A method and system for calculating longitudinal uneven deformation in corrugated steel plate support structures

Abstract

This invention proposes a method and system for calculating longitudinal uneven deformation of corrugated steel plate support structures, belonging to the field of transportation infrastructure structural design technology. The method includes: constructing an orthotropic equivalent stiffness model of the corrugated steel plate, treating the corrugated steel plate support structure as an equivalent Timoshenko beam, and calculating the equivalent section bending stiffness and equivalent section shear stiffness; constructing a calculation model for longitudinal uneven deformation, determining the longitudinal differential load distribution based on the actual soil cover conditions and soil arching effect above the corrugated steel plate support structure; and calculating the longitudinal differential load distribution based on the longitudinal uneven deformation calculation model to obtain the longitudinal uneven deformation of the corrugated steel plate support structure. This invention enables effective and rapid assessment of the longitudinal uneven deformation of shallow-buried corrugated steel plate support structures.

Description

Technical Field

[0001] This invention belongs to the field of structural design technology for transportation infrastructure, and particularly relates to a method and system for calculating longitudinal uneven deformation of corrugated steel plate support structures. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Corrugated steel plate support structures, due to their outstanding advantages such as lightweight, high strength, adaptability to large deformations, and ease of construction, have been widely used in the support structures of transportation infrastructure such as culverts, bridges, tunnels, and sheds. Compared with traditional concrete support structures, their material usage is only 1 / 25 to 1 / 30 of that of concrete, and their weight is about 1 / 200 to 1 / 300 of concrete. Furthermore, they can better utilize the self-supporting capacity of the surrounding rock, showing significant application prospects in complex geological conditions such as shallowly buried weak surrounding rock and fault crossings.

[0004] In practical engineering, shallow-buried corrugated steel plate support structures often face longitudinally uneven loads, such as abrupt changes in geological conditions, tunnel excavation disturbances, fault displacement, and local overloading. These loads easily induce longitudinally uneven settlement and deformation of the structure. Corrugated steel plates have low longitudinal torsional stiffness and complex deformation modes. Excessive uneven deformation can not only lead to buckling and weld cracking damage to the structure itself, but may also trigger a chain reaction of instability of the support system, subsidence of the surrounding roadbed, and failure of traffic facilities, seriously threatening the operational safety of infrastructure and causing economic losses.

[0005] However, due to the longitudinal corrugated structure of corrugated steel plates, their mechanical properties exhibit significant anisotropy. The structure primarily achieves soil-structure interaction and bearing capacity with the surrounding soil through cross-sectional (lateral) deformation coordination. Therefore, existing research mostly focuses on the stress mechanism, bearing characteristics, and design methods of the cross-section, failing to analyze the longitudinal mechanical response of the structure. Consequently, the analysis of the safety and stability of the support structure system lacks real-time performance and reliability. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, the present invention provides a method and system for calculating longitudinal uneven deformation of corrugated steel plate support structures, which can effectively and quickly assess the longitudinal uneven deformation of shallow-buried corrugated steel plate support structures.

[0007] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0008] The first aspect of the present invention provides a method for calculating longitudinal non-uniform deformation of corrugated steel plate support structures.

[0009] Methods for calculating longitudinal uneven deformation in corrugated steel plate support structures include:

[0010] An orthotropic equivalent stiffness model of a corrugated steel plate is constructed to obtain the equivalent stiffness parameters of the corrugated steel plate in the corrugation direction, the perpendicular direction, and the out-of-plane direction; wherein, the equivalent stiffness parameters include equivalent tensile stiffness, equivalent bending stiffness, and equivalent shear stiffness.

[0011] Based on the obtained equivalent stiffness parameters, the corrugated steel plate support structure is equivalent to a Timoshenko beam, and its equivalent section bending stiffness and equivalent section shear stiffness are calculated.

[0012] Based on Pasternak's two-parameter foundation model and Timoshenko's beam theory, the equilibrium differential equation of the corrugated steel plate support structure under longitudinal load is established, and the finite difference method is used for discretization to construct a calculation model for longitudinal non-uniform deformation.

[0013] Based on the actual soil cover conditions and soil arching effect above the corrugated steel plate support structure, the longitudinal differential load distribution acting on the corrugated steel plate support structure is determined.

