A calculation method for post-buckling of cold-rolled strip with initial flatness defects

Abstract

The present invention proposes a post-buckling calculation method for cold-rolled strip steel with initial plate shape defects inside, which relates to the field of buckling technology. First, the geometric size parameters and property parameters of the cold-rolled strip steel with initial plate shape defects inside the production site are collected, and then the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip steel with initial plate shape defects inside are established to form a post-buckling calculation model for the cold-rolled strip steel with initial plate shape defects inside. Finally, the perturbation method and Hamilton method are used to solve the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip steel with initial plate shape defects inside, and the general analytical model formula for the post-buckling of the cold-rolled strip steel with initial plate shape defects inside is obtained. The calculation method for solving the post-buckling of the cold-rolled strip steel with initial plate shape defects proposed in the present invention can better improve the post-buckling mechanical mechanism of the cold-rolled strip steel with initial plate shape defects inside, improve the quality of the plate, and eliminate the defects of the plate.

Description

Technical Field

[0001] The invention relates to the technical field of buckling, and in particular to a post-buckling calculation method for a cold-rolled steel strip with an initial plate shape defect inside. Background Art

[0002] As a key basic material in the manufacturing industry, cold-rolled strip plays a vital role in the field of metal processing and manufacturing. One of the core indicators of its quality is the plate shape, and the strip usually has certain plate shape defects in its initial state. These defects are mostly caused by the uneven distribution of internal residual stress generated during production, curling, stacking or transportation, resulting in initial plate shape defects such as edge waves and middle waves. Therefore, it is of great theoretical and practical significance to establish a buckling deformation model of cold-rolled strip that includes initial plate shape defects.

[0003] The strip buckling deformation analysis model mainly consists of two parts: pre-buckling instability judgment and post-buckling stress-strain analysis. In the application of cold-rolled strip, the study of post-buckling behavior is particularly critical. However, there are still some aspects that have not been explored in depth in current research: First, although the research on the pre-buckling instability judgment model by domestic and foreign scholars has become mature, there are relatively few studies on the post-buckling deformation of strip with initial plate shape defects, and there is a lack of a mechanism model with strong applicability to systematically explain the post-buckling behavior of strip; second, when solving the post-buckling problem, it often involves the solution of nonlinear high-order partial differential equations. The calculation process of the existing solution method is complicated and lengthy, and a calculation method that is both accurate and simple has not yet been formed; third, the existing research mainly focuses on the buckling phenomenon under the action of external forces, while ignoring the buckling phenomenon caused by the uneven stress distribution inside the strip without the application of external forces. Therefore, the study of post-buckling of cold-rolled strip requires not only the study of the buckling behavior mechanism of the strip with initial plate shape defects, but also the development of more efficient and concise solution methods to better solve the buckling deformation problem of cold-rolled strip in actual processing. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a calculation method for the post-buckling of cold-rolled strip with initial plate shape defects inside in view of the deficiencies of the above-mentioned prior art. The calculation model of the post-buckling of cold-rolled strip with initial plate shape defects inside is solved by the perturbation method and the Hamiltonian method, so as to better improve the mechanical mechanism of the post-buckling of cold-rolled strip with initial plate shape defects inside, improve the quality of the plate, and eliminate the defects of the plate.

[0005] A post-buckling calculation method for a cold-rolled steel strip with an initial flatness defect comprises the following steps:

[0006] Step 1: Collect the geometric size parameters and property parameters of the cold-rolled strip with initial plate shape defects at the production site;

[0007] The geometric dimension parameters of the cold-rolled steel strip include the length, width and thickness of the cold-rolled steel strip, and the property parameters of the cold-rolled steel strip include the density, Young's modulus, Poisson's ratio, yield strength and tangent modulus of the cold-rolled steel strip;

[0008] Step 2: Establish the large deflection equilibrium equation and deformation coordination equation of cold-rolled strip with initial defect terms inside, and form the post-buckling calculation model of cold-rolled strip with initial plate shape defect terms inside;

