Co-optimization design method for structural stiffeners and support locations

Abstract

This invention discloses a method for the collaborative optimization design of stiffeners and support positions in a structure, comprising the following steps: 1. Establishing an initial base structure model based on the external dimensions of the box-shaped structure; 2. Initializing design parameters; 3. Performing mechanical performance analysis on the box-shaped structure, calculating the sensitivity of the support units and the number of support units to be retained in the current iteration step; 4. Entering a sub-loop for support position optimization; 5. Optimizing the stiffener layout based on the optimization results of the support positions and updating the box-shaped structure model; 6. Repeating the iterative process from steps 3 to 5, stopping the iteration when the change in the objective function is less than the convergence tolerance. This invention relates to the field of mechanical construction design technology and can solve the problem in the prior art where the optimization design of stiffener distribution is limited by pre-given support conditions, resulting in suboptimal design results.

Description

Technical Field

[0001] This invention relates to the field of mechanical construction design technology, and in particular to a method for the coordinated optimization design of structural stiffeners and support positions. Background Technology

[0002] The foundation structure of mechanical equipment must possess sufficient static and dynamic characteristics to meet the equipment's performance requirements. Such foundation structures often employ box-type structures with internal reinforcing ribs. Clearly, the arrangement of these ribs is related to the load-bearing method and support locations of the foundation structure. Given a fixed working load on the mechanical equipment, the arrangement of the ribs varies with the number and location of supports at the bottom of the foundation structure. The number and location of these supports are also design parameters that can vary within a certain range.

[0003] Currently, when optimizing the distribution of stiffeners in a structure, the support conditions are generally predetermined based on design experience, neglecting the impact of support locations on the structure's load-bearing capacity and other performance characteristics, thus reducing the possibility of further improving structural performance. In fact, since the loads borne by the structure need to be transferred to the supports through the stiffeners, the distribution of stiffeners and the support locations are interdependent, causing the optimization design of stiffener distribution to be limited by the predetermined support conditions. Therefore, there is a need to provide a method for the collaborative optimization design of structural stiffeners and support locations, which can solve the problem in existing technologies where the optimization design of stiffener distribution is limited by predetermined support conditions, resulting in suboptimal design results. Summary of the Invention

[0004] The purpose of this invention is to provide a method for the coordinated optimization design of the stiffener and support positions of a structure, which can solve the problem that the optimization design of stiffener distribution in the prior art is limited by the pre-given support conditions, resulting in suboptimal design results.

[0005] This invention is implemented as follows:

[0006] A method for coordinating and optimizing the design of stiffeners and support locations in a structure, comprising the following steps:

[0007] Step 1: Based on the external dimensions of the box-shaped structure, establish an initial basic structure model, which includes the main body of the box-shaped structure (1) and the supporting structure;

[0008] Step 2: Initialize design parameters: seed point, support degradation rate V d The final number of support units to be retained, N * ;

[0009] Step 3: Perform mechanical performance analysis on the box-type structure, and calculate the sensitivity α of the j-th support unit (2) according to equation (2). j eThe number N of support units to be retained in the i-th iteration step is calculated according to equation (3). i * :

[0010]

[0011] In the formula, α j e The sensitivity of the j-th support unit (2); x j To support the pseudo-density variable of the unit; K st K is the stiffness matrix of the main body of the box-shaped structure (1); su Here is the stiffness matrix of the support structure composed of support elements (2); p is the penalty factor; K j su,e u is the stiffness matrix of the j-th support element (2); j Let be the displacement vector of the j-th support element (2);

[0012]

[0013] Step 4: Enter the sub-loop for support position optimization;

[0014] Step 5: Optimize the layout of the reinforcing ribs based on the optimization results of the support positions, and update the box-type structure model;

[0015] Step 6: Repeat the iterative process from Step 3 to Step 5. According to Equation (13), stop the iteration when the change in the objective function is less than the convergence tolerance.

