Dynamic boundary equivalent design method considering heat influence
By constructing a finite element model and optimizing the dimensional parameters of the boundary support plate, the problems of structural stiffness degradation and dynamic coupling effects under thermal load were solved, and the equivalent design of the dynamic boundary was realized, which improved the accuracy of dynamic analysis and the accuracy of structural life prediction.
Patent Information
- Application Number
- CN202511778206.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-28
- Publication Date
- 2026-03-03
AI Technical Summary
Existing technologies fail to effectively characterize the structural stiffness degradation effect under thermal loads, leading to distorted boundary conditions, which affects the accuracy of dynamic analysis and the prediction of structural fatigue life. Furthermore, they neglect the dynamic coupling effect between local structures and the overall frame.
A finite element model is constructed, the thermal stress distribution is calculated and boundary conditions are applied. By optimizing the dimensional parameters of the boundary support plate, an equivalent design of the dynamic boundary is formed, and the dynamic characteristics under thermal influence are accurately reconstructed.
It improves the accuracy of dynamic characteristic modeling, reduces modal frequency error, and enhances the accuracy of dynamic analysis and fatigue life prediction of structures under complex thermal environments.
Smart Images
Figure CN121598508A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of aircraft dynamic strength design technology, specifically relating to a dynamic boundary equivalent design method that considers thermal effects. Background Technology
[0002] Against the backdrop of aerospace equipment evolving towards lower detectability and higher maneuverability, panel structures, as core carriers supporting critical functional components, directly impact the vibration control and long-life reliability of aircraft due to their dynamic characteristics. Traditional boundary condition design, based on the assumption of rigid support, simplifies computational models but fails to account for the structural stiffness degradation effect caused by thermal loads. Studies show that when structures are in the typical operating temperature range of 500-800℃ for thermal protection systems, the material properties at the connection interfaces undergo nonlinear degradation, leading to a reduction in boundary stiffness of approximately 30%-45%. Existing design methods lack effective characterization of such dynamic changes. This distorted modeling of boundary conditions directly induces local modal frequency shifts exceeding 10% and mode shape distortion rates exceeding 25%, significantly weakening the engineering guidance value of dynamic analysis.
[0003] On the other hand, under the combined effects of extreme temperature rise and thermoacoustic vibration loads, the dynamic response characteristics of local regions of aircraft panel structures are highly susceptible to the influence of the boundary constraints of surrounding auxiliary structures. The currently prevalent rigid-supported boundary condition design strategy often neglects the dynamic coupling effect between local structures and the overall frame, leading to significant deviations between local modal parameters and global dynamic characteristics, thus negatively impacting the accuracy of structural fatigue life prediction. Currently, research on equivalent modeling and optimization design methods for structural boundaries under thermal conditions is still in the exploratory stage, lacking a systematic theoretical framework and engineering application schemes, which directly restricts the ability to accurately reconstruct structural dynamic characteristics. Summary of the Invention
[0004] To address the aforementioned issues, this application provides a dynamic boundary equivalent design method that considers thermal effects, applicable to the design of aerospace stiffened panel structures, to achieve accurate reconstruction of the dynamic characteristics of local structures such as stiffened panels.
[0005] The dynamic boundary equivalent design method considering thermal effects provided in this application mainly includes:
[0006] Step S1: Construct a finite element model of the overall structure including the target structure, and calculate the thermal stress distribution of the overall structure under a specified temperature load;
[0007] Step S2: After applying boundary conditions to the overall structure, calculate the low-order modal frequencies and mode shapes of the overall structure caused by thermal stress;
[0008] Step S3: Based on the connection relationship between the target structure and the surrounding structures in the overall structure, extend the target structure to construct an equivalent initial design model that includes the target structure and the surrounding structures.
[0009] Step S4: After applying fixed boundary conditions to the equivalent design initial model, calculate the low-order modal frequencies and mode shapes of the target structure caused by thermal stress.
[0010] Step S5: Using the maximum low-order modal frequency of the target structure as the constraint as the objective function, optimize the surrounding structure into multiple boundary support thin plates to form an optimal topology model;
[0011] Step S6: After applying fixed boundary conditions to the optimal topology model, calculate the low-order modal frequencies and mode shapes of the target structure caused by thermal stress.
[0012] Step S7: Optimize the dimensional parameters of each boundary support plate with the goal of maximizing the similarity between the low-order modal frequencies and mode shapes of the target structure and the overall structure, and obtain the equivalent design parameters of the dynamic boundary for the target structure.
