Layering-reinforcement collaborative optimization method for composite material wallboard structure

Abstract

The invention belongs to the technical field of aerospace and topological optimization, and particularly relates to a layering-reinforcement collaborative optimization method for a composite material wallboard structure. Comprising a rib layout description method, a laminated plate laying angle description method, composite material wall plate structure laying-reinforcement collaborative optimization, and flexibility minimization design and fundamental frequency maximization design of the composite material wall plate structure laying-reinforcement collaborative optimization. According to the rib layout description method, a reinforcement optimization design method based on an MMC method is adopted to explicitly describe rib information, the rib information serves as a design variable, and a rib path is obtained. According to the method, the influence of the laminated plate design variable and the rib design variable is considered at the same time, the global optimization configuration can be obtained, the effects of the laminated plate and the rib can be fully played, the problem of flexibility minimization of the laminated plate reinforced structure is solved, the strength and rigidity of the structure can be improved from the side face, and the reliability of the structure is improved. The problem of fundamental frequency maximization of a laminated plate reinforced structure is solved, and unfavorable conditions such as resonance are prevented.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace and topology optimization technology, and specifically relates to a composite material wall panel structure ply-reinforcement collaborative optimization method. Background Art

[0002] In the past few decades, the application of fiber-reinforced composite parts in various industries has increased significantly due to the characteristics of composite materials such as light weight, high strength and corrosion resistance. This composite material has made progress in some fields where metals once dominated. For example, in the aerospace field, fiber-reinforced plastics (FRP) are used in the manufacture of aircraft fuselages and wings to reduce their weight. Composite laminates also provide superior design flexibility. By selecting single-layer plates of different materials, performing different stacking sequences and orientation angles, the laminates can exhibit different mechanical properties. In addition, in the field of thin-walled structure reinforcement, the application of stiffeners is favored because of its simplicity and ease. For thin-walled structures, in order to meet the stiffness and vibration (fundamental frequency) requirements required in various working environments, reinforcing thin-walled structures is a commonly used method. The shape and layout of these stiffeners are usually the key to increasing strength and reducing resonance.

[0003] For the current thin-walled structure, composite laminates can be used as thin-walled substrates, and ribs can be laid to supplement the strength. By optimizing the ply angles and rib layout of the laminates, the material properties can be more fully utilized, so that the structure can achieve the strength and vibration indicators that meet the working requirements with less material usage.

[0004] Although there have been many studies on the optimization design of reinforcement and laminate, and remarkable results have been achieved, there are still some challenging problems that need to be further solved. First, the existing research work basically focuses on the optimization research of laminates alone or the optimization research of ribs alone. The two optimization methods of laminate reinforced structures are carried out separately. The structure is optimized without comprehensive consideration, which often leads to the miss of some mutually coupled and global optimal structures. Secondly, the commonly used implicit optimization methods often have many design variables, difficult to control explicit dimensions, and complicated post-processing. In the optimization of laminates, the analysis and calculation are often based on solid units, which takes a long time and requires a lot of calculation. In addition, for the laminated plate structures commonly used in actual engineering, each single layer usually selects one of the angles from -45°, 0°, 45°, and 90°, so the design variables of the laminated plate structure are discrete, while the design variables of the ribs, such as the coordinates of the nodes at both ends of the ribs, the thickness of the ribs, and other design variables are within a specific range of values. The design variables are continuous design variables. Achieving coordinated optimization of these two different types of design variables is also a difficulty in this work. Summary of the invention

[0005] The purpose of the present invention is to provide a collaborative optimization method for ply-reinforcement of a composite material wall panel structure, which simultaneously considers the influence of the laminate design variables and the rib design variables, and can obtain a global optimized configuration, which can give full play to the role of the laminate and the ribs, solve the problem of minimizing the flexibility of the laminate reinforced structure, and can improve the strength and stiffness of the structure from the side, solve the problem of maximizing the fundamental frequency of the laminate reinforced structure, and prevent the occurrence of adverse conditions such as resonance.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A composite wall panel structure ply-reinforcement collaborative optimization method, including a description method of rib layout, a description method of laminate ply angle, composite wall panel structure ply-reinforcement collaborative optimization, and a flexibility minimization design and a fundamental frequency maximization design of the composite wall panel structure ply-reinforcement collaborative optimization;

[0008] The description method of the rib layout adopts a reinforcement optimization design method based on the MMC method to explicitly describe the rib information and use it as a design variable to obtain the rib path;

[0009] The method for describing the angle of the ply of the laminate adopts a parameterization method using a shape function with penalty to determine the orientation angle of the laminate;

[0010] The ply-reinforcement collaborative optimization of composite wall structure requires the given thickness and quantity information of the laminate, and the ply angle of each layer is determined through optimization to obtain the most suitable orientation angle of each layer of the laminate. For the ribs, the upper limit of the mass constraint needs to be given, and the coordinates of the end points of each rib and the thickness of the rib are obtained through optimization.

