Connection hole site iterative optimization method based on multi-dimensional stress characteristic driving

Abstract

The invention relates to a connection hole site iterative optimization method based on multi-dimensional stress characteristic driving. The problems existing in layout optimization of connecting hole sites of plate / shell components at present are solved. Firstly, the center position of a design domain inner hole is parameterized; calculating at least two of equivalent stress, stress gradient, principal stress direction and strain energy density under a predefined load; calculating a comprehensive influence function through a method of normalizing and weighting the multi-dimensional features; carrying out iterative optimization on the position of the guide hole in the first principal stress direction, calculating a multi-dimensional stress feature and a comprehensive influence function in each iteration, and carrying out dynamic updating on a feasible region by considering geometric and process constraints at the same time; after iterative calculation convergence, a calculation result is output, and key index verification is carried out; checking whether geometric constraints and process manufacturing conditions are met or not; and generating a sample piece and carrying out physical test verification. According to the method, optimization of multiple performance targets such as strength, rigidity and fatigue life can be achieved, and the method can also be closely combined with engineering practical application.

Description

Technical Field

[0001] This invention belongs to the field of engineering structure connection design optimization technology, and relates to a method for iteratively optimizing the position of connection holes of mechanical fasteners based on multidimensional stress characteristics. It is applicable to the position layout optimization of connection holes such as bolts and rivets in plate / shell components. Background Technology

[0002] In fields such as mechanical engineering and transportation, the layout of connection holes (e.g., bolt and rivet connection holes) in plate / shell components directly affects the strength, fatigue life, and manufacturability of the structure.

[0003] Existing methods generally suffer from the following drawbacks: the placement of connection holes often relies on design experience; they are arranged all at once within a fixed design space; finite element analysis is mostly used for verification after design completion; a single index (such as maximum equivalent stress) is often used as the optimization objective; and geometric constraints are not considered during the optimization process. These limitations result in evaluation indices failing to fully reflect the impact of hole placement on structural performance and hinder the real-time guidance of hole placement towards more favorable stress regions during optimization. Therefore, there is an urgent need for an optimization method that can integrate stress characteristics and geometric constraints to achieve real-time iterative adjustment of the hole placement optimization direction. Summary of the Invention

[0004] This invention addresses the following problems in the current optimization of connection hole layout for plate / shell components by providing an iterative optimization method for connection hole positions driven by multidimensional stress characteristics: reliance on experience to determine hole positions, limited and fixed design space, application of finite element analysis only after design completion, use of a single evaluation index, and lack of real-time optimization and adjustment of hole movement direction.

[0005] This invention is achieved through the following technical solutions:

[0006] A method for iterative optimization of connection hole positions driven by multidimensional stress characteristics includes the following steps:

[0007] Step 1: Parameterize the center position of the connecting holes within the design space of the target structure, and set geometric constraints such as minimum hole spacing and minimum edge distance;

[0008] Step 2: Perform calculations under the initial hole arrangement and working conditions to obtain at least two stress characteristics from the equivalent stress, stress gradient, first principal stress direction, and strain energy density;

[0009] Step 3: Normalize and weight the stress characteristics, and adjust the weighting coefficients adaptively to construct a comprehensive influence function for evaluating candidate hole locations;

[0010] Step 4: Using the direction of the first principal stress as a reference, and combining the changing trend of the comprehensive influence function, determine the direction of iterative movement of the hole center position;

[0011] Step 5: Repeat the above steps until the convergence condition is met.

[0012] Furthermore, the design space is a pre-defined geometric space in the target structure that allows for hole position adjustment. The design space satisfies both geometric and process constraints and is dynamically updated during the optimization iteration process.

[0013] Furthermore, the comprehensive influence function is obtained by combining the equivalent stress, stress gradient, strain energy density, and principal stress direction with normalized weights.

[0014] Furthermore, the moving step size of the hole center position is adaptively adjusted according to the decreasing trend of the comprehensive influence function.