[0013] Preferably, in step S1, the finite element model of the overall structure includes a high-temperature alloy using GH5188 material, and thermodynamic performance parameters are input, including elastic modulus, thermal conductivity, coefficient of linear expansion and specific heat capacity as they change with temperature.
[0014] Preferably, the order of the low-order modal frequency is 1-N, where N is 3-6.
[0015] Preferably, in step S5, optimizing the surrounding structure further includes:
[0016] The constraint condition is set that the volume of the optimized boundary support plate is no more than 55% of the volume of the surrounding structure before optimization;
[0017] The design variable is set as element density;
[0018] The iteration termination condition is set as either the maximum number of iterations or error convergence.
[0019] Preferably, in step S7, optimizing the dimensional parameters of each boundary support plate includes:
[0020] The optimization objectives include: minimizing the sum of the low-order modal frequency errors between the overall structure and the target structure, and minimizing the structural mass of the target structure;
[0021] The constraints include: maximizing the MAC value of the lower-order mode shape, and ensuring that all dimensional parameters are within their ranges.
[0022] The dimensional parameters to be optimized include the length, width, and thickness of the support plates at each boundary.
[0023] Preferably, when optimizing the dimensional parameters of each boundary support plate, the constraints also include the minimum thickness of the boundary support plate that is process-feasible.
[0024] This application realizes the boundary equivalent design of local structures of wall panels under complex thermal environments, and improves the accuracy of dynamic characteristic modeling of structures. Attached Figure Description
[0025] Figure 1 This is a flowchart of a preferred embodiment of the dynamic boundary equivalent design method considering thermal effects in this application.
[0026] Figure 2 This is a schematic diagram of the initial structure for boundary equivalent design.
[0027] Figure 3 This is a schematic diagram of the topology optimization results.
[0028] Figure 4 This is a schematic diagram of the boundary equivalent optimization structure.
[0029] Figure 5 This is a diagram showing the comparison of mode MAC values. Detailed Implementation
[0030] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, not all, of the embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings.
[0031] This application provides a dynamic boundary equivalent design method that considers thermal effects, such as Figure 1 As shown, it mainly includes:
[0032] Step S1: Construct a finite element model of the overall structure including the target structure, and calculate the thermal stress distribution of the overall structure under a specified temperature load;
[0033] Step S2: After applying boundary conditions to the overall structure, calculate the low-order modal frequencies and mode shapes of the overall structure caused by thermal stress;
[0034] Step S3: Based on the connection relationship between the target structure and the surrounding structures in the overall structure, extend the target structure to construct an equivalent initial design model that includes the target structure and the surrounding structures.
[0035] Step S4: After applying fixed boundary conditions to the equivalent design initial model, calculate the low-order modal frequencies and mode shapes of the target structure caused by thermal stress.
[0036] Step S5: Using the maximum low-order modal frequency of the target structure as the constraint as the objective function, optimize the surrounding structure into multiple boundary support thin plates to form an optimal topology model;
[0037] Step S6: After applying fixed boundary conditions to the optimal topology model, calculate the low-order modal frequencies and mode shapes of the target structure caused by thermal stress.
[0038] Step S7: Optimize the dimensional parameters of each boundary support plate with the goal of maximizing the similarity between the low-order modal frequencies and mode shapes of the target structure and the overall structure, and obtain the equivalent design parameters of the dynamic boundary for the target structure.
[0039] In contrast to the traditional approach of simply applying fixed boundary conditions to the target structure, this application optimizes the boundary conditions, referencing... Figure 1 The method used is as follows: First, in steps S1-S2, the low-order frequencies and mode shapes of the target structure within the overall structure are studied and selected as the required low-order frequencies and mode shapes. Then, in step S6, the target structure is isolated, and the corresponding low-order frequencies and mode shapes are calculated for different boundary conditions. Finally, in step S7, the boundary conditions that make the subsequently calculated low-order frequencies and mode shapes consistent with or very close to the required low-order frequencies and mode shapes are found are identified. This process uses a genetic algorithm to solve for the optimal boundary conditions.
[0040] In addition, in steps S3-S5, the number of supports and support points of the boundary support structure are further optimized using an optimization algorithm, that is, to find the optimal number of supports and support positions of the boundary support plates. Thus, in the optimization algorithm of steps S6-S7, only the size parameters of each boundary support plate need to be considered.