[0011] The flexibility minimization design of the composite panel structure ply-reinforcement collaborative optimization is to minimize the total strain energy of the reinforced panel structure;

[0012] The fundamental frequency maximization design of collaborative optimization is to minimize the inverse of the first-order eigenvalue of the stiffened panel structure, which is equivalent to maximizing the first-order frequency of the structure.

[0013] Furthermore, the reinforcement optimization design method based on the MMC method includes the following steps:

[0014] Use components to describe each rib in the design domain. Each rib is connected through a spatial node in the design domain, so that the position of the rib changes with the movement of the node, thereby changing the layout of the rib. The position of different spatial nodes determines the change of the rib shape.

[0015] During the optimization process, the node-driven adaptive base structure method is used to establish the reinforcement model. The design variables are the node coordinates and the reinforcement thickness. An efficient shape sensitivity analysis method is used to iteratively update the entire structure by moving a series of driving nodes and changing some dimensional parameters of the components until convergence to obtain the optimal reinforcement layout.

[0016] Furthermore, during the optimization process, the lower limit of the rib thickness range is t ε (t ε < t ), the Heaviside function (1) is used to penalize it, and the thickness penalty form of formula (2) is used to penalize the thickness of the i-th rib t i Multiply by the Heaviside function to get the thickness after penalty Take t ε =α=0.001,ε=0.1;

[0017]

[0018]

[0019] Furthermore, the parameterization method using the penalized shape function writes the stiffness matrix of the k-th layer of the laminate as a weighted sum of the stiffness matrices of the candidate materials:

[0020]

[0021] Among them, C (k) represents the elastic matrix of the k-th layer of the laminate, C 1 , C 2 , C 3 , C 4 They represent the stiffness matrix corresponding to the fiber orientation of -45°, 0°, 45°, and 90°, respectively, and their weight factors are represents the weight of the i-th orientation angle in the k-th layer of the laminate. The weight factor of the k-th layer of the laminate is obtained by the design variable R (k) , S (k) Indicates that R (k) and S (k) The value of varies between -1 and 1:

[0022]

[0023] satisfy

[0024]

[0025] The weight factors need to satisfy equations (5) and (6) to obtain physically meaningful results; in the best case, the kth layer should consist of one candidate layer with material properties C 1, C 2 , C 3 or C 4 Therefore, one of the solutions needs to be is equal to 1 and the others =0; In order to obtain this result, it is necessary to penalize the intermediate values ​​of the design variables, and impose an exponent p on the shape function (SF), i.e., equation (4), to obtain the penalized shape function parameterized expression as shown in equation (7). This expression still satisfies equation (6), but for the design variable R (k) and S (k) The intermediate value of does not satisfy equation (5), but it does at the solution;

[0026]

[0027] In SFP parameterization, when the parameter R corresponding to the kth layer (k) and S (k) When both are 1 or -1, the orientation angle of the laminate of that layer can be determined.

[0028] Furthermore, the ply angle of each layer is determined by optimization, and the most suitable orientation angle of each layer of the laminate is obtained, and the orientation angle is one of -45°, 0°, 45°, and 90°.

[0029] Furthermore, the optimization formula corresponding to the flexibility minimization design of the composite panel structure layup-reinforcement collaborative optimization is formula (8);

[0030]

[0031] Among them, P i is the coordinate of the i-th moving node describing the position of the rib, t i is the thickness of the i-th rib, R i ,S i is the parameter describing the ply angle of the i-th layer of the laminate, np is the total number of nodes controlling the position of the ribs, ns is the total number of ribs, and nl is the total number of layers of the laminate.

[0032] Furthermore, the optimization formula corresponding to the collaboratively optimized fundamental frequency maximization design is formula (9);

[0033]

[0034] Among them, P i is the coordinate of the i-th moving node describing the position of the rib, t i is the thickness of the i-th rib, R i ,S i is the parameter describing the ply angle of the i-th layer of the laminate, np is the total number of nodes controlling the position of the ribs, ns is the total number of ribs, and nl is the total number of layers of the laminate.