[0014] The longitudinal differential load distribution is substituted into the calculation model of longitudinal non-uniform deformation for analysis, and the longitudinal non-uniform deformation of the corrugated steel plate support structure is obtained through numerical calculation.

[0015] Furthermore, the construction of the orthotropic equivalent stiffness model includes: equipping a corrugated periodic element of the corrugated steel plate with an orthotropic plate element in terms of mechanical behavior, and solving for the equivalent tensile stiffness, equivalent bending stiffness, and equivalent shear stiffness of the corrugated steel plate in the global coordinate system based on the principle of force equivalence and the principle of strain energy equivalence.

[0016] Furthermore, the calculation of the equivalent section bending stiffness and equivalent section shear stiffness includes: solving the integral term according to the section shape, and combining the bending and shear stiffness correction coefficients affected by the section shape deformation, obtaining the equivalent section stiffness of the Timoshenko beam through elasticity theory and the law of conservation of energy.

[0017] Furthermore, the construction of the equilibrium differential equation includes: placing the equivalent Timoshenko beam on the Pasternak foundation, establishing a coupled equilibrium equation for vertical deformation and rotation based on the principles of mechanics of materials and Timoshenko beam theory, and obtaining a fourth-order differential equation only concerning vertical deformation after decoupling.

[0018] Furthermore, the foundation reaction coefficient and stratum shear coefficient in the Pasternak foundation model were determined using the Vlasov method.

[0019] Furthermore, the determination of the longitudinal differential load distribution includes: calculating the soil pressure load distributed along the longitudinal direction based on the changes in soil cover height and structural cross-sectional dimensions, combined with the load reduction effect of the soil arching effect.

[0020] Furthermore, the soil arching coefficient, which reduces the load in the soil arching effect, is determined based on the ratio of the soil cover height to the structural span, and in conjunction with design standards.

[0021] A second aspect of the present invention provides a calculation system for longitudinal non-uniform deformation of corrugated steel plate support structures.

[0022] A system for calculating longitudinal non-uniform deformation in corrugated steel plate support structures includes:

[0023] The orthotropic equivalent stiffness calculation module is configured to: construct an orthotropic equivalent stiffness model of the corrugated steel plate, and obtain the equivalent stiffness parameters of the corrugated steel plate in the corrugation direction, the perpendicular direction and the out-of-plane direction; wherein, the equivalent stiffness parameters include equivalent tensile stiffness, equivalent bending stiffness and equivalent shear stiffness;

[0024] The equivalent section stiffness calculation module is configured to: based on the obtained equivalent stiffness parameters, convert the corrugated steel plate support structure into a Timoshenko beam, and calculate its equivalent section bending stiffness and equivalent section shear stiffness.

[0025] The module for constructing the longitudinal non-uniform deformation calculation model is configured to: establish the equilibrium differential equation of the corrugated steel plate support structure under longitudinal load based on the Pasternak two-parameter foundation model and Timoshenko beam theory, and use the finite difference method for discretization to construct the calculation model of longitudinal non-uniform deformation.

[0026] The longitudinal differential load distribution calculation module is configured to: determine the longitudinal differential load distribution acting on the corrugated steel plate support structure based on the actual soil cover conditions and soil arching effect above the corrugated steel plate support structure.

[0027] The longitudinal uneven deformation calculation module is configured to: substitute the longitudinal differential load distribution into the longitudinal uneven deformation calculation model for analysis, and obtain the longitudinal uneven deformation of the corrugated steel plate support structure through numerical calculation.

[0028] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps in the method for calculating longitudinal non-uniform deformation of a corrugated steel plate support structure as described in the first aspect of the present invention.

[0029] The fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the longitudinal non-uniform deformation calculation method for corrugated steel plate support structures as described in the first aspect of the present invention.

[0030] The above one or more technical solutions have the following beneficial effects:

[0031] This invention constructs an orthotropic equivalent stiffness model for corrugated steel plates, equating the corrugated steel plate support structure to a Timoshenko beam, and calculates the equivalent section bending stiffness and equivalent section shear stiffness. By constructing a calculation model for longitudinal uneven deformation, the longitudinal differential load distribution is determined based on the actual soil cover conditions and soil arching effect above the corrugated steel plate support structure. Based on the longitudinal uneven deformation calculation model, the longitudinal differential load distribution is calculated to obtain the longitudinal uneven deformation of the corrugated steel plate support structure. Therefore, this invention overcomes the limitations of existing theoretical calculations of longitudinal uneven deformation in shallow-buried corrugated steel plate support structures, providing industry professionals with a reliable method for quickly determining the longitudinal uneven deformation of shallow-buried corrugated steel plate support structures to guide engineering design, thereby timely and effectively preventing structural collapse caused by excessive longitudinal uneven deformation of shallow-buried corrugated steel plate support structures.

