Optimization algorithm of wing tensegrity frame structure based on genetic algorithm

Abstract

The invention discloses an optimization algorithm of a wing tensegrity frame structure based on a genetic algorithm, and relates to the technical field of aircraft wing structure design. A frame structure serves as a unit, connection between the frame structure and a skin is considered, the positions of connecting nodes are defined, every two connecting nodes are connected to serve as an initial base structure, components are all defined as pressing rods, the components are classified into a fixed component set and an optimized component set, and the whole frame structure is tensioned. The method comprises the following steps: performing component deletion and type change according to a stress condition, keeping as a pressing rod, changing as a stay cable or deleting, giving an optimization column formula by taking minimization of structural mass as an optimization target, calculating the optimization column formula based on a genetic algorithm, and performing iterative search to obtain a final base structure as an optimization configuration. The components of the tensegrity frame base structure are deleted based on the genetic algorithm, a more remarkable weight reduction effect is achieved on the premise of meeting the structural requirements, and the result is more accurate and reasonable.

Description

Technical Field

[0001] The invention relates to the technical field of aircraft wing structure design, in particular to an optimization algorithm for a wing tensegrity frame structure based on a genetic algorithm. Background Art

[0002] During the flight of an aircraft, the wing structure is the main structure responsible for providing lift and bearing gravity and inertial loads. As the speed of the aircraft increases and the flight time increases, higher requirements are placed on the lightweight of the wing structure. In order to achieve ultra-lightweight, the wing structure needs to use high-strength, low-density materials such as composite materials and titanium alloys. The traditional wing structure consists of a wing spar extending along the span direction and a wing rib extending along the chord direction, which cannot meet the requirements of controlling the autonomous deformation of the wing. By topologically optimizing the wing spars and wing ribs, a thin-walled plate with complex holes is finally formed, which places extremely high requirements on the manufacturing process of the composite material and requires a high manufacturing cost.

[0003] Therefore, using a tensegrity frame structure to replace traditional wing beams and ribs as the support structure of the wing skin is an effective means to solve the above problems. The tensegrity frame structure is a self-balancing spatial structural system composed of discrete struts and continuous cables. The reasonable distribution of prestress between components provides the initial structural stiffness and ensures the stability of the system. It is widely used in the fields of architecture, soft robotics, aerospace engineering, and metamaterials. As a typical structure with clear force and tension and compression separation, the tensegrity frame structure has a higher strength-to-weight ratio than the traditional structural system. It can meet the strength requirements with less material and achieve lightweight structure. In addition, the manufacture of struts and cables is simple, and there are a variety of standard parts to choose from, without the need for complex processes. At the same time, the struts and cables can adjust the length of the components through the linkage actuator, change the distribution of prestress, and realize intelligent control of structural deformation. However, the layout design of the tensegrity frame structure currently relies too much on the engineering experience of the designers. It is difficult to design a structural layout that meets the requirements for complex working conditions based on experience alone. Summary of the invention

[0004] In order to solve the shortcomings of the background technology, the present invention provides an optimization algorithm for the wing tensegrity frame structure based on a genetic algorithm, which deletes the components of the tensegrity frame base structure based on the genetic algorithm, and achieves a more significant weight reduction effect while meeting the structural requirements, and the result is more accurate and reasonable.

[0005] To achieve the above object, the present invention adopts the following technical solution: an optimization algorithm for a wing tensegrity frame structure based on a genetic algorithm, comprising the following steps:

[0006] S1. For the overall frame of the wing, a frame structure is used as a unit, the connection between the frame structure and the skin is considered, the position of the connection node is predefined, and all the connection nodes are connected in pairs as the initial base structure. In the initial base structure, all components are defined as compression bars. Then, the components of the initial base structure are classified into a fixed component group and an optimized component group, wherein the fixed component group is composed of components connected to the skin, and the optimized component group is composed of the remaining components;