[0009] Step 2.1: According to the geometric equation, physical equation and equilibrium equation of the cold-rolled strip, a large deflection mechanical model of the cold-rolled strip is constructed, and then the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip are derived;

[0010] The large deflection equilibrium equation of cold-rolled strip steel is shown in the following formula:

[0011] ;in, is the bending stiffness of cold-rolled strip per unit width, ; is the Young’s modulus of cold-rolled steel strip; is the thickness of cold-rolled strip; is Poisson's ratio; is the Laplace operator, ; is the internal stress function of cold-rolled strip; is the deflection of cold-rolled strip; is the length direction coordinate of the cold-rolled strip; is the width direction coordinate of the cold-rolled strip;

[0012] The deformation coordination equation of cold rolled strip is shown in the following formula:

[0013] ;in, ;

[0014] Step 2.2: Add the initial defect term to the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip to obtain the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip with the initial plate shape defect term inside;

[0015] The large deflection equilibrium equation of cold-rolled strip steel with the initial plate defect term inside is as follows:

[0016] ;in, is the initial plate defect item;

[0017] The deformation coordination equation of cold-rolled strip with initial plate shape defect term inside is as follows:

[0018] ;

[0019] Step 3: Using the perturbation method and Hamiltonian method, the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip with the initial plate defect term are solved, and the general analytical model formula of post-buckling of the cold-rolled strip with the initial plate defect term is obtained;

[0020] Step 3.1: Use the perturbation method to perform perturbation expansion on the deflection, stress function and internal stress of the cold-rolled strip. The perturbation expansion process is shown in the following formula:

[0021] , , ;in, Expand the parameters for the perturbation; is the zero-order deflection of the cold-rolled strip, is the first-order deflection of cold-rolled strip, is the second-order deflection of the cold-rolled strip; is the zero-order stress function of cold-rolled strip, is the first-order stress function of cold-rolled strip, is the second-order stress function of cold-rolled strip; is the internal stress of cold-rolled strip, is the critical internal residual stress for buckling of cold-rolled strip, is the first-order internal stress of the cold-rolled strip, is the second-order internal stress of the cold-rolled strip;

[0022] Step 3.2: Combine step 2.2 with step 3.1, expand the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip with initial plate defect terms into control equations, obtain the post-buckling control equation of the cold-rolled strip with initial plate defect terms, and import it into the Hamiltonian system for solution, and obtain the general analytical model formula for post-buckling calculation of the cold-rolled strip with initial plate defect terms;

[0023] Perturb expansion parameters 0th power The coefficient of is set to 0, and the zero-order control equation of the cold-rolled strip with the initial defect term inside is obtained, as shown in the following formula:

[0024] ;

[0025] Perturb expansion parameters 1st power The coefficient of is set to 0, and the first-order control equation of the cold-rolled strip with the initial defect term inside is obtained, as shown in the following formula:

[0026] ;in, is the amplitude of the initial shape defect of the cold-rolled strip, is the width of the cold-rolled strip;

[0027] Hamiltonian is used to solve the first-order control equation of the cold-rolled strip with the initial defect term inside, and the first-order deflection control equation of the cold-rolled strip is obtained, as shown in the following formula:

[0028] ;in, is the local longitudinal buckling of the strip i Order parameter; is the modal order of strip buckling, and the first-order governing equation is Take 1; is the length of the strip;

[0029] Perturb expansion parameters The power of 2 The coefficient of is set to 0, and the second-order control equation of the cold-rolled strip with the initial defect term inside is obtained, as shown in the following formula: ;

[0030] Combining the second-order control equation of the cold-rolled strip with the initial defect term and the first-order deflection control equation of the cold-rolled strip, the post-buckling control equation of the cold-rolled strip with the initial plate shape defect is obtained, as shown in the following formula:

[0031] ;in, is the local longitudinal buckling of the strip j Order parameter; , is a non-zero eigenvalue, ;

[0032] The post-buckling control equation of cold-rolled strip with initial flatness defects is introduced into the Hamiltonian system and solved to obtain the general analytical model formula for post-buckling calculation of cold-rolled strip with initial flatness defects, as shown in the following formula:

[0033] ;in, These are all parameters to be fitted, and their specific values ​​are solved according to the different boundary conditions to which the cold-rolled strip is subjected; They represent the first i The first mode and j Order mode.

