A topology optimization method for large spacecraft structures based on optimal flexibility method

Abstract

This invention discloses a topology optimization method for large spacecraft structures based on the optimal flexibility method, which relates to the field of aerospace technology. The method comprises the following steps: using the geometric parameters of deformable components as design variables to perform explicit parametric modeling of the spacecraft structure; establishing a finite element analysis model based on the explicit parameter model of the spacecraft structure; constructing an updated objective function for the design variables with respect to flexibility based on the established finite element analysis model; and iteratively updating and optimizing the design variables based on the updated objective function to obtain the optimal design variables. This invention provides a high-performance, high-efficiency, and high-reliability optimization paradigm for large-scale, multi-constrained, and complex optimization scenarios such as large spacecraft, significantly reducing computational costs and engineering risks compared to traditional methods.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and more particularly to a large spacecraft structure topology optimization method based on an optimal flexibility method. Background Art

[0002] High-performance optimization design methods are an eternal theme in the field of aerospace engineering research and development, which has a decisive impact on the comprehensive performance and service effectiveness of spacecraft.

[0003] With the continuous development of aerospace technology, the demand for comprehensive performance and multifunctionality of new-generation spacecraft continues to increase. A series of structural optimization design methods, represented by topology optimization methods, have great development potential and enormous application value. As the application level of spacecraft increases, the requirements for spacecraft structural performance are also increasingly higher. Finding a structure that meets these requirements has become the most critical link in the entire design process.

[0004] When performing topology optimization design on large spacecraft, their structures are typically large and complex, requiring them to meet requirements such as lightweight, high strength, stiffness, and dynamic stability. Traditional topology optimization methods, however, often suffer from issues such as high computational resource consumption, limited multi-objective optimization results, and the inability to avoid the application limitations of single topology optimization methods, resulting in low efficiency. A range of structural optimization design methods, represented by existing topology optimization methods, have provided some insights into large spacecraft manufacturing. However, most of these methods are based on a single topology optimization method, with little consideration given to combining multiple topology optimization methods for spacecraft structural optimization. This leads to limitations in the application of topology optimization methods, and further research is needed on topology optimization methods for high-performance, lightweight spacecraft structures. When applying topology optimization methods to spacecraft structural design, combining multiple topology optimization methods based on the structural characteristics and mechanical properties of the optimization target can overcome the shortcomings of a single method and achieve better optimization results. Summary of the Invention

[0005] In view of this, the present invention provides a large spacecraft structure topology optimization method based on the optimal flexibility method, which is used to at least solve some of the technical problems in the background technology.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A large spacecraft structure topology optimization method based on an optimal flexibility method includes the following steps:

[0008] Explicit parametric modeling of spacecraft structures using geometric parameters of deformable components as design variables;

[0009] Establish a finite element analysis model based on the explicit parameter model of the spacecraft structure;

[0010] An updated objective function of the design variables with respect to flexibility is constructed according to the established finite element analysis model, and the design variables are iteratively updated and optimized according to the updated objective function to obtain the optimal design variables.

[0011] Furthermore, in the step of using geometric parameters of a deformable component as a design variable, the deformable component includes a rectangle and a beam unit, and the geometric parameters include position coordinates, angles and specifications and dimensions.

[0012] Furthermore, an updated objective function of the design variables with respect to flexibility is constructed based on the established finite element analysis model, and the design variables are iteratively updated and optimized based on the updated objective function; specifically, the method includes:

[0013] Construct the updated objective function of the design variables with respect to flexibility:

[0014]

[0015] in, represents the design variable at k+1 steps after the update, X represents the design variable in the updated objective function, represents the flexibility function of the design variables, represents the volume function of the design variables, It plays a role in balancing different objectives in optimization and is a constant parameter.

[0016] The updated objective function is iteratively updated. During each iteration, it is determined whether the updated design variables meet the constraint conditions. If not, the step size or direction of the updated objective function is adjusted to ensure that the optimization process is always carried out within the feasible domain. If so, normal iteration is performed until the iterative convergence condition is met.