[0016]

[0017] Where C is the objective function; i is the current iteration step; δ is the convergence tolerance; and M is an integer from 3 to 5.

[0018] Step 1 includes the following sub-steps:

[0019] Step 1.1: Discretize the box-shaped structure main body (1), i.e. the structural design domain, using hexahedral elements, and establish shell elements with a certain thickness on the surface and inside of the box-shaped structure main body (1) according to the corresponding element node information, i.e., surface shell elements (3) and internal shell elements (4), the internal shell elements (4) being the stiffeners;

[0020] Step 1.2: Introduce a support design domain at the bottom periphery of the structural design domain. The support design domain includes several support units (2) connected to the main body of the box structure (1). The several support units (2) constitute the support structure, and the support position of the several support units (2) is optimized.

[0021] Each of the aforementioned support units (2) is a three-degree-of-freedom spring unit; wherein, the node located at the top of the spring unit is connected to the node of the surface shell unit (3) on the bottom periphery of the box-shaped main body (1), and the node located at the bottom of the spring unit is used to define the boundary constraint conditions.

[0022] During the optimization process, based on the mechanical properties of the current structure in each iteration, the support positions are optimized using a two-way progressive structural optimization method. Then, based on the obtained support positions, the internal stiffeners are optimized using an adaptive growth method based on the growth mechanism of natural branching systems. This process is repeated until the optimal layout of the two is obtained. The optimization mathematical model is shown as (a1) to (a8) in equation (1):

[0023] find X = [x1, ... x j ,...,x n (a1)

[0024] T = [T1,...,T] k ,...,T l (a2)

[0025] min C(X,T)=U T KU (a3)

[0026] stF=KU (a4)

[0027] NN * =0 (a5)

[0028] V-ηV0≤0 (a6)

[0029] x min ≤x j ≤1j=[1,...,n] (a7)

[0030] 0 < T min ≤T k ≤T max k = [1,...,l] (a8) (1)

[0031] In the formula, x j To support the pseudo-density variable of the unit; T k For stiffener thickness, C is the global strain energy of the structure, i.e., the objective function; U is the displacement vector; K is the stiffness matrix; F is the load vector; N is the number of support elements retained after optimization convergence; V is the optimized stiffener volume; V0 is the initial stiffener volume; η is the stiffener volume fraction; x min The minimum value of the pseudo-density of the supporting element; T min and T max These are the minimum and maximum thicknesses of the reinforcing ribs, respectively.

[0032] Step 4 includes the following sub-steps:

[0033] Step 4.1: Based on the maximum sensitivity value max(α1) of the support unit (2) e :α n e ) and minimum sensitivity min(α1) e :α n e The sensitivity threshold τ of the support unit (2) at the r-th iteration step of the current sub-loop is calculated using equations (4) and (5). r :

[0034]

[0035]

[0036] Where τ1 is the initial sensitivity threshold for support position optimization;

[0037] Step 4.2: Based on the sensitivity threshold τ r The support unit (2) can be added or deleted as shown in equation (6). The principle for adding or deleting the support unit (2) is: if the sensitivity value of the support unit (2) is greater than the sensitivity threshold τ r If the support unit (2) is a solid, then the sensitivity value of the support unit (2) is less than or equal to the sensitivity threshold τ. r If so, then delete the support unit (2);

[0038]

[0039] Where, x j To support the pseudo-density variable of the unit; x min To support the minimum pseudo-density of the element, x min Take 0.0001;

[0040] Step 4.3: Based on the sensitivity threshold τ of the support unit (2) r and its maximum sensitivity max(α1) e :α n e ) and minimum sensitivity min(α1) e :α n e ), calculate the tolerance e1 for the optimized support position according to equation (7);

[0041]

[0042] Where ε represents the iterative tolerance for supporting position optimization;

[0043] When the iteration tolerance ε is satisfied, exit the sub-loop of support position optimization.

