Large spacecraft structure topological optimization method based on optimal flexibility method

Abstract

The invention discloses a large spacecraft structure topological optimization method based on an optimal flexibility method, and relates to the technical field of aerospace, and the method comprises the following steps: taking geometric parameters of a deformable assembly as design variables, and carrying out the explicit parametric modeling of a spacecraft structure; establishing a finite element analysis model according to the explicit parameter model of the spacecraft structure; and according to the established finite element analysis model, constructing an update target function of the design variable about flexibility, and according to the update target function, performing iterative update and optimization on the design variable to obtain an optimal design variable. According to the method, a high-performance, high-efficiency and high-reliability optimization normal form is provided for the optimization problem of large-scale and multi-constraint complex scenes such as large spacecrafts, and the calculation cost and the engineering risk are remarkably reduced compared with a traditional method.

Description

Technical Field

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

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

[0003] With the continuous development of space technology, the comprehensive performance and multi-functional requirements for new-generation spacecraft are increasing continuously. A series of structural optimization design methods represented by the topology optimization method have great development potential and huge application value. With the development of the application level of spacecraft, higher standards are also put forward for the structural performance of spacecraft. Finding a structure that meets the requirements has become the most critical link in the entire design process.

[0004] When conducting topology optimization design for large spacecraft, their structures are usually large in volume and high in complexity, and need to meet requirements such as light weight, high strength, stiffness, and dynamic stability. However, traditional topology optimization methods often may have problems such as high consumption of computing resources, insignificant multi-objective optimization effects, and inability to avoid the application limitations of a single topology optimization method, and often have low efficiency. A series of structural optimization design methods represented by the existing topology optimization method provide certain ideas in the field of large spacecraft manufacturing, but most of them are based on the application of a single topology optimization method, and rarely consider using multiple topology optimization methods combined for the structural optimization design of spacecraft, resulting in the application limitations of the topology optimization method. The topology optimization method for high-performance and light-weight design of spacecraft structures needs to be further studied. When applying the topology optimization method to the research of spacecraft structural design, according to the structural characteristics and mechanical properties of the optimization target, selecting appropriate multiple topology optimization methods combined for optimization can avoid the deficiencies of a single method and obtain better optimization effects. Summary of the Invention

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

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for structural topology optimization of large spacecraft based on the optimal flexibility method, comprising the following steps:

[0008] Using the geometric parameters of deformable components as design variables to perform explicit parametric modeling of the spacecraft structure;

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

[0010] Construct an updated objective function of the design variables with respect to flexibility based on the established finite element analysis model, and iteratively update and optimize the design variables according to the updated objective function to obtain the optimal design variables.

[0011] Further, use the geometric parameters of the deformable components as design variables. In this step, the deformable components include rectangles and beam elements, and the geometric parameters include position coordinates, angles, and specification dimensions.

[0012] Further, construct an updated objective function of the design variables with respect to flexibility based on the established finite element analysis model, and iteratively update and optimize the design variables according to the updated objective function; specifically including:

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

[0014]

[0015] Among them, represents the design variables at the (k + 1)-th step after update, X 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, plays a role in balancing different objectives in the optimization and is a constant parameter.

[0016] Iteratively update the updated objective function. In each iteration process, judge whether the updated design variables meet the constraint conditions; if not, adjust the step size or direction of the updated objective function to ensure that the optimization process is always within the feasible domain; if so, perform normal iteration; until the iteration convergence condition is met.

[0017] Further, in the updated objective function of the design variables with respect to flexibility, the flexibility function of the design variables specifically includes the following expressions:

[0018]

[0019] In the formula, is the value of the flexibility function of the design variables, n represents the total number of iterations, represents the flexibility function of the design variables at the k-th step, represents the geometric parameters in the design variables is the flexibility sensitivity, and respectively represent the upper limit value and the lower limit value of the design variable in the k-th iteration, and are defined by the following formula The value range of , represents the compliance sensitivity coefficient of the geometric parameter in the design variable .

[0020] Furthermore, in the updated objective function of the design variable with respect to compliance, the volume function of the design variable specifically includes the following expressions:

[0021]

[0022] where is the value of the volume function of the design variable, n represents the total number of iterations, represents the volume sensitivity of the geometric parameter in the design variable, and respectively represent the upper limit value and the lower limit value of the design variable in the k-th iteration, and define the value range of , represents the compliance sensitivity coefficient of the geometric parameter in the design variable, represents the volume sensitivity coefficient of the geometric parameter in the design variable.

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

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

[0025] ,

[0026] where is the design variable at the k-th step, and x k+1 represents the design variable at the (k + 1)-th step;

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

[0028]

[0029] where V(x k ) represents the volume of the design variable at the k-th step, and V target represents the optimized final target volume.

[0030] Furthermore, in each update iteration, it is judged whether the updated design variable satisfies the constraint conditions, which specifically includes the following constraint conditions:

[0031]

[0032] where V(X) is the volume of the design variable X, is the maximum allowable volume; represents the element density, , is the element volume.