[0017] Furthermore, in the update objective function of the design variable with respect to flexibility, the flexibility function of the design variable specifically includes the following expression:

[0018]

[0019] Where, The flexibility function value of the design variable, n represents the total number of iterations, represents the flexibility function of the design variables at step k, Represents the geometric parameters in the design variables Softness sensitivity, and are the design variables in the kth iteration The upper and lower limits of The value range of , Represents the geometric parameters in the design variables The flexibility sensitivity coefficient.

[0020] Furthermore, in the update objective function of the design variable with respect to flexibility, the volume function of the design variable specifically includes the following expression:

[0021]

[0022] Where, The volume function value of the design variable, n represents the total number of iterations, Represents the geometric parameters in the design variables Volume sensitivity, and are the design variables in the kth iteration The upper and lower limits of The value range of , Represents the geometric parameters in the design variables The flexibility sensitivity coefficient, Represents the geometric parameters in the design variables The volume sensitivity coefficient.

[0023] Furthermore, the iterative convergence condition specifically includes:

[0024] The update amount of the design variable is less than the set threshold:

[0025] ,

[0026] in, is the design variable for step k, x k+1 represents the design variable of the k+1th step;

[0027] The volume constraint deviation is less than the threshold;

[0028]

[0029] Among them, V(x k ), represents the volume of the design variable in step k, V target represents the final target volume after optimization.

[0030] Furthermore, in each update iteration, it is determined whether the updated design variables meet the constraints, including the following constraints:

[0031]

[0032] Where V(X) is the volume of the design variable X, is the maximum volume allowed; represents the cell density, , is the unit volume.

[0033] Furthermore, the geometric parameters in the design variables The flexibility sensitivity of is calculated by the following expression:

[0034]

[0035] Where C represents flexibility, represents the i-th component parameter of the design variable, represents the stiffness matrix, Represents a displacement vector.

[0036] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a method for topology optimization of large spacecraft structures based on the optimal flexibility method, which has the following beneficial effects:

[0037] Large-scale spacecraft structures mean a large number of grids, which leads to a dramatic increase in the amount of computation required for finite element analysis. Topology optimization is an iterative process, and each step requires a large amount of computation. This places high demands on memory and computing time, which may result in an excessively long optimization cycle. The present invention introduces the optimal flexibility method into the explicit topology optimization method, and utilizes its relaxation factor to adjust the update step size of the solution in each iteration to optimize the convergence speed of the iterative process. This can significantly accelerate the convergence speed and reduce the number of iterations. In addition, the optimal flexibility method is relatively simple to implement and can be easily implemented in a computer program. At the same time, it minimizes the flexibility of the structure under load, thereby effectively improving the stiffness of the optimized structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0039] Figure 1 The present invention provides a schematic diagram of the overall process of the method.

[0040] Figure 2 This is a schematic diagram of the design variable definition for the rectangular component example provided by the present invention. DETAILED DESCRIPTION

[0041] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0042] The embodiment of the present invention discloses a method for topology optimization of a large spacecraft structure based on an optimal flexibility method, comprising the following steps:

[0043] Explicit parametric modeling of spacecraft structures using geometric parameters of deformable components as design variables;

[0044] Construct objective functions and constraints for design variables;

[0045] Use differentiation to calculate the sensitivity of the objective function with respect to the design variables;

[0046] Constructing iterative equations for flexibility-design variable optimization algorithm;

[0047] According to the calculated sensitivity, the optimization algorithm is used to iteratively optimize and adjust the design variables of the objective function to obtain the optimal design variables.

[0048] The following combination Figure 1 、 Figure 2 The specific steps of the present invention are further described to illustrate the specific implementation process and beneficial effects of the present invention.

