cold-formed steel are clarified, and a model of the probability distribution characteristic parameters of mechanical properties and the weight loss rate is established. Combining the relationship between the weight loss rate and time, a method for establishing a time-varying stochastic constitutive model of rusted cold-formed steel based on random fields is further proposed. This invention, based on corrosion degree parameters and a two-dimensional power spectral density equation, can not only characterize the degree of uniform corrosion but also evaluate the degree of non-uniform corrosion. Furthermore, it can generate a large number of cold-formed steel corrosion surface morphologies that satisfy a certain statistical distribution through computer simulation. Based on the generated corrosion surface morphology data, a finite element model of the cold-formed steel is used for numerical calculation of mechanical properties. This method imports the large-scale generated corrosion surface data into the finite element model of the cold-formed steel through a program, taking into account the discreteness and uncertainty caused by corrosion. The finite element numerical calculation results are highly consistent with the experimental results. Based on the mechanical property results of the cold-formed steel, the degradation law of its parameters is analyzed, clarifying the probability distribution characteristics of the mechanical property indicators of the rusted cold-formed steel. A model of the probability distribution characteristic parameters of mechanical properties and the weight loss rate is established. Combining the relationship between the weight loss rate and time, a time-varying stochastic constitutive model of the rusted cold-formed steel based on a random field is further established. This solves the problem that the establishment of constitutive models for rusted cold-formed steel is still based on deterministic experiments, and realizes the prediction of time-varying stochastic constitutive models of cold-formed steel.

[0230] The above embodiments are merely one of the implementation methods for achieving the technical solution of the present invention. The scope of protection claimed by the present invention is not limited to this embodiment, but also includes any variations, substitutions and other implementation methods that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention.

Claims

1. A method for establishing a time-varying stochastic constitutive model for rusted cold-formed steel based on random fields, characterized in that, Includes the following steps: Step 1: Based on the surface morphology and corrosion characteristic parameter variation law of the rusted cold-formed steel, the surface morphology of the rusted cold-formed steel is reconstructed, and a random field model of corrosion depth is established. Step 2: Based on the established random field model of corrosion depth, establish a finite element model of cold-formed steel considering random corrosion surface; In step 2, based on the established random field model of corrosion depth, the process of establishing a finite element model of cold-formed steel considering random corrosion surfaces is as follows: S2-1. The reconstructed surface morphology of the cold-formed steel is converted from relative values ​​to absolute coordinates to obtain the surface morphology data of the rusted cold-formed steel: 1) Treat the upper and lower surfaces symmetrically: （14） in, It is the total length of the model in the x-direction; It is the original lower surface node. coordinate; It is the original lower surface coordinate; It is the original lower surface coordinate; It is the node on the upper surface after symmetry coordinate; It is the node on the upper surface after symmetry coordinate; It is the node on the upper surface after symmetry coordinate; 2) Transformation of relative z-coordinate values: （15） in, The upper surface after treatment coordinate; The lower surface after treatment coordinate; It is the highest point on the surface; It is an overall offset of the upper surface; 3) Mesh sparsification: （16） in, It is the height value of the new mesh after sparsening; These are interpolation weighting coefficients; It is the height of the original dense grid; It is to be interpolated coordinate; It is to be interpolated coordinate; , It is the original grid number , column corners coordinate; , It is the original grid number , Line corner point coordinate; S2-2. Import the rust surface morphology data of the cold-formed steel into the node coordinates of the cold-formed steel finite element model to obtain the cold-formed steel finite element model considering random rust surface: 1) Node coordinate calculation: （17） in, yes List, OK, Layer coordinate vector; It refers to the number of layers; It is the layer number where the node is located; It is the vertical height increment between floors; 2) Hexahedral element node index: （18） in, It is the first The global numbering vector of the 8 nodes of the unit; From three-dimensional position Mapped to a global node number; 6) Node tolerance merging: （19） in, For the finite element method The three-dimensional coordinates of node number 1; For the first The three-dimensional coordinates of node number 1; To consolidate tolerances; S2-3. For the finite element model of cold-formed steel considering random rust surface morphology, set material properties, set analysis steps, and apply boundary conditions and loads. Step 3: Numerical simulation using finite element method is performed to conduct large-scale parametric analysis of cold-formed steel considering random rust surface, and the mechanical properties of cold-formed steel considering random rust surface are obtained. Combined with the rust degree parameter of cold-formed steel, the degradation law of mechanical property parameters of rusted cold-formed steel is analyzed. Step 4: Based on the degradation law of mechanical properties of cold-formed steel with randomly corroded surfaces and the corrosion degree parameters, determine its probability distribution characteristics and the relationship between its parameters and the corrosion degree parameters; Step 5: Based on the relationship between the corrosion degree parameter and time, and combined with the probability distribution characteristics of the mechanical property parameters of cold-formed steel, establish a time-varying stochastic constitutive model of rusted cold-formed steel based on random fields; In step 5, based on the relationship between the corrosion degree parameter and time, the mechanical property parameters of cold-formed steel with random rust surface morphology are considered in large batches, and the relationship between the probability distribution characteristic parameters and the corrosion degree parameter is obtained, thus obtaining the time-varying stochastic constitutive model of the rusted cold-formed steel based on the random field.