[0044] Step 5 includes the following sub-steps:

[0045] Step 5.1: Calculate the sensitivity of the stiffener according to equation (8);

[0046]

[0047] Among them, u k Let be the displacement vector of the k-th stiffener; Let K be the stiffness matrix of the k-th stiffener, derived from the plane stress term K. k stress and bending term K k bend Therefore, its sensitivity needs to be calculated in two parts:

[0048]

[0049]

[0050] in, and , respectively, are matrices independent of design variables in the plane stress and bending terms, mainly determined by the element size and Poisson's ratio of the shell element; μ is the Poisson's ratio of the stiffener; to reduce the influence of the base structure on the structural stiffening optimization process, the stiffener material properties are penalized according to the stiffener thickness, and the elastic modulus E of the k-th stiffener after penalty is... k for:

[0051]

[0052] Among them, E * The true elastic modulus of the material; T k T represents the thickness of the k-th reinforcing rib. init T represents the initial thickness of the reinforcing rib. m Let the stiffness matrix of the k-th stiffener be the mature thickness. Therefore, the sensitivity of the stiffness matrix of the k-th stiffener with respect to the stiffener thickness can be obtained from equations (11) and (12):

[0053]

[0054]

[0055] in, and They are respectively of thickness T m The plane stress and bending terms of the true stiffness matrix of the stiffeners at that time;

[0056] Step 5.2: Update the stiffener thickness using the MMA algorithm based on the stiffener's sensitivity. In the initial iteration of optimization, the stiffener starts growing from the seed point and continues to diverge and degenerate based on the sensitivity information in subsequent optimization processes.

[0057] Step 5.3: Update the box-type structure model according to the new stiffener thickness;

[0058] Step 5.4: Return to step 3 and re-analyze the mechanical properties of the box structure.

[0059] Compared with the prior art, the present invention has the following advantages:

[0060] This invention updates the stiffeners after iteratively optimizing the support positions and performs collaborative optimization of the stiffeners and support units. Under the same stiffener volume constraint, compared with the traditional optimization results of pre-given support conditions, the collaborative optimization results of this invention are conducive to forming the optimal stiffener distribution and support position distribution. Under the same structural volume, it can improve the stiffness of the box structure, thereby improving the performance of the structure. Attached Figure Description

[0061] Figure 1 This is a flowchart of the method for coordinating and optimizing the design of the reinforcing ribs and support positions in the structure of this invention;

[0062] Figure 2 This is a schematic diagram of step 1 in the collaborative optimization design method for the reinforcing ribs and support positions of the structure of the present invention;

[0063] Figure 3 This is a schematic diagram of step 1.1 in the collaborative optimization design method for the stiffeners and support positions of the structure of the present invention;

[0064] Figure 4 This is a schematic diagram of steps 1 and 2 in Embodiment 1 of the method for coordinated optimization design of the stiffeners and support positions of the structure of the present invention;

[0065] Figure 5 This is a schematic diagram of the iterative process in Embodiment 1 of the method for coordinating the design of the stiffeners and support positions of the structure of the present invention, wherein (a) is a cross-sectional view of the box structure in the 10th iteration step, (b) is a cross-sectional view of the box structure in the 35th iteration step, (c) is a cross-sectional view of the box structure in the 70th iteration step, and (d) is a structural view of the box structure in the 70th iteration step.

[0066] Figure 6 This is an iterative process diagram of the objective function in Embodiment 1 of the collaborative optimization design method for the stiffeners and support positions of the structure of the present invention;

[0067] Figure 7This is an optimization iteration diagram of the stiffener volume and the number of supports in Embodiment 1 of the co-optimization design method for the stiffener and support positions of the present invention. The straight line represents the iteration process diagram of the stiffener volume, and the dashed line represents the iteration process diagram of the number of supports.

[0068] Figure 8 These are the design results of the optimized distribution of stiffeners under known support positions in the traditional design. Among them, (e) is the cross-sectional view of the optimized result of the four sides fixed at the midpoint, (f) is the structural view of the optimized result of the four sides fixed at the midpoint, (g) is the cross-sectional view of the optimized result of the four corner points fixed, and (h) is the structural view of the optimized result of the four corner points fixed.