[0015] Furthermore, the dynamic design space is generated in the initial stage by a comprehensive influence function combining the first principal stress direction with multidimensional stress characteristics, and is adjusted according to the latest stress characteristics after each iteration.

[0016] Furthermore, spaces where the stress gradient exceeds the threshold are eliminated, and spaces with low values ​​of the comprehensive influence function are extended along the direction of the first principal stress.

[0017] Furthermore, the comprehensive objectives include maximum equivalent stress, fatigue damage, etc., and the weights are adaptively adjusted according to the convergence speed of each objective.

[0018] Furthermore, when updating the design space, it is simultaneously determined whether the constraints such as minimum hole spacing, minimum edge distance, and non-design space are met.

[0019] Furthermore, methods for calculating stress characteristics include, but are not limited to, the finite element method, the boundary element method, or the meshless method.

[0020] Furthermore, the method is applicable to bolts, rivets, and other similar mechanical fasteners for plate / shell components.

[0021] This invention parameterizes the position of the connecting hole, using the direction of the first principal stress as the primary guide, and combines this with a comprehensive influence function of stress characteristics to guide the iterative optimization of the hole position. Each iteration calculates multi-dimensional stress characteristics while also considering geometric and process constraints, thereby achieving optimization of multiple performance objectives such as strength and fatigue life, and is closely integrated with engineering practice. Attached Figure Description

[0022] Figure 1 This is a flowchart of the invention;

[0023] Figure 2 This is a schematic diagram of the method of the present invention. Detailed Implementation

[0024] The following is in conjunction with the appendix Figure 1 , 2 Specific embodiments of the present invention will be described below.

[0025] S1 Design Space and Hole Position Parameterization

[0026] In structural components, the allowable space area (i.e., design space, denoted as Ω) used for adjusting the position of holes d ).

[0027] In the design space Ω d The following parameters and constraints will be established:

[0028] The initial center position coordinates (x0, y0) of the hole are used as an adjustable design variable.

[0029] Minimum spacing d of holes min To ensure that the distance between adjacent holes is not too small, thus preventing localized strength reduction.

[0030] Minimum edge distance b of the hole min To prevent the hole position from being too close to the edge of the design space and avoid machining interference;

[0031] Aperture range [r] min ,r max ]: Ensure it matches the specifications of the connecting components;

[0032] Ω und Spaces where holes cannot be placed, such as welding areas or reinforcing ribs.

[0033] S2 Multidimensional Stress Feature Acquisition

[0034] Based on predefined loads and boundary conditions, a mechanical response analysis is performed on the structure to extract a multidimensional stress feature set S = {S1, S2, ...}. This set must include at least two of the following indices:

[0035] Equivalent stress σ eq : A characteristic quantity that reflects the stress state of the material around the connecting hole and measures whether the material will undergo plastic deformation:

[0036] stress gradient It reflects the variation of stress with spatial location. Areas with higher stress gradients are prone to failure modes such as fatigue fracture and brittle fracture, thus affecting fatigue life.

[0037] The direction of the first principal stress, n1, reflects the directionality of the applied stress and corresponds to the direction vector of the maximum principal stress, which is of great significance for guiding the crack path.

[0038] Strain energy density per unit volume U: This represents the elastic deformation energy stored in a localized area of ​​the material per unit volume. It is a key parameter reflecting the material's deformation energy state, and it helps to prevent energy concentration in localized areas such as connecting holes, sharp corners, and other geometric discontinuities.

[0039]

[0040] σ i ε i τ ij γ ij These represent normal stress, normal strain, shear stress, and shear strain, respectively.

[0041] S3 Constructing the Comprehensive Influence Function and Adjusting Adaptive Weights

[0042] The stress characteristics are normalized to construct a unified comprehensive influence function FI, which guides iterative optimization in areas with better hole orientation performance. The specific implementation steps are as follows:

[0043] S3.1 Normalization Processing: The maximum-minimum value normalization method is used to calculate the stress characteristic S. i Dimensionless normalized value:

[0044]

[0045] in, S is the i-th feature after normalization; i,max S i,min These are the maximum and minimum values ​​of the i-th feature in the current design space, respectively.

[0046] S3.2 Adjust adaptive weights:

[0047] 1. Define the initial weight w i Before iterative optimization begins, each stress characteristic is evaluated based on engineering requirements or design experience, and an initial weight w is assigned. i .

[0048] 2. Index convergence: After each iteration, calculate the normalized improvement rate R of each stress characteristic. i,k+1 :

[0049]

[0050] Among them, S i,k Let represent the normalized value of the stress characteristic after the k-th iteration.

[0051] 3. Calculate the weight adjustment:

[0052] Method 1: Adjust according to the convergence rate. If the R of the i-th stress characteristic iA smaller R-value indicates a slower convergence rate for this indicator, therefore its weight should be increased. Conversely, if the R-value of this indicator is smaller... i If the value is close to 0, its weight should be appropriately reduced.

[0053] Method 2: Adjust based on the gap between the current indicator value and the target value.

[0054] 4. Adjust the weights:

[0055] w i,k+1 =w i,k +Δw i,k+1

[0056] Among them, the weight adjustment amount Δw i,k+1 =α·(1-R) i,k+1 ), where α is the adjustment coefficient.

[0057] The updated weights are then normalized.

[0058]

[0059] S3.3 Calculation of Comprehensive Influence Function: The normalized features are weighted according to their respective weights to calculate the comprehensive influence function FI at the current hole position.

[0060]

[0061] The smaller the FI value, the better the overall performance at that location.

[0062] S3.4 Constructing the FI distribution field: A continuous FI distribution field is formed throughout the entire design space using numerical or contour methods such as gradient descent.

[0063] S4 Hole Position Iterative Adjustment

[0064] Based on the principle of minimizing FI and the coupling relationship between the principal stress direction n1, the hole position is iteratively optimized and adjusted. The steps are as follows:

[0065] S4.1 Determine the migration direction: For the current hole center position (x... k ,y k Obtain the unit vector n1 = (cosθ, sinθ) in the direction of the first principal stress, and evaluate the trend of change along the two directions of FI value ±n1:

[0066] The FI value decreases along the n1 direction, so the n1 direction is selected as the current preferred migration direction.

[0067] The FI value decreases along the -n1 direction; choose the opposite direction.

[0068] If the change in FI is not significant in either direction, then retain the current position.

[0069] S4.2 Update Hole Position Coordinates: Based on the migration direction selected in S4.1, update the hole center position according to the initial step size Δs.

[0070] (x k+1 ,y k+1 )=(x k ,y k )+Δs·n1

[0071] Δs can be a fixed value, or it can be adaptively adjusted according to the rate of change of FI, which can be defined as:

[0072]

[0073] When η is small, it indicates that the performance improvement is relatively limited. In this case, the step size Δs should be reduced for a more refined search. When η is large, the step size Δs can be increased to speed up the convergence.

[0074] S4.3 Constraint Check: Check whether the new hole location meets the following constraints: located in the design space Ω d Within; meets constraints such as minimum hole spacing, minimum edge distance, and processing area; does not interfere with existing structures or other hole positions.

[0075] Building and updating the S5 dynamic design space

[0076] Taking into account both the FI value of S3 and the migration direction of S4, a global search method for updating the hole position is established in the design space Ω. d The system searches for the globally optimal solution.

[0077] The dynamic design space proposed in this invention refers to a design space that can change with the stress field during the optimization process, making the optimization results more practical for actual engineering applications.

[0078] At the beginning of the optimization process, a larger step size is used to explore from multiple directions to avoid local optima. In the later stages, the step size is gradually reduced, focusing on more refined iterative optimization within the low-FI design space.

[0079] In the same iteration, several possible candidate hole positions are generated simultaneously. Based on the FI value of the candidate hole, the starting point of the next iteration is selected.

[0080] After each iteration, the generated candidate positions are evaluated based on constraints such as minimum hole spacing and manufacturing process requirements. Positions that do not meet these constraints are eliminated.

[0081] S6 Convergence Condition

[0082] Method 1: In N consecutive iterations, the improvement in FI is lower than the threshold ε or reaches the preset maximum number of iterations N. max When the iteration converges;

[0083] Method 2: In N consecutive iterations, the standard deviation of FI is less than the threshold ∈ std When the iteration converges, this method helps prevent premature termination of the iteration due to a single fluctuation in FI. The mathematical expression is as follows:

[0084] Iteration terminated.

[0085] S7 Result Output and Verification

[0086] Output optimal hole center coordinates (x * ,y * And the iterative convergence curve.

[0087] Calculate the key stress parameters under the optimal hole position condition and compare them with the initial hole position to verify the improvement.

[0088] Check whether the final optimization results meet the engineering constraints such as processing and assembly.

[0089] S8 Process Integration and Application

[0090] The final hole coordinates are updated to a 3D CAD model and machining drawings are generated.

[0091] Adjust the stamping, welding and other process routes based on the optimized model data.

[0092] Physical tests were conducted on the samples to verify the improvement effect on structural performance (strength, fatigue, etc.).

[0093] Example:

[0094] The specific application process of this invention is illustrated using a longitudinal beam sheet metal connector of a commercial vehicle frame as an example. This 6mm thick structure is made of Q345B steel plate and is bolted to the frame, bearing the vertical and torsional loads generated during vehicle operation.

[0095] S1 Design Space and Hole Position Parameterization

[0096] Based on the overall vehicle layout and installation requirements, the design space Ω is determined. d Given a rectangular space with a length of 40mm and a width of 30mm, and initial hole position coordinates (x0, y0), set the following constraints:

[0097] Minimum hole spacing: d min =12mm;

[0098] Minimum margin: b min =10mm;

[0099] Aperture range: r min =6mm, r max =8mm;

[0100] Non-design space Ω und : Welding area and space for reinforcing ribs, etc.

[0101] S2 Multidimensional Stress Characteristic Calculation

[0102] Finite element modeling was performed on the structural components, and typical vehicle loads (vertical impact + local torsion) were applied, constraining the nodes at the connection surfaces with the frame. The design space Ω... d Multidimensional stress characteristics around the initial hole: equivalent stress σ eq Stress gradient The first principal stress direction n1, strain energy density per unit volume U.

[0103] S3 Constructing the Comprehensive Influence Function and Adjusting Adaptive Weights

[0104] For each stress characteristic, perform maximum / minimum value normalization. Set the initial weights to...

[0105] w n1 =0.3, w U =0.4.

[0106] During the iteration process, the convergence of each indicator is monitored in real time.

[0107] For example, stress gradient When the improvement rate is lower than expected, increase its weight, for example, by... The value was adjusted to 0.4, while other weights were reduced to accelerate the optimization of the high-stress-concentration space.

[0108] For each candidate aperture, calculate the comprehensive influence function FI according to the updated weights. The smaller the value, the better the comprehensive performance at that location.

[0109] S4 Hole Position Iterative Adjustment

[0110] A search method for updating the location of the connecting hole is established based on the principle of minimizing FI and the direction of the first principal stress n1.

[0111] Using the principal stress direction n1 as a reference, and considering the decreasing trend of the FI value, the direction of the connecting hole movement is determined. A relatively large initial step size Δs = 2mm is used for global exploration, and the step size is gradually reduced to Δs = 0.5mm in the later stages, focusing on the design space with low FI and making more refined iterative adjustments.

[0112] After each iteration update, check whether the candidate connection hole positions meet constraints such as minimum hole spacing, minimum edge distance, and non-design space.

[0113] Building and updating the S5 dynamic design space

[0114] After each iteration, the design space is dynamically adjusted based on the latest changes in multidimensional stress characteristics. For example, if the stress gradient in a certain space consistently exceeds a preset threshold, that region will be excluded from the design space. If the FI value in a certain direction continues to decrease, the design space will expand in that direction.

[0115] S6 Convergence Condition

[0116] Robust convergence criteria are adopted. If the standard deviation of FI at the hole location is less than ε over 30 consecutive iterations... std =1×10 -4 If convergence is achieved, then the maximum number of iterations N is calculated. max =50 is used as a backup convergence condition.

[0117] S7 Hole Position Optimization Results Output and Verification

[0118] Output the final hole center coordinates (x * ,y * The radius of curvature is (6.5, -8.0) mm, and FI has decreased by 23.4% compared to the initial value. Verification steps:

[0119] Finite element analysis of the optimized connection hole positions showed that the maximum equivalent stress decreased by 17.3%, the local strain energy density decreased by 18.5%, and the fatigue life increased by approximately 13%.

[0120] The optimized hole arrangement was checked and found to meet geometric and process constraints, with no potential interference or local failure risk.

[0121] S8 Process Integration and Application Deployment

[0122] The final hole positions were updated, a CAD model was created, machining drawings were generated, and drilling, welding, and other processes were adjusted. Field testing of the prototype showed that the structure with optimized hole positions met the strength and fatigue performance requirements.

Claims

1. A method for iterative optimization of connection hole positions based on multidimensional stress characteristics, characterized in that: Includes the following steps: Step 1: Parameterize the center position of the connecting holes within the design space of the target structure, and set the minimum hole spacing and minimum edge distance geometric constraints; Step 2: Perform calculations under the initial hole arrangement and working conditions to obtain at least two stress characteristics from the equivalent stress, stress gradient, first principal stress direction, and strain energy density; Step 3: Normalize and weight the stress characteristics, and adjust the weighting coefficients adaptively to construct a comprehensive influence function for evaluating candidate hole locations; Step 4: Using the direction of the first principal stress as a reference, and combining the changing trend of the comprehensive influence function, determine the direction of iterative movement of the hole center position; Step 5: Repeat the above steps until the convergence condition is met.

2. The method for iterative optimization of connection hole positions based on multidimensional stress characteristics according to claim 1, characterized in that: The design space is a pre-defined geometric space in the target structure that allows for hole position adjustment. The design space satisfies both geometric and process constraints and is dynamically updated during the optimization iteration process.

3. The method for iterative optimization of connection hole positions based on multidimensional stress characteristics according to claim 1, characterized in that: The comprehensive influence function is obtained by combining the equivalent stress, stress gradient, strain energy density and principal stress direction with normalized weights.

4. The method for iterative optimization of connection hole positions based on multidimensional stress characteristics according to claim 1, characterized in that: The movement step size of the hole center position is adaptively adjusted according to the decreasing trend of the comprehensive influence function.

5. The method for iterative optimization of connection hole positions based on multidimensional stress characteristics according to claim 2, characterized in that: The dynamic design space is generated in the initial stage by a comprehensive influence function combining the first principal stress direction and multidimensional stress characteristics, and is further refined after each iteration based on the latest stress characteristics.

6. The method for iterative optimization of connection hole positions based on multidimensional stress characteristics according to claim 5, characterized in that: Spaces with stress gradients exceeding the threshold are discarded, and spaces with low values ​​of the comprehensive influence function are extended along the direction of the first principal stress.

7. The method for iterative optimization of connection hole positions based on multidimensional stress characteristics according to claim 1, characterized in that: The comprehensive objective includes maximum equivalent stress and fatigue damage, and the weights are adaptively adjusted according to the convergence speed of each objective.

8. The method for iterative optimization of connection hole positions based on multidimensional stress characteristics according to claim 1, characterized in that: When updating the design space, it is simultaneously determined whether the minimum hole spacing, minimum edge distance, and non-design space constraints are met.

9. The method for iterative optimization of connection hole positions based on multidimensional stress characteristics according to claim 1, characterized in that: Methods for calculating stress characteristics include, but are not limited to, the finite element method, the boundary element method, or the meshless method.

10. The method for iterative optimization of connection hole positions based on multidimensional stress characteristics according to claim 1, characterized in that: The method is applicable to bolts, rivets, and other similar mechanical fasteners for plate / shell components.

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