[0032] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0033] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0034] Figure 1 This is a flowchart of the longitudinal uneven deformation calculation method for corrugated steel plate support structure in Embodiment 1 of the present invention.

[0035] Figure 2 This is a schematic diagram of the corrugated steel plate cross-sectional parameters defined in Embodiment 1 of the present invention.

[0036] Figure 3 This is a schematic diagram illustrating how a corrugated steel plate is equivalent to an orthotropic plate in Embodiment 1 of the present invention.

[0037] Figure 4 This is a schematic diagram illustrating the dimensional parameters of the circular cross-section corrugated steel plate support structure as defined in Embodiment 1 of the present invention.

[0038] Figure 5This is a schematic diagram illustrating the dimensional parameters of the corrugated steel plate support structure with a pipe arch cross-section as defined in Embodiment 1 of the present invention.

[0039] Figure 6 This is a schematic diagram of the theoretical calculation model of the corrugated steel plate support structure placed on the Pasternak foundation in Embodiment 1 of the present invention.

[0040] Figure 7 This is a schematic diagram of the finite difference discretization of the corrugated steel plate support structure in Embodiment 1 of the present invention.

[0041] Figure 8 This is a schematic diagram of some geometric parameters of the circular cross-section corrugated steel plate support structure in Embodiment 1 of the present invention.

[0042] Figure 9 This is a comparison chart showing the results of the calculation method of this invention and the solution obtained by finite element software under the circular cross-section corrugated steel plate support structure in Embodiment 1 of this invention.

[0043] Figure 10 This is a schematic diagram of some geometric parameters of the corrugated steel plate support structure with a tube arch cross section in Embodiment 1 of the present invention.

[0044] Figure 11 This is a comparison chart showing the results of the calculation method of this invention and the solution obtained by finite element software under the tube arch cross-section corrugated steel plate support structure in Embodiment 1 of this invention. Detailed Implementation

[0045] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0046] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0047] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0048] Example 1

[0049] This embodiment discloses a method for calculating longitudinal uneven deformation of corrugated steel plate support structures.

[0050] like Figure 1 As shown, the calculation method for longitudinal uneven deformation of corrugated steel plate support structures includes:

[0051] Step S1: Construct an orthotropic equivalent stiffness model of the corrugated steel plate and obtain the equivalent stiffness parameters of the corrugated steel plate in the corrugation direction, the perpendicular direction and the out-of-plane direction; wherein, the equivalent stiffness parameters include equivalent tensile stiffness, equivalent bending stiffness and equivalent shear stiffness.

[0052] Step S2: Based on the obtained equivalent stiffness parameters, the corrugated steel plate support structure is equivalent to a Timoshenko beam, and its equivalent section bending stiffness and equivalent section shear stiffness are calculated.

[0053] Step S3: Based on the Pasternak two-parameter foundation model and Timoshenko beam theory, establish the equilibrium differential equation of the corrugated steel plate support structure under longitudinal load, and use the finite difference method for discretization to construct a calculation model for longitudinal non-uniform deformation.

[0054] Step S4: Determine the longitudinal differential load distribution acting on the corrugated steel plate support structure based on the actual soil cover conditions and soil arching effect above the corrugated steel plate support structure.

[0055] Step S5: Substitute the longitudinal differential load distribution into the calculation model of longitudinal uneven deformation for analysis, and obtain the longitudinal uneven deformation of the corrugated steel plate support structure through numerical calculation.

[0056] Based on the above process, this invention can achieve effective and rapid assessment of longitudinal uneven deformation in shallow-buried corrugated steel plate support structures. To facilitate understanding of the technical solution of this invention, the specific implementation methods of this invention will be further explained and described below.

[0057] In step S1, an orthotropic equivalent stiffness model of the corrugated steel plate is constructed to obtain the equivalent stiffness parameters of the corrugated steel plate in the corrugation direction, the vertical direction, and the out-of-plane direction.