[0034] The beneficial effects of adopting the above technical solution are: At present, there is a lack of research on the post-buckling deformation of steel strip, and the post-buckling calculation involves the solution of nonlinear high-order partial differential equations. The calculation process is complicated and cumbersome. There is a lack of a post-buckling analytical model of cold-rolled steel strip that only considers the internal plate shape defects of the steel strip and has strong applicability, and it is studied in a more accurate and simpler way. The present invention establishes a post-buckling calculation method for cold-rolled steel strip with initial plate shape defects inside, solves the post-buckling model of the steel strip based on the Hamilton method and the perturbation method, and achieves a better explanation of the mechanical behavior of the post-buckling of the cold-rolled steel strip from a mechanical point of view, and achieves no assumptions about the strip buckling deflection function. The strip post-buckling formula can be obtained through rigorous derivation, so as to better improve the mechanical mechanism of post-buckling of cold-rolled steel strip with initial plate shape defects inside, improve the quality of the plate, and eliminate plate defects. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A flow chart of a method for calculating post-buckling of a cold-rolled steel strip with an initial flatness defect provided by an embodiment of the present invention;

[0036] Figure 2 A schematic diagram of three-dimensional coordinates of a cold-rolled steel strip provided in an embodiment of the present invention;

[0037] Figure 3 A diagram of a large deflection mechanical model of cold-rolled steel strip provided in an embodiment of the present invention;

[0038] Figure 4 A stress change comparison diagram of the finite element results and simulation results of post-buckling of cold-rolled strip provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0040] At present, there are few studies on the post-buckling deformation of cold-rolled strip in the prior art, and the calculation process is complex and cumbersome. There is a lack of a cold-rolled strip post-buckling mechanism model with strong applicability, making it difficult to explain the mechanical relationship of the post-buckling of cold-rolled strip and the internal mechanism problems in a more accurate and simpler way. The present invention proposes a post-buckling calculation method for cold-rolled strip with initial plate shape defects inside, and solves the post-buckling model of the strip based on the Hamilton method and the perturbation method, thereby clarifying the post-buckling mechanism of the strip with initial plate shape defects inside. This embodiment obtains the post-buckling formula of cold-rolled strip through rigorous derivation without making any assumptions on the deflection function of the cold-rolled strip, so as to better improve the mechanical mechanism of post-buckling of cold-rolled strip;

[0041] This embodiment takes the study of the post-buckling calculation model of cold-rolled strip with initial plate shape defects as the starting point, establishes the large deflection equilibrium equation and deformation coordination equation of cold-rolled strip with initial plate shape defects without considering the external force, and then studies the post-buckling calculation model of cold-rolled strip based on the large deflection equilibrium equation and deformation coordination equation of cold-rolled strip with initial plate shape defects, and solves it by expansion through the perturbation method and then comprehensively solves it according to the Hamilton method, and solves the general analytical model formula of post-buckling of cold-rolled strip under different boundary conditions, and at the same time, combines the on-site process data, compiles a simulation program, and simulates the strip, so as to better explain the mechanical mechanism of post-buckling of cold-rolled strip with initial plate shape defects;

[0042] In this embodiment, a post-buckling calculation method for a cold-rolled steel strip with an initial flatness defect is provided. Figure 1 As shown, the following steps are included:

[0043] Step 1: Collect the geometric size parameters and property parameters of the cold-rolled strip with initial plate shape defects at the production site;