[0007] S2. Use a tensegrity frame structure, and delete and change the components of the initial base structure according to the stress conditions:

[0008] When the member is compressed, it remains a compression rod;

[0009] When the member is under tension, it is changed to a cable;

[0010] If the component is not subjected to force, delete the component;

[0011] Taking minimizing the structural mass as the optimization goal, the optimization formula is as follows:

[0012] min(a s ρ s ) T s+(a c ρ c ) T c

[0013] stAt=f

[0014]

[0015]

[0016]

[0017] In the formula, the first line is the objective function, and the second to fifth lines are constraints, where: represents the equilibrium matrix composed of the direction cosines of all components, t represents the actual axial force of the component, f represents the applied external load, u represents the node displacement, represents the axial stiffness matrix of the structure, K g represents the geometric stiffness matrix related to the prestress, a s and a c denote the cross-sectional areas of the compression rod and the cable, respectively, and ρ s and ρ c denote the density of the compression rod and the cable respectively, l denotes the length vector of the component, and They represent the ultimate strength of the compression rod and the cable respectively, t represents the axial force of any component, s and c represent binary variables, and their meanings are as follows:

[0018]

[0019] The optimization formula is calculated based on the genetic algorithm, and the final base structure is obtained through iterative search as the optimized configuration of the tensegrity frame structure.

[0020] Furthermore, the genetic algorithm includes the following:

[0021] (1) Encoding: Binary encoding is performed on the binary variables s and c in the optimization column. The initial base structure has m components, called genes. Each component is represented by two binary numbers, forming the genotype g of the individual.

[0022] (2) Population: All components of the initial base structure are compression rods. The gene fragment of genotype g is represented by gi = (1,0) i = 1,2…m. The initial base structure is subjected to stress analysis. i From (1,0) to (0,1) or (0,0), a number of individuals form a population;

[0023] (3) Selection: Define the inverse of the objective function as the fitness, use the tournament algorithm for selection, randomly select two individuals to compare their fitness, and take the smaller one as the excellent individual. Repeat the selection process to obtain several excellent individuals.

[0024] (4) Crossover: Cross the gene fragments of every two excellent individuals to produce new individuals;

[0025] (5) Mutation: Randomly change the gene fragments of some individuals i From (1,0) to (0,1) or (0,0);

[0026] (6) New population: Sort the new and old individuals in the population according to their fitness from large to small, and eliminate individuals from the back to the front until the number of individuals is the same as the initial population, forming a new population;

[0027] Repeat steps (3) to (6). When the fitness of the excellent individuals in the population no longer changes or reaches the maximum number of iterations, the calculation is terminated to obtain the final base structure as the optimized configuration of the tensegrity frame structure.

[0028] Compared with the prior art, the beneficial effects of the present invention are: the present invention optimizes the layout and lightweight designs the wing support frame of the tensegrity frame structure, and deletes the components of the tensegrity frame base structure based on the genetic algorithm to obtain a spatial layout that meets the stiffness, strength and weight reduction requirements. Compared with the traditional wing spar and rib frame structure, the weight reduction effect is more significant, avoiding over-reliance on the engineering experience of designers, and the optimization result is more accurate and reasonable. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a flow chart of the optimization algorithm of the present invention;

[0030] Figure 2 is a schematic diagram of a frame structure selected for a conventional wing in the embodiment;

[0031] Figure 3 is a schematic diagram of classifying components of an initial base structure in an embodiment;

[0032] Figure 4 It is a schematic diagram of an optimized configuration obtained by changing components of the base structure in the embodiment. DETAILED DESCRIPTION

[0033] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than 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 work are within the scope of protection of the present invention.