[0058] like Figure 2 As shown, the corrugated steel plate is composed of a combination of circular arc segments and straight line segments, with the dividing point being the tangent point between the straight line segment and the circular arc segment. Based on this, the following parameters are used: Indicates the angle of inclination of a straight line segment. Indicates the length of a straight line segment, Indicates the inner radius of the arc segment, Indicates the radius corresponding to the axis of the arc segment. Indicates half the wavelength. Indicates half the wave height. This represents half the length of a single periodic ripple. This indicates the plate thickness. Meanwhile, corrugated steel plates can be considered orthotropic plates, with the corrugation direction of the corrugated steel plate as... The direction, perpendicular to the ripples, is The direction of the corrugated steel plate is the out-of-plane direction. The direction, the elastic modulus of corrugated steel plate is expressed as Poisson's ratio is expressed as .

[0059] like Figure 3 As shown, corrugated steel plates can be viewed in the global coordinate system. The lower equivalent is an orthotropic plate. Therefore, according to the basic theory of elasticity, the corrugated steel plate in the global coordinate system... The constitutive equation below can be expressed as:

[0060] ;

[0061] In the formula, , , They are respectively x direction, y direction, xy directional force component, , , They are respectively x direction, y direction, xy The bending moment component in the direction; , They are respectively x direction, y The transverse shear force component in the direction of the shear force. , , They are respectively x direction, y direction, xy Strain components in the direction, , , They are respectively x direction, y direction, xy Curvature components in the direction; , They are respectively xz direction, yz The transverse shear strain component in the direction. , , , , All are equivalent tensile stiffness coefficients corresponding to the force and strain components, where, This is the in-plane longitudinal stiffness coefficient. and These are the first and second Poisson coupling stiffness coefficients in the plane, respectively. This is the in-plane lateral stiffness coefficient. This is the in-plane shear stiffness coefficient. , , , , All are equivalent bending stiffness coefficients corresponding to the bending moment component and the curvature component, where, This is the longitudinal bending stiffness coefficient. and These are the first and second bending Poisson coupling stiffness coefficients, respectively. This is the transverse bending stiffness coefficient. This is the torsional stiffness coefficient. , All are equivalent shear stiffness coefficients corresponding to the transverse shear force component and the transverse shear strain component, where, for x Transverse shear stiffness coefficient for y Transverse shear stiffness coefficient.

[0062] Take a corrugated steel plate unit ( Take one cycle in the direction. (Taking the direction as a unit width), its stress behavior is compared with that of the corresponding element of the orthotropic plate. Using the principles of equivalence of stress, equivalence of strain energy, and the law of conservation of energy, the equivalent stiffness coefficient of the corrugated steel plate is solved.

[0063] ;

[0064] Furthermore, the various parameters in the above formula can be obtained in the following ways:

[0065] 1) Tensile stiffness parameters of flat steel plate , , , , Obtained through the following methods:

[0066] ;

[0067] 2) Bending stiffness parameters of flat steel plates , , , , Obtained through the following methods:

[0068] ;

[0069] 3) Shear stiffness parameters of flat steel plates , Obtained through the following methods:

[0070] ;

[0071] 4) Integral coefficient , , Obtained through the following methods:

[0072] ;

[0073] ;

[0074] ;

[0075] 5) Stiffness coefficient It is the stiffness coefficient generated when solving the relationship between internal forces and deformation of corrugated steel plate elements according to Castiglione's theorem, and can be obtained in the following ways:

[0076] ;

[0077] in, , , , , , The compliance coefficient, generated when solving the relationship between internal forces and deformation of a corrugated steel plate element according to Castiglione's theorem, reflects the flexibility characteristics of the corrugated steel plate element. The calculation method is as follows:

[0078] ;

[0079] The integral term in the above formula is solved in the following way:

[0080] ;

[0081] ;

[0082] ;

[0083] ;

[0084] ;

[0085] ;

[0086] ;

[0087] ;

[0088] After solving the above integral formula, substitute it into the solution above. , , , , , Wait, calculate these parameters, and then solve for the result. .

[0089] In step S2, based on the obtained equivalent stiffness parameters, the corrugated steel plate support structure is equivalent to a Timoshenko beam, and its equivalent section bending stiffness and equivalent section shear stiffness are calculated.

