Method and device for determining layout of bolted structure based on grey wolf algorithm

Abstract

The embodiment of the present application provides a method and device for determining the layout of a bolted structure based on a grey wolf algorithm, which comprises: determining the maximum stress, maximum shear stress and critical bending stress of a target bolt as an optimized stress based on the distribution position of the target bolt on a plate and the external force applied to the plate; determining a cost function of the target bolt based on a price table of the diameter and unit price of the bolt; determining a target function corresponding to the target bolt based on the optimized stress and the cost function; and minimizing and optimizing the target function based on the grey wolf algorithm to obtain the distance between the target bolts and the diameter of the target bolts. The present application determines the minimum optimization solution of a target function composed of the target maximum stress, maximum shear stress, critical bending stress and cost function of the target bolt through the grey wolf algorithm, thereby optimizing the layout of the target bolt on the plate, and helping to improve the safety and reliability of the load-bearing connection structure in large and complex equipment.

Description

Technical Field

[0001] This invention relates to the field of large and complex equipment technology, and in particular to a method and apparatus for determining the layout of bolted connection structures based on the Grey Wolf algorithm. Background Technology

[0002] Bolted connections are a crucial connection method in large, complex equipment, aerospace, and other mechanical structures. The variation in preload of this connection directly affects the service life of the bolts and the normal operation of the mechanical structure. Among these factors, the peri-hole stress in bolted connections is a key factor influencing the lifespan of the structure. To make structures more robust and reduce stress on load-bearing structures, it is necessary to optimize the layout of multi-bolted connections to achieve better connection performance. Many scholars have conducted extensive research on bolt layout optimization.

[0003] However, the optimization of multi-bolt connection structures by related technologies is limited to symmetrical bolt structures, while there is little research on asymmetrical bolt structures, especially the optimization of multi-bolt layout structures in triangular positions.

[0004] Therefore, determining the optimal layout of asymmetrically distributed bolts has become a pressing technical problem in this field. Summary of the Invention

[0005] To address the technical problems existing in the prior art, the present invention provides a method and apparatus for determining the layout of bolted connection structures based on the Grey Wolf algorithm.

[0006] In a first aspect, the present invention provides a method for determining the layout of bolted connection structures based on the Grey Wolf algorithm, comprising:

[0007] Based on the distribution of the target bolts on the plate, the external force applied to the plate determines the maximum force, maximum shear stress, and critical bending stress of the target bolts, which are then used as the force to be optimized. The target bolts are three identical bolts, and their distribution on the plate satisfies the condition of forming an equilateral triangle and being asymmetrically distributed. The external force applied to the plate is the tensile force in the positive X-axis direction and the tensile force in the negative Y-axis direction of the coordinate system in which the plate is located.

[0008] Based on the price list of bolt diameter and unit price, determine the cost function of the target bolt;

[0009] Based on the stress to be optimized and the cost function, determine the objective function corresponding to the target bolt;

[0010] Based on the Grey Wolf algorithm, the objective function is minimized and optimized to obtain the spacing and diameter of the target bolts.

[0011] Optionally, the step of determining the maximum force, maximum shear stress, and critical bending stress of the target bolt based on the distribution position of the target bolt on the plate, and applying external force to the plate as the force to be optimized, includes:

[0012] Based on mechanical principles, the distribution position of the target bolt on the plate and the external force applied to the plate are used to determine the force analysis results of the target bolt;

[0013] Based on the force analysis results of the target bolt, the maximum force analysis result is determined as the maximum force of the target bolt;

[0014] Based on the diameter of the target bolt and the maximum force on the target bolt, determine the maximum shear stress of the target bolt;

[0015] Based on the principle of torque analysis, the torque and moment of inertia with the largest torque in the target bolt are determined, and the critical bending stress is determined.

[0016] The stress to be optimized is determined based on the maximum force on the target bolt, the maximum shear stress on the target bolt, and the critical bending stress.

[0017] Optionally, determining the maximum shear stress of the target bolt based on its diameter and the maximum force it experiences includes:

[0018] Based on the maximum force F of the target bolt max The maximum shear stress of the target bolt is determined by using the diameter d of the target bolt and the shear stress formula.

[0019] The shear stress formula is:

[0020] Where, τ max This represents the maximum shear stress of the target bolt.

[0021] Optionally, determining the maximum torque and moment of inertia in the target bolt based on the torque analysis principle, and determining the critical bending stress, includes:

[0022] Based on the principle of torque analysis, the torque M and moment of inertia I with the largest torque in the target bolt are determined;

[0023] Based on the ratio of the maximum torque M to the moment of inertia I, the critical bending stress σ is determined. max .

[0024] Optionally, the cost function for determining the target bolt based on the price list of bolt diameter and unit price includes:

[0025] Based on the square method, a price list of bolt diameters and unit prices is used to fit the relationship between the price of the target bolt and the diameter of the target bolt, thereby determining the cost function of the target bolt.