[0034] like Figure 1 As shown, an optimization algorithm for a wing tensegrity frame structure based on a genetic algorithm comprises the following steps:

[0035] Step 1: Pre-treatment process

[0036] The overall frame of the wing is taken as a unit with a frame structure. First, the connection between the frame structure and the skin is considered, and the position of the connection node is predefined by the designer. Then, all the connection nodes are connected in pairs as the initial base structure. In the initial base structure, all components are defined as compression rods. In the subsequent optimization process, the components are deleted and the types are changed according to the stress conditions to update the base structure. When the component is compressed, it remains as a compression rod; when the component is tensile, it is changed to a cable; if the component is not under stress, the component is deleted. Then, the components of the initial base structure are classified into a fixed component group and an optimized component group. The fixed component group is composed of components connected to the skin, which are not optimized during the optimization process; the optimized component group is composed of the remaining components, which can be deleted and changed during the optimization process.

[0037] Step 2: Optimization process

[0038] After the pre-processing is completed, the optimized component group of the initial base structure is deleted based on the genetic algorithm to achieve lightweight design optimization. The tensegrity frame structure is adopted. The tensegrity frame structure must be in a self-balanced state, that is, when no external load is applied, the structure as a whole maintains static balance under the action of prestress. For a tensegrity frame structure with m components and n connection nodes, its equilibrium state can be expressed as follows:

[0039] At 0 =0

[0040] In the formula, represents the equilibrium matrix composed of the direction cosines of all components, t 0 Indicates the axial preload generated by prestressing.

[0041] For a self-balanced tensegrity frame structure with redundant components (hyperstatic), there are usually multiple feasible sets of axial preloads. The formula for determining the axial preload is as follows:

[0042] t 0 =Rα

[0043] Where R = null(A) represents the null space matrix of A, with dimensions m rows and n s Column, indicating that the structure has n s An axial preload mode, α represents the coefficient vector, and the value of the axial preload is determined by α.

[0044] After applying the external load f, the equilibrium equation of the tensegrity frame structure is expressed as follows:

[0045] At=f

[0046] Where t represents the actual axial force of the component.

[0047] The presence of external loads generates nodal displacements u, and the constitutive relation of the structure is:

[0048]

[0049] In the formula, represents the axial stiffness matrix of the structure, K g Represents the geometric stiffness matrix associated with the prestress.

[0050] In addition to the self-balancing condition, tensegrity frames must also satisfy stability conditions. Structural balance does not guarantee stability. If the potential energy of a tensegrity frame is in a strict local minimum, the structure is stable and will return to its equilibrium position after a small disturbance. The stability of a tensegrity frame is determined by the following conditions:

[0051]

[0052] Based on the above theory, all components in the initial base structure are regarded as a set M, and these components are divided into three subsets according to the stress conditions of the components: S represents compression rods, C represents cables, and E represents deleted components, M=S∪C∪E.

[0053] Taking minimizing the structural mass as the optimization goal, the optimization formula is as follows:

[0054] min(a s ρ s ) T s+(a c ρ c ) T c

[0055] stAt=f

[0056]

[0057]

[0058]

[0059] In the formula, the first line is the objective function, and the second to fifth lines are constraint conditions, which are the self-balance condition, stability condition, and the maximum stress constraint of the compression rod and the cable. s and a c denote the cross-sectional areas of the compression rod and the cable, respectively, and ρ s and ρ c denote the density of the compression rod and the cable respectively, l denotes the length vector of the component, and They represent the ultimate strength of the compression rod and the cable respectively, t represents the axial force of any component, s and c represent binary variables, and their meanings are as follows:

[0060]

[0061] The optimization problem is a nonlinear mixed integer optimization problem, and the gradient of the objective function cannot be obtained explicitly. Therefore, a genetic algorithm in the heuristic algorithm is used to calculate it.