[0090] The corrugated steel plate support structure is equivalent to a Timoshenko beam, and the equivalent flexural stiffness and equivalent shear stiffness of the Timoshenko beam are obtained through the basic theory of elasticity and the law of conservation of energy:

[0091] ;

[0092] ;

[0093] in, Indicates the equivalent cross-sectional bending stiffness. Indicates the shear stiffness of the equivalent cross section; This represents the bending stiffness correction factor considering cross-sectional shape deformation, with a value of 0.885; This represents the shear stiffness correction factor considering cross-sectional shape deformation, with a value of 0.833. This represents the Poisson's ratio determined based on the equivalent tensile stiffness. This represents the Poisson's ratio determined based on the equivalent bending stiffness. , This represents the integral term in the solution process for the flexural stiffness of the equivalent cross section. For a circular cross section, it is represented as... , For a tubular arch cross-section, it is represented as , ; , This represents the integral term in the solution process for the shear stiffness of the equivalent cross section. For a circular cross section, it is expressed as: , For a tubular arch cross-section, it is represented as , .

[0094] stiffness coefficient in the formula , , , , , The solution is obtained through step S2, and the coefficients are... and The calculation is performed using the following formula:

[0095] ;

[0096] ;

[0097] Integral term in the formula , , , Then it is necessary to solve based on the cross-sectional shape, for example... Figure 4 The radius shown is For a circular cross-section, the integral term is calculated as follows:

[0098] ;

[0099] ;

[0100] ;

[0101] ;

[0102] For example Figure 5 The illustrated tubular arch cross-section shows that the arch axis is composed of three circular arcs of different radii, with the dividing point being the tangent point of two adjacent arcs. , and These represent the radii of the arcs at the positions of the invert, the axle, and the crown, respectively. α, β, γ These represent the angle ranges of the invert section, the axle section, and the crown section, respectively. S , H These are the cross-sectional span and height, respectively. The distance from the center of the arc at the axle position to the bottom of the structure is the height. The distance from the centerline of the cross-section to the bottom of the structure is [height / value]. and These represent the heights of the two dividing points (tangent points) of the three circular arcs from the bottom of the structure. β 1 、β 2 represents the arc angle (angle with the vertical) corresponding to the boundary point between the arc at the axle position and the other two arc segments. Based on this, the integral term calculation method for the tubular arch cross-section is as follows:

[0103] ;

[0104] ;

[0105] ;

[0106] .

[0107] In step S3, based on the Pasternak two-parameter foundation model and Timoshenko beam theory, the equilibrium differential equation of the corrugated steel plate support structure under longitudinal load is established, and the finite difference method is used for discretization to construct a calculation model for longitudinal non-uniform deformation.

[0108] like Figure 6 As shown, the equivalent Timoshenko beam of the corrugated steel plate structure is placed on the Pasternak two-parameter foundation. A micro-element is taken along the longitudinal direction of the structure for force equilibrium analysis. Based on the basic principles of mechanics of materials and Timoshenko beam theory, the external loads are obtained. The Timoshenko beam on the Pasternak foundation under action regarding vertical deformation and corner The equilibrium differential equation is expressed as:

[0109] ;

[0110] Among them, coefficient k and Let V represent the foundation reaction coefficient and the formation shear coefficient of the Pasternak two-parameter foundation model, respectively, which are determined using the Vlasov method. k and The expression is:

[0111] ;

[0112] ;

[0113] in, and These are the elastic modulus and Poisson's ratio of the foundation, respectively. The thickness of the subgrade. By simultaneously solving and decoupling the two equilibrium differential equations, the vertical deformation can be obtained. The expression is:

[0114] ;

[0115] Vertical deformation The expression is a fourth-order differential equation, which is solved discretly using the finite difference method for the corrugated steel plate support structure, such as... Figure 7 As shown, substituting the boundary conditions at both ends, we obtain the formula for calculating the longitudinal uneven settlement of the corrugated steel plate support structure:

[0116] ;

[0117] in, Here is the displacement stiffness matrix. Here is the shear stiffness matrix. Here is the bending stiffness matrix; This is the vertical deformation vector; For the first load column vector, For the second load column vector, This is the third load column vector.