[0026] Optionally, the step of minimizing and optimizing the objective function based on the Grey Wolf algorithm to obtain the spacing and diameter of the target bolts includes:

[0027] Set the gray wolf population size, maximum number of iterations, solution dimension, and boundary range;

[0028] The position of each individual gray wolf in the gray wolf population is initialized as a candidate set for the initial position of the target bolt;

[0029] The objective function is used as the fitness function of individual gray wolves to determine the fitness value of each gray wolf in the gray wolf population. The gray wolf with the smallest fitness value is designated as the global best gray wolf α, the gray wolf with the second smallest fitness value is designated as the global second best gray wolf β, and the gray wolf with the third smallest fitness value is designated as the global third best gray wolf δ.

[0030] According to the iteration rules, update the position information of each individual gray wolf in the gray wolf population at the next moment; the iteration rules include:

[0031]

[0032] in, Let α, β, and δ be the distance vectors between α and the other gray wolves, respectively. and Let be vectors representing the current positions of α, β, and δ, respectively. and It is a random vector. A vector representing the current position of the gray wolf population;

[0033]

[0034]

[0035] Where A1, A2, and A3 represent intermediate parameters, and A vector representing the current position of other gray wolves in the gray wolf population; A vector representing the next position of the gray wolf population; the intermediate parameters A1, A2, and A3 and the random vector. and The following formula is used for calculation:

[0036]

[0037]

[0038]

[0039] in, The convergence factor is and The modulus of is a random number between [0-1], t represents the current iteration number, and T represents the maximum number of iterations.

[0040] Based on the position information of each individual gray wolf in the gray wolf population at the next moment, the globally optimal gray wolf α, the globally second-best gray wolf β, and the globally third-best gray wolf δ are updated until the maximum number of iterations is reached, so as to obtain the spacing and diameter of the target bolts.

[0041] Secondly, the present invention also provides a device for determining the layout of bolted connection structures based on the Grey Wolf algorithm, comprising:

[0042] The target module is used to determine the target function corresponding to the target bolt based on the distribution position of the target bolt on the plate, the external force applied to the plate, the type and unit price of the target bolt;

[0043] The layout determination module is used to minimize and optimize the objective function based on the Grey Wolf algorithm to obtain the spacing and diameter of the target bolts.

[0044] Thirdly, the present invention also provides an electronic device, including a memory, a transceiver, and a processor;

[0045] A memory for storing computer programs; a transceiver for sending and receiving data under the control of the processor; and a processor for reading the computer programs in the memory and implementing the method for determining the layout of bolted connections based on the Grey Wolf algorithm as described in the first aspect above.

[0046] Fourthly, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for determining the layout of bolted connection structures based on the Grey Wolf algorithm as described in the first aspect above.

[0047] Fifthly, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the method for determining the layout of bolted connection structures based on the Grey Wolf algorithm as described in the first aspect.

[0048] This invention provides a method and apparatus for determining the layout of bolted connections based on the Grey Wolf algorithm. By analyzing the stress on target bolts asymmetrically distributed on a nickel-steel plate, an objective function is constructed, consisting of the target maximum stress, maximum shear stress, critical bending stress, and the cost function of the target bolts. The Grey Wolf algorithm is then used to determine the minimum optimal solution of the objective function, yielding the bolt spacing and diameter. This reduces the stress around the holes in the nickel-steel plate and the maximum stress on the bolt surface, providing a new approach to optimizing the layout of asymmetrical bolted connections. It can improve the strength and stiffness of the structure, extend the service life and reliability of the bolted connection structure and the bolts themselves. When designing bolts and connection structures, the optimal solution of the Grey Wolf algorithm allows for the selection of bolt diameters and spacing within a reasonable range, keeping the stress around the bolt holes within a reasonable range, avoiding excessive material use, and reducing material costs. This contributes to improving the safety and reliability of load-bearing connection structures in complex mechanical fields such as large and complex equipment, long-distance ship voyages, and aerospace. Attached Figure Description

[0049] 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 some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0050] Figure 1 This is a flowchart illustrating the method for determining the layout of bolted connection structures based on the Grey Wolf algorithm provided in an embodiment of the present invention.

[0051] Figure 2 This is a cross-sectional schematic diagram of the target bolts at the distribution position on the flat plate according to an embodiment of the present invention;

[0052] Figure 3 This is one of the top views of the target bolts distributed on the flat plate according to an embodiment of the present invention;

[0053] Figure 4 This is a cross-sectional view of bolt B cut along the Y-axis according to an embodiment of the present invention;

[0054] Figure 5 This is a torque diagram of the flat plate provided in an embodiment of the present invention;

[0055] Figure 6 This is a second top view of the target bolts distributed on the flat plate according to an embodiment of the present invention;

[0056] Figure 7 This is a schematic diagram illustrating the principle of updating the position of individual wolves in the gray wolf algorithm provided in this embodiment of the invention;

[0057] Figure 8This is a schematic diagram of the device for determining the layout of bolted connections based on the gray wolf algorithm provided in an embodiment of the present invention;

[0058] Figure 9 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0059] In this embodiment of the invention, the term "and / or" describes the relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The character " / " generally indicates that the preceding and following associated objects have an "or" relationship.

[0060] In this embodiment of the invention, the term "multiple" refers to two or more, and other quantifiers are similar.

