A panel structure stiffened layout topology optimization method for sound radiation suppression

Abstract

The application discloses a panel structure stiffening layout topology optimization method for sound radiation suppression and belongs to the technical field of structural acoustics and intelligent optimization design. 1) a base structure is established, structure load, boundary conditions, optimization parameters and design variables are defined, and seed point positions are determined; 2) finite element analysis is performed to obtain structure dynamics response; 3) real element set and empty element set are obtained, and sensitivity is calculated; 4) a global moving asymptote algorithm is adopted to dynamically update the width of the real element; 5) according to the width of the real element, a growth competition criterion is introduced to guide the branching and degeneration of the corresponding element and to update the material properties of the element, so that a new stiffening configuration is obtained; 6) whether the optimization process converges is judged based on the target function value, if the optimization process does not converge, finite element analysis is performed again, and the optimal stiffening configuration is obtained until the optimal stiffening configuration is obtained. The application can effectively reduce the radiation sound power of the panel structure, improve the acoustic performance, obtain an optimal configuration with clear boundaries and easy manufacturing, improve the calculation efficiency, and guarantee the stability and convergence.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of structural acoustics and intelligent optimization design, and relates to a stiffener layout topology optimization method for sound radiation suppression of a plate shell structure, in particular to a stiffener layout topology optimization design method for sound radiation suppression of a plate shell structure. BACKGROUND

[0002] Plate shell structures are widely used in aerospace, shipbuilding, rail transportation and mechanical equipment engineering fields due to their lightweight and efficient load transmission characteristics [Loughlan J. Thin-walled structures: advances in research, design and manufacturing technology [J]. 2018]. However, due to their thin-walled characteristics, they are prone to vibration under external excitation, which can cause significant sound radiation problems. This noise not only affects the service performance of the structure itself, but also has an adverse impact on the surrounding environment. Therefore, how to effectively reduce the sound radiation level of plate shell structures has become an important research topic in the engineering field.

[0003] Currently, the optimization design for sound radiation of plate shell structures mainly focuses on two schemes: laying damping layers and arranging stiffeners. Laying damping layers on the surface of plate shell structures can suppress vibration noise by dissipating energy, but to achieve the desired effect, a certain thickness and mass are usually required, which significantly increases the weight of the structure [Li Zongji, Wang Xudong, Zhu Yonyong, et al. Optimization of noise reduction damping layer for strongly coupled acoustic-vibration thin plate structure [J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2021, 49(09): 120-125. DOI: 10.13245 / j.hust.210921.]. This has obvious limitations for weight-sensitive applications such as aircraft and underwater vehicles. At the same time, damping materials also have problems such as durability and environmental temperature sensitivity [Lv Ping, Gao Jingang, Li Jing, et al. Factors affecting the damping performance of constrained damping structures [J]. Noise and Vibration Control, 2014, 34(05): 234-238. DOI: CNKI: SUN: ZSZK.0.2014-05-051.]. In contrast, optimizing the arrangement of stiffeners on the plate shell structure can improve the stiffness of the structure without significantly increasing the weight, thereby effectively suppressing low-frequency vibration and sound radiation.

[0004] Currently, researchers have carried out research on the layout optimization design of stiffened plate and shell structures. For example, a design method for stiffened plate structures is proposed in Chinese invention patent (application number 202211259512.0). Based on the variable density method, i.e., the SIMP method, the method maximizes the stiffness of the stiffened plate. Through the introduction of a three-stage continuation technique with gradually increasing penalty factors and an automated batch processing technique, the optimization of the stiffened plate in terms of panel thickness and stiffener layout is achieved. Chinese invention patent (application number 202510244938.6) proposes a design method for stiffened flat plates with embedded acoustic black holes. The method establishes a collaborative optimization mathematical model by minimizing the average external force input power. The density of solid elements is used as a design variable to perform topology optimization on the stiffened area. Meanwhile, variable-thickness shell elements are used to simulate the acoustic black holes in the flat plate area. Various geometric and topological constraints are introduced to achieve the collaborative design of the two, thereby improving the suppression of mid-high frequency vibrations and achieving the suppression of vibration noise of the stiffened flat plate.

[0005] Existing stiffened design schemes mostly rely on continuum topology optimization methods (such as the SIMP method mentioned above), and the results often present ambiguous and complex configurations, which are difficult to directly apply to actual engineering manufacturing. In addition, when considering the acoustic radiation performance of plate and shell structures, acoustic-structure coupling analysis needs to be performed, but this process significantly increases the degrees of freedom of finite element analysis, leading to a decrease in computational efficiency. Therefore, there is still an urgent need to develop a stiffened layout topology optimization method that can generate clear configurations and has higher computational efficiency, for the purpose of realizing the acoustic radiation suppression design of plate and shell structures.

