Method for calculating whole-process stress distribution and deformation of flexural steel member

Abstract

The invention belongs to the technical field of structural engineering calculation, and particularly relates to a method for calculating whole-process stress distribution and deformation of a flexural steel member, which comprises the following specific steps: S1, defining parameters and establishing an initial model; s2, load grading and theoretical ultimate bending moment calculation: calculating a yield bending moment Me in a loading direction according to section parameters and material characteristics, carrying out segmented loading on an external load from zero to a preset ultimate load, adopting different fixed step lengths before and after a yield point for segmented loading step lengths, constructing a self-adaptive grading algorithm through a yield state detection mechanism, and calculating a theoretical ultimate bending moment according to the self-adaptive grading algorithm; accurately capturing a yield point; s3, section stress distribution initial assumption and mathematical model construction; s4, performing two-dimensional fine discretization on the cross section; s5, constructing a nonlinear equilibrium equation and solving a numerical value; s6, calculating the curvature, the deflection and the displacement; and S7, performing whole-process response analysis and limit state judgment. According to the method, the nonlinear balance relation between the internal force and the external load is established, automatic solving is achieved, and the calculation efficiency is remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural engineering calculations, and particularly relates to a calculation method for the full-process stress distribution and deformation of flexural steel members. Background Technique

[0002] Steel members are key load-bearing units in modern civil engineering structures, and their internal stress states and deformation characteristics are directly related to the safety and stability of the structures. In practical engineering, accurately predicting the mechanical responses of steel members under complex loads is of great significance for design and safety assessment. Currently, the mainstream finite element analysis methods (such as commercial software like Abaqus, ANSYS, etc.) have the following obvious deficiencies in practical applications: (1) Low modeling efficiency: The preprocessing processes such as geometric modeling, mesh generation, and boundary condition setting are cumbersome and time-consuming; (2) High consumption of computing resources: Nonlinear analysis requires fine mesh generation, resulting in a large computational scale, many iteration times, and prone to convergence difficulties; (3) High economic cost: The licensing fees of commercial software are expensive, and high-performance computing hardware is required; (4) Insufficient parameterization: It is difficult to achieve rapid modeling and batch analysis, and the calculation results are easily affected by the mesh quality and the artificial setting of boundary conditions, with large uncertainties. Summary of the Invention

[0003] The purpose of the present invention is to provide a calculation method for the full-process stress distribution and deformation of flexural steel members to solve the deficiencies in the above background technique.

[0004] To achieve the above purpose, the present invention adopts the following technical solutions: A calculation method for the full-process stress distribution and deformation of flexural steel members, the specific steps are as follows: S1: Parameter definition and initial model establishment: Determine the cross-sectional type, geometric dimensions, material parameters, external load direction α and loading method of the member. The material parameters include the yield strength fy and the elastic modulus E, and establish a preliminary mechanical model to provide basic data for subsequent analysis.

[0005] S2: Load grading and theoretical ultimate moment calculation: Calculate the yield moment Me in the loading direction according to the cross-sectional parameters and material properties. The external load is loaded in segments from zero to the predetermined ultimate load, and different fixed step sizes are adopted before and after the yield point for the segmented loading step size. Through the yield state detection mechanism, an adaptive grading algorithm is constructed to accurately capture the yield point.

[0006] S3: Initial assumption of cross-sectional stress distribution and mathematical model construction: Based on the plane section assumption, the angle θn between the neutral axis and the strong axis and the stress development angle θf are introduced to establish a mathematical model for the cross-section stress distribution.

[0007] S4: Two-dimensional fine discretization of the cross-section: Adopt two-dimensional discretization technology to divide the cross-section into multiple tiny elements, and determine the area and geometric position parameters of each element.

[0008] S5: Construction and numerical solution of the nonlinear equilibrium equation: Based on the stress distribution assumption obtained in step 3 and the discretization data in step 4, calculate the bending moment contribution of each element in the principal axis direction, and construct a nonlinear equilibrium equation describing the relationship between internal forces and external loads. Using the numerical iteration method, through minimizing the error criterion, iteratively correct θn and θf until the accuracy requirement is met.

[0009] S6: Calculation of curvature, deflection and displacement: After obtaining the true stress distribution of the cross-section, use the cross-section mechanics theory to calculate the local curvature k, and calculate the deflection and displacement of the component by integrating the curvature distribution and combining with the actual boundary conditions.