[0044] The geometric dimension parameters of the cold-rolled steel strip include the length, width and thickness of the cold-rolled steel strip, and the property parameters of the cold-rolled steel strip include the density, Young's modulus, Poisson's ratio, yield strength and tangent modulus of the cold-rolled steel strip;

[0045] In this example, a local cold-rolled steel strip of linearly strengthened elastic-plastic material is selected for study. The geometric size parameters and property parameters of the local cold-rolled steel strip are as follows: the length of the cold-rolled steel strip is 100 mm, the width is 100 mm, the thickness is 2 mm, and the density is 7850 kg / m 3 , Young's modulus is 2.1×10 5 (MPa), Poisson's ratio is 0.3, yield strength is 215MPa, and tangent modulus is 610Mpa;

[0046] Step 2: Establish the large deflection equilibrium equation and deformation coordination equation of cold-rolled strip with initial defect terms inside, and form the post-buckling calculation model of cold-rolled strip with initial plate shape defect terms inside;

[0047] Step 2.1: According to the geometric equation, physical equation and equilibrium equation of the cold-rolled strip, a large deflection mechanical model of the cold-rolled strip is constructed, and then the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip are derived;

[0048] In this embodiment, Figure 2 is a schematic diagram of the three-dimensional coordinates of cold-rolled strip steel, where Indicates the length direction coordinate of the cold-rolled strip, Indicates the width direction coordinate of cold rolled strip, Indicates the thickness direction coordinate of cold rolled strip, lis the length of the cold-rolled strip, is the thickness of the cold rolled strip, is the width of the cold-rolled strip;

[0049] Different from the solution of the post-buckling process of cold-rolled steel in the prior art, this embodiment does not consider the external force applied to the cold-rolled strip, but only considers the stress distribution inside the cold-rolled strip. According to the geometric equation, physical equation and equilibrium equation of the cold-rolled strip, the following is constructed: Figure 3 The large deflection mechanical model of cold-rolled strip steel is shown, and the large deflection equilibrium equation and deformation coordination equation of cold-rolled strip steel are derived. Figure 3 middle, , For strip steel , The normal stress distribution in the direction, , For strip steel , Shear stress distribution between directions, , For strip steel , Direction of shear force, , For strip steel , Bending moment in direction, , For strip steel , Twist between directions, For external force, , Indicated in , A short distance in the direction , After, along , Bending moment in direction , changes, , Indicated in , A short distance in the direction , After, along , Shear force in direction , changes, , Indicated in , A short distance in the direction , After, along , Normal stress in the direction , changes, , Indicated in , A short distance in the direction , After, along , Direction , changes, , Indicated in , A short distance in the direction , After, along , Direction , changes;

[0050] The large deflection equilibrium equation of cold-rolled strip steel is shown in the following formula (1):

[0051] (1);

[0052] in, is the bending stiffness of cold-rolled strip per unit width, ; is the Young’s modulus of cold-rolled steel strip; is the thickness of cold-rolled strip; is Poisson's ratio; is the Laplace operator, ; is the internal stress function of cold-rolled strip; is the deflection of cold-rolled strip; is the length direction coordinate of the cold-rolled strip; is the width direction coordinate of the cold-rolled strip;

[0053] The deformation coordination equation of cold-rolled strip is shown in the following formula (2):

[0054] (2);

[0055] in, ;

[0056] Step 2.2: Add the initial defect term to the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip to obtain the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip with the initial plate shape defect term inside;

[0057] In order to study the post-buckling calculation of the cold-rolled strip with initial plate shape defects inside, an initial plate shape defect term is introduced into the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip obtained in step 2.1, and the large deflection equilibrium equation and deformation coordination equation with initial plate shape defect terms inside are obtained; this example takes the strip with edge wave defects initially as the research object, so the initial plate shape defect type in this embodiment is edge wave defect;

[0058] The large deflection equilibrium equation of cold-rolled strip steel with the initial plate defect term inside is shown in the following formula (3):

[0059] (3);

[0060] in, is the initial plate defect item;

[0061] The deformation coordination equation of cold-rolled strip with the initial plate shape defect term inside is shown in the following formula (4):

[0062] (4);

[0063] The large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip with the initial plate defect term are solved. Since it is very difficult to directly solve the above partial differential equations, the perturbation method and Hamiltonian method are combined to solve the post-buckling calculation model of the strip.