[0035] Furthermore, the rib mass constraint includes a maximum thickness constraint, a minimum thickness constraint, a rib layout and thickness being symmetrical in a certain rectangular coordinate system, or being symmetrical in a certain rectangular coordinate system.

[0036] The technical effects achieved by the present invention are:

[0037] (1) The composite material wall panel structure ply-reinforcement collaborative optimization method of the present invention can solve the problem of minimizing the flexibility of the laminated reinforced structure and can improve the strength and stiffness of the structure from the side.

[0038] (2) The composite wall panel structure ply-reinforcement collaborative optimization method of the present invention can solve the fundamental frequency maximization problem of the laminated reinforced structure and prevent the occurrence of adverse conditions such as resonance.

[0039] (3) The composite wall panel structure ply-reinforcement collaborative optimization method of the present invention simultaneously considers the influence of the laminate design variables and the rib design variables, and can obtain a global optimized configuration, which can give full play to the role of the laminate and the rib.

[0040] (4) The composite wall panel structure ply-reinforcement collaborative optimization method of the present invention adopts an efficient analytical sensitivity method for optimization and performs analysis based on shell elements. Compared with the optimization analysis method of solid elements, it greatly reduces the number of finite elements and shortens the analysis time of finite elements, thereby improving the optimization efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a schematic diagram of the node-driven adaptive base structure method of the present invention;

[0042] Figure 2 It is the principle of SFP parameterization of the present invention;

[0043] Figure 3 It is the collaborative optimization design content of the present invention;

[0044] Figure 4 It is the optimization flow chart of the present invention;

[0045] Figure 5 is a schematic diagram of a square plate flexibility optimization calculation example of the present invention;

[0046] Figure 6 It is the flexibility optimization rib layout of the square simply supported plate of the present invention;

[0047] Figure 7 is an optimization iteration curve of the objective function, the rib volume and the penalized rib volume in the square plate flexibility optimization of the present invention;

[0048] Figure 8 The stress cloud diagram and displacement cloud diagram of the comparative layout and the optimized layout of the present invention;

[0049] Fig. 9 This is a schematic diagram of a square plate fundamental frequency optimization calculation example of the present invention;

[0050] Fig.10 It is the fundamental frequency optimized rib layout of the square simply supported plate of the present invention;

[0051] Fig.11 It is an optimization iteration curve of the objective function, the rib volume and the penalized rib volume in the fundamental frequency optimization of the square plate of the present invention;

[0052] Fig.12 It is a vibration mode cloud diagram of the comparative layout and the optimized layout of the present invention. DETAILED DESCRIPTION

[0053] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

[0054] This technical solution proposes a collaborative optimization method for the ply-reinforcement of composite wall panel structures. By collaboratively optimizing the ply angle of the laminate and the reinforcement layout, the flexibility minimization design and fundamental frequency maximization design of the composite laminate reinforced structure are achieved; the optimization contents include the ply angle of the laminate, the reinforcement path of the rectangular stiffener and the thickness of the ribs.

[0055] In addition, through constraint setting, the optimization results can meet the manufacturing constraints in the project, including the maximum and minimum thickness constraints of the ribs and the symmetrical distribution constraints of the ribs that need to be met in engineering manufacturing, as well as the balanced ply constraints in the laminate ply settings (the same number of plies at ±45°), symmetrical ply constraints, the maximum number of adjacent repeated plies at the same angle, and the constraint that adjacent plies do not exceed 45°, so that the optimized structure can be directly applied to actual production and manufacturing.

[0056] Different from the prior art, this technical solution realizes the sensitivity analysis of the collaborative optimization of ply reinforcement for the first time. It has a strict sensitivity derivation and can optimize the ply reinforcement of thin-walled structures of any shape. The accuracy of the analytical sensitivity is verified by differential sensitivity, ensuring fast and accurate sensitivity analysis. Gradient optimization algorithms such as the moving asymptote method (MMA) can be used directly for optimization, and the optimization speed is fast. In addition, the sensitivity analysis can be analyzed using shell elements, which greatly reduces the calculation time of finite elements and improves the calculation efficiency compared to the solid element topology optimization method. The optimization uses the moving deformable component (MMC) method with explicit description features to describe the rib information, so that the optimization results are composed of a set of components with clear geometric parameters, which greatly simplifies post-processing and improves the accuracy of the analysis.