[0010] S7: Whole-process response analysis and ultimate state determination: Conduct a whole-process response analysis for all loading conditions, repeat steps 3 to 6, obtain the stress distribution and deformation data of the component under different conditions, and form a complete force-deformation response curve; under multiple loading conditions, if the solution of the nonlinear equilibrium equation does not converge, it is determined that the component has reached the ultimate bearing capacity, and thus the calculation is ended.

[0011] Preferably, in step S1, the cross-section type of the component is box-shaped, H-shaped or T-shaped.

[0012] Preferably, in step S2, the ultimate load is 2Me.

[0013] Preferably, the specific steps of step S4 are as follows: (1) Generation of the basic grid: Generate the initial grid division according to the cross-section characteristics; (2) Strain gradient detection: Based on the calculation results of the previous step, mark the high strain gradient areas; (3) Dynamic local refinement: Implement grid refinement for the strain concentration areas to improve the accuracy.

[0014] Preferably, in step S4, the strain concentration area in (3) is the corner area.

[0015] Compared with the prior art, the beneficial effects obtained by the present invention: (1) Through segmented loading, different fixed step sizes are adopted before and after the yield point for the segmented loading steps. By utilizing the yield state detection mechanism, an adaptive hierarchical algorithm is constructed, significantly reducing the computational amount. At the same time, the accuracy of the yield inflection point is ensured, the computational efficiency is optimized, and computational redundancy is avoided; (2) Through two-dimensional discretization technology, the cross-section is divided into multiple tiny units to form an adaptive mesh generation technology, which can intelligently identify stress concentration areas, avoid ineffective calculations, and is not affected by the artificial setting of mesh quality and boundary conditions. While ensuring accuracy, it controls the use of computational resources, significantly improving the computational accuracy of local stress; (3) A nonlinear equilibrium equation describing the relationship between internal forces and external loads is constructed, and the convergence is accelerated through a hybrid optimization algorithm to ensure fast solution under complex working conditions. The software cost is not high, reducing costs, and at the same time, it has low requirements for the performance of computational hardware; (4) A mathematical model of the cross-section stress distribution is established, providing a theoretical basis for subsequent stress evolution and deformation calculations; by integrating the curvature distribution and combining with actual boundary conditions, the deflection and displacement of the component are calculated, providing a quantitative description of the component deformation response, laying a foundation for the force-deformation response curve, and realizing fast modeling and batch analysis; (5) This method establishes a nonlinear equilibrium relationship between internal forces and external loads, realizes automatic solution, significantly shortens the computational cycle, and significantly improves the computational efficiency; it avoids the cumbersome pre- and post-processing links of traditional finite element methods, simplifies the operation process, and reduces human errors; it can be widely applied to the mechanical analysis of common steel component cross-sections such as box-shaped, H-shaped, and T-shaped, with strong applicability; through fine discretization of the cross-section, it accurately reflects the true stress and deformation behavior of the component, improving the computational accuracy; the algorithm supports multi-process parallel computing and is suitable for large-scale engineering analysis. Description of the Drawings

[0016] Figure 1 Schematic diagram of the geometric parameters of the H-shaped cross-section in Embodiment 1 of the present invention; Figure 2 Schematic diagram of the initial assumption of the cross-section stress distribution in Embodiment 1 of the present invention; Figure 3 Schematic diagram of the two-dimensional discretization of the cross-section in Embodiment 1 of the present invention; Figure 4 Parameter curve of the whole-process microscopic stress distribution under the action of bidirectional bending moment in Embodiment 1 of the present invention; Figure 5 Force-displacement curve of the whole process under the action of bidirectional bending moment in Embodiment 1 of the present invention; Figure 6 Schematic diagram of the geometric parameters of the box-shaped cross-section in Embodiment 2 of the present invention; Figure 7 Schematic diagram of the initial assumption of the stress distribution of the box-shaped cross-section in Embodiment 2 of the present invention; Figure 8 Schematic diagram of two-dimensional discretization of the box section in Embodiment 2 of the present invention; Figure 9 Parameter curve of the whole-process microscopic stress distribution of the box-section steel member under the action of bidirectional bending moments in Embodiment 2 of the present invention; Figure 10 Force-displacement curve of the whole process of the box-section steel member under the action of bidirectional bending moments in Embodiment 2 of the present invention. Detailed implementation manners