[0069] In the figure, 1 is the main box structure, 2 is the support unit, 3 is the surface shell unit, and 4 is the internal shell unit. Detailed Implementation

[0070] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0071] Please see the appendix Figure 1 A method for coordinating and optimizing the design of stiffeners and support locations in a structure, comprising the following steps:

[0072] Please see the appendix Figure 2 Step 1: Based on the external dimensions of the box-shaped structure, establish an initial base structure model. The initial base structure model includes the main body 1 of the box-shaped structure (as the structural design domain) and the supporting structure (as the supporting design domain).

[0073] Step 1 includes the following sub-steps:

[0074] Please see the appendix Figure 3 Step 1.1: Discretize the box-shaped structure 1 using hexahedral elements, and establish shell elements with a certain thickness on the surface and inside of the box-shaped structure 1 according to the corresponding element node information, namely surface shell element 3 and internal shell element 4.

[0075] In the structural design domain, the surface shell unit 3 located on the surface of the box-shaped main body 1 is used to characterize the outer wall of the box-shaped structure and serves as a non-design domain; the internal shell unit 4 serves as the optimization design domain for the reinforcing ribs.

[0076] Step 1.2: Introduce a support design domain at the bottom periphery of the structural design domain. The support design domain includes several support units 2 connected to the main body 1 of the box structure. The several support units 2 constitute the support structure, and the support position of the several support units 2 is optimized.

[0077] Each of the aforementioned support units 2 is a three-degree-of-freedom spring unit; wherein, the node located at the top of the spring unit is connected to the node of the surface shell unit 3 on the bottom periphery of the box-shaped main body 1, and the node located at the bottom of the spring unit is used to define boundary constraint conditions.

[0078] During the optimization process, based on the mechanical properties of the current structure in each iteration step, the support position of support unit 2 is optimized using a two-way progressive structural optimization method. Then, based on the obtained support position, the internal stiffeners of the structure are optimized using an adaptive growth method based on the growth mechanism of natural branching systems. This process is repeated until the optimal layout of the two is obtained. The optimization mathematical model is shown in equations (a1) to (a8) in equation (1).

[0079] find X = [x1, ... x j ,...,x n (a1)

[0080] T = [T1,...,T] k ,...,T l (a2)

[0081] min C(X,T)=U T KU (a3)

[0082] stF=KU (a4)

[0083] NN * =0 (a5)

[0084] V-ηV0≤0 (a6)

[0085] x min ≤x j ≤1j=[1,...,n] (a7)

[0086] 0 < T min ≤T k ≤T max k = [1,...,l] (a8) (1)

[0087] In the formula, x j To support the pseudo-density variable of the unit; T k For stiffener thickness, C is the global strain energy of the structure, i.e., the objective function; U is the displacement vector; K is the stiffness matrix; F is the load vector; N is the number of support elements retained after optimization convergence; V is the optimized stiffener volume; V0 is the initial stiffener volume; η is the stiffener volume fraction; x min The minimum value of the pseudo-density of the supporting element; T min and T max These are the minimum and maximum thicknesses of the reinforcing ribs, respectively.

[0088] Step 2: Initialize design parameters: seed point, support degradation rate V d The final number of support units to be retained, N * .

[0089] The determination of seed points is mainly based on the location of loads and constraints, and there is no specific limit to the number. In order to obtain the shortest force flow transmission path between loads and constraints, seed points are set at the loading and constraint locations. Only in the initial stage of rib optimization, the rib begins to grow at the seed points, and then grows on the basis of the existing ribs.

[0090] Step 3: Perform mechanical performance analysis (i.e., finite element analysis) on the box-type structure, and calculate the sensitivity α of the j-th support element 2 according to equation (2). j e The number N of support units to be retained in the i-th iteration step is calculated according to equation (3). i * .