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

[0034]

[0035] where C represents compliance, represents the i-th component parameter of the design variable, represents the stiffness matrix, represents the displacement vector.

[0036] From the above technical solutions, it can be seen that compared with the prior art, the present invention discloses a large spacecraft structure topology optimization method based on the optimal compliance method, which has the following beneficial effects:

[0037] A large spacecraft structure means a large number of grids, and the computational load of finite element analysis increases sharply. Topology optimization is an iterative process, and a large amount of calculation is required for each step. This places high requirements on memory and calculation time, which may lead to an overly long optimization cycle. The present invention introduces the optimal compliance method into the explicit topology optimization method, uses its relaxation factor to adjust the update step of the solution in each iteration, so as to optimize the convergence speed of the iterative process. In this way, the convergence speed can be significantly accelerated, the number of iterations can be reduced, and the implementation of the optimal compliance method is relatively simple and easy to implement in a computer program; at the same time, the compliance of the structure under the action of the load is minimized, thereby effectively improving the stiffness of the optimized structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0039] Figure 1 is a schematic diagram of the overall process flow of the method provided by the present invention.

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

[0041] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

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

[0043] Use the geometric parameters of deformable components as design variables to perform explicit parametric modeling of the spacecraft structure;

[0044] Construct the objective function and constraint conditions of the design variables;

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

[0046] Construct the iterative equation of the flexibility-design variable optimization algorithm;

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

[0048] Next, in conjunction with Figure 1 、 Figure 2 The specific steps of the present invention will be further described to elaborate 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 by the present invention are as follows:

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

[0053]

[0054] Represents component parameters (such as the center coordinates of a rectangle , dimensions , rotation angle etc.; for beam elements, in addition to the center coordinates , dimensions , rotation angle also includes the cross-sectional area , = (thickness × width))

[0055] Material distribution function:

[0056]

[0057] SS2: Establish the objective function and perform compliance calculation; where is the external force vector, is the displacement vector;

[0058] Construct the compliance matrix according to the results and calculate the objective function:

[0059] Objective function (minimum compliance):

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

[0061] Taking volume as the constraint:

[0062] Where, is the compliance, is the stiffness matrix, is the displacement field, is the external load, is the material volume, is the maximum allowable volume.

[0063] SS3: Sensitivity analysis and gradient calculation, using differentiation to calculate the sensitivity (i.e., gradient) of the objective function with respect to the design variables to identify the influence of the design variables on the objective function and guide the optimization process. During the entire optimization process, sensitivity analysis is the key to guiding the iterative process of the optimization algorithm. By analyzing the sensitivity information of the structure to the design variables, the optimization process can be more effective and accurate.

[0064] Compliance sensitivity analysis calculation:

[0065] SS4: Optimization Algorithm and Parameter Update. The optimization iteration is the core part of the whole process. According to the sensitivity information, an optimization algorithm is adopted to update the design variables. By repeatedly adjusting the design variables, the optimal solution is gradually approximated; in each iteration, constraint handling is carried out to ensure that the updated design meets all the constraint conditions. If the design does not meet the constraints, adjust the step size or direction of the optimization algorithm to ensure that the optimization process is always within the feasible region.

[0066] The design variables are updated to: , where and are the established approximate models.

[0067] The optimization algorithm is:

[0068]

[0069]

[0070] SS5: Convergence Check. If the design meets the convergence criterion, the iteration can be stopped; otherwise, return to perform a new round of function calculation and optimization iteration. After reaching the convergence condition, the results are updated and the optimal design result is output. Post-processing of the optimization results includes evaluating the structural performance, performing visual display, and preparing for manufacturing. This stage 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 at the k-th step.

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

[0075]

[0076] If the function calculation does not meet the convergence condition, return to SS4 for recalculation.

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

[0078] Compared with 3D modeling, display parametric modeling uses parameters and constraints to define the model, which has significant advantages, such as: convenient modification, efficient design change, support for complex constraint relationships, suitable for parametric optimization and finite element analysis design processes, and relatively more suitable for scenarios that require multiple iterations and precise control, as follows:

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

[0080] It significantly improves the collaboration efficiency. The parametric model can be directly associated with simulation tools for simulation calculation and analysis, and multi-objective optimization of dimensions and shapes can be achieved.

[0081] The parametric model relies on precise mathematical constraints for modeling rather than manual operations, improving the design accuracy and controllability.

[0082] The optimal flexibility method mainly focuses on minimizing the structural flexibility, which is usually associated with maximizing the stiffness; the explicit topology optimization method achieves the optimization goal by explicitly controlling the material distribution. After combining the two, especially for the high-performance, lightweight, and complex constraint requirements of large aerospace structures, there are the following advantages in topology optimization:

[0083] High computational efficiency. The gradient of the flexibility with respect to the design variables can be directly analytically derived using the differential method, and then combined with the iteration criterion of explicit topology optimization. Especially for large-scale problems such as the optimization of large spacecraft structures, the combination of the two can reduce the number of iterations and significantly reduce the computational cost.