[0064] Step 3: Using the perturbation method and Hamiltonian method, the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip with the initial plate defect term are solved, and the general analytical model formula of post-buckling of the cold-rolled strip with the initial plate defect term is obtained;

[0065] Step 3.1: The deflection, stress function and internal stress of the cold-rolled strip are perturbation-developed using the perturbation method. The perturbation-development process is shown in the following formula (5):

[0066] (5);

[0067] in, Expand the parameters for the perturbation; is the zero-order deflection of the cold-rolled strip, is the first-order deflection of cold-rolled strip, is the second-order deflection of the cold-rolled strip; is the zero-order stress function of cold-rolled strip, is the first-order stress function of cold-rolled strip, is the second-order stress function of cold-rolled strip; is the internal stress of cold-rolled strip, is the critical internal residual stress for buckling of cold-rolled strip, is the first-order internal stress of the cold-rolled strip, is the second-order internal stress of the cold-rolled strip;

[0068] When the internal residual stress of the strip does not exceed the critical buckling stress, the strip buckles forward, and when the internal residual stress of the strip exceeds the critical buckling stress, the strip buckles backward. The critical residual internal stress is the dividing point between the pre-buckling and post-buckling.

[0069] Step 3.2: Combine step 2.2 with step 3.1, expand the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip with initial plate defect terms into control equations, obtain the post-buckling control equation of the cold-rolled strip with initial plate defect terms, and import it into the Hamiltonian system for solution, and obtain the general analytical model formula for post-buckling calculation of the cold-rolled strip with initial plate defect terms;

[0070] Perturb expansion parameters 0th power The coefficient of is set to 0, and the zero-order control equation of the cold-rolled strip with the initial defect term inside is obtained, as shown in the following formula (6):

[0071] (6);

[0072] Perturb expansion parameters 1st power The coefficient of is set to 0, and the first-order control equation of the cold-rolled strip with the initial defect term inside is obtained, as shown in the following formula (7):

[0073] (7);

[0074] in, is the amplitude of the initial shape defect of the cold-rolled strip, is the width of the cold-rolled strip;

[0075] The Hamiltonian is used to solve the first-order control equation of the cold-rolled strip with the initial defect term inside, and the first-order deflection control equation of the cold-rolled strip is obtained, as shown in the following formula (8): (8);

[0076] in, is the local longitudinal buckling of the strip i The order parameter is obtained according to the boundary conditions of the strip (the boundary is subject to simple support constraints, fixed support constraints or free edges). In this embodiment, the strip boundary of the edge wave defect is SfSS / SfSC, and the strip boundary of the middle wave defect is SSSS / SSSC / SSCS, where S means that the boundary is subject to simple support constraints. indicates that the boundary is subject to fixed support constraints. Indicates that the boundary is a free edge; is the modal order of strip buckling, and the first-order governing equation is Take 1; is the length of the strip;

[0077] Perturb expansion parameters The power of 2 The coefficient of is set to 0, and the second-order control equation of the cold-rolled strip with the initial defect term inside is obtained, as shown in the following formula (9): (9);

[0078] Combining formula (9) and formula (8), and using Mathmatica software to sort out, the post-buckling control equation of cold-rolled strip with initial plate shape defects is obtained, as shown in the following formula (10):

[0079] (10);

[0080] in, is the local longitudinal buckling of the strip j The order parameters need to be solved according to the actual boundary conditions; , is a non-zero eigenvalue, ;

[0081] Formula (10) is introduced into the Hamiltonian system and solved to obtain the general analytical model formula for post-buckling calculation of cold-rolled strip with initial plate shape defects, as shown in the following formula (11):

[0082] (11);

[0083] in, , These are all parameters to be fitted, and their specific values ​​are solved according to the different boundary conditions to which the cold-rolled strip is subjected; They represent the first i The first mode and j In this embodiment, i , j Take 1, 2, 3, 4;

[0084] Based on the Hamiltonian method and the perturbation method, the whole process model of post-buckling of strip steel with initial plate shape defects inside was solved. After rigorous derivation, different from the previous assumptions on the buckling deflection function, the general analytical model formula of post-buckling of cold-rolled strip steel was obtained.