[0062] Genetic algorithm is a mathematical calculation method that imitates the biological evolution process by simulating the natural selection and genetic mechanism in Darwin's theory of biological evolution. It is an intelligent algorithm that searches for the optimal solution by simulating the natural evolution process. According to the optimization formula, the initial base structure is subjected to stress analysis, the tension components are changed into cables, and the unstressed components are randomly deleted to generate several feasible configurations as the initial population. Then, the selection, crossover and mutation operations of the genetic algorithm are used to perform iterative search, and finally the optimized configuration is obtained. The specific steps are as follows:

[0063] (1) Coding: Binary variables s and c in the optimization column are encoded directly using binary coding without the need for data conversion. For the m components, called genes, each component is represented by two binary numbers, totaling 2m binary numbers, which constitute the individual's genotype g;

[0064] (2) Population: The components of the initial base structure are all struts, and the gene fragment of genotype g is represented by g i =(1,0)i=1,2…m, perform stress analysis on the initial base structure, change the tension components into cables, and randomly delete the unstressed components. The operation method in the individual is to replace the gene fragment g i From (1,0) to (0,1) or (0,0), the individuals formed constitute a population;

[0065] (3) Selection: The individuals in the population are screened by simulating the law of survival of the fittest in nature. The inverse of the objective function is defined as the fitness to simulate the degree of adaptation of the individual to the environment. The greater the fitness, the smaller the mass of the tensegrity frame structure, and the more it meets the lightweight requirements. The tournament algorithm is used for selection. Two individuals are randomly selected to compare their fitness. The one with the smaller fitness is selected as the excellent individual. The selection process is repeated to obtain several excellent individuals.

[0066] (4) Crossover: Simulating the reproduction process of individuals in nature, cross the gene fragments of every two excellent individuals to produce new individuals;

[0067] (5) Mutation: In nature, the genes of organisms may mutate with a small probability. In this genetic algorithm, the gene fragments g of some individuals are randomly replaced. i From (1,0) to (0,1) or (0,0);

[0068] (6) New population: Sort the new and old individuals in the population according to their fitness from large to small, and eliminate individuals from the back to the front until the number of individuals is the same as the initial population, forming a new population.

[0069] Repeat steps (3) to (6). When the fitness of the excellent individuals in the population no longer changes or reaches the maximum number of iterations, the calculation is terminated to obtain the final base structure as the optimized configuration of the tensegrity frame structure.

[0070] Step 3: Post-processing

[0071] For the optimized configuration of the tensegrity frame structure, the initial prestress is calculated. Under the condition of applying the initial prestress, the bearing performance of the structure is analyzed to verify whether the optimized configuration meets the stiffness, strength and weight reduction requirements.

[0072] Example

[0073] Taking the optimization of a frame structure as an example, combined with Figure 2 The figure shows the overall shape and size information of a one-fifth frame structure (called a frame) of a conventional wing after holes are dug for the wing spars and rib webs. In the figure, part (a) is an axonometric structure diagram, part (b) is a main view structure diagram, and part (c) is a top view structure diagram. The frame structure is 1.2m wide, 0.6m long, and 0.3-0.5m high. It is divided into 4×2 grids, and each grid measures 0.3m×0.3m. All wing spars and ribs are made of 2024-T4 aluminum alloy with a density of 2700kg / m 3 , the elastic modulus is 72 GPa, the Poisson's ratio is 0.3, all webs are modeled as flat plate structures with a thickness of 1 mm. The total mass of the frame structure is 1.73 kg.

[0074] The nodes are connected in pairs to obtain the initial base structure, and its components are classified into fixed component group and optimized component group. Figure 3 As shown in the figure, part (a) is a schematic diagram of the initial base structure as a whole, and part (b) is a schematic diagram of the fixed component group therein.

[0075] Based on the genetic algorithm, the initial base structure changes the component type according to the stress conditions of the components. According to the stress conditions of the components, the components are changed to compression rods, cables or deleted. The compression rods are made of the same material as the ribs with a radius of 11.8mm. The cables are made of braided steel cables with a radius of 1mm and a density of 6450kg / m 3 , the elastic modulus is 137GPa. A uniform pressure of 2kPa is applied to the top of the structure and the pressure is converted to the frame nodes. The initial population contains 100 individuals, the maximum number of iterations is 100, and the optimized configuration is obtained after 55 generations of calculation. The initial structure has 135 components, while the optimized configuration obtained by this method has 73 components. Figure 4 As shown, the optimized configuration after the components of the base structure are changed is shown. In the figure, part (a) is the overall schematic diagram of the optimized configuration, part (b) is the main view of the optimized configuration, and part (c) is the top view of the optimized configuration. The red line segment represents the compression rod, and the blue line segment represents the cable.