[0049] The specific implementation steps of the large spacecraft structure topology optimization method based on the optimal flexibility method disclosed in the present invention are as follows:

[0050] SS1: Explicit parametric modeling, using the geometric parameters (position, angle, size) of deformable components (such as rectangles and beam elements) as design variables; each component is parameterized as ,in For the central location, is the length, is the tilt angle, such as Figure 2 The set of design variables is:

[0051]

[0052] It is used to explicitly describe the shape and distribution of the structure, and can optimize the spacecraft structure with high flexibility, intuitiveness and manufacturing compatibility. For example, the design variables are defined as:

[0053]

[0054] Represents component parameters (such as the center coordinates of a rectangle ,size , rotation angle etc.; beam element except center coordinates ,size , rotation angle In addition, the cross-sectional area , = (thickness × width)

[0055] Material distribution function:

[0056]

[0057] SS2: Establishing the objective function and performing flexibility calculation ;in is the external force vector, is the displacement vector;

[0058] Construct the flexibility matrix based on the results and calculate the objective function:

[0059] Objective function (minimum flexibility): ;

[0060] Establish constraints (volume constraints, manufacturing constraints, etc.):

[0061] Using volume as constraint: ;

[0062] in, It's softness. is the stiffness matrix, is the displacement field, is the external load, is the material volume, is the maximum volume allowed.

[0063] SS3: Sensitivity Analysis and Gradient Calculation. This technique uses differentials to calculate the sensitivity (i.e., gradient) of the objective function with respect to design variables. This method identifies the impact of these variables on the objective function and guides the optimization process. Throughout the optimization process, sensitivity analysis is key to guiding the iterations of the optimization algorithm. By analyzing the sensitivity of the structure to the design variables, the optimization process can be more efficient and accurate.

[0064] Flexibility sensitivity analysis calculation: .

[0065] SS4: Optimization Algorithm and Parameter Update. Iterative optimization is the core of the entire process. Based on sensitivity information, an optimization algorithm is used to update the design variables. By repeatedly adjusting the design variables, the optimal solution is gradually approached. Constraints are processed during each iteration to ensure that the updated design satisfies all constraints. If the design does not meet the constraints, the step size or direction of the optimization algorithm is adjusted to ensure that the optimization process remains within the feasible region.

[0066] The design variables are updated as follows: ,in and It is an approximate model established.

[0067] The optimization algorithm is:

[0068]

[0069]

[0070] SS5: Convergence Check. If the design meets the convergence criteria, the iterations are terminated; otherwise, a new round of function calculation and optimization iterations is resumed. Once convergence is achieved, the results are updated and the optimal design is output. The optimized results are then post-processed, including structural performance evaluation, visualization, and preparation for fabrication. This phase ensures that the optimization results are not only theoretically valid but also feasible in practical applications.

[0071] Convergence conditions and criteria:

[0072] The update amount of the design variables is small enough;

[0073] , is the design variable for step k.

[0074] The volume constraint deviation is less than the threshold;

[0075]

[0076] If the function calculation does not meet the convergence conditions, it returns to SS4 and recalculates.

[0077] Through the above steps, combined with the optimal flexibility method and the explicit topology optimization method, when optimizing the structure of large spacecraft, an efficient and stable optimization process can be ensured. It can systematically explore all possibilities of spacecraft structural design and find the design with the best performance under given constraints. It has broad application prospects in structural design and can effectively generate innovative structures with high stiffness, lightweight and meeting manufacturing requirements.

[0078] Compared to 3D modeling, parametric modeling uses parameters and constraints to define the model. This offers significant advantages, such as ease of modification, efficient design changes, support for complex constraint relationships, and suitability for parameter optimization and finite element analysis design processes. It is also more suitable for scenarios requiring multiple iterations and precise control, as follows:

[0079] Display parameter modeling has design flexibility and efficient iteration. The model is defined by algebraic parameters (such as dimensions such as length, width, and height, position, angle, and other parameters). Adjusting the parameters can automatically update the associated features without manual reconstruction, facilitating subsequent algorithm iterations.

[0080] The collaboration efficiency has been significantly improved. The parametric model can be directly linked to the simulation tool for simulation calculation and analysis, and can achieve multi-objective optimization of size and shape.

[0081] Parametric models rely on precise mathematical constraints for modeling rather than manual operations, improving design accuracy and controllability.