[0057] Embodiment 1:

[0058] like Figure 1-12 As shown, a composite material wall panel structure ply-reinforcement collaborative optimization method includes a description method of rib layout, a description method of laminate ply angle, composite material wall panel structure ply-reinforcement collaborative optimization, flexibility minimization design and fundamental frequency maximization design of composite material wall panel structure ply-reinforcement collaborative optimization;

[0059] Among them, see Figure 1 As shown in the figure, the description method of the reinforcement layout adopts the reinforcement optimization design method based on the MMC method. The reinforcement optimization design method based on the MMC method can explicitly describe the reinforcement information and use it as a design variable. This method can obtain a clear and accurate reinforcement path without any post-processing.

[0060] The reinforcement optimization design method based on the MMC method comprises the following steps:

[0061] Components are used to describe each rib in the design domain. Each rib is connected through a spatial node in the design domain, so that the position of the rib changes with the movement of the node, thereby changing the layout of the rib. The position of different spatial nodes determines the change in the shape of the rib.

[0062] During the optimization process, the node-driven adaptive base structure method is used to establish the reinforcement model. The design variables are the node coordinates and the reinforcement thickness. An efficient shape sensitivity analysis method is used to iteratively update the entire structure by moving a series of driving nodes and changing some dimensional parameters of the components until convergence to obtain the optimal reinforcement layout.

[0063] Specifically, during the optimization process, due to the existence of volume constraints, some thicknesses less than the lower limit of the manufacturable thickness (denoted as t) may contribute less to the stiffness in their current position, so their thickness is small, but they cannot be deleted directly because as the layout changes during optimization, their contribution to the stiffness may increase, and their thickness will increase.

[0064] To ensure that the thickness is less than the lower limit t The ribs can be deleted in the final structure. In this technical solution, the lower limit of the thickness range of the ribs in the optimization process is set to t ε (t ε < t ), the Heaviside function (1) is used to penalize it, and the thickness penalty form of formula (2) is used to penalize the thickness of the i-th rib t i Multiply by the Heaviside function to get the thickness after penalty In this work, t ε =α=0.001, ε=0.1, this penalty method can effectively reduce the thickness The number of ribs and the thickness is taken to the lower limit t ε When , due to its extremely small thickness, it has almost no contribution to the stiffness of the structure and can be eliminated in the result to obtain a simple reinforcement layout.

[0065]

[0066] See also Figure 2 As shown in the figure, for the description method of the ply angle of the constant stiffness laminate, the parameterization method using the shape function with penalty (SFP) proposed by M. Bruyneel et al. is adopted. This method writes the stiffness matrix of the k-th layer of the laminate as the weighted sum of the stiffness matrices of the candidate materials:

[0067]

[0068] Among them, c (k) represents the elastic matrix of the k-th layer of the laminate, c 1 、c 2 、c 3 、c 4 They represent the stiffness matrix corresponding to the fiber orientation of -45°, 0°, 45°, and 90°, respectively, and their weight factors are represents the weight of the i-th orientation angle in the k-th layer of the laminate. The weight factor of the k-th layer of the laminate is obtained by the design variable R (k) , S (k) Indicates that R (k) and S (k) The value of varies between -1 and 1:

[0069]

[0070] satisfy

[0071]

[0072] The weight factors need to satisfy equations (5) and (6) to obtain physically meaningful results; in the best case, the kth layer should consist of one candidate layer with material properties C 1 , C 2 , C 3 or C 4 Therefore, one of the solutions needs to be is equal to 1 and the others =0. In order to obtain this result, it is necessary to penalize the intermediate values ​​of the design variables, and impose an exponent p on the shape function (SF), i.e., equation (4), to obtain the parameterized expression of the shape function with penalty (SFP), as shown in equation (7). This expression still satisfies equation (6), but for the design variable R (k) and S (k) The intermediate value of does not satisfy equation (5), but it does at the solution. Numerical tests show that this is allowed.

[0073]

[0074] In SFP parameterization, the relationship between the parameter value and the corresponding orientation angle is as follows: Figure 2 As shown, when the parameter R corresponding to the kth layer (k) and S (k) When both are 1 or -1, the orientation angle of the laminate of that layer can be determined.

[0075] In the collaborative optimization of ply-reinforcement of composite panel structures, for the laminate base plate, the thickness and number of the laminates need to be given, and the ply angle of each layer needs to be determined through optimization, such as Figure 3 As shown in (a), the purpose of optimization is to obtain the most suitable orientation angle of each layer of the laminate, which is one of the angles of -45°, 0°, 45°, and 90°. For the ribs, the upper limit of the mass constraint needs to be given, and the coordinates of the end points of each rib and the thickness of the rib are obtained through optimization, as shown in Figure 3 (b) as shown.