[0085] This embodiment also establishes a finite element simulation model for post-buckling of cold-rolled strip steel and verifies the analytical numerical results obtained by the general analytical model formula.

[0086] In this embodiment, according to the general analytical model formula derived in step 3, boundary conditions are set with the strip steel initially having edge wave defects, and a finite element simulation model of the cold-rolled strip steel is established to perform model verification.

[0087] In this embodiment, the analysis steps Buckle and Static Riks of the Abaqus software are performed, and the post-buckling model results obtained by the general analytical model formula in step 3 are used as the initial defects of the cold-rolled strip stretch bending and straightening process. The embedded sigin program is used to perform a three-dimensional stretch bending and straightening finite element simulation of the cold-rolled strip. The strip material is selected as a linear strengthening elastic-plastic material with a density of , elastic modulus is 2.1×105 (MPa), Poisson's ratio is 0.3, yield strength is 215 (MPa), tangent modulus is 610 (MPa);

[0088] Figure 4 The stress changes of the post-buckling equilibrium path of the strip in the finite element simulation results and the analytical results in this embodiment are shown. It can be seen that the critical buckling stress of the strip is 25.6 (MPa), after which the post-buckling path of the strip changes. In addition, the simulation results and the finite element results are within the allowable error range, indicating the accuracy of the results and verifying the effectiveness of the calculation method of the present invention.

[0089] The calculation method for solving the post-buckling of cold-rolled strip with initial plate shape defects established in this embodiment solves the post-buckling model of the strip based on the Hamilton method and the perturbation method, so as to better explain the mechanical behavior of the post-buckling of the cold-rolled strip from a mechanical point of view, and obtain the post-buckling formula of the strip through rigorous derivation without making any assumptions about the buckling deflection function of the strip, so as to better improve the mechanical mechanism of post-buckling of cold-rolled strip with initial plate shape defects, improve the quality of the plate, and eliminate the defects of the plate.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A method for calculating post-buckling of cold-rolled steel strip with initial flatness defects, characterized in that: The following steps are involved: Step 1: Collect geometric dimension parameters and property parameters of cold-rolled steel strip with initial plate shape defects at the production site; Step 2: Establish the large deflection equilibrium equation and deformation coordination equation of cold-rolled strip with initial defect terms inside, and construct the post-buckling calculation model of cold-rolled strip with initial plate shape defect terms inside; Step 2.1: A large deflection mechanical model of cold-rolled strip is constructed according to the geometric equation, physical equation and equilibrium equation of cold-rolled strip, and then the large deflection equilibrium equation and deformation coordination equation of cold-rolled strip are derived; The large deflection equilibrium equation of cold-rolled strip steel is shown in the following formula: ;in, is the bending stiffness of cold-rolled strip per unit width, ; is the Young’s modulus of cold-rolled steel strip; is the thickness of cold-rolled strip; is Poisson’s ratio; is the Laplace operator, ; is the internal stress function of cold-rolled strip; is the deflection of cold-rolled strip; is the length direction coordinate of the cold-rolled strip; is the width direction coordinate of the cold-rolled strip; The deformation coordination equation of cold rolled strip is shown in the following formula: ;in, ; Step 2.2: Add the initial defect term to the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip to obtain the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip with the initial plate shape defect term inside; The large deflection equilibrium equation of cold-rolled strip steel with the initial plate defect term inside is as follows: ;in, is the initial plate defect item; The deformation coordination equation of cold-rolled strip with initial plate shape defect term inside is as follows: ； Step 3: Use the perturbation method and Hamilton method to solve the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip with the initial plate defect term inside, and obtain the general analytical model formula for the post-buckling of the cold-rolled strip with the initial plate defect term inside.