[0091]

[0092] In the formula, α j e Let x be the sensitivity of the j-th support unit 2 (1≤j≤n, n≥1); j To support the pseudo-density variable of the unit; K st K represents the stiffness matrix of the box-shaped main body 1, which consists of surface shell elements 3 and internal shell elements 4. su Here is the stiffness matrix of the support structure composed of support unit 2; p is the penalty factor; K j su,e Let u be the stiffness matrix of the j-th support element 2; j Let be the displacement vector of the j-th support unit 2.

[0093]

[0094] Step 4: Enter the sub-loop for support position optimization.

[0095] Step 4 includes the following sub-steps:

[0096] Step 4.1: Based on the maximum sensitivity value of support unit 2, max(α1) e :α n e ) and minimum sensitivity min(α1) e :α n e The sensitivity threshold τ of support unit 2 at the r-th iteration step of the current sub-loop is calculated using equations (4) and (5). r.

[0097]

[0098]

[0099] Where τ1 is the initial sensitivity threshold for support position optimization.

[0100] Step 4.2: Based on the sensitivity threshold τ r The support unit 2 can be added or deleted as shown in equation (6). The principle for adding or deleting the support unit 2 is: if the sensitivity value of the support unit 2 is greater than the sensitivity threshold τ r If the support unit 2 is a solid, then the sensitivity value of the support unit 2 is less than or equal to the sensitivity threshold τ. r If so, then delete support unit 2.

[0101]

[0102] Where, x j To support the pseudo-density variable of the unit; x min To support the minimum pseudo-density of the element, x min A value of 0.0001 can be used to avoid the spring element stiffness matrix being singular, while ensuring that the deleted support element 2 has a certain degree of recoverability.

[0103] Step 4.3: Based on the sensitivity threshold τ of support unit 2 r and its maximum sensitivity max(α1) e :α n e ) and minimum sensitivity min(α1) e :α n e ), calculate the tolerance e1 for the support position optimization according to equation (7).

[0104]

[0105] Where ε is the iterative tolerance for support position optimization.

[0106] When the iteration tolerance ε is satisfied, exit the sub-loop of support position optimization.

[0107] Step 5: Optimize the layout of the reinforcing ribs based on the optimization results of the support positions, and update the box-type structure model.

[0108] Step 5 includes the following sub-steps:

[0109] Step 5.1: Calculate the sensitivity of the stiffener according to equation (8).

[0110]

[0111] Among them, u k Let be the displacement vector of the k-th stiffener; Let K be the stiffness matrix of the k-th stiffener, derived from the plane stress term K. k stress and bending term K k bend Therefore, its sensitivity needs to be calculated in two parts:

[0112]

[0113]

[0114] in, and , respectively, are matrices independent of design variables in the plane stress and bending terms, mainly determined by the element size and Poisson's ratio of the shell element; μ is the Poisson's ratio of the stiffener; to reduce the influence of the base structure on the structural stiffening optimization process, the stiffener material properties are penalized according to the stiffener thickness, and the elastic modulus E of the k-th stiffener after penalty is... k for:

[0115]

[0116] Among them, E * The true elastic modulus of the material; T k T represents the thickness of the k-th reinforcing rib. init T represents the initial thickness of the reinforcing rib. m Let be the mature thickness of the stiffener. Therefore, the sensitivity of the stiffness matrix of the k-th stiffener with respect to the stiffener thickness can be obtained from equations (11) and (12):

[0117]

[0118]

[0119] in, and They are respectively of thickness T m The plane stress term and bending term of the true stiffness matrix of the stiffener.

[0120] Step 5.2: Update the stiffener thickness using the MMA algorithm based on the stiffener's sensitivity. In the initial iteration of optimization, the stiffener starts growing from the seed point and continues to diverge and degenerate based on the sensitivity information in subsequent optimization processes.