[0041] In step S1 of this application, a finite element model of the overall structure (including the local target structure) is established. In some optional embodiments, in step S1, the finite element model of the overall structure includes a high-temperature alloy using GH5188 material, and thermodynamic performance parameters are input, including the elastic modulus, thermal conductivity, coefficient of linear expansion, and specific heat capacity as a function of temperature.
[0042] Then, a specified temperature load, such as 600°C, is applied, and the thermal stress distribution of the structure at high temperature is calculated. ;
[0043] ;
[0044] in: The elastic modulus of the material as a function of temperature; The coefficient of thermal expansion; Temperature field distribution; The initial temperature of the structure.
[0045] In step S2, modal analysis of the overall structure is then performed. Boundary conditions are applied, the structural support stiffness caused by thermal stress is calculated, and the structural stiffness matrix and mass matrix considering thermal effects are extracted. Modal analysis and calculation are then performed to obtain the low-order modal frequencies and mode shapes of the overall structure considering thermal effects. Here, the low-order modal frequencies of the overall structure are consistent with the "required low-order frequencies" of the target structure mentioned above, and the mode shapes of the overall structure necessarily include the "required mode shapes" of the target structure.
[0046] To further illustrate the technical effects of this application, the structural support stiffness caused by thermal stress is calculated for the target structure after applying the traditional fixed-support boundary conditions. Modal analysis is then performed to extract the low-order frequencies and mode shapes corresponding to the target structure, and these are compared with the target structure, as shown in Table 1 below.
[0047] Table 1. Error of fixed support frequency between target structure and local wall panel
[0048]
[0049] As can be seen from Table 1 above, the traditional method provides low-order modal frequencies for the target structure with an error of over 30%.
[0050] Table 1 lists the modal frequencies of orders 1-4, but modal frequency parameters of other orders can also be used. In some optional embodiments, the lower-order modal frequencies are of orders 1-N, where N is 3-6.
[0051] Returning to this application, in step S3, the locally stiffened wall panel is extended to simulate the supporting effect of the surrounding structure, and the boundary equivalent design of the initial structure is constructed, such as... Figure 2 As shown, the middle wall panel structure is the target structure, and the area around the wall panel structure is the boundary design area. Together, they form an equivalent initial design structure. After calculating its parameters in step S4, the boundary design area is optimized in step S5.
[0052] Specifically, the objective function of step S5 is to maximize the sum of low-order modal frequencies, thereby seeking the optimal force transmission path, i.e. ;in, Let be the i-th modal frequency of the target structure.
[0053] In some alternative implementations, step S5, optimizing the surrounding structure, further includes:
[0054] The constraint condition is set that the volume of the optimized boundary support plate is no more than 55% of the volume of the surrounding structure before optimization;
[0055] The design variable is set as element density;
[0056] The iteration termination condition is set as either the maximum number of iterations or error convergence.
[0057] In this embodiment, the optimal layout of the boundary support structure is generated through density-based iterative optimization, such as... Figure 3 As shown, based on the topology optimization results, the local structural boundary support structure is reconstructed, as follows: Figure 4 As shown, multiple boundary support thin plates are formed. Figure 4 In the middle, three thin plates are used on the top and bottom sides of the target structure: the Y1 plate in the middle and two identical Y2 plates on both sides of the Y1 plate. Three thin plates are used on the left and right sides of the target structure: the X2 plate in the middle and two identical X1 plates on both sides of the X2 plate.
[0058] Steps S6 and S7 are used to optimize the dimensional parameters of the four types of boundary support plates mentioned above.
[0059] In some alternative implementations, step S7, optimizing the dimensional parameters of each boundary support plate, includes:
[0060] The optimization objectives include: minimizing the sum of the low-order modal frequency errors between the overall structure and the target structure, and minimizing the structural mass of the target structure;
[0061] The constraints include: maximizing the MAC value of the lower-order mode shape, and ensuring that all dimensional parameters are within their ranges.
[0062] The dimensional parameters to be optimized include the length, width, and thickness of the support plates at each boundary.
[0063] In this embodiment, a multi-objective optimization model is constructed:
[0064] ;
[0065] The multi-objective function Obj aims to minimize the sum of low-order modal frequency errors and minimize structural mass. In the formula, Let i be the i-th modal frequency of the target structure. Let i be the i-th modal frequency of the overall structure. For structural quality.