[0061] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0062] Figure 1 This is a flowchart illustrating the method for determining the layout of bolted connections based on the Grey Wolf algorithm provided in an embodiment of the present invention. Figure 1 As shown, the method includes:

[0063] Step 101: Based on the distribution position of the target bolts on the plate, determine the maximum force, maximum shear stress, and critical bending stress of the target bolts by applying external force to the plate, as the force to be optimized; the target bolts are three identical bolts, and their distribution position on the plate satisfies the condition of forming an equilateral triangle and being asymmetrically distributed; the external force applied to the plate is the tensile force in the positive X-axis direction and the tensile force in the negative Y-axis direction of the coordinate system in which the plate is located;

[0064] Specifically, Figure 2 This is a cross-sectional schematic diagram of the target bolts at the distribution position on the flat plate according to an embodiment of the present invention; Figure 3 This is one of the top views of the target bolts distributed on the flat plate according to an embodiment of the present invention; such as Figure 2 and 3As shown, the target bolts include three bolts, namely bolt A, bolt B, and bolt C. These three bolts are arranged in an equilateral triangle in a flat plate, with the centroid of the equilateral triangle at O. The distance between any two bolts, i.e., the side length of the equilateral triangle, is a. The flat plate is made of nickel steel, with a length of L, a width of W, and a height of H. A tensile force F1 along the positive X direction and a tensile force F2 along the negative Y direction are applied at point K on the flat plate. The point of application of force K is at the midpoint of the width of the nickel steel flat plate. Simplifying the force at point K to point O, a moment about point O is formed. Force analysis is performed on bolts A, B, and C:

[0065]

[0066]

[0067]

[0068] Among them, F A F B and F C These represent the forces acting on bolts A, B, and C, respectively; Q represents the distance from the centroid O to the center of the bolt, satisfying...

[0069] Based on the stress analysis results corresponding to bolts A, B, and C, the maximum stress, maximum shear stress, and critical bending stress of the target bolt are determined as the stress to be optimized.

[0070] Step 102: Based on the price list of bolt diameter and unit price, determine the cost function of the target bolt;

[0071] Bolts of different diameters have different unit prices; the larger the diameter, the higher the unit price, and vice versa. However, larger diameter bolts generally have higher strength and hardness, and can withstand greater torsional and shear forces. Therefore, both of these factors need to be considered when determining the bolt diameter to select the one offering the best cost-performance ratio.

[0072] By utilizing the price list of bolt diameters and unit prices collected from the existing market, the cost function of the target bolt can be determined, which is beneficial for subsequently using the Grey Wolf algorithm to determine the diameter of the target bolt.

[0073] Step 103: Based on the force to be optimized and the cost function, determine the objective function corresponding to the target bolt;

[0074] Step 104: Based on the Grey Wolf algorithm, minimize and optimize the objective function to obtain the spacing and diameter of the target bolts.

[0075] Based on the aforementioned forces to be optimized and the cost function, the objective function for the target bolt is determined. Then, the Grey Wolf algorithm is used to minimize and optimize this objective function.

[0076] The Gray Wolf Algorithm is designed based on the hunting system and leadership hierarchy of gray wolves. The algorithm's hierarchical pyramid consists of four layers. The top layer, α, is responsible for decision-making events such as hunting and item allocation. The second layer is the think tank of the top gray wolf α, called β. β primarily assists α in decision-making and fills vacancies at the top layer. The third layer, δ, follows the orders of the first two layers and is mainly responsible for tasks such as guarding and sentry duty. The bottom layer, ω, primarily balances internal relationships.

[0077] The Grey Wolf algorithm boasts fast convergence speed, high global search capability, applicability across diverse problem domains, no need for complex computer models, and the ability to automatically adapt to problem characteristics and changes in the search space. Furthermore, the Grey Wolf algorithm is particularly well-suited for solving asymmetric structure problems. Therefore, this invention selects the Grey Wolf algorithm for layout optimization of multi-bolted connection structures.

[0078] This invention provides a method for determining the layout of bolted connections based on the Grey Wolf algorithm. By analyzing the stress on target bolts asymmetrically distributed on a nickel-steel plate, an objective function is constructed, consisting of the target maximum stress, maximum shear stress, critical bending stress, and the cost function of the target bolts. The Grey Wolf algorithm is then used to determine the minimum optimal solution of the objective function, yielding the bolt spacing and diameter. This reduces the peripheral stress of the nickel-steel plate and the maximum stress on the bolt surface, providing a new approach to optimizing the layout of asymmetrical bolted connections. It can improve the strength and stiffness of the structure, extend the service life and reliability of the bolted connection structure and the bolts themselves. When designing bolts and connection structures, the optimal solution of the Grey Wolf algorithm allows for the selection of bolt diameters and spacing within a reasonable range, keeping the peripheral stress of the bolt holes within a reasonable range, avoiding excessive material use, and reducing material costs. This contributes to improving the safety and reliability of load-bearing connection structures in complex mechanical fields such as large and complex equipment, long-distance ship voyages, and aerospace.