[0121] The adaptive optimization method is a topology optimization approach that optimizes the design based on the base structure and the thickness of each shell element. The main structure is discretized using shell elements, with all shell elements in the design domain forming the base structure (which already exists before optimization begins, at which point the shell element thickness is small). Then, based on this, the thickness of the corresponding shell elements in the base structure is optimized according to the optimization algorithm. Therefore, the number of stiffeners does not change, but different material properties are assigned to them according to the shell element thickness. Small-thickness stiffeners are degenerated, thus forming the optimal stiffener distribution. The final design result is stiffeners that have grown to a certain thickness.

[0122] The MMA algorithm is a conventional calculation method in this field for calculating the thickness of stiffeners based on their sensitivity, and the calculation process of the MMA algorithm will not be described in detail here.

[0123] Step 5.3: Update the box-type structure model according to the new stiffener thickness.

[0124] Step 5.4: Return to step 3 and re-analyze the mechanical properties of the box structure.

[0125] Step 6: Repeat the iterative process from Step 3 to Step 5. According to Equation (13), stop iterating when the change in the objective function is less than the convergence tolerance.

[0126]

[0127] Where C is the objective function; i is the current iteration step; δ is the convergence tolerance; and M is usually an integer from 3 to 5.

[0128] Example 1:

[0129] Taking a box-shaped structure subjected to a concentrated load at its center as an example, the length-to-width-to-height ratio of this box-shaped structure is 1:1:0.5. The elastic modulus of the material is 2×1 1 Pa, Poisson's ratio is 0.3, and density is 7800 kg / m³. 3 Please see the appendix. Figure 4 The upper surface of the box-shaped main body 1 is subjected to a concentrated load perpendicular to the surface and inward, with a load magnitude of 1000N. There are 40 seed points around the top of the box-shaped main body 1, and 40 support elements 2 are constructed around the bottom. The bifurcation thickness, maturity thickness, maximum thickness, and minimum thickness are defined as 5mm, 10mm, 15mm, and 0.1mm, respectively. The support degradation rate is defined as 4, and it is assumed that the number of support elements 2 to be retained after optimization convergence is 4, and the normal and axial stiffness of the support elements 2 is 1×10⁻⁶. 12 N / m. The volume fraction η in equation (1) is 0.3. The convergence tolerances in equations (7) and (13) are 1×10 N / m. -10 and 1×10-5 .

[0130] An adaptive growth algorithm and a two-way progressive structural optimization method were used to collaboratively optimize the positions of the stiffeners and support units 2 of the box-shaped structure. Dots represent the locations of support units 2. (See appendix.) Figure 5 During each growth of the reinforcing rib, the position of the support unit 2 will change as the layout of the reinforcing rib changes.

[0131] Please see the appendix Figure 5 and attached Figure 6 As shown in the optimization iteration curve, the optimization process reached convergence after 70 iterations. The final result shows that support element 2 is located at the midpoint of the four sides of the structure, with stiffeners forming a cross-shaped rib, and local reinforcement at the loading point of load F1. The strain energy of this box-type structure is 1.152 × 10⁻⁶. -3 J.

[0132] To verify the effectiveness of the collaborative optimization algorithm, the results were compared with those of the traditional optimization method based on the distribution of stiffeners at known support locations. The known support locations were set at the midpoints of the four sides and the four corners of the box-shaped structure, under the same volume constraint (the stiffener volume was 0.034 m³). 3 The adaptive growth method was used for stiffener optimization design, and the optimization results are as follows: Figure 8 As shown.

[0133] Both optimization results for known support locations show a cross-stiffener layout, forming the shortest load transfer path to effectively transfer the load to the support unit. The optimization result for the box-shaped structure with the four-sided midpoint support unit is consistent with the collaborative optimization result of Embodiment 1 of this invention, where the strain energy of the box-shaped structure is 1.259 × 10⁻⁶. -3 J; while the strain energy of the box-shaped structure supported at four corners is 3.170 × 10⁻⁶. -3 J.

[0134] With the same stiffening plate volume of 0.034m 3 Below, the strain energy of the box-type structure in Example 1 is 1.152 × 10⁻⁶. -3 J, the strain energy of the box-shaped structure at the midpoint of its four sides is 1.259 × 10⁻⁶. -3 J, the strain energy of the box-shaped structure supported at four corners is 3.170 × 10⁻⁶. -3 J, the optimization result of Example 1 using the collaborative optimization method of the present invention shows a performance improvement of 63.7% compared to the optimization result under known support positions, and Example 1 has a thicker rib plate distributed at the center (e.g. Figure 5 (d) The thickness of the intermediate stiffening plate is 10.9 mm and 10 mm. Figure 8 (e) The stiffener thickness is 9.9 mm and 3.5 mm), and its performance is improved by 8.5%, which proves the effectiveness of the collaborative optimization method of the present invention.

[0135] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the invention. Therefore, any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for co-optimizing the design of stiffeners and support locations in a structure, characterized by: Includes the following steps: Step 1: Based on the external dimensions of the box-shaped structure, establish an initial basic structure model, which includes the main body of the box-shaped structure (1) and the supporting structure; Step 2: Initialize design parameters: seed point, support degradation rate V d The final number of support units to be retained, N * ; Step 3: Perform mechanical performance analysis on the box-type structure, and calculate the sensitivity α of the j-th support unit (2) according to equation (2). j e The number N of support units to be retained in the i-th iteration step is calculated according to equation (3). i * : In the formula, α j e The sensitivity of the j-th support unit (2); x j To support the pseudo-density variable of the unit; K st K is the stiffness matrix of the main body of the box-shaped structure (1); su Here is the stiffness matrix of the support structure composed of support elements (2); p is the penalty factor; K j su,e u is the stiffness matrix of the j-th support element (2); j Let be the displacement vector of the j-th support element (2); Step 4: Enter the sub-loop for support position optimization; Step 5: Optimize the layout of the reinforcing ribs based on the optimization results of the support positions, and update the box-type structure model; Step 6: Repeat the iterative process from Step 3 to Step 5. According to Equation (13), stop the iteration when the change in the objective function is less than the convergence tolerance. Where C is the objective function; i is the current iteration step; δ is the convergence tolerance; and M is an integer from 3 to 5.

2. The method for coordinated optimization design of stiffeners and support positions in a structure according to claim 1, characterized in that: Step 1 includes the following sub-steps: Step 1.1: Discretize the box-shaped structure main body (1), i.e. the structural design domain, using hexahedral elements, and establish shell elements with a certain thickness on the surface and inside of the box-shaped structure main body (1) according to the corresponding element node information, i.e., surface shell elements (3) and internal shell elements (4), the internal shell elements (4) being the stiffeners; Step 1.2: Introduce a support design domain at the bottom periphery of the structural design domain. The support design domain includes several support units (2) connected to the main body of the box structure (1). The several support units (2) constitute the support structure, and the support position of the several support units (2) is optimized.

3. The method for coordinated optimization design of stiffeners and support positions in a structure according to claim 2, characterized in that: Each of the aforementioned support units (2) is a three-degree-of-freedom spring unit; wherein, the node located at the top of the spring unit is connected to the node of the surface shell unit (3) on the bottom periphery of the box-shaped main body (1), and the node located at the bottom of the spring unit is used to define the boundary constraint conditions.