[0076] In the flexibility minimization design of composite panel structure ply-reinforcement collaborative optimization, the optimization goal is to minimize the total strain energy of the reinforced panel structure. The corresponding optimization formula is shown in formula (8), where P i is the coordinate of the i-th moving node describing the position of the rib, t i is the thickness of the i-th rib, R i ,S iis the parameter describing the ply angle of the i-th layer of the laminate. np is the total number of nodes controlling the position of the ribs, ns is the total number of ribs, and nl is the total number of layers of the laminate.

[0077]

[0078] The optimization formula corresponding to the collaborative optimization fundamental frequency maximization design is shown in formula (9). The optimization goal is to minimize the inverse of the first-order eigenvalue of the stiffened wall panel structure, which is equivalent to maximizing the first-order frequency of the structure.

[0079]

[0080]

[0081] In this technical solution, in order to make the optimization results meet the manufacturing requirements or engineering constraints, in the collaborative optimization, by setting the constraint function, the results can meet the required constraints. For example, in the ribs, due to the limitations of the manufacturing process, there are restrictions on the maximum and minimum thickness of the ribs. In the optimization process, we use the Heaviside function to penalize the density and stiffness of the thin ribs, so that the ribs below the thickness requirements can be deleted from the optimization results, so that the results meet the minimum thickness manufacturing requirements. In addition, a symmetrical rib layout can be set to make the optimization results meet some quality symmetry requirements. In terms of laminates, in order to prevent excessive local stress between laminates, avoid the influence of tension-bending coupling, tension-shear coupling and other effects, there will be some constraints on the ply rules in the engineering, such as the maximum and minimum proportion of each ply angle, balanced ply, symmetrical ply, maximum continuous identical ply restrictions, and the angle difference between two adjacent layers does not exceed 45°. Corresponding constraint functions are proposed as restrictions to make the results meet the required constraints. The constraints that have been implemented are summarized as follows.

[0082] Rib constraint:

[0083] 1. Maximum thickness constraint, minimum thickness constraint

[0084] 2. The rib layout and thickness are symmetrical up and down or left and right in a certain rectangular coordinate system

[0085] 3. The rib layout and thickness are symmetrical in a certain rectangular coordinate system.

[0086] Layup Constraints:

[0087] (1) Maximum and minimum volume proportions at each angle

[0088] (2) Balanced ply (the number of plies at 45° is equal to the number of plies at -45°)

[0089] (3) Symmetrical ply

[0090] (4) The number of consecutive layers with the same angle does not exceed n, and n can be any value.

[0091] (5) The angle difference between two adjacent layers does not exceed 45°

[0092] Among them, the optimization design process of composite wall panel structure ply-reinforcement collaborative optimization is as follows: Figure 4 As shown. At the beginning of the optimization, different optimization results can be obtained by arranging different numbers of reinforced components in the design domain. After the initial design variables are given, due to the advantage of the MMC method in explicitly describing the components, the given initial design variables can be used directly in the Abaqus commercial finite element analysis software through Python scripts to automatically perform parameterized modeling, perform finite element analysis, extract field output results, and calculate analytical sensitivity in Python. The design variables are updated through the MMA solver, and the updated model data is obtained to automatically perform the next step of modeling and analysis. The entire iterative process does not require manual operation. As long as the initial information is given, the loop steps in the optimization process can be automatically performed in the Python script. Only the initial parameters need to be entered, and the optimization results can be waited for. The optimized model can be exported without post-processing, saving labor costs.

[0093] Embodiment 2:

[0094] In this embodiment, a four-corner simply supported embodiment of a square plate will be demonstrated. The flexibility optimization design and fundamental frequency optimization design of the square laminated plate stiffened structure are performed to verify the effectiveness of this method. The material properties selected in the optimization are set in Abaqus according to Table 1.

[0095] Table 1 Material properties of ribs and laminates

[0096]

[0097] In order to verify the flexibility optimization of the square laminate reinforced structure, the side length of the square laminate in this embodiment is 100 mm, and simply supported displacement constraints are set at four right angles of the plate. A concentrated force load of 100 N is applied vertically downward at the center of the plate, as shown in FIG. Figure 5 shown.

[0098] In this embodiment, the total number of plies of the given square laminate is 20, the thickness of each layer is 0.2 mm, the rib height is 5 mm, and the total volume of the ribs is limited to 10000 mm. 3 The ribs are set with up-down symmetry constraints and left-right symmetry constraