Dichotomy-based stability limit load calculation method and computer program product

Abstract

The invention relates to the technical field of metal structure stability finite element analysis, in particular to a stability limit load calculation method based on a dichotomy and a computer program product, and the method comprises the steps: carrying out the structural modeling of a target structural part, completing the finite element pretreatment, applying an initial load to a modeled structure, obtaining an initial maximum Mises stress value of the structure, and calculating the stability limit load of the target structural part. According to the elastic field linear superposition principle and the stability upper limit principle, the initial load range [Flower, Fupper] of the stability limit load is calculated, then the load range is iteratively updated by adopting a dichotomy method until the convergence condition is met, the final stability limit load is obtained, the total calculation frequency is reduced by 40%-60%, and the final stability limit load is obtained. Meanwhile, full-process automation from load setting to result judgment is achieved, and the requirement for manual intervention is remarkably reduced.

Description

Technical Field

[0001] This invention relates to the field of finite element analysis technology for the stability of metal structures, and in particular to a method and computer program product for calculating the stability limit load based on the bisection method. Background Technology

[0002] For giant hydraulic presses, due to the discontinuity of their structure, localized high-stress zones inevitably appear, characterized by "extremely small areas with extremely high stress." Current methods to address these localized high stresses primarily involve increasing size or extreme manufacturing processes, but neither can completely eliminate their impact. The elastic safety principle of avoiding plastic deformation is now difficult to achieve, and designing structures according to this principle sacrifices a significant portion of the material's load-bearing capacity between its elastic limit and tensile strength. This means that the utilization of material strength is still minimal, and significant mass waste remains in the structure.

[0003] The study of structural stability (shakedown) originated in the 1930s, with its core theory driven by the development of plasticity mechanics. It aimed to analyze the long-term stability and load-bearing capacity of structures under cyclic or varying loads. In 1938, Austrian scholar Melan proposed the lower bound theorem of stability, laying the foundation for classical stability theory. This theorem states that if there exists a time-independent self-equilibrium residual stress field that ensures the structure always satisfies the yield condition under cyclic loading, then the structure can reach a stable state. In 1960, Dutch scholar Koiter proposed the upper bound theorem of stability, further supplementing the theoretical framework and extending stability analysis to kinematically permissible plastic deformation mechanisms. Research at this stage focused on elastic stability problems, applicable to ideal elastoplastic materials, and did not consider factors such as geometric nonlinearity and material damage.

[0004] Since the 1970s, with the advancement of computer technology, stability analysis has shifted from analytical methods to numerical calculations, such as linear programming and the finite element method. For example, linear programming-based algorithms have been used to solve multi-factor coupled studies of the stability limit load of complex structures: the research scope has been expanded to practical engineering problems such as thermal effects, geometric nonlinearity, strain hardening, and material damage, forming a generalized concept of stability (including elastic stability and plastic stability).

[0005] Since 2010, the finite element method (FEM) has been used to determine the stable ultimate load of a giant hydraulic press, thus demonstrating the long-term ultimate bearing capacity of the equipment structure. However, the mesh size of giant equipment models is enormous, requiring significant computational power. Limited by the current level of computer hardware development, completing a single calculation still takes a long time. Furthermore, existing manual incremental methods for solving the stable ultimate load involve too many calculations and are excessively time-consuming. Summary of the Invention

[0006] In view of this, the purpose of this invention is to propose a method and computer program product for calculating the stability limit load based on the bisection method, so as to solve the problems of low calculation efficiency and frequent manual intervention in the prior art.