[0079] Optionally, the step of determining the maximum force, maximum shear stress, and critical bending stress of the target bolt based on the distribution position of the target bolt on the plate, and applying external force to the plate as the force to be optimized, includes:

[0080] Based on mechanical principles, the distribution position of the target bolt on the plate and the external force applied to the plate are used to determine the force analysis results of the target bolt;

[0081] Based on the force analysis results of the target bolt, the maximum force analysis result is determined as the maximum force of the target bolt;

[0082] Based on the diameter of the target bolt and the maximum force on the target bolt, determine the maximum shear stress of the target bolt;

[0083] Based on the principle of torque analysis, the torque and moment of inertia with the largest torque in the target bolt are determined, and the critical bending stress is determined.

[0084] The stress to be optimized is determined based on the maximum force on the target bolt, the maximum shear stress on the target bolt, and the critical bending stress.

[0085] Specifically, after determining the force analysis results for bolts A, B, and C using the method described above, F is determined. A F B and F C If the maximum force is on bolt C, then the maximum force on the target bolt is:

[0086] F max =F C (4)

[0087] Because all target bolts in this invention are of the same size, meaning they all have the same diameter d, the maximum shear stress of the target bolt is further determined based on its diameter and the aforementioned maximum force. For example, the formula for determining the maximum shear stress received by the target bolt at this point can be expressed as:

[0088]

[0089] Where, τ max The maximum shear stress of the target bolt is represented by d, and the diameter of the target bolt is represented by d.

[0090] Furthermore, based on the principle of torque analysis, a torque analysis was performed on the target bolt. Figure 4 This is a cross-sectional view of bolt B cut along the Y-axis according to an embodiment of the present invention. Figure 5 This is a torque diagram of the flat plate provided in an embodiment of the present invention; as shown below. Figure 4 and 5 As shown, it is clear that bolt B experiences the greatest torque, and the moment of inertia and torque at bolt B are also the greatest. Therefore, based on the moment of inertia and torque at bolt B, the critical bending stress of the target bolt can be determined. Figure 4 Z represents the central axis of the flat plate.

[0091] The stress to be optimized is determined based on the maximum force, maximum shear stress, and critical bending stress of the target bolt. This can be understood as the maximum force, maximum shear stress, and critical bending stress of the target bolt being closely related to the bolt diameter and its positional distribution. Optimizing these maximum forces, maximum shear stresses, and critical bending stresses ensures that the stress around the bolt hole is within a reasonable range, avoiding excessive material usage and reducing material costs.

[0092] Optionally, determining the maximum torque and moment of inertia in the target bolt based on the torque analysis principle, and determining the critical bending stress, includes:

[0093] Based on the principle of torque analysis, the torque M and moment of inertia I with the largest torque in the target bolt are determined;

[0094] Based on the ratio of the maximum torque M to the moment of inertia I, the critical bending stress σ is determined. max .

[0095] Specifically, such as Figure 4 and 5 As shown, the torque and moment of inertia are greatest at bolt B, which can be expressed by the formula:

[0096]

[0097]

[0098] Where I represents the moment of inertia; I max I represents the maximum moment of inertia; 孔 The moment of inertia corresponding to the hole diameter of the plate on which the target bolt is located; I 偏移 The value represents the offset moment of inertia; L represents the length of the plate, W represents the width of the plate, H represents the height of the plate, a represents the spacing between any bolts, d represents the diameter of the bolts; Q represents the distance from the bolt center to the centroid O; F B This indicates the force applied to bolt B.

[0099] Based on the ratio of the maximum torque M to the moment of inertia I, the critical bending stress σ is determined. max , can be represented as:

[0100] Where, σ max M represents the critical bending stress; I represents the maximum torque; and M represents the maximum moment of inertia.

[0101] Optionally, the cost function for determining the target bolt based on the price list of bolt diameter and unit price includes:

[0102] Based on the square method, a price list of bolt diameters and unit prices is used to fit the relationship between the price of the target bolt and the diameter of the target bolt, thereby determining the cost function of the target bolt.

[0103] Specifically, the price list for bolt diameters and unit prices is shown in Table 1.

[0104] Table 1

[0105]

[0106]

[0107] The price of the bolts is the cost of 100 bolts. The price curve is fitted into a function using the square method. The cost function of the target bolts is: K1 = 0.4601d-4; (9)

[0108] Furthermore, based on the maximum force on the target bolt, the maximum shear stress of the target bolt, the critical bending stress, and the cost function shown above, the objective function is determined, which can be expressed as:

[0109]

[0110] Where Fitness represents the objective function of the target bolt, and K2 represents the adjustment parameter. From this formula (10), it can be seen that the objective function is a function of the two independent variables: the spacing of the target bolts and the diameter of the target bolts.

[0111] Optionally, the step of minimizing and optimizing the objective function based on the Grey Wolf algorithm to obtain the spacing and diameter of the target bolts includes:

[0112] Set the gray wolf population size, maximum number of iterations, solution dimension, and boundary range;

[0113] The position of each individual gray wolf in the gray wolf population is initialized as a candidate set for the initial position of the target bolt;

[0114] The objective function is used as the fitness function of individual gray wolves to determine the fitness value of each gray wolf in the gray wolf population. The gray wolf with the smallest fitness value is designated as the global best gray wolf α, the gray wolf with the second smallest fitness value is designated as the global second best gray wolf β, and the gray wolf with the third smallest fitness value is designated as the global third best gray wolf δ.