[0084] Clear optimization goal. The core of the optimal flexibility method is to minimize the structural flexibility (i.e., maximize the structural stiffness), and its objective function highly matches the requirements of large spacecraft structures for stiffness and stability; by adding the flexibility goal to the update iteration of the 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, driven by the goal of minimum flexibility and combined with the iteration of the explicit topology optimization algorithm, provides a high-performance, high-efficiency, and high-reliability optimization paradigm for large-scale, multi-constraint complex scenario optimization problems such as large spacecraft, significantly reducing the computational cost and engineering risk compared with traditional methods.

[0086] In the present specification, the various embodiments are described in a progressive manner. Each embodiment focuses on the differences from other embodiments, and the same or similar parts among the various embodiments can be referred to each other. 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 description of the method part.

[0087] The foregoing description of the disclosed embodiments enables those skilled in the art to practice or use the present invention. Various modifications to these embodiments will be readily apparent to those 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 invention. Thus, the invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A topology optimization method for large spacecraft structures based on the optimal flexibility method, characterized in that It includes the following steps: Using the geometric parameters of the deformable components as design variables, perform explicit parametric modeling of the spacecraft structure; Establish a finite element analysis model based on the explicit parameter model of the spacecraft structure; Construct an updated objective function of the design variables with respect to flexibility according to the established finite element analysis model, and iteratively update and optimize the design variables according to the updated objective function to obtain the optimal design variables.

2. The large spacecraft structure topology optimization method based on the optimal flexibility method according to claim 1, wherein In the step of using the geometric parameters of the deformable components as design variables, the deformable components include rectangles and beam elements, and the geometric parameters include position coordinates, angles, and specification dimensions.

3. A topology optimization method for a large spacecraft structure based on the optimal flexibility method according to claim 1, characterized in that, Construct an updated objective function of the design variables with respect to flexibility according to the established finite element analysis model, and iteratively update and optimize the design variables according to the updated objective function; specifically including: Construct an updated objective function of the design variables with respect to flexibility: ； Among them, represents the design variable at the (k + 1)-th step after update, represents the design variable in the updated objective function, represents the compliance function of the design variable, represents the establishment of the volume function of the design variable, represents the constant parameter that plays a role in balancing different objectives in the optimization, Iteratively update the updated objective function. In each iteration process, judge whether the updated design variables meet the constraint conditions; if not, adjust the step size or direction of the updated objective function to ensure that the optimization process is always carried out within the feasible region; if so, perform normal iteration; until the iteration convergence conditions are met.

4. A topology optimization method for a large spacecraft structure based on the optimal flexibility method according to claim 3, characterized in that, In the updated objective function of the design variables with respect to flexibility, the flexibility function of the design variables specifically includes the following expressions: ； In the formula, The flexibility function value of the design variable, n represents the total number of iterations, Represents the flexibility function of the design variable at the k-th step, Represents the geometric parameter in the design variable The flexibility sensitivity, And Respectively represent the upper limit value and the lower limit value of the design variable In the k-th iteration, Represents the geometric parameter in the design variable The flexibility sensitivity coefficient.

5. A topology optimization method for a large spacecraft structure based on the optimal flexibility method according to claim 3, characterized in that In the updated objective function of the design variables with respect to flexibility, the volume function of the design variables specifically includes the following expressions: ； In the formula, The volume function value of the design variable, n represents the total number of iterations, Represents the geometric parameter in the design variable The volume sensitivity of And Respectively represent the upper limit value and the lower limit value of the design variable In the k-th iteration, Represents the geometric parameter in the design variable The volume sensitivity coefficient of 6. A topology optimization method for large spacecraft structures based on the optimal flexibility method according to claim 3, characterized in that, The iteration convergence conditions specifically include: The update amount of the design variables is less than the set threshold: , Among them, is the design variable at the k-th step, represents the design variable at the (k + 1)-th step; The deviation of the volume constraint is less than the threshold; ； Among them, represents the volume of the design variable at the k-th step, represents the final target volume after optimization.

7. A topology optimization method for large spacecraft structures based on the optimal flexibility method according to claim 3, characterized in that, In each update iteration, judge whether the updated design variables meet the constraint conditions, specifically including the following constraint conditions: ； Among them, V(X) is the design variable volume, is the maximum allowable volume; represents the element density, , is the element volume.

8. A topology optimization method for large spacecraft structures based on the optimal flexibility method according to claim 4, characterized in that, Geometric parameters among the design variables The compliance sensitivity is calculated by the following expression: ； Among them, denotes flexibility, denotes the i-th component parameter of the design variable, denotes the stiffness matrix, denotes the displacement vector.

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