[0006] The present invention aims to address the above-mentioned problems and proposes a plate and shell structure stiffened layout topology optimization method for acoustic radiation suppression. This method simulates the growth mechanism of plant leaf veins, introduces growth competition criteria and high-frequency approximate acoustic impedance theory, significantly improves computational efficiency while reducing structural acoustic radiation levels, achieves collaborative optimization of stiffener layout and size, and obtains clear and manufacturable optimization results. SUMMARY

[0007] The present invention aims to overcome the shortcomings of existing noise reduction design methods for plate and shell structures and provides a plate and shell structure stiffened layout topology optimization method for acoustic radiation suppression. This method can effectively reduce the acoustic radiation level of plate and shell structures, significantly improve computational efficiency, and obtain clear and easily manufactured stiffener optimization configurations.

[0008] To achieve the above-mentioned objectives, the present invention adopts the following technical solutions:

[0009] A plate and shell structure stiffened layout topology optimization method for acoustic radiation suppression includes the following steps:

[0010] First step: Establish the base structure, define the structure load, boundary condition, optimization parameter and design variable. According to the structure load and boundary condition, the acoustic power sensitivity analysis is carried out on the base structure to determine the seed point position. Specifically:

[0011] Step 1.1, after the plate shell structure is discretized into shell elements, any two nodes on the shell element are connected by beam element as stiffener to form the basic structure model required for design, that is, the base structure is obtained; define the structure load, boundary condition, optimization parameter and design variable.

[0012] Step 1.2, set the material properties of all beam elements in the base structure to weak material, that is, empty element.

[0013] Step 1.3, acoustic power sensitivity analysis is carried out on the base structure, and any node of the beam element in the region with minimum acoustic power sensitivity is selected as the seed point, and the material properties of the beam element connected with the seed point are changed from weak material to solid material, that is, from empty element to solid element.

[0014] Further, the optimization parameters include the initial width of the stiffener, the height of the stiffener, the upper and lower limits of the width of the stiffener, the branch threshold, the degradation threshold, the material properties, the acoustic medium properties, the volume constraint, and the convergence precision.

[0015] Further, the design variables include the width of the stiffener and the material properties.

[0016] Further, the seed point refers to the preset starting growth position in the base structure, and the connected stiffener is used as the starting unit of evolution to guide the growth direction and distribution of the subsequent stiffener.

[0017] Further, the weak material has extremely low Young's modulus and density.

[0018] Second step: Perform finite element analysis on the base structure in the first step and obtain the structure dynamics response, wherein the structure dynamics response is the total displacement vector.

[0019] Third step: Obtain the solid element set and the empty element set, and calculate the target function value based on the structure dynamics response obtained in the second step and the high-frequency approximate acoustic impedance theory. Calculate the sensitivity of each solid element in the solid element set and the sensitivity of each empty element in the empty element set. Specifically:

[0020] Step 3.1, in the first iteration, the initial empty element set and the initial solid element set are obtained based on steps 1.2 to 1.3. From the second iteration to the end of each iteration, the solid element set and the empty element set are reacquired according to the update of the material properties of each beam element.

[0021] Step 3.2: Calculate the objective function value based on the high-frequency approximate acoustic impedance theory. The optimized mathematical model is shown in formula (1), where the objective function is the acoustic power, i.e., in formula (1). The design goal is to minimize the acoustic power of the plate and shell structure.

[0022] (1)

[0023] In equation (1), It is a collection of the properties of reinforcing rib materials. It is the material property of the first beam element. It refers to the material properties of the second beam element. It is the first Material properties of individual beam elements It is the first Material properties of individual beam elements; It is a collection of the widths of the reinforcing ribs. It is the width of the first beam element. It is the width of the second beam element. It is the first The width of each beam element, It is the first The width of each beam element, where the subscript... Indicates the first Individual beam element, subscript Represents the total number of beam elements; design variables include a set. middle Material properties and sets of beam elements middle The width of each beam element. It is sound power; It is the density of the acoustic medium; It is the speed of sound; It is the external excitation angular frequency; It is the global displacement vector The conjugate transpose of; It is the normal vector coefficient matrix; It is a preset volume limit. It is the first Volume of each beam element; K d It is the structural dynamic stiffness matrix; It is an external excitation column vector; It is the first The width of each beam element, and These are the upper and lower limits of the beam element width, respectively; x i It is the first Material properties of individual beam elements 1 represents a weak material, and 1 represents a solid material. and 1 represent different properties of beam element material, i.e. empty element is set as weak material, represented by 0 and solid element is set as solid material, represented by 1.

[0024] Step 3.3, in the optimization process, the first iteration, the sound power sensitivity of N empty elements in the initial empty element set is calculated by formula (2), and the sound power sensitivity of M solid elements in the initial solid element set is calculated by formula (2) by the same reason, where N+M=p. From the second iteration to the end of each iteration, based on the updated empty element set and solid element set in step 3.1, the sound power sensitivity of each empty element in the empty element set is calculated by formula (2), and the sound power sensitivity of each solid element in the solid element set is calculated by formula (2) by the same reason. The sound power sensitivity calculation formula of solid element and empty element is:

[0025] (2)

[0026] In formula (2), is the width of the first beam element; is a defined formula artificially introduced to simplify the formula; is the transpose of the local coordinate to global coordinate conversion matrix T; K B and M B are beam element stiffness matrix and mass matrix respectively.