[0082] Optimal flexibility methods focus on minimizing structural flexibility, often associated with maximizing stiffness. Explicit topology optimization methods achieve optimization goals by explicitly controlling material distribution. The combination of these two approaches offers the following advantages for topology optimization, particularly for large aerospace structures requiring high performance, lightweight construction, and complex constraints:

[0083] The computational efficiency is high, and the gradient of flexibility with respect to design variables can be directly analytically derived using the differential method. Combined with the iterative criteria of explicit topology optimization, this approach can reduce the number of iterations and significantly lower computational costs, especially for large-scale problems such as the optimization of large spacecraft structures.

[0084] The optimization goal is clear. The core of the optimal flexibility method is to minimize structural flexibility (i.e., maximize structural stiffness). Its objective function is highly consistent with the stiffness and stability requirements of large spacecraft structures. By adding the flexibility goal to the update and iteration of design variables through the explicit topology optimization method, more accurate and efficient optimization can be achieved.

[0085] In summary, the combination of the optimal flexibility method and explicit topology optimization, through the goal-driven minimum flexibility combined with the iterative explicit topology optimization algorithm, provides a high-performance, high-efficiency, and high-reliability optimization paradigm for large-scale, multi-constrained and complex optimization problems such as large spacecraft, significantly reducing computational costs and engineering risks compared to traditional methods.

[0086] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0087] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A large spacecraft structure topology optimization method based on the optimal flexibility method, characterized in that: The following steps are involved: Explicit parametric modeling of spacecraft structures using geometric parameters of deformable components as design variables; Establish a finite element analysis model based on the explicit parameter model of the spacecraft structure; An updated objective function of the design variables with respect to flexibility is constructed based on the established finite element analysis model, and the design variables are iteratively updated and optimized based on the updated objective function to obtain optimal design variables. Specifically, the updated objective function of the design variables with respect to flexibility is constructed: in, represents the design variable at k+1 steps after the update, represents the design variables in the updated objective function, represents the flexibility function of the design variables, represents the volume function of the design variables, Represents a constant parameter that balances different objectives in optimization; The flexibility function of the design variable specifically includes the following expressions: Where, The flexibility function value of the design variable, n represents the total number of iterations, represents the flexibility function of the design variables at step k, Represents the geometric parameters in the design variables Softness sensitivity, and are the design variables in the kth iteration The upper and lower limits of Represents the geometric parameters in the design variables The flexibility sensitivity coefficient of The volume function of the design variable specifically includes the following expressions: Where, The volume function value of the design variable, Represents the geometric parameters in the design variables Volume sensitivity, Represents the geometric parameters in the design variables Volume sensitivity coefficient; The updated objective function is iteratively updated. During each iteration, it is determined whether the updated design variables meet the constraint conditions. If not, the step size or direction of the updated objective function is adjusted to ensure that the optimization process is always carried out within the feasible domain. If so, normal iteration is performed until the iterative convergence condition is met.

2. A large spacecraft structure topology optimization method based on the optimal flexibility method according to claim 1, characterized in that: In the step of using geometric parameters of a deformable component as a design variable, the deformable component includes a rectangle and a beam unit, and the geometric parameters include position coordinates, angles and specifications and dimensions.

3. The method for topology optimization of large spacecraft structures based on the optimal flexibility method according to claim 1, characterized in that: The iterative convergence conditions specifically include: The update amount of the design variable is less than the set threshold: in, is the design variable for step k, represents the design variable of the k+1th step; The volume constraint deviation is less than the threshold; in, represents the volume of the design variable at step k, represents the final target volume after optimization.

4. The method for topology optimization of large spacecraft structures based on the optimal flexibility method according to claim 1, characterized in that: In each update iteration, it is determined whether the updated design variables meet the constraints, including the following constraints: Where V(X) is the design variable The volume, is the maximum volume allowed; represents the cell density, , is the unit volume.

5. The method for topology optimization of large spacecraft structures based on the optimal flexibility method according to claim 1, characterized in that: Geometric parameters in design variables The flexibility sensitivity of is calculated by the following expression: in, Indicates softness, represents the i-th component parameter of the design variable, represents the stiffness matrix, Represents a displacement vector.

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