[0118] Furthermore, some of the parameters designed in the formula can be calculated using the following methods:

[0119] 1) Vertical deformation vector to be solved The expression is as follows:

[0120] ;

[0121] 2) Stiffness matrix , , The expression is as follows:

[0122] ;

[0123] ;

[0124] ;

[0125] in, A 1. A 2. A 3. B To calculate the process coefficients, the following method can be used:

[0126] ;

[0127] ;

[0128] ;

[0129] ;

[0130] 3) Load vector , , The expression is as follows:

[0131] ;

[0132] ;

[0133] ;

[0134] in, C 1. C 2. C 3. C 4 represents the coefficients used in the calculation process, which can be solved using the following methods:

[0135] ;

[0136] ;

[0137] ;

[0138] .

[0139] In step S4, the longitudinal differential load distribution acting on the support structure is determined based on the actual soil cover conditions and soil arching effect above the corrugated steel plate support structure.

[0140] Based on the actual soil cover above the corrugated steel plate support structure and considering the soil-knot interaction caused by the flexibility of the corrugated steel plate, the longitudinal load acting on the structure is determined. As an optional embodiment, longitudinal load The calculation formula is:

[0141] ;

[0142] in, The weight of the soil column directly above the structure within the width of the arch line per unit length; is the soil arching coefficient, which is related to the soil cover height and structural dimensions; S is the cross-sectional span of the corrugated steel plate support structure.

[0143] Will Discretization allows us to determine the load column vector. , , .

[0144] In step S5, the longitudinal differential load distribution is substituted into the established calculation model of longitudinal uneven deformation for analysis, and the longitudinal uneven deformation of the corrugated steel plate support structure is obtained through numerical calculation.

[0145] To further verify the significant advancements of this invention, the following comparative experiment was conducted in this embodiment:

[0146] Experiment 1: The problem of longitudinal uneven deformation in a corrugated steel plate support structure caused by uneven soil cover, with geometric parameters as follows. Figure 8As shown, the length of the corrugated steel plate support structure is 89870mm, the height is 5500mm, the width of the top surface of the soil cover is 30360mm, the height of the soil cover slope is 11665mm, and the width of the soil cover slope is 20221mm. The cross-sectional parameters of the corrugated steel plate in this embodiment are: α = 47.3°, lt = 25.5mm, r = 53mm, R = 56.25mm, c = 100mm, f = 27.5mm, l = 118.37mm, t = 6.5mm; the elastic modulus of the corrugated steel plate in this embodiment is E = 206000MPa, and the Poisson's ratio is ν = 0.3; the cross-sectional shape of the corrugated steel plate support structure in this embodiment is circular, with specific parameters as follows: = 5500mm.

[0147] The method of this invention is used to solve the longitudinal non-uniform deformation of the corrugated steel plate support structure under non-uniform soil load, such as... Figure 9 As shown. To verify the accuracy of the calculation results, ABAQUS finite element software was used to perform refined simulation calculations on the corrugated steel plate support structure in this embodiment. The obtained calculation results are consistent with those obtained in this invention. Figure 9 The results were compared with those of the simulation results; it can be seen that the calculation results of the present invention are in high agreement with the simulation results, which verifies the accuracy of the calculation method of the present invention.

[0148] Experiment 2: Another problem of uneven longitudinal deformation of corrugated steel plate support structure caused by uneven soil cover, with geometric parameters as follows: Figure 10 As shown, the length of the corrugated steel plate support structure is 38000mm, the height is 7490mm, the width of the top surface of the soil cover is 25750mm, the height of the soil cover slope is 3975mm, and the width of the soil cover slope is 6125mm. The cross-sectional parameters of the corrugated steel plate in this embodiment are: α = 51.1°, lt = 102.07mm, r = 76.2mm, R = 81.2mm, c = 190.5mm, f = 70mm, l = 246.91mm, t = 10mm; the elastic modulus of the corrugated steel plate in this embodiment is E = 206000MPa, and the Poisson's ratio is ν = 0.3; the cross-sectional shape of the corrugated steel plate support structure in this embodiment is a tubular arch shape, with specific parameters as follows: = 9650mm = 1660mm = 5140mm, S = 10277.56mm, H = 7505mm, B = 2457.07mm, = 3503.55mm = 962.67mm = 2500.99mm.

[0149] The method of this invention is used to solve the longitudinal non-uniform deformation of the corrugated steel plate support structure under non-uniform soil load, such as... Figure 11 As shown. To verify the accuracy of the calculation results, ABAQUS finite element software was used to perform refined simulation calculations on the corrugated steel plate support structure in this embodiment. The obtained calculation results are consistent with those obtained in this invention. Figure 11 The results were compared with those of the simulation results; it can be seen that the calculation results of the present invention are in high agreement with the simulation results, which verifies the accuracy of the calculation method of the present invention.

[0150] Example 2

[0151] This embodiment discloses a longitudinal non-uniform deformation calculation system for corrugated steel plate support structures.

[0152] A system for calculating longitudinal non-uniform deformation in corrugated steel plate support structures includes:

[0153] The orthotropic equivalent stiffness calculation module is configured to: construct an orthotropic equivalent stiffness model of the corrugated steel plate, and obtain the equivalent stiffness parameters of the corrugated steel plate in the corrugation direction, the perpendicular direction and the out-of-plane direction; wherein, the equivalent stiffness parameters include equivalent tensile stiffness, equivalent bending stiffness and equivalent shear stiffness;

[0154] The equivalent section stiffness calculation module is configured to: based on the obtained equivalent stiffness parameters, convert the corrugated steel plate support structure into a Timoshenko beam, and calculate its equivalent section bending stiffness and equivalent section shear stiffness.

[0155] The module for constructing the longitudinal non-uniform deformation calculation model is configured to: establish the equilibrium differential equation of the corrugated steel plate support structure under longitudinal load based on the Pasternak two-parameter foundation model and Timoshenko beam theory, and use the finite difference method for discretization to construct the calculation model of longitudinal non-uniform deformation.

[0156] The longitudinal differential load distribution calculation module is configured to: determine the longitudinal differential load distribution acting on the corrugated steel plate support structure based on the actual soil cover conditions and soil arching effect above the corrugated steel plate support structure.

[0157] The longitudinal uneven deformation calculation module is configured to: substitute the longitudinal differential load distribution into the longitudinal uneven deformation calculation model for analysis, and obtain the longitudinal uneven deformation of the corrugated steel plate support structure through numerical calculation.

[0158] Example 3

[0159] The purpose of this embodiment is to provide a computer-readable storage medium.

[0160] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the longitudinal non-uniform deformation calculation method for corrugated steel plate support structures as described in Embodiment 1 of this disclosure.

[0161] Example 4

[0162] The purpose of this embodiment is to provide an electronic device.

[0163] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the longitudinal non-uniform deformation calculation method for corrugated steel plate support structures as described in Embodiment 1 of this disclosure.

[0164] The steps and methods involved in the apparatuses of Embodiments 2, 3, and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0165] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0166] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for calculating longitudinal uneven deformation of corrugated steel plate support structures, characterized in that, include: An orthotropic equivalent stiffness model of a corrugated steel plate is constructed to obtain the equivalent stiffness parameters of the corrugated steel plate in the corrugation direction, perpendicular direction, and out-of-plane direction. The equivalent stiffness parameters include equivalent tensile stiffness, equivalent bending stiffness, and equivalent shear stiffness. The construction of the orthotropic equivalent stiffness model includes: equipping a corrugated periodic element of the corrugated steel plate with an orthotropic plate element in terms of mechanical behavior, and solving for the equivalent tensile stiffness, equivalent bending stiffness, and equivalent shear stiffness of the corrugated steel plate in the global coordinate system based on the principles of force equivalence and strain energy equivalence. Based on the obtained equivalent stiffness parameters, the corrugated steel plate support structure is equivalent to a Timoshenko beam, and its equivalent sectional bending stiffness and equivalent sectional shear stiffness are calculated. The calculation of the equivalent sectional bending stiffness and equivalent sectional shear stiffness includes: solving for the integral term based on the cross-sectional shape, and combining the bending and shear stiffness correction coefficients affected by cross-sectional shape deformation, obtaining the equivalent sectional bending stiffness and equivalent sectional shear stiffness of the Timoshenko beam through elasticity theory and the law of conservation of energy. ； ； in, Indicates the equivalent cross-sectional bending stiffness. Indicates the shear stiffness of the equivalent cross section; This represents the bending stiffness correction factor that takes into account cross-sectional shape deformation. This represents the shear stiffness correction factor that takes into account cross-sectional shape deformation; This represents the Poisson's ratio determined based on the equivalent tensile stiffness. This represents the Poisson's ratio determined based on the equivalent bending stiffness. , This represents the integral term in the process of solving the flexural stiffness of the equivalent section. This represents the integral term in the process of solving the shear stiffness of the equivalent section; , , , , and This is the stiffness coefficient; Based on the Pasternak two-parameter foundation model and Timoshenko beam theory, the equilibrium differential equations of a corrugated steel plate support structure under longitudinal loads are established, and discretized using the finite difference method to construct a computational model for longitudinal non-uniform deformation. The construction of the equilibrium differential equations includes: placing the equivalent Timoshenko beam of the corrugated steel plate structure on the Pasternak two-parameter foundation; performing force equilibrium analysis on a micro-element along the longitudinal direction of the structure; and obtaining the external loads based on the principles of mechanics of materials and Timoshenko beam theory. The Timoshenko beam on the Pasternak foundation under action regarding vertical deformation and corner The equilibrium differential equation is used as the coupled equilibrium equation, and after decoupling, a fourth-order differential equation is obtained only with respect to vertical deformation; the equilibrium differential equation is expressed as: ； Among them, coefficient k and These represent the foundation reaction coefficient and the stratum shear coefficient of the Pasternak two-parameter foundation model, respectively. S Indicates the cross-sectional span; Based on the actual soil cover conditions and soil arching effect above the corrugated steel plate support structure, the longitudinal differential load distribution acting on the corrugated steel plate support structure is determined. The longitudinal differential load distribution is substituted into the calculation model of longitudinal uneven deformation for analysis, and the longitudinal uneven deformation of the corrugated steel plate support structure is obtained through numerical calculation.