[0076] The results of the maximum displacement, mass and weight reduction effect are compared for the conventional wing spar rib frame structure and the tensegrity frame structure optimized by the present invention, as shown in Table 1:

[0077] Table 1 Comparison of traditional wing section structure and optimized wing section results

[0078]

[0079] It can be seen that the optimized tensegrity frame structure of the present invention reduces weight by 48% under the condition that the maximum displacement increases by 2.7%.

[0080] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms of assembly without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0081] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. An optimization algorithm for a wing tensegrity frame structure based on a genetic algorithm, characterized in that: The following steps are involved: S1. For the overall frame of the wing, a frame structure is used as a unit, the connection between the frame structure and the skin is considered, the position of the connection node is predefined, and all the connection nodes are connected in pairs as the initial base structure. In the initial base structure, all components are defined as compression bars. Then, the components of the initial base structure are classified into a fixed component group and an optimized component group, wherein the fixed component group is composed of components connected to the skin, and the optimized component group is composed of the remaining components; S2. Use a tensegrity frame structure, and delete and change the components of the initial base structure according to the stress conditions: When the member is compressed, it remains a compression rod; When the member is under tension, it is changed to a cable; If the component is not subjected to force, delete the component; Taking minimizing the structural mass as the optimization goal, the optimization formula is as follows: min(a s r s )l T s+(a c r c )l T c stAt=f In the formula, the first line is the objective function, and the second to fifth lines are constraints, where: represents the equilibrium matrix composed of the direction cosines of all components, t represents the actual axial force of the component, f represents the applied external load, u represents the node displacement, represents the axial stiffness matrix of the structure, K g represents the geometric stiffness matrix related to the prestress, a s and a c denote the cross-sectional areas of the compression rod and the cable, ρ s and ρ c denote the density of the compression rod and the cable respectively, l denotes the length vector of the component, and They represent the ultimate strength of the compression rod and the cable respectively, t represents the axial force of any component, s and c represent binary variables, and their meanings are as follows: The optimization formula is calculated based on the genetic algorithm, and the final base structure is obtained through iterative search as the optimized configuration of the tensegrity frame structure.

2. The optimization algorithm of a wing tensegrity frame structure based on a genetic algorithm according to claim 1, characterized in that: The genetic algorithm includes the following: (1) Encoding: Binary encoding is performed on the binary variables s and c in the optimization column. The initial base structure has m components, called genes. Each component is represented by two binary numbers, forming the genotype g of the individual. (2) Population: All components of the initial base structure are compression rods. The gene fragment of genotype g is represented by gi = (1,0) i = 1,2…m. The initial base structure is subjected to stress analysis. i From (1,0) to (0,1) or (0,0), a number of individuals form a population; (3) Selection: Define the inverse of the objective function as the fitness, use the tournament algorithm for selection, randomly select two individuals to compare their fitness, and take the smaller one as the excellent individual. Repeat the selection process to obtain several excellent individuals. (4) Crossover: Cross the gene fragments of every two excellent individuals to produce new individuals; (5) Mutation: Randomly change the gene fragments of some individuals i From (1,0) to (0,1) or (0,0); (6) New population: Sort the new and old individuals in the population according to their fitness from large to small, and eliminate individuals from the back to the front until the number of individuals is the same as the initial population, forming a new population; Repeat steps (3) to (6). When the fitness of the excellent individuals in the population no longer changes or reaches the maximum number of iterations, the calculation is terminated to obtain the final base structure as the optimized configuration of the tensegrity frame structure.

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