[0007] To achieve the above objectives, this invention provides a method for calculating the stability limit load based on the bisection method, comprising the following steps:

[0008] S1. Perform structural modeling on the target structural component and complete finite element preprocessing;

[0009] S2. After completing the finite element preprocessing, apply initial loads to the modeled structure. Calculate the stress distribution of the structure and extract the maximum Mises stress value of the structure. ;

[0010] S3, based on the maximum Mises stress value Based on the principle of linear superposition of elastic fields and the principle of upper limit of stability, the initial load range [F] of the stability limit load is calculated. lower , F upper ]:

[0011] S4, Take the load range [F] lower , F upper The midpoint load F mid The corresponding maximum stress value is calculated based on finite element analysis. Determine whether it is less than the material's yield strength. And update the load range based on the calculation results:

[0012] If the current < Then let F lower = F mid ;

[0013] If the current ≥ Then let F upper = F mid ;

[0014] S5. Repeat step S4 until the convergence condition is met, and output the lower limit load of the final ultimate load range as the final stable ultimate load.

[0015] Preferably, modeling and finite element preprocessing are performed in Abaqus, and stress distribution calculation, stress value calculation, and finite element analysis are performed through Abaqus.

[0016] Preferably, this method automates the following operations using a Python script:

[0017] Modify the Load option in the Abaqus input file to set the initial load in step S2. ;

[0018] Submit a calculation task by calling the Abaqus solver to calculate the stress distribution and stress values;

[0019] Extract full-field Mises stress data from the ODB results file obtained from Abaqus and determine the maximum Mises stress value. .

[0020] Preferably, during the iteration of step S4, the Python program executes automatically:

[0021] According to the current F lower and F upper Values ​​are dynamically generated to create new F values. mid ;

[0022] Reset the load parameters and submit a new calculation using the Abaqus-Python interface;

[0023] The system monitors the convergence status of the calculation in real time and automatically terminates the iteration when the accuracy requirements are met.

[0024] The preferred method for calculating the initial load range is as follows:

[0025] F lower = (σ y / )× ;

[0026] F upper = m×F lower ;

[0027] Where m is the search space magnification factor.

[0028] Preferably, the convergence condition is that |F upper - F lower | ≤ α×F lower , where α is the error coefficient.

[0029] Preferably, the initial load Take 10% of the design load.

[0030] The present invention also provides a computer program product for implementing the above method, comprising:

[0031] Initial Calculation Module: Used to perform finite element calculations for initial loads and extract the maximum Mises stress value. ;

[0032] Load estimation module: used to calculate the initial load range [F] lower , Fupper ];

[0033] The binary search control module is used to automatically perform load updates, calculation submissions, and result judgments in step S4.

[0034] Output module: Used to generate a report containing the stability limit load values ​​and the iteration process.

[0035] The beneficial effects of this invention are:

[0036] 1. Computational efficiency is greatly improved. By using the principle of linear superposition of elastic fields, only one initial calculation is needed to determine the reasonable search space. Combined with the logarithmic convergence property of the bisection method, the total number of calculations is reduced by 40%-60%. In typical cases, only 9 iterations are needed to reach the convergence criterion.

[0037] 2. It achieves full-process automation, automatically completing the entire process of load setting, calculation submission, result extraction and parameter adjustment through Python scripts, eliminating manual intervention and supporting 24 / 7 unattended continuous calculation.

[0038] 3. Controllable computational accuracy. The initial range is determined based on the principles of elasticity and the upper limit of stability. A dual convergence criterion is used to control the iterative process. Load space accuracy control ensures that the relative error of the final result is kept within the required accuracy range. The number of iterations is controlled to avoid convergence stalling under special circumstances. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a flowchart of the stability limit load calculation method based on the bisection method according to an embodiment of the present invention;

[0041] Figure 2 This is a schematic diagram of the structure of the computer program product of the present invention;

[0042] Figure 3 This is a schematic diagram of the dimensions of the target structural component in an embodiment of the present invention;

[0043] Figure 4 This is a force diagram of the target structural component according to an embodiment of the present invention;

[0044] Figure 5 This is a schematic diagram of the incremental method and the loading path of the method of the present invention according to an embodiment of the present invention;

[0045] Figure 6 This is a comparison chart showing the search speed and effectiveness of the incremental method and the method of the present invention in an embodiment of the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0047] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0048] Example 1:

[0049] like Figure 1 As shown in the embodiments of this specification, a method for calculating the stability limit load based on the bisection method is provided, including the following steps:

[0050] S1. Perform structural modeling of the target structural component and complete finite element preprocessing in Abaqus;

[0051] S2. After completing the finite element preprocessing, apply initial loads to the modeled structure. initial load Taking 10% of the design load, calculate the stress distribution of the structure and extract the maximum Mises stress value of the structure. ;

[0052] S3, based on the maximum Mises stress value Based on the principle of linear superposition of elastic fields and the principle of upper limit of stability, the initial load range [F] of the stability limit load is calculated. lower , F upper ]:

[0053] Based on the principle of linear superposition of elastic fields, the lower limit load F of stability is calculated. lower = (σ y / )× , where σ yThis represents the material's yield strength. Since (σ... y / The ratio of ) is relatively large, and the error is amplified, resulting in a decrease in the actual obtained F. lower It is usually slightly less than the actual structural elastic limit load.

[0054] Based on the upper limit of stability theory, determine the upper limit of stability load F. upper = m×F lower m is the search space magnification factor. To reduce the impact of errors and avoid secondary calculation of the upper limit, m is set to 4.

[0055] S4, Take the load range [F] lower , F upper The midpoint load F mid The corresponding maximum stress value is calculated based on finite element analysis. Determine whether it is less than the material's yield strength. And update the load range based on the calculation results:

[0056] If the current < Then let F lower = F mid ;

[0057] If the current ≥ Then let F upper = F mid ;

[0058] S5. Repeat step S4 until |F is satisfied. upper - F lower | ≤ α×F lower α is the error coefficient, which can be modified according to the requirements before calculation. The default value is 0.01. The lower limit load of the final ultimate load range is output as the final ultimate load, i.e., Fmax = Flower.

[0059] As one implementation method, this approach automates the following operations using a Python script:

[0060] Modify the Load option in the Abaqus input file to set the initial load. ;

[0061] Submit a computation task by calling the Abaqus solver;

[0062] Extract full-field Mises stress data from the ODB results file and determine... .

[0063] Furthermore, during the iteration of step S4, the Python program executes automatically:

[0064] According to the current F lower and F upper Values ​​are dynamically generated to create new F values. mid ;

[0065] Reset the load parameters and submit a new calculation using the Abaqus-Python interface;

[0066] The system monitors the convergence status of the calculation in real time and automatically terminates the iteration when the accuracy requirements are met.

[0067] Example 2:

[0068] like Figure 2 As shown. This specification also provides a computer program product for rapid calculation of stable ultimate load based on Python-Abaqus integration, including:

[0069] Initial calculation module—initial load calculation and initial domain calculation of stability limit load;

[0070] Bisection Iteration Module – Fast Convergence Stability Limit Load Domain:

[0071] Results output module – outputs the stability limit load results and calculation history.

[0072] Example 3:

[0073] This embodiment uses, as follows Figure 3 (a) shows a square plate model with a circular hole, and as shown in Figure 1. Figure 3 (b) shows the experiment of calculating the stability limit load on the thin-walled square-hole circular tube model. Figure 4 This refers to the loading methods for these two models.

[0074] See Figure 5 This section describes two sets of loading processes for the circular hole square plate model. The loading processes for the two calculation methods can be observed in the circular hole square plate model example.

[0075] See Figure 6 The numbers represent the number of calculations required for the two methods under specified accuracy requirements. It can be seen that the method provided by this invention can quickly narrow down the range of the stability limit load. Under the same error requirements, this method reduces the number of calculations by 30%–50% compared to the traditional incremental method. In practical applications, since the load does not need to be manually modified after the program runs, the actual reduction in working time will be even higher.

[0076] This invention is particularly suitable for stability analysis of heavy equipment with complex structures but relatively simple load conditions. Typical application scenarios include, but are not limited to, the following two types of structures:

[0077] Firstly, there are hydraulic press frame structures, including four-column hydraulic press beams and integral cast hydraulic press frames. These structures have complex geometric features (such as transition fillets and bolted connection areas), leading to significant stress concentration effects. However, the working loads are usually unidirectional pressure or simple cyclic loads, perfectly matching the program's advantage of "complex structure + simple loading." Secondly, there are pressure vessel equipment, such as reactor shells, tank heads, and pipeline connections. These structures often have discontinuous areas such as openings and nozzles, forming complex local stress fields. The pressure conditions are mostly constant internal pressure or regular pressure fluctuations. This program can accurately capture the stress characteristics of these key parts through a single initial calculation, thereby quickly determining the overall structural stability limit load. Both types of engineering structures share the characteristics of large-scale finite element models (usually containing millions of elements) and dramatic changes in local stress gradients, but the external load forms are simple and clear, allowing the program's computational efficiency advantage to be maximized.

[0078] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of the invention is limited to these examples; within the framework of the invention, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity. Any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for calculating the stability limit load based on the bisection method, characterized in that, The method includes the following steps: S1. Perform structural modeling on the target structural component and complete finite element preprocessing; S2. After completing the finite element preprocessing, apply an initial load F0 to the modeled structure, calculate the stress distribution of the structure, and extract the maximum Mises stress value of the structure. ; S3, based on the maximum Mises stress value Based on the principle of linear superposition of elastic fields and the principle of upper limit of stability, the initial load range [F] of the stability limit load is calculated. lower , F upper ]: S4, Take the load range [F] lower , F upper The midpoint load F mid The corresponding maximum stress value is calculated based on finite element analysis. Determine whether it is less than the material's yield strength. And update the load range based on the calculation results: If the current < Then let F lower = F mid ; If the current ≥ Then let F upper = F mid ; S5. Repeat step S4 until the convergence condition is met, and output the lower limit load of the final ultimate load range as the final stable ultimate load.

2. The method for calculating the stability limit load based on the bisection method according to claim 1, characterized in that, Modeling and finite element preprocessing are performed in Abaqus. Stress distribution calculation, stress value calculation, and finite element analysis are all conducted using Abaqus.

3. The method for calculating the stability limit load based on the bisection method according to claim 2, characterized in that, The method automatically performs the following operations using a Python script: Modify the Load option in the Abaqus input file to set the initial load in step S2. ; Submit a calculation task by calling the Abaqus solver to calculate the stress distribution and stress values; Extract full-field Mises stress data from the ODB results file obtained from Abaqus and determine the maximum Mises stress value. .

4. The method for calculating the stability limit load based on the bisection method according to claim 2, characterized in that, During the iteration of step S4, the Python program executes automatically: According to the current F lower and F upper Values ​​are dynamically generated to create new F values. mid ; Reset the load parameters and submit a new calculation using the Abaqus-Python interface; The system monitors the convergence status of the calculation in real time and automatically terminates the iteration when the accuracy requirements are met.

5. The method for calculating the stability limit load based on the bisection method according to claim 1, characterized in that, The method for calculating the initial load range is as follows: F lower = (σ y / )× ; F upper = m×F lower ; Where m is the search space magnification factor.

6. The method for calculating the stability limit load based on the bisection method according to claim 1, characterized in that, The convergence condition is that |F upper - F lower | ≤ α×F lower , where α is the error coefficient.

7. The method for calculating the stability limit load based on the bisection method according to claim 1, characterized in that, The initial load Take 10% of the design load.

8. A computer program product implementing the method of any one of claims 1-7, characterized in that, Include: Initial Calculation Module: Used to perform finite element calculations for initial loads and extract the maximum Mises stress value. ; Load estimation module: used to calculate the initial load range [F] lower , F upper ]; The binary search control module is used to automatically perform load updates, calculation submissions, and result judgments in step S4. Output module: Used to generate a report containing the stability limit load values ​​and the iteration process.

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