2. The post-buckling calculation method for cold-rolled steel strip with initial flatness defects according to claim 1, characterized in that: The geometric dimension parameters of the cold-rolled steel strip include the length, width and thickness of the cold-rolled steel strip, and the property parameters of the cold-rolled steel strip include the density, Young's modulus, Poisson's ratio, yield strength and tangent modulus of the cold-rolled steel strip.

3. The post-buckling calculation method for cold-rolled steel strip with initial flatness defects according to claim 2, characterized in that: The specific method of step 3 is: Step 3.1: Use the perturbation method to perform perturbation expansion on the deflection, stress function and internal stress of the cold-rolled strip; Step 3.2: Combine step 2.2 with step 3.1, expand the large deflection equilibrium equation and deformation coordination equation of the cold-rolled strip with initial plate shape defects into control equations, obtain the post-buckling control equation of the cold-rolled strip with initial plate shape defects and import it into the Hamiltonian system for solution, and obtain the general analytical model formula for post-buckling calculation of the cold-rolled strip with initial plate shape defects.

4. The post-buckling calculation method for cold-rolled steel strip with initial flatness defects according to claim 3, characterized in that: The perturbation expansion process in step 3.1 is shown in the following formula: , , ;in, Expand the parameters for the perturbation; is the zero-order deflection of the cold-rolled strip, is the first-order deflection of cold-rolled strip, is the second-order deflection of the cold-rolled strip; is the zero-order stress function of cold-rolled strip, is the first-order stress function of cold-rolled strip, is the second-order stress function of cold-rolled strip; is the internal stress of cold-rolled strip, is the critical internal residual stress for buckling of cold-rolled strip, is the first-order internal stress of the cold-rolled strip, is the second-order internal stress of cold-rolled strip.

5. The post-buckling calculation method for cold-rolled steel strip with initial flatness defects according to claim 4, characterized in that: The specific method of step 3.2 is: Perturb expansion parameters 0th power The coefficient of is set to 0, and the zero-order control equation of the cold-rolled strip with the initial defect term inside is obtained, as shown in the following formula: ； Perturb expansion parameters 1st power The coefficient of is set to 0, and the first-order control equation of the cold-rolled strip with the initial defect term inside is obtained, as shown in the following formula: ;in, is the amplitude of the initial shape defect of the cold-rolled strip, is the width of the cold-rolled strip; Hamiltonian is used to solve the first-order control equation of the cold-rolled strip with the initial defect term inside, and the first-order deflection control equation of the cold-rolled strip is obtained, as shown in the following formula: ;in, is the local longitudinal buckling of the strip i Order parameter; is the modal order of strip buckling, and the first-order governing equation is Take 1; is the length of the strip; Perturb expansion parameters The power of 2 The coefficient of is set to 0, and the second-order control equation of the cold-rolled strip with the initial defect term inside is obtained, as shown in the following formula: ; Combining the second-order control equation of the cold-rolled strip with the initial defect term and the first-order deflection control equation of the cold-rolled strip, the post-buckling control equation of the cold-rolled strip with the initial plate shape defect is obtained, as shown in the following formula: ;in, is the local longitudinal buckling of the strip j Order parameter; , is a non-zero eigenvalue, ; The post-buckling control equation of cold-rolled strip with initial flatness defects is introduced into the Hamiltonian system and solved to obtain the general analytical model formula for post-buckling calculation of cold-rolled strip with initial flatness defects, as shown in the following formula: ； in, These are all parameters to be fitted, and their specific values ​​are solved according to the different boundary conditions to which the cold-rolled strip is subjected; They represent the first i The first mode and j Order mode.

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