[0066] Constraint st: Maximize the MAC value of lower-order mode shapes The closer the MAC value is to 1, the more consistent the mode shapes of the two components are. (In the formula...) Let i be the i-th mode shape parameter of the target structure. Let be the i-th mode shape parameter of the overall structure.
[0067] In some alternative implementations, when optimizing the dimensional parameters of each boundary support plate, the constraints also include a minimum processable thickness for the boundary support plate. In the formula, For dimensional parameters, This is the lower limit of the dimensional parameters. This represents the upper limit of the size parameter.
[0068] A multi-parameter genetic optimization algorithm is used to iteratively solve for the optimal size parameters.
[0069] The optimized dimensional parameters are shown in Table 2.
[0070] Table 2 Optimal Results of Size Optimization
[0071]
[0072] Redesign with optimal parameters based on size optimization Figure 4 The boundary equivalent optimization structure was constructed, and modal analysis was performed to obtain the first four modal frequencies and mode shapes corresponding to the target structure. The results show that the frequency error is within 3%, as shown in Figure 3, and the MAC values are all greater than 0.97, indicating a high degree of consistency in mode shapes. Figure 5 As shown.
[0073] Table 3 Comparison of modal frequencies of the front and rear wall plates before and after the boundary equivalent
[0074]
[0075] Through comparative verification, the equivalent design of the dynamic boundary of the target structure in this application results in a low-order frequency error of ≤3% and consistent mode shapes, which is significantly better than the traditional fixed-support method. This application provides a high-precision technical solution for the equivalent design of local structural boundaries under complex thermal environments.
[0076] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A dynamic boundary equivalent design method considering thermal effects, characterized in that, The method includes: Step S1: Construct a finite element model of the overall structure including the target structure, and calculate the thermal stress distribution of the overall structure under a specified temperature load; Step S2: After applying boundary conditions to the overall structure, calculate the low-order modal frequencies and mode shapes of the overall structure caused by thermal stress; Step S3: Based on the connection relationship between the target structure and the surrounding structures in the overall structure, extend the target structure to construct an equivalent initial design model that includes the target structure and the surrounding structures. Step S4: After applying fixed boundary conditions to the equivalent design initial model, calculate the low-order modal frequencies and mode shapes of the target structure caused by thermal stress. Step S5: Using the maximum low-order modal frequency of the target structure as the constraint as the objective function, optimize the surrounding structure into multiple boundary support thin plates to form an optimal topology model; Step S6: After applying fixed boundary conditions to the optimal topology model, calculate the low-order modal frequencies and mode shapes of the target structure caused by thermal stress. Step S7: Optimize the dimensional parameters of each boundary support plate with the goal of maximizing the similarity between the low-order modal frequencies and mode shapes of the target structure and the overall structure, and obtain the equivalent design parameters of the dynamic boundary for the target structure.
2. The dynamic boundary equivalent design method considering thermal effects according to claim 1, characterized in that, In step S1, the finite element model of the overall structure is constructed using a high-temperature alloy made of GH5188 material, and thermodynamic performance parameters are input, including elastic modulus, thermal conductivity, coefficient of linear expansion and specific heat capacity as they change with temperature.
3. The dynamic boundary equivalent design method considering thermal effects according to claim 1, characterized in that, The order of the low-order modal frequencies is 1 to N, where N is 3 to 6.
4. The dynamic boundary equivalent design method considering thermal effects according to claim 1, characterized in that, Step S5, further optimization of the surrounding structure includes: The constraint condition is set that the volume of the optimized boundary support plate is no more than 55% of the volume of the surrounding structure before optimization; The design variable is set as element density; The iteration termination condition is set as either the maximum number of iterations or error convergence.
5. The dynamic boundary equivalent design method considering thermal effects according to claim 1, characterized in that, In step S7, optimizing the dimensional parameters of each boundary support plate includes: The optimization objectives include: minimizing the sum of the low-order modal frequency errors between the overall structure and the target structure, and minimizing the structural mass of the target structure; The constraints include: maximizing the MAC value of the lower-order mode shape, and ensuring that all dimensional parameters are within their ranges. The dimensional parameters to be optimized include the length, width, and thickness of the support plates at each boundary.
6. The dynamic boundary equivalent design method considering thermal effects according to claim 5, characterized in that, When optimizing the dimensional parameters of each boundary support plate, the constraints also include the minimum thickness of the boundary support plate that is process-feasible.