[0027] Further, the high-frequency approximate acoustic impedance theory refers to: the acoustic impedance of the structure surface can be replaced by the characteristic impedance of the acoustic medium, which means that the sound pressure and normal velocity of the structure surface satisfy the following linear relationship: (3)

[0028] In formula (3), is the structure surface sound pressure vector, is the structure surface normal velocity.

[0029] Step 4: according to the sensitivity genetic mechanism, the empty element sensitivity and solid element sensitivity obtained in step 3 are processed, and the global moving asymptote algorithm is used to dynamically update the solid element width. Specifically:

[0030] Step 4.1, according to the sensitivity genetic mechanism, the sensitivity of each solid element in the solid element set and the sensitivity of each empty element in the empty element set are processed, and the sensitivity genetic mechanism is:

[0031] Step 4.1.1, based on the sound power sensitivity obtained in step 3.3, the first iteration, formula (4) is used to process the sound power sensitivity of each of the N empty cells in the initial empty cell set, and formula (4) is used to process the sound power sensitivity of each of the M real cells in the initial real cell set, where N+M=p.

[0032] (4)

[0033] In formula (4), is the sensitivity of the jth beam element; the superscript 1 is the first iteration.

[0034] From the second iteration to the end of each iteration, based on step 3.1 and step 3.3, formula (5) is used to process the sound power sensitivity of each empty cell in the empty cell set, and formula (5) is used to process the sound power sensitivity of each real cell in the real cell set.

[0035] (5)

[0036] In formula (5), is the sensitivity of the jth beam element; the superscript 1 is the first iteration. is the sensitivity of the jth beam element; the superscript 1 is the first iteration. is the sensitivity of the jth beam element; the superscript 1 is the first iteration. is the sensitivity of the jth beam element; the superscript 1 is the first iteration.

[0037] In this step, the significance of the sensitivity genetic mechanism is to average the sound power sensitivity of each real cell in the real cell set and the sound power sensitivity of each empty cell in the empty cell set corresponding to the sound power sensitivity of each cell in the previous iteration, to ensure good convergence of the iteration process.

[0038] Step 4.2, after processing the beam element sensitivity using the method described in step 4.1, the global moving asymptote algorithm, i.e. GCMMA algorithm, is used to update the width of the real cell.

[0039] Step 5: According to the width of the real cell obtained in step 4, introduce the "growth competition criterion" to guide the branching, degeneration and update of the material properties of the corresponding cell, and obtain a new stiffened configuration. Specifically:

[0040] Step 5.1, branching operation: if the width of the jth real cell in the real cell set exceeds the branching threshold, i.e. Step 5.2, degeneration operation: if the width of the jth real cell in the real cell set is less than the degeneration threshold, i.e.​​​If the width of the i-th solid cell is lower than the branch threshold, i.e.

[0041] (6)

[0042] In formula (6), the minimum sensitivity of the void cell is denoted as , and the subscript i represents the i-th void cell. The number of void cells is denoted as N. The weak material is denoted as 0, and the solid material is denoted as 1. The branch threshold is denoted as

[0043] In this step, the mathematical meaning of the "growth competition criterion" is that the sensitivity reflects the influence of a small change in the design variable on the performance of the structure. The smaller the sensitivity, the greater the influence of the unit on the reduction of the objective function, and therefore, such a unit is preferentially selected for growth.

[0044] Step 5.2, degradation operation: if the width of the i-th solid cell in the solid cell set is lower than the degradation threshold, i.e. , the degradation operation is activated. At this time, the unit is selected from the solid cell set and its material property is reset to the weak material, thereby achieving removal from the structure. The degradation threshold is denoted as Step 5.3, keep unchanged: if the width of the i-th solid cell in the solid cell set is within the interval of the branch threshold and the degradation threshold, i.e.

[0045] , no treatment is performed on the unit, and its current state is maintained. Step 5.4, the "growth competition criterion" is obtained based on steps 5.1 to 5.3, and a new stiffened configuration is obtained based on the "growth competition criterion".

[0046] Further, the branch threshold and the degradation threshold need to be selected according to different problems, and the beam theory is not invalid.

[0047] Step 6: based on the objective function obtained in formula (1) , it is determined whether the optimization process converges. When it is determined that the optimization process does not converge, the second step is returned, and the design variable obtained in the fifth step is further optimized. When it is determined that the optimization process converges, the optimization process is ended, and the optimal reinforcement distribution is obtained.

[0048]

[0049] ​​​​Further, the convergence criterion is that the rate of change of the objective function value between two consecutive iteration steps is less than or equal to the convergence precision; and the convergence precision is 0.001% to 0.01%.