[0017] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments. Embodiment 1

[0018] Taking an H-shaped section steel member as an example, the following gives a specific calculation method for the whole-process stress distribution and deformation of the flexural steel member. The specific steps are as follows: S1: As shown in Figure 1 , determine the cross-sectional geometric dimensions of the member, the member length L, and the material parameters yield strength fy and elastic modulus E, and set the loading direction α; assume that in the cross-sectional dimensions, the cross-sectional width b = 200 mm, the cross-sectional height h = 300 mm, the web thickness tw = 12 mm, the flange thickness tf = 16 mm, the material length L = 3000 mm, the yield strength fy = 355 Mpa, the elastic modulus E = 206000 Mpa, and α = 30°; S2: Calculate the yield moment Me according to the parameters, and divide the external load from 0 to 2Me at intervals of 0.1Me and 0.2Me to obtain several selected moment conditions: 0, 0.1Me, 0.2Me, 0.3Me,..., 1.6Me, 1.8Me, 2Me; S3: As shown in Figure 2 , assume the angle θn between the neutral axis and the strong axis of the H-shaped section and the stress development angle θf, and construct a preliminary cross-sectional stress distribution diagram; S4: As shown in Figure 3 , perform mesh division on the cross-section to obtain the area and position data of each unit; S5: For all the units obtained in step S4, calculate their sectional moments about the two principal axes respectively according to the actual unit area and the stress values extracted from the cross-sectional stress distribution diagram at the center point of the unit, and establish a moment-stress nonlinear equilibrium equation. Using the nonlinear solution method, by comparing with the selected moments obtained in step S1 and minimizing the error, finally determine the true neutral axis angle and stress distribution parameters of the cross-section under a specific selected moment; through calculation, the results of the angle θn between the neutral axis and the strong axis and the stress development angle θf of the member during the whole process are shown in the following table;

[0019] S6: Calculate the curvature k of the component under the corresponding bending moment according to the cross-section performance parameters determined in step S5, and then calculate the deflection and displacement of the component based on the curvature k to accurately evaluate the deformation performance of the component. The results of the curvature k, the deflections wx and wy of the mid-span cross-section of the component obtained through calculation are shown in the following table;

[0020] S7: For all selected bending moment loads, repeat steps S3 to S6 to obtain the complete mechanical response data of the component under different loading conditions. When the non-linear solution fails under consecutive multiple load conditions, it can be determined that the component has reached the ultimate bearing capacity and the calculation ends.

[0021] Finally, obtain Figure 4 the curve of the microscopic stress distribution parameters during the whole process under the action of bi-directional bending moment as shown in Figure 5 and the force-displacement curve at any position (taking the mid-span cross-section as an example) during the whole process under the action of bi-directional bending moment as shown in Figure 4 to realize the visual analysis of the whole process of the structural response. Figure 5 It can accurately capture the evolution law of the cross-section-level microscopic stress field at any time history node, Example 2

[0022] The following takes a box-section steel component as an example to give a specific calculation method for the stress distribution and deformation of the flexural steel component during the whole process. The specific steps are as follows: S1: As Figure 6 shown, determine the cross-section geometric dimensions, the length L of the component, and the material parameters yield strength fy and elastic modulus E of the component, and set the loading direction α. Assume that in the cross-section dimensions, the cross-section width b = 200 mm, the cross-section height h = 300 mm, the web thickness tw = 12 mm, the flange thickness tf = 12 mm, the material length L = 3000 mm, the yield strength fy = 355 Mpa, the elastic modulus E = 206000 Mpa, and α = 30°; S2: Calculate the yield moment Me according to the parameters, and divide the external load from 0 to 2Me at intervals of 0.1Me and 0.2ME respectively to obtain several selected bending moment conditions: 0, 0.1Me, 0.2Me, 0.3Me ……, 1.6Me, 1.8Me, 2Me; S3: AsFigure 7 As shown, assuming the angle θn between the neutral axis and the strong axis of the box section and the stress development angle θf, a preliminary cross-section stress distribution diagram is constructed; S4: As Figure 8 shown, the cross-section is meshed to obtain the area and position data of each element; S5: For all the elements obtained in step S4, based on the actual element area and the stress values extracted from the cross-section stress distribution diagram at the center point of the element, calculate their cross-section moments about the two principal axis directions respectively, and establish a moment-stress nonlinear equilibrium equation. Using a nonlinear solution method, by comparing with the selected moment obtained in step S1 and minimizing the error, finally determine the true neutral axis angle and stress distribution parameters of the cross-section under a specific selected moment; The results of the angle θn between the neutral axis and the strong axis and the stress development angle θf of this member during the whole process are shown in the following table;

[0023] S6: According to the cross-section performance parameters determined in step S5, calculate the curvature k of the member under the corresponding moment, and then calculate the deflection and displacement of the member based on the curvature k to accurately evaluate the deformation performance of the member; The results of the curvature k, the deflections wx and wy of the mid-span cross-section of this member during the whole process are shown in the following table;

[0024] S7: For all selected moment loads, repeat steps S3 to S6 to obtain the complete mechanical response data of the member under different loading conditions; When the nonlinear solution fails under consecutive multiple load conditions, it can be determined that the member has reached the ultimate bearing capacity and the calculation ends.

[0025] Finally, obtain the microscopic stress distribution parameter curve during the whole process under the action of bidirectional moments as shown in Figure 9 and the force-displacement curve at any position (taking the mid-span cross-section as an example) during the whole process under the action of bidirectional moments as shown in Figure 10 , realizing the visual analysis of the whole process of structural response. Figure 9 It can accurately capture the evolution law of the cross-section-level microscopic stress field at any time history node, Figure 10 while completely recording the macroscopic deformation dynamic development process of the typical cross-section (such as the mid-span position). Compared with the complex post-processing steps (such as data extraction, contour reconstruction, parameter fitting, etc.) in traditional finite element analysis, this method improves the engineering analysis efficiency by more than 60% by establishing a real-time dynamic mapping model between the stress field and the displacement field. At the same time, the obtained calculation results are basically consistent with the traditional finite element analysis method, verifying its accuracy and reliability. This method provides a new idea for the real-time mapping analysis of the three-dimensional dynamic response of steel structures.

Claims

1. A calculation method for the whole-process stress distribution and deformation of a flexural steel member, characterized in that The specific steps are as follows: S1: Parameter definition and initial model establishment: Determine the cross-section type, geometric dimensions, material parameters, external load direction α and loading mode of the component. The material parameters include the yield strength fy and elastic modulus E. Establish a preliminary mechanical model to provide basic data for subsequent analysis; S2: Load grading and theoretical ultimate moment calculation: Calculate the yield moment Me in the loading direction according to the cross-section parameters and material properties. The external load is loaded in segments from zero to the predetermined ultimate load. Different fixed step sizes are adopted before and after the yield point for the segmented loading steps. Through the yield state detection mechanism, an adaptive grading algorithm is constructed to accurately capture the yield point; S3: Initial assumption of cross-section stress distribution and mathematical model construction: Based on the plane section assumption, introduce the angle θn between the neutral axis and the strong axis and the stress development angle θf, and establish a mathematical model for the cross-section stress distribution; S4: Two-dimensional fine discretization of the cross-section: Adopt two-dimensional discretization technology to divide the cross-section into multiple tiny units, and determine the area and geometric position parameters of each unit; S5: Construction and numerical solution of the nonlinear equilibrium equation: Based on the stress distribution assumption obtained in step 3 and the discretization data in step 4, calculate the moment contribution of each unit in the main axis direction, and construct a nonlinear equilibrium equation describing the relationship between internal force and external load. Using the numerical iteration method, through the minimum error criterion, iteratively correct θn and θf until the accuracy requirement is met; S6: Calculation of curvature, deflection and displacement: After obtaining the true stress distribution of the cross-section, use the cross-section mechanics theory to calculate the local curvature k, and calculate the deflection and displacement of the component by integrating the curvature distribution and combining the actual boundary conditions; S7: Whole-process response analysis and ultimate state determination: Conduct a whole-process response analysis for all loading conditions, repeat steps 3 to 6, obtain the stress distribution and deformation data of the component under different conditions, and form a complete force-deformation response curve; Under multiple loading conditions, if the solution of the nonlinear equilibrium equation does not converge, it is determined that the component has reached the ultimate bearing capacity, and the calculation is terminated.

2. The calculation method for the whole-process stress distribution and deformation of a flexural steel member according to claim 1, characterized in that, In step S1, the cross-section type of the component is box-shaped, H-shaped or T-shaped.

3. The calculation method for the whole-process stress distribution and deformation of a flexural steel member according to claim 1, characterized in that, In step S2, the ultimate load is 2Me.

4. The calculation method for the whole-process stress distribution and deformation of a flexural steel member according to claim 1, characterized in that, The specific steps of step S4 are as follows: (1) Basic grid generation: Generate an initial grid division according to the cross-section characteristics; (2) Strain gradient detection: Based on the calculation results of the previous step, mark the high strain gradient areas; (3) Dynamic local refinement: Implement grid refinement for the strain concentration areas to improve the accuracy.

5. A calculation method for the whole-process stress distribution and deformation of a flexural steel member according to claim 4, characterized in that In step S4, the strain concentration area in (3) is the corner area.

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