2. The method for establishing a time-varying stochastic constitutive model of rusted cold-formed steel based on random fields according to claim 1, characterized in that, In step 1, the random field model for the corrosion depth of the cold-formed steel is for comprehensive corrosion, and the specific operation is as follows: 1) Multi-size corrosion depth field: （1） in, The coordinates are the location; The number of rust pits, The depth coefficient of the k-th rust pit; , The center coordinates of the kth rust pit; , It is the radius of expansion of the k-th pit in the x and y directions; It is the amplitude of the micro-component; It is a wavenumber function; It is a random phase angle; , These are the harmonic component numbers in the x and y directions, respectively; 2) The adaptive anisotropic power spectral density is calculated by the following formula: （2） （3） in, It is the corrosion depth proportionality coefficient; It is an isotropic weighting factor; It is the average spatial correlation length; , These are the relevant lengths in the x and y directions, respectively. It is the directional modulation coefficient; These are the wavenumbers in the x and y directions; 3) The directional modulation wavenumber function is calculated by the following formula: （4） （5） in, , These are the discrete wavenumbers in the x and y directions, respectively. It is the frequency coupling coefficient; It is the zero-frequency stability factor; 4) Calculation of micro-component amplitude: （6） （7） （8） in, Dimensions in the x-direction of the surface; Dimensions in the y-direction of the surface; Anisotropic adaptive factor; It is the wavenumber resolution coefficient in the x-direction; It is the wavenumber resolution coefficient in the y-direction; 5) The cutoff wave number is calculated as follows: （9） The radial power spectrum is calculated as follows: （10） in, It is the power spectrum cutoff wavenumber; It is the standard deviation of corrosion depth; It is the energy cutoff threshold; It is the cutoff wavenumber; 6) The step size and minimum harmonic component number are calculated as follows: （11） （12） （13） in, , These are the sampling intervals in the x and y directions, respectively; M and N are the number of sampling points in the x and y directions, respectively; P and Q are the number of harmonic components in the x and y directions, respectively. It is the wavenumber resolution in the x-direction; It is the wavenumber resolution in the y-direction; S1-1, Standard deviation of rust depth Power spectral density parameters include Substituting into formula (2), the power spectral density of the fully corroded surface is determined. The power spectrum is cut off by wavenumber. and standard deviation of corrosion depth Substitute into formula (9) to determine the cutoff wave number. ; S1-2, Determine the harmonic component parameters and the surface dimensions. Cutoff wavenumber and related length Substituting into formulas (11) and (13), determine: sampling interval , Number of sampling points M, N; Number of harmonic components P, Q; S1-3, Generate micro-roughness, including the determined parameters. Substituting into formulas (3)-(6) generates: random phase angle Evenly distributed in Directional modulation function wavenumber function ;amplitude ; S1-4. Generate macroscopic corrosion pits, including microscopic roughness and corrosion pit parameters. Substituting into formula (1), we generate the morphology of multi-scale corrosion pits.

3. The method for establishing a time-varying stochastic constitutive model of rusted cold-formed steel based on random fields according to claim 1, characterized in that, In step 3, the finite element method is used to perform numerical calculations on the finite element model of the cold-formed steel considering random rust surface morphology, obtaining the mechanical properties of the cold-formed steel considering random rust surface morphology. Combined with the rust degree parameters of the cold-formed steel, the degradation law of the mechanical property parameters of the rusted cold-formed steel is analyzed, as follows: S3-1. Perform finite element numerical calculations on a large batch of cold-formed steel sections considering random rust surface morphology to obtain their load-displacement curves. S3-2. Perform engineering stress-strain transformation on the load-displacement curve of the large batch of rusted cold-formed steel to obtain the stress-strain curve of the large batch of rusted cold-formed steel. S3-3. The stress-strain curves of the large batch of rusted cold-formed steel are processed to obtain the mechanical properties of rusted cold-formed steel with different degrees of rust, including elastic modulus, yield plateau slope, yield plateau length, ultimate strength, and ultimate strain. （20） in, It is the elastic modulus; It refers to the strain and stress at the end of the linear region; （21） in, It is the slope of the yield plateau; , These are the stress and strain at the end of the yield plateau; , These are the stress and strain at the starting point of the yield plateau; （22） in, The length of the yield plateau; (23) in, It is the ultimate strength; It is an engineering stress-strain curve function; (24) in, It is the ultimate strain; S3-4. Based on the mechanical properties of the aforementioned rusted cold-formed steel and the rust degree parameters of the aforementioned rusted cold-formed steel, analyze its degradation law.

4. The method for establishing a time-varying stochastic constitutive model of rusted cold-formed steel based on random fields according to claim 1, characterized in that, In step 4, the mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology are analyzed to clarify the probability distribution characteristics of the mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology. The relationship between the probability distribution characteristics of the mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology and the rust degree parameters is established, as follows: S4-1. The mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology, including elastic modulus, yield plateau slope, yield plateau length, ultimate strength, and ultimate strain, are analyzed to obtain their probability distribution histogram and perform KS test. S4-2. The mechanical property parameters of the cold-formed steel considering random rust surface morphology in a large batch, including elastic modulus, yield plateau slope, yield plateau length, ultimate strength, and ultimate strain, are calculated to obtain the mean and variance of the mechanical property parameters of the cold-formed steel considering random rust surface morphology in a large batch. S4-3. By combining the mean and variance of the mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology with the rust degree parameter, the relationship between the probability distribution characteristic parameter of the mechanical property parameters of the large batch of cold-formed steel considering random rust surface morphology and the rust degree parameter is obtained.

Images