[0050] Compared with the prior art, the present application has the following beneficial effects:

[0051] The plate-shell structure stiffening layout topology optimization method for sound radiation suppression can significantly weaken the vibration response of the structure under excitation, thereby reducing the radiated sound power and improving the acoustic performance of the structure; meanwhile, the high-frequency approximate acoustic impedance theory is introduced in the acoustic analysis, thereby avoiding the solving process of the large-scale Helmholtz integral equation, so that the calculation cost is significantly reduced and the optimization efficiency is improved. Unlike the traditional continuum topology optimization which is prone to produce ambiguous results, the present application explicitly describes the stiffener, and the generated stiffener configuration has clear geometric boundaries and explicit size parameters, which is convenient for manufacturing and engineering application. In addition, the present application introduces the growth competition criterion and the sensitivity genetic mechanism, so that the optimization process is stable and reliable, and the convergence and robustness are maintained in the complex iteration. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 is a flow chart of the plate-shell structure stiffening layout topology optimization method for sound radiation suppression;

[0053] Figure 2 is a schematic diagram of the base structure;

[0054] Figure 3 is a case setting schematic diagram of the rectangular plate structure in the embodiment of the present application; Figure 3 (a) in the above is a case model; Figure 3 (b) in the above is the sound power sensitivity analysis result; Figure 3 (c) in the above is the seed point setting;

[0055] Figure 4 is a schematic diagram of the optimization process of the rectangular plate structure in the embodiment of the present application; Figure 4 (a) in the above is a 10-time iteration result graph; Figure 4 (b) in the above is a 30-time iteration result graph; Figure 4 (c) in the above is a 50-time iteration result graph; Figure 4 (d) in the above is a 70-time iteration result graph; Figure 4 (e) in the above is a 90-time iteration result graph; Figure 4 (f) in the above is a final optimization result graph.

[0056] Figure 5 is a schematic diagram of the optimization iteration history curve in the embodiment of the present application; Figure 5 (a) in the above is an iteration history graph of the sound power level ratio; Figure 5 (b) in the above is an iteration history graph of the total volume of the stiffener;

[0057] Figure 6 is the comparison chart of the optimized results in the embodiment of the present application and the optimization results of the built-in variable density method, i.e., the SIMP method, in the COMSOL software. Figure 6 (a) in the figure is the optimization result of the method of the present application when the volume constraint is 0.15; Figure 6 (b) in the figure is the optimization result of the method of the present application when the volume constraint is 0.3; Figure 6 (c) in the figure is the optimization result of the method of the present application when the volume constraint is 0.45; Figure 6 (d) in the figure is the optimization result of the SIMP method when the volume constraint is 0.15; Figure 6 (e) in the figure is the optimization result of the SIMP method when the volume constraint is 0.3; Figure 1 (f) in the figure is the optimization result of the SIMP method when the volume constraint is 0.45. DETAILED DESCRIPTION

[0058] The present application is further described below in combination with specific implementation cases.

[0059] Embodiment:

[0060] Figure 1 The implementation flowchart of the plate and shell structure stiffening layout topology optimization method for sound radiation suppression provided in the embodiment of the present application. As shown in Figure 2 , the plate and shell structure stiffening layout topology optimization method for sound radiation suppression provided in the embodiment of the present application specifically includes the following steps:

[0061] Step 1: Establish the base structure, define the structure load, boundary condition, optimization parameter and design variable. Perform the sound power sensitivity analysis on the base structure according to the structure load and boundary condition, and determine the seed point position. Specifically:

[0062] Step 1.1, the case model optimized in the embodiment is a rectangular plate embedded in an infinite barrier plate in a semi-infinite space. After discretizing the plate and shell structure into shell elements, connect any two nodes on the shell element with a beam element as a stiffener to form the basic structure model required for design, i.e., the base structure. The base structure schematic diagram is shown in Figure 3 . The length , the width , and the thickness of the case model in the embodiment; the geometric center is subjected to a vertical downward simple harmonic force as the structure load, the amplitude is , and the excitation frequency is ; the boundary condition is four-edge simply supported, as shown in Figure 3 (a).

[0063] Step 1.2, set the material properties of all beam elements in the base structure to weak material, i.e. empty elements.

[0064] Step 1.3, perform a sound power sensitivity analysis on the base structure, as shown in (b) of FIG. 1C. Among them, the sound power sensitivity of the four corners and the center area is the smallest, so the beam element node with the smallest sound power sensitivity in the area is selected as the seed point, as shown in (c) of FIG. 1C, and the material properties of the beam elements connected to the seed point are changed from weak material to solid material, i.e. from empty elements to solid elements. Figure 3 Figure 4

[0065] In this embodiment, the optimization parameters include the initial width of the stiffener , the height of the stiffener ; the upper limit of the width of the stiffener , the lower limit of the width of the stiffener ; the branch threshold , the degradation threshold ; Young's modulus , Poisson's ratio , material density ; the acoustic medium is air, the air density , the sound speed ; volume constraint , where is the total volume of the shell element; the convergence accuracy is 0.001%.

[0066] In this embodiment, the design variables include the width of the stiffener and the material properties.

[0067] In this embodiment, the seed point refers to a preset starting growth position in the base structure, and the connected stiffener is used as the starting element of evolution to guide the growth direction and distribution of the subsequent stiffener.

[0068] In this embodiment, the weak material has extremely low Young's modulus and density, and the Young's modulus .

[0069] Second step: perform finite element analysis on the base structure in the first step and obtain the structure dynamics response, wherein the structure dynamics response is the total displacement vector.

[0070] Third step: obtain the solid element set and the empty element set, and combine the structure dynamics response obtained in the second step and the high-frequency approximate acoustic impedance theory to calculate the objective function value. Calculate the sensitivity of each solid element in the solid element set and the sensitivity of each empty element in the empty element set. Specifically:

[0071] ​​Step 3.1, in the first iteration, the initial empty element set and initial solid element set are obtained based on step 1.2 and step 1.3 respectively. From the second iteration to the end of each iteration, the solid element set and empty element set are re-obtained according to the update of the material properties of each beam element.

[0072] Step 3.2, the target function value is calculated based on the high-frequency approximate acoustic impedance theory, the mathematical model of the optimization design is shown in formula (1), the target function is the sound power, i.e. formula (1) , the design goal is to minimize the sound power of the plate shell structure.

[0073] (1)

[0074] In formula (1), is the set of stiffener material properties, is the material property of the first beam element, is the material property of the second beam element, is the material property of the th beam element, is the material property of the th beam element; is the set of stiffener widths, is the width of the 1st beam element, is the width of the 2nd beam element, is the width of the th beam element, is the width of the th beam element, wherein the subscript represents the th beam element, and the subscript represents the total number of beam elements; the design variables include the material properties of the beam elements in the set and the widths of the beam elements in the set . is the sound power; is the density of the acoustic medium; is the sound speed; is the outer excitation circular frequency; is the conjugate transpose of the total displacement vector ; is the normal vector coefficient matrix; V * is the preset upper limit of the volume, is the volume of the th beam element; K d is the structural dynamic stiffness matrix; is the outer excitation column vector; is the width of the th beam element, and are the upper and lower limits of the beam element width, respectively; is the material property of the th beam element, represents weak material, and 1 represents solid material, i.e. and 1 represent different properties of the beam element material, i.e. the empty element is set to weak material, and the solid element is set to solid material.

[0075] Step 3.3, in the optimization process, the first iteration, formula (2) is used to calculate the sound power sensitivity of the N empty elements in the initial empty element set, and similarly, formula (2) is used to calculate the sound power sensitivity of the M solid elements in the initial solid element set, where N+M=p. From the second iteration to the end of each iteration, based on the updated empty element set and solid element set in step 3.1, formula (2) is used to calculate the sound power sensitivity of each empty element in the empty element set, and similarly, formula (2) is used to calculate the sound power sensitivity of each solid element in the solid element set. The sound power sensitivity calculation formula of the solid element and the empty element is:

[0076] (2)

[0077] In formula (2), is the width of the th beam element; is a defined formula artificially introduced to simplify the formula; T T is the transpose of the local coordinate to global coordinate conversion matrix T; K B and M B are the beam element stiffness matrix and mass matrix, respectively.

[0078] In this embodiment, the high-frequency approximate acoustic impedance theory refers to: the acoustic impedance of the structure surface can be replaced by the characteristic impedance of the acoustic medium, which means that the sound pressure and the normal velocity of the structure surface satisfy the following linear relationship:

[0079] (3)

[0080] In formula (3), is the sound pressure vector of the structure surface, is the normal velocity of the structure surface.

[0081] Step 4: Process the empty element sensitivity and solid element sensitivity obtained in step 3 based on the sensitivity genetic mechanism, and dynamically update the solid element width using the global moving asymptote algorithm. Specifically:

[0082] ​Step 4.1: Process the sensitivity of each real unit in the set of real units and the sensitivity of each empty unit in the set of empty units according to the sensitivity inheritance mechanism. The sensitivity inheritance mechanism is as follows:

[0083] Step 4.1.1: Based on the acoustic power sensitivity obtained in step 3.3, in the first iteration, the acoustic power sensitivity of the N empty units in the initial empty unit set is processed by formula (4). Similarly, the acoustic power sensitivity of the M real units in the initial real unit set is processed by formula (4), where N+M=p.

[0084] (4)

[0085] In equation (4), It is the first Sensitivity of individual beam elements; the superscript 1 indicates the first iteration.

[0086] From the beginning of the second iteration to the end of each iteration, based on steps 3.1 and 3.3, the acoustic power sensitivity of each empty cell in the empty cell set is processed by formula (5). Similarly, the acoustic power sensitivity of each real cell in the real cell set is processed by formula (5).

[0087] (5)

[0088] In equation (5), It is the first Individual beam element sensitivity; superscript It is the first Next iteration, superscript It is the first The next iteration.

[0089] In this step, the significance of the sensitivity inheritance mechanism lies in averaging the acoustic power sensitivity of each real unit in the real unit set with the acoustic power sensitivity of each empty unit in the empty unit set with the acoustic power sensitivity of each unit corresponding to the previous iteration, thus ensuring good convergence of the iteration process.

[0090] Step 4.2: After processing the sensitivity of each beam element using the method described in Step 4.1, the width of the real element is updated using the Global Moving Asymptote Algorithm (GCMMA).

[0091] Step 5: Based on the real element width obtained in Step 4, a "growth competition criterion" is introduced to guide the branching, degradation, and updating of the element's material properties, resulting in a new stiffened configuration. Specifically:

[0092] Step 5.1, Branch Operation: If the set of real cells contains the first branch... The width of each real cell exceeds the branch threshold (in this embodiment) is 0.002 m, i.e. the branch operation is activated. Specifically, the empty cell with the minimum acoustic power sensitivity value in the empty cell set is selected and converted into a solid cell, i.e. the material property of the cell is converted from weak material to solid material, and the direction is the growth direction, which is mathematically expressed as formula (6):

[0093] (6)

[0094] In formula (6), represents the minimum value of the sensitivity of the empty cell, and the subscript i represents the i-th empty cell; represents the number of empty cells; represents weak material, and 1 represents solid material. The branch threshold value is denoted as

[0095] In this step, the mathematical meaning of the "growth competition criterion" is that the sensitivity reflects the influence of the small change of the design variable on the performance of the structure, and the smaller the sensitivity, the greater the influence of the unit on the reduction of the objective function, and therefore such a unit is preferentially selected for growth.

[0096] Step 5.2, degradation operation: if the width of the i-th solid cell in the solid cell set is lower than the degradation threshold (0.001 m in this embodiment), i.e. the degradation operation is activated. At this time, the cell is selected from the solid cell set and its material property is reset to weak material, thereby achieving removal from the structure. The degradation threshold is denoted as

[0097] Step 5.3, keep unchanged: if the width of the i-th solid cell in the solid cell set is within the interval of the branch threshold and the degradation threshold, i.e. no treatment is performed on the cell, and its current state is kept.

[0098] Step 5.4, the "growth competition criterion" is obtained based on steps 5.1 to 5.3, and a new stiffened configuration is obtained based on the "growth competition criterion".

[0099] In this embodiment, the branch threshold and the degradation threshold need to be selected according to different problems, and the beam theory is not invalid.

[0100] Step 6: the objective function obtained based on formula (1) ​​​​determining whether the optimization process converges, when it is determined that it does not converge, returning to the second step and further optimizing based on the design variables obtained in the fifth step; when it is determined that it converges, ending the optimization process and obtaining the optimal reinforcement distribution. In this embodiment, the convergence criterion is that the rate of change of the objective function value between two consecutive iteration steps is less than or equal to the convergence precision, which is specifically 0.001% in this embodiment.

[0101] Figure 4 The reinforcement layout optimization process of the rectangular plate under the volume constraint of 0.45 is shown, specifically, Figure 4 (a) in FIG. 10 is a result graph of 10 iterations, Figure 4 (b) in FIG. 10 is a result graph of 30 iterations, Figure 4 (c) in FIG. 10 is a result graph of 50 iterations, Figure 4 (d) in FIG. 10 is a result graph of 70 iterations, Figure 5 (e) in FIG. 10 is a result graph of 90 iterations, Figure 5 (f) in FIG. 10 is a final optimization result graph. It can be analyzed that, with the increase of the number of iterations, the real elements gradually branch, reconstruct and degenerate from the seed points in the four corners and the central region. The optimization process converges after 134 iterations, forming a reinforcement topology configuration that meets the optimal structure performance under the given parameters. In order to intuitively evaluate the optimization effect, the sound power level is used as a relative index: the sound power level after optimization decreases from 127.32 dB to 99.79 dB, with a decrease of 27.53 dB.

[0102] Figure 5 The iteration process curve is given, wherein, Figure 6 (a) in FIG. 11 gives the iteration process graph of the ratio of the sound power level, Figure 6 (b) in FIG. 11 gives the iteration process graph of the total volume of the reinforcement. It can be analyzed that, thanks to the introduction of the "growth competition criterion" and the sensitivity genetic mechanism, although the branching and degeneration operations cause the elements to dynamically switch between existing (real elements) and missing (empty elements), the entire iteration process still exhibits high efficiency and stability. This feature ensures the convergence of the optimization algorithm in complex topology evolution, verifying the reliability and practicality of the proposed method in engineering structure design.

[0103] In order to verify the superiority of the proposed method, a comparative model with completely consistent optimization parameters is established in COMSOL, and the built-in variable density method, i.e., the SIMP algorithm, is called to carry out topology optimization under three working conditions of volume constraints of 0.15, 0.30 and 0.45, respectively. The results are compared with the proposed method. The optimization results are shown in ​ (a) in FIG. 12, ​ (f) in FIG. 12, and the post-optimization data are shown in Table 1.

[0104] Table 1 Comparison of optimization results

[0105]

[0106] For the same optimization problem, the optimization results show that the proposed optimization method and the SIMP method have topological consistency in the spatial distribution of the reinforcement region, both identifying the four corners and the central region as the main reinforcement regions. However, the sound power level obtained by the proposed method is significantly lower than that of the SIMP method, and the difference between the two further increases as the volume constraint decreases. The reason is that the SIMP method defines the element density based on the density interpolation model, where there are many "pseudo densities", which leads to the deviation of the calculation of the overall stiffness matrix. In contrast, the proposed optimization method directly spreads the reinforcement stiffness to the shell element, which can more accurately solve the dynamic response; at the same time, the optimization results of the present application do not require a complex feature extraction process, and have significant advantages in structural clarity and manufacturability.

[0107] In terms of computational efficiency, the proposed optimization method consumes less computational resources compared to the SIMP method. The SIMP method is highly sensitive to mesh size and sensitivity filtering radius, and requires a finer mesh and appropriate filtering radius to obtain clear optimization results. This inevitably leads to a significant increase in the number of design variables and degrees of freedom, resulting in high computational cost. The proposed optimization method significantly improves efficiency in the following ways: on the one hand, it simplifies the structure-acoustic analysis and avoids the calculation of large-scale Helmholtz integral equations; on the other hand, since there is no need for mesh reconstruction, the shell element stiffness and mass matrix only need to be assembled once. More importantly, the growth competition criterion proposed in the present application only allows the beam element that wins in the competition to participate in subsequent calculations, thereby further reducing the computational cost.

[0108] The above-described embodiments only express the implementation of the present application, but cannot be interpreted as limiting the scope of the present application. It should be pointed out that for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the scope of protection of the present application.

Claims

1. A panel structure stiffener layout topology optimization method for sound radiation suppression, characterized in that, The method comprises the following steps: The first step is to establish a base structure, define the structural load, boundary conditions, optimization parameters and design variables, perform acoustic power sensitivity analysis on the base structure according to the structural load and boundary conditions, determine the seed point position, obtain the empty cell and the real cell, and obtain the total displacement vector as the structural dynamic response. The second step is to perform finite element analysis on the base structure in the first step and obtain the structural dynamic response. The third step is to obtain the real cell set and the empty cell set, combine the structural dynamic response obtained in the second step and the high-frequency approximate acoustic impedance theory to calculate the target function value, and calculate the sensitivity of each real cell in the real cell set and the sensitivity of each empty cell in the empty cell set. The fourth step is to process the sensitivities of the real cells and the empty cells obtained in the third step according to the sensitivity genetic mechanism, and dynamically update the width of the real cells by using the global moving asymptote algorithm. The fifth step is to introduce the "growth competition criterion" to guide the branching and degradation of the corresponding cells and update the material properties of the cells according to the width of the real cells obtained in the fourth step, and obtain a new stiffened configuration. The fifth step is specifically: Step 5.1, branch operation: if the width of the first real unit in the real unit set exceeds the branch threshold value , i.e. , , the branch operation is activated; select the empty unit with the minimum sound power sensitivity value in the empty unit set and convert it into a real unit, i.e. convert the material attribute of the unit from weak material to solid material, and the direction is the growth direction, which is expressed as formula (6): (6) ； In formula (6), represents the minimum value of the air cell sensitivity, the subscript represents the number of air cells; represents a weak material, 1 represents a solid material; Step 5.2, Degradation operation: If the width of the first real cell in the real cell set is below the degradation threshold , i.e. , , the degradation operation is activated; at this point, the cell is selected from the real cell set and its material properties are reset to weak material, thus enabling its removal from the structure. Step 5.3, remains the same: if the width of the i-th real unit in the set of real units is in the interval between the branch threshold and the degenerate threshold, i.e. then no action is taken on this unit, and its current state is maintained. ​ Step 5.4, the growth competition criterion is steps 5.1 to 5.3, and a new stiffened configuration is obtained based on the growth competition criterion. The sixth step is to judge whether the optimization process converges based on the obtained target function value, and if the judgment is not convergent, return to the second step and further optimize based on the design variables obtained in the fifth step; if the judgment is convergent, end the optimization process and obtain the optimal stiffener distribution.

2. The method according to claim 1, wherein, The first step is specifically: Step 1.1, after discretizing the plate and shell structure into shell elements, connect any two nodes on the shell element with a beam element as a stiffener to form a basic structure model required for design, that is, obtain the base structure; define the structural load, boundary conditions, optimization parameters and design variables; Step 1.2, set the material properties of all beam elements in the base structure to weak material, that is, empty cell; Step 1.3, perform acoustic power sensitivity analysis on the base structure, select any node of the beam element in the region with the smallest acoustic power sensitivity as the seed point, and change the material properties of the beam element connected to the seed point from weak material to solid material, that is, from empty cell to real cell.