[0115] According to the iteration rules, update the position information of each individual gray wolf in the gray wolf population at the next moment; the iteration rules include:

[0116]

[0117] in, Let α, β, and δ be the distance vectors between α and the other gray wolves, respectively. and Let be vectors representing the current positions of α, β, and δ, respectively. and It is a random vector. A vector representing the current position of the gray wolf population;

[0118]

[0119]

[0120] Where A1, A2, and A3 represent intermediate parameters, and A vector representing the current position of other gray wolves in the gray wolf population; A vector representing the next position of the gray wolf population; the intermediate parameters A1, A2, and A3 and the random vector. and The following formula is used for calculation:

[0121]

[0122]

[0123] in, The convergence factor is and The modulus of is a random number between [0-1].

[0124] Based on the position information of each individual gray wolf in the gray wolf population at the next moment, the globally optimal gray wolf α, the globally second-best gray wolf β, and the globally third-best gray wolf δ are updated until the maximum number of iterations is reached, so as to obtain the spacing and diameter of the target bolts.

[0125] Specifically, in order to more clearly explain the method for determining the layout of bolted connections based on the gray wolf algorithm provided by the present invention, the principle of the gray wolf algorithm will be introduced first.

[0126] The Grey Wolf algorithm mainly includes three aspects: surrounding the prey, hunting, and attacking the prey.

[0127] 1. Encirclement and capture of prey

[0128] The behavior of gray wolf packs hunting prey is defined as follows:

[0129]

[0130]

[0131] in, The distance between the wolf and its prey is represented by t, where t represents the current iteration number. and These are the current position vectors of the prey and the gray wolf, respectively. and For the coefficient vector, This represents the position vector of the gray wolf at the next moment.

[0132] calculate and The formula is as follows:

[0133]

[0134]

[0135] in, The convergence factor is denoted as , which decreases linearly from 2 to 0 as the number of iterations decreases. and The modulus of is a random number between [0-1].

[0136] 2. Hunting

[0137] Gray wolves can pinpoint the exact location of their prey and, led by the wolf at the top of the pyramid, gradually surround the prey, ensuring that each wolf reaches the optimal position. Therefore, this invention simulates the behavior of gray wolves by selecting three optimal positions around the prey and using these three positions to determine the prey's exact location. Simultaneously, it forces other gray wolves to update their own positions based on the optimal wolf's location. By gradually approaching the prey, they encircle and capture it. The principle behind the individual gray wolf's position updating is as follows... Figure 7 As shown.

[0138] 3. Attacking prey

[0139] To realistically simulate the movement of a gray wolf approaching its prey, When the value of decreases linearly from 2 to 0, its The range also gradually decreased. The value range of is [-α, α], when When within this range, the gray wolf can freely change between its own position and the position of its prey. A larger value will cause the gray wolves to move away from their prey in hopes of finding a more suitable prey, thus prompting the wolf pack to conduct a global search. like A smaller value will cause the gray wolves to approach their prey, prompting the pack to conduct a localized search.

[0140]

[0141] Where t represents the current iteration number, and T is the set maximum number of iterations.

[0142] Before using the Grey Wolf algorithm to minimize and optimize the objective function of the target bolt proposed in this invention, the population size, maximum number of iterations, solution dimension, and boundary range are set.

[0143] Assuming the population size (pop) is 50, the variable dimension (dim) is 2, the maximum number of iterations (maxIter) is 500, the upper boundary velocity is [2, 2], and the lower boundary velocity is [-2, -2]. For M8 bolts, the distance between the bolt and the nickel steel plate, and the distance between bolts, cannot be too small. According to steel structure design specifications, the bolt spacing should not be less than 3d, and the bolt end distance should not be less than 1.5d. A schematic diagram is shown below. Figure 6 As shown. Considering the diameter of the small bolt as well, the bolt diameter d varies from 1.4 to 36. Therefore, this paper selects the following ranges for the spacing a and the bolt diameter d:

[0144] 2.8mm <a<142.5mm

[0145] 1.4mm <d<36mm

[0146] The position of each individual gray wolf in the gray wolf population is initialized as a candidate set for the initial position of the target bolt.

[0147] Using the fitness function as the objective function for the target bolt, the fitness value of each gray wolf in the gray wolf population is determined. The gray wolf with the smallest fitness value is designated as the globally optimal gray wolf α, the gray wolf with the second smallest fitness value as the globally second optimal gray wolf β, and the gray wolf with the third smallest fitness value as the globally third optimal gray wolf δ. The specific positions of the three bolts in the target bolt that this invention needs to solve for need to be infinitely close to the positions of the globally optimal gray wolf α, the globally second optimal gray wolf β, and the globally third optimal gray wolf δ, which can be expressed as follows: and

[0148] Based on an iterative rule, the position information of each individual gray wolf in the gray wolf population at the next time step is updated. This iterative rule includes:

[0149]

[0150] Determine the distances between the current global best gray wolf α, the current second best gray wolf β, and the current global third best gray wolf δ, and the gray wolf population at that time.