4. The method for coordinated optimization design of stiffeners and support positions in a structure according to claim 2, characterized in that: During the optimization process, based on the mechanical properties of the current structure in each iteration step, a two-way progressive structural optimization method is used to optimize the design of its support positions. Then, based on the obtained support positions, an adaptive growth method based on the growth mechanism of natural branching systems is used to optimize the design of the internal stiffeners of the structure. This process is repeated until the optimal layout of the two is obtained. The optimization mathematical model is shown as (a1) to (a8) in equation (1): find X=[x1,...x j ,...,x n ] (a1) T=[T1,...,T k ,...,T l ] (a2) min C(X,T)=U T KU (a3) stF=KU (a4) NN * 0 (a5) V-ηV0≤0 (a6) x min ≤x j ≤1j=[1,...,n] (a7) 0<T min ≤T k ≤T max k=[1,...,l] (a8) (1) In the formula, x j To support the pseudo-density variable of the unit; T k For stiffener thickness, C is the global strain energy of the structure, i.e., the objective function; U is the displacement vector; K is the stiffness matrix; F is the load vector; N is the number of support elements retained after optimization convergence; V is the optimized stiffener volume; V0 is the initial stiffener volume; η is the stiffener volume fraction; x min The minimum value of the pseudo-density of the supporting element; T min and T max These are the minimum and maximum thicknesses of the reinforcing ribs, respectively.

5. The method for coordinated optimization design of stiffeners and support positions in a structure according to claim 1, characterized in that: Step 4 includes the following sub-steps: Step 4.1: Based on the maximum sensitivity value max(α1) of the support unit (2) e :α n e ) and minimum sensitivity min(α1) e :α n e The sensitivity threshold τ of the support unit (2) at the r-th iteration step of the current sub-loop is calculated using equations (4) and (5). r : Where τ1 is the initial sensitivity threshold for support position optimization; Step 4.2: Based on the sensitivity threshold τ r The support unit (2) can be added or deleted as shown in equation (6). The principle for adding or deleting the support unit (2) is: if the sensitivity value of the support unit (2) is greater than the sensitivity threshold τ r If the support unit (2) is a solid, then the sensitivity value of the support unit (2) is less than or equal to the sensitivity threshold τ. r If so, then delete the support unit (2); Where, x j To support the pseudo-density variable of the unit; x min To support the minimum pseudo-density of the element, x min Take 0.0001; Step 4.3: Based on the sensitivity threshold τ of the support unit (2) r and its maximum sensitivity max(α1) e :α n e ) and minimum sensitivity min(α1) e :α n e ), calculate the tolerance e1 for the optimized support position according to equation (7); Where ε represents the iterative tolerance for supporting position optimization; When the iteration tolerance ε is satisfied, exit the sub-loop of support position optimization.

6. The method for coordinated optimization design of stiffeners and support positions in a structure according to claim 1, characterized in that: Step 5 includes the following sub-steps: Step 5.1: Calculate the sensitivity of the stiffener according to equation (8); Among them, u k Let be the displacement vector of the k-th stiffener; Let K be the stiffness matrix of the k-th stiffener, derived from the plane stress term K. k stress and bending term K k bend Therefore, its sensitivity needs to be calculated in two parts: in, and , respectively, are matrices independent of design variables in the plane stress and bending terms, mainly determined by the element size and Poisson's ratio of the shell element; μ is the Poisson's ratio of the stiffener; to reduce the influence of the base structure on the structural stiffening optimization process, the stiffener material properties are penalized according to the stiffener thickness, and the elastic modulus E of the k-th stiffener after penalty is... k for: Among them, E * The true elastic modulus of the material; T k T represents the thickness of the k-th reinforcing rib. init T represents the initial thickness of the reinforcing rib. m Let the stiffness matrix of the k-th stiffener be the mature thickness. Therefore, the sensitivity of the stiffness matrix of the k-th stiffener with respect to the stiffener thickness can be obtained from equations (11) and (12): in, and They are respectively of thickness T m The plane stress and bending terms of the true stiffness matrix of the stiffeners at that time; Step 5.2: Update the stiffener thickness using the MMA algorithm based on the stiffener's sensitivity. In the initial iteration of optimization, the stiffener starts growing from the seed point and continues to diverge and degenerate based on the sensitivity information in subsequent optimization processes. Step 5.3: Update the box-type structure model according to the new stiffener thickness; Step 5.4: Return to step 3 and re-analyze the mechanical properties of the box structure.

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