3. The method according to claim 2, wherein, In the first step: The optimization parameters include the initial width of the stiffener, the height of the stiffener, the upper and lower limits of the width of the stiffener, the branching threshold, the degradation threshold, the material properties, the acoustic medium properties, the volume constraint and the convergence precision; The design variables include the width of the stiffener and the material properties; The seed point refers to the initial growth position preset in the base structure, and the stiffener connected to the seed point is used as the initial unit for evolution to guide the growth direction and distribution of the subsequent stiffeners.

4. The panel skin structure stiffener layout topology optimization method of claim 3, wherein, The third step is specifically: Step 3.1, in the first iteration, obtain the initial empty cell set and the initial real cell set based on steps 1.2 to 1.3; from the second iteration to the end of each iteration, reacquire the real cell set and the empty cell set according to the update of the material properties of each beam element; Step 3.2, the target function value is calculated based on the high-frequency approximate acoustic impedance theory, and the mathematical model of the optimization design is shown in formula (1), and the target function is the sound power, i.e. formula (1) , and the design goal is to minimize the sound power of the plate shell structure; （1）； In equation (1), It is a collection of the properties of reinforcing rib materials. It is the material property of the first beam element. It refers to the material properties of the second beam element. It is the first Material properties of individual beam elements It is the first Material properties of individual beam elements; It is a collection of the widths of the reinforcing ribs. It is the width of the first beam element. It is the width of the second beam element. It is the first The width of each beam element, It is the first The width of each beam element, where the subscript... Indicates the first Individual beam element, subscript Represents the total number of beam elements; design variables include a set. middle Material properties and sets of beam elements middle The width of each beam element; It is sound power; It is the density of the acoustic medium; It is the speed of sound; It is the external excitation angular frequency; It is the global displacement vector The conjugate transpose of; It is the normal vector coefficient matrix; It is a preset volume limit. It is the first Volume of each beam element; K d It is the structural dynamic stiffness matrix; It is an external excitation column vector; It is the first The width of each beam element, and These are the upper and lower limits of the beam element width, respectively. It is the first Material properties of individual beam elements 1 represents a weak material, and 1 represents a solid material. The values ​​1 and 1 represent different properties of the beam element material, i.e., empty elements are set as weak materials, using... This indicates that the real element is set as a solid material, represented by 1; In step 3.3, in the first iteration, the sound power sensitivity of each of the N null elements in the initial null element set is calculated, and the sound power sensitivity of each of the M real elements in the initial real element set is calculated. In each iteration from the second iteration to the end, based on the updated null element set and real element set in step 3.1, the sound power sensitivity of each of the null elements in the null element set is calculated, and the sound power sensitivity of each of the real elements in the real element set is calculated.

5. The method according to claim 4, wherein, In step 3.3, the sound power sensitivity calculation formula of the real element and the null element is as follows: (2) ； In formula (2), is the width of the beam element; is a definition introduced artificially for simplifying the formula; is the transpose of the local coordinate to global coordinate conversion matrix T; K B and M B are the beam element stiffness matrix and mass matrix, respectively.

6. The panel skin structure stiffener layout topology optimization method of claim 5, wherein, The fourth step is specifically as follows: In step 4.1, the sensitivity genetic mechanism is used to process the sensitivity of each real element in the real element set and the sensitivity of each null element in the null element set. In step 4.2, after the sensitivity of each beam element is processed in step 4.1, the global moving asymptote algorithm (GCMMA) is used to update the width of the real element.

7. The method according to claim 6, wherein, In step 4.1, the sensitivity genetic mechanism is as follows: In step 4.1.1, in the first iteration, the sound power sensitivity of each of the N null elements in the initial null element set is processed by using formula (4), and the sound power sensitivity of each of the M real elements in the initial real element set is processed by using formula (4). (4) ； In formula (4), is the sensitivity of the first beam unit; the superscript 1 is the first iteration; In each iteration from the second iteration to the end, based on step 3.1 and step 3.3, the sound power sensitivity of each of the null elements in the null element set is processed by using formula (5), and the sound power sensitivity of each of the real elements in the real element set is processed by using formula (5). (5) ； In formula (5), is the sensitivity of the first beam unit; the superscript is the iteration number; the superscript is the iteration number; the superscript is the iteration number; the superscript is the iteration number.

8. The method of topology optimization of stiffened layout of panel-shell structure for sound radiation suppression according to claim 1, characterized in that, The branch threshold and the degradation threshold need to be selected according to different problems, and the beam theory should not be disabled.

9. The method according to claim 8, wherein, In the sixth step, the convergence criterion is that the change rate of the objective function value between two consecutive iterations is less than or equal to the convergence precision, and the convergence precision is 0.001% to 0.01%.

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