[0151]

[0152]

[0153] Based on formulas (12) and (13), the current positions of other gray wolves in the gray wolf pack are determined, and the positions of each gray wolf in the pack are further updated. The meanings of the parameters in the above formulas can be found in the relevant explanations above.

[0154] In addition, the intermediate parameters and random vectors included in formulas (11) to (13) are updated according to the following formula:

[0155]

[0156]

[0157]

[0158] in, The convergence factor is denoted as , which decreases linearly from 2 to 0 as the number of iterations decreases. and The modulus is a random number between [0-1], t represents the current iteration number, and T represents the maximum number of iterations.

[0159] After the update is complete, meaning the position information of each individual gray wolf in the gray wolf population at the next moment is determined, the third gray wolf with the lowest fitness is determined based on the fitness function. The globally optimal gray wolf α, the globally second-best gray wolf β, and the globally third-best gray wolf δ are then updated until the maximum number of iterations is reached. This allows us to determine the position of the final globally optimal gray wolf α at the maximum number of iterations, and the corresponding minimum value of the fitness function. Since the objective function and fitness function correspond in this invention, the minimum value of the fitness function is the minimum value of the objective function. Simultaneously, based on the final position of the globally optimal gray wolf α and the position of the centroid O of the target bolts, the side length of the equilateral triangle distribution of the target bolts is determined, which is the bolt spacing d. Furthermore, the objective function is a function of two independent variables: the bolt spacing and the bolt diameter. With the minimum value of the objective function and the bolt spacing determined, the bolt diameter can naturally be obtained.

[0160] This invention provides a method for determining the layout of bolted connections based on the Grey Wolf algorithm. By analyzing the stress on target bolts asymmetrically distributed on a nickel-steel plate, an objective function is constructed, consisting of the target maximum stress, maximum shear stress, critical bending stress, and the cost function of the target bolts. The Grey Wolf algorithm is then used to determine the minimum optimal solution of the objective function, yielding the bolt spacing and diameter. This reduces the peripheral stress of the nickel-steel plate and the maximum stress on the bolt surface, providing a new approach to optimizing the layout of asymmetrical bolted connections. It can improve the strength and stiffness of the structure, extend the service life and reliability of the bolted connection structure and the bolts themselves. When designing bolts and connection structures, the optimal solution of the Grey Wolf algorithm allows for the selection of bolt diameters and spacing within a reasonable range, keeping the peripheral stress of the bolt holes within a reasonable range, avoiding excessive material use, and reducing material costs. This contributes to improving the safety and reliability of load-bearing connection structures in complex mechanical fields such as large and complex equipment, long-distance ship voyages, and aerospace.

[0161] Figure 8 This is a schematic diagram of the device for determining the layout of bolted connections based on the Grey Wolf algorithm provided in an embodiment of the present invention; as shown. Figure 8 As shown, the device includes:

[0162] The force determination module 801 is used to determine the maximum force, maximum shear stress, and critical bending stress of the target bolts based on their distribution position on the plate, and to optimize the force. The target bolts are three identical bolts, and their distribution on the plate satisfies the condition of forming an equilateral triangle and being asymmetrical. The external force applied to the plate is a tensile force in the positive X-axis direction and a tensile force in the negative Y-axis direction of the coordinate system in which the plate is located.

[0163] Cost module 802 is used to determine the cost function of the target bolt based on a price list of bolt diameter and unit price;

[0164] The objective function module 803 is used to determine the objective function corresponding to the target bolt based on the force to be optimized and the cost function;

[0165] The solver module 804 is used to minimize and optimize the objective function based on the Grey Wolf algorithm to obtain the spacing and diameter of the target bolts.

[0166] Optionally, the force-determining module 801, based on the distribution position of the target bolt on the plate, applies external forces to the plate, and determines the maximum force, maximum shear stress, and critical bending stress of the target bolt. This is used in the process of optimizing the force, specifically for:

[0167] Based on mechanical principles, the distribution position of the target bolt on the plate and the external force applied to the plate are used to determine the force analysis results of the target bolt;

[0168] Based on the force analysis results of the target bolt, the maximum force analysis result is determined as the maximum force of the target bolt;

[0169] Based on the diameter of the target bolt and the maximum force on the target bolt, determine the maximum shear stress of the target bolt;

[0170] Based on the principle of torque analysis, the torque and moment of inertia with the largest torque in the target bolt are determined, and the critical bending stress is determined.

[0171] The stress to be optimized is determined based on the maximum force on the target bolt, the maximum shear stress on the target bolt, and the critical bending stress.

[0172] It should be noted that the division of units in the embodiments of the present invention is illustrative and only represents one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated units described above can be implemented in hardware or as software functional units.

[0173] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a processor-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0174] It should be noted that the apparatus provided in this embodiment of the invention can implement all the method steps implemented in the above method embodiment and can achieve the same technical effect. Therefore, the parts and beneficial effects that are the same as those in the method embodiment will not be described in detail here.

[0175] Figure 9 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention, such as... Figure 9 As shown, the electronic device includes a memory 920, a transceiver 910, and a processor 900; wherein the processor 900 and the memory 920 can also be physically arranged separately.

[0176] The memory 920 is used to store computer programs; the transceiver 910 is used to send and receive data under the control of the processor 900.

[0177] Specifically, the transceiver 910 is used to receive and send data under the control of the processor 900.

[0178] Among them, Figure 9 In this embodiment, the bus architecture may include any number of interconnected buses and bridges, specifically linking various circuits of one or more processors represented by processor 900 and memory represented by memory 920 together. The bus architecture may also link various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and therefore will not be further described herein. A bus interface provides an interface. Transceiver 910 may be multiple elements, including transmitters and receivers, providing a unit for communicating with various other devices over a transmission medium, including wireless channels, wired channels, optical fibers, and other transmission media.

[0179] The processor 900 is responsible for managing the bus architecture and general processing, while the memory 920 can store the data used by the processor 900 during operation.

[0180] The processor 900 can be a central processing unit (CPU), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a complex programmable logic device (CPLD). The processor can also adopt a multi-core architecture.

[0181] The processor 900 executes any of the methods provided in the embodiments of the present invention by calling logical instructions stored in the memory 920, for example:

[0182] Based on the distribution of the target bolts on the plate, the external force applied to the plate determines the maximum force, maximum shear stress, and critical bending stress of the target bolts, which are then used as the force to be optimized. The target bolts are three identical bolts, and their distribution on the plate satisfies the condition of forming an equilateral triangle and being asymmetrically distributed. The external force applied to the plate is the tensile force in the positive X-axis direction and the tensile force in the negative Y-axis direction of the coordinate system in which the plate is located.

[0183] Based on the price list of bolt diameter and unit price, determine the cost function of the target bolt;

[0184] Based on the force to be optimized and the cost function, determine the objective function corresponding to the target bolt;

[0185] Based on the Grey Wolf algorithm, the objective function is minimized and optimized to obtain the spacing and diameter of the target bolts.

[0186] Furthermore, the logical instructions in the aforementioned memory 920 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0187] It should be noted that the electronic device provided in this embodiment of the invention can implement all the method steps implemented in the above method embodiment and achieve the same technical effect. Therefore, the parts and beneficial effects that are the same as those in the method embodiment will not be described in detail here.

[0188] On the other hand, the present invention also provides a computer program product, the computer program product including a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions, and when the program instructions are executed by a computer, the computer is able to execute the method for determining the bolt connection structure layout based on the gray wolf algorithm provided in the above embodiments.

[0189] On the other hand, embodiments of the present invention also provide a processor-readable storage medium storing a computer program for causing the processor to execute the method for determining the bolt connection structure layout based on the gray wolf algorithm provided in the above embodiments.

[0190] The processor-readable storage medium can be any available medium or data storage device that the processor can access, including but not limited to magnetic memory (e.g., floppy disk, hard disk, magnetic tape, magneto-optical disk (MO)), optical memory (e.g., CD, DVD, BD, HVD), and semiconductor memory (e.g., ROM, EPROM, EEPROM, non-volatile memory (NAND FLASH), solid-state drive (SSD)).

[0191] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0192] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0193] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining the layout of bolted connection structures based on the Grey Wolf algorithm, characterized in that, include: Based on the distribution of the target bolts on the plate, the external force applied to the plate determines the maximum force, maximum shear stress, and critical bending stress of the target bolts, which are then used as the force to be optimized. The target bolts are three identical bolts, and their distribution on the plate satisfies the condition of forming an equilateral triangle and being asymmetrically distributed. The external force applied to the plate is the tensile force in the positive X-axis direction and the tensile force in the negative Y-axis direction of the coordinate system in which the plate is located. Based on the price list of bolt diameter and unit price, determine the cost function of the target bolt; Based on the stress to be optimized and the cost function, determine the objective function corresponding to the target bolt; Based on the Grey Wolf algorithm, the objective function is minimized and optimized to obtain the spacing and diameter of the target bolts. The critical bending stress is determined in the following manner: Based on the principle of torque analysis, the torque with the largest torque in the target bolt is determined. and moment of inertia I; ； ； in, The torque representing the maximum torque. Represents the moment of inertia; Indicates the maximum moment of inertia; The moment of inertia corresponding to the hole diameter of the plate on which the target bolt is located; Indicates the offset moment of inertia; L Indicates the length of the plate. W H represents the width of the plate, and H represents the height of the plate. Indicates the spacing of any bolt. d Indicates the diameter of the bolt; Q This indicates the distance from the bolt center to the centroid O; This indicates the force applied to bolt B; Based on the maximum torque The ratio of the moment of inertia I to the critical bending stress is used to determine the critical bending stress. .

2. The method for determining the layout of bolted connections based on the gray wolf algorithm according to claim 1, characterized in that, The method of determining the maximum force, maximum shear stress, and critical bending stress of the target bolts based on their distribution position on the plate, and using these as the stresses to be optimized, includes: Based on mechanical principles, the distribution position of the target bolt on the plate and the external force applied to the plate are used to determine the force analysis results of the target bolt; Based on the force analysis results of the target bolt, the maximum force analysis result is determined as the maximum force of the target bolt; Based on the diameter of the target bolt and the maximum force on the target bolt, determine the maximum shear stress of the target bolt; Based on the principle of torque analysis, the torque and moment of inertia with the largest torque in the target bolt are determined, and the critical bending stress is determined. The stress to be optimized is determined based on the maximum force on the target bolt, the maximum shear stress on the target bolt, and the critical bending stress.

3. The method for determining the layout of bolted connections based on the gray wolf algorithm according to claim 2, characterized in that, Determining the maximum shear stress of the target bolt based on its diameter and maximum force includes: Based on the maximum force of the target bolt The diameter of the target bolt And the shear stress formula is used to determine the maximum shear stress of the target bolt; The shear stress formula is: ; in, This represents the maximum shear stress of the target bolt.

4. The method for determining the layout of bolted connections based on the gray wolf algorithm according to claim 1, characterized in that, The price list based on bolt diameter and unit price determines the cost function of the target bolt, including: Based on the square method, a price list of bolt diameters and unit prices is used to fit the relationship between the price of the target bolt and the diameter of the target bolt, thereby determining the cost function of the target bolt.

5. The method for determining the layout of bolted connections based on the gray wolf algorithm according to claim 1, characterized in that, The method based on the Grey Wolf algorithm minimizes and optimizes the objective function to obtain the spacing and diameter of the target bolts, including: Set the gray wolf population size, maximum number of iterations, solution dimension, and boundary range; The position of each individual gray wolf in the gray wolf population is initialized as a candidate set for the initial position of the target bolt; The objective function is used as the fitness function for individual gray wolves to determine the fitness value for each gray wolf in the population. The gray wolf with the smallest fitness value is then selected as the globally optimal gray wolf. The gray wolf with the second lowest fitness value is considered the second best gray wolf globally. The gray wolf with the third lowest fitness value is considered the third best gray wolf globally. ; According to the iteration rules, update the position information of each individual gray wolf in the gray wolf population at the next moment; the iteration rules include: ； in, , , They are respectively , , Distance vector between the wolf and other gray wolves , and They represent , , The vector of the current position. , and For random vectors, A vector representing the current position of the gray wolf population; ； ； in, , and Indicates intermediate parameters. , and A vector representing the current position of other gray wolves in the gray wolf population; A vector representing the next position of the gray wolf population; the intermediate parameters , and and random vectors , and The following formula is used for calculation: ； ； ； in, The convergence factor is and The modulus of is a random number between [0-1], t represents the current iteration number, and T represents the maximum number of iterations. Based on the position information of each individual gray wolf in the gray wolf population at the next moment, update the globally optimal gray wolf. The second best overall performance comes from the Grey Wolves. And the third best overall, the Grey Wolf The process continues until the maximum number of iterations is reached, at which point the spacing and diameter of the target bolts are obtained.

6. A device for determining the layout of bolted connection structures based on the Grey Wolf algorithm, characterized in that, The apparatus for implementing the method for determining bolt connection structure layout based on the Grey Wolf algorithm as described in any one of claims 1 to 5, the apparatus comprising: A force determination module is used to determine the maximum force, maximum shear stress, and critical bending stress of the target bolts based on their distribution positions on the plate. These are used as the force to be optimized. The target bolts are three identical bolts, and their distribution positions on the plate satisfy an equilateral triangle and an asymmetrical distribution. The external force applied to the plate is a tensile force in the positive X-axis direction and a tensile force in the negative Y-axis direction of the coordinate system in which the plate is located. The cost estimation module is used to determine the cost function of the target bolt based on a price list of bolt diameter and unit price; The objective function module is used to determine the objective function corresponding to the target bolt based on the force to be optimized and the cost function; The solution module is used to minimize and optimize the objective function based on the Grey Wolf algorithm to obtain the spacing and diameter of the target bolts.

7. The device for determining the layout of bolted connections based on the gray wolf algorithm according to claim 6, characterized in that, The force determination module, based on the distribution position of the target bolt on the plate, applies external forces to the plate to determine the maximum force, maximum shear stress, and critical bending stress of the target bolt. These parameters are then used in the process of optimizing the force distribution. Specifically, this is used for: Based on mechanical principles, the distribution position of the target bolt on the plate and the external force applied to the plate are used to determine the force analysis results of the target bolt; Based on the force analysis results of the target bolt, the maximum force analysis result is determined as the maximum force of the target bolt; Based on the diameter of the target bolt and the maximum force on the target bolt, determine the maximum shear stress of the target bolt; Based on the principle of torque analysis, the torque and moment of inertia with the largest torque in the target bolt are determined, and the critical bending stress is determined. The stress to be optimized is determined based on the maximum force on the target bolt, the maximum shear stress on the target bolt, and the critical bending stress.

8. An electronic device, characterized in that, Includes memory, transceiver, and processor; Memory, used to store computer programs; Transceiver, used to send and receive data under the control of the processor; A processor for executing a computer program in the memory and implementing the method for determining the layout of bolted connections based on the Grey Wolf algorithm as described in any one of claims 1 to 5.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program for causing a computer to perform the method for determining the layout of bolted connections based on the Grey Wolf algorithm as described in any one of claims 1 to 5.

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