2. The method for calculating longitudinal uneven deformation of corrugated steel plate support structures as described in claim 1, characterized in that, The foundation reaction coefficient and stratum shear coefficient in the Pasternak foundation model were determined using the Vlasov method.

3. The method for calculating longitudinal uneven deformation of corrugated steel plate support structures as described in claim 1, characterized in that, The determination of the longitudinal differential load distribution includes: calculating the soil pressure load distributed along the longitudinal direction based on the changes in soil cover height and structural cross-sectional dimensions, combined with the load reduction effect of the soil arching effect.

4. The method for calculating longitudinal uneven deformation of corrugated steel plate support structures as described in claim 3, characterized in that, The soil arching coefficient, which reduces the load in the soil arching effect, is determined based on the ratio of soil cover height to structural span, and in conjunction with design standards.

5. A calculation system for longitudinal uneven deformation of corrugated steel plate support structures, employing the calculation method for longitudinal uneven deformation as described in any one of claims 1-4, characterized in that, include: The orthotropic equivalent stiffness calculation module is configured to: construct an orthotropic equivalent stiffness model of the corrugated steel plate, and obtain the equivalent stiffness parameters of the corrugated steel plate in the corrugation direction, the perpendicular direction and the out-of-plane direction; wherein, the equivalent stiffness parameters include equivalent tensile stiffness, equivalent bending stiffness and equivalent shear stiffness; The equivalent section stiffness calculation module is configured to: based on the obtained equivalent stiffness parameters, convert the corrugated steel plate support structure into a Timoshenko beam, and calculate its equivalent section bending stiffness and equivalent section shear stiffness. The module for constructing the longitudinal non-uniform deformation calculation model is configured to: establish the equilibrium differential equation of the corrugated steel plate support structure under longitudinal load based on the Pasternak two-parameter foundation model and Timoshenko beam theory, and use the finite difference method for discretization to construct the calculation model of longitudinal non-uniform deformation. The longitudinal differential load distribution calculation module is configured to: determine the longitudinal differential load distribution acting on the corrugated steel plate support structure based on the actual soil cover conditions and soil arching effect above the corrugated steel plate support structure. The longitudinal uneven deformation calculation module is configured to: substitute the longitudinal differential load distribution into the longitudinal uneven deformation calculation model for analysis, and obtain the longitudinal uneven deformation of the corrugated steel plate support structure through numerical calculation.

6. A computer-readable storage medium having a program stored thereon, characterized in that, When executed by the processor, the program implements the steps in the longitudinal non-uniform deformation calculation method for corrugated steel plate support structures as described in any one of claims 1-4.

7. An electronic device, comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the longitudinal non-uniform deformation calculation method for corrugated steel plate support structures as described in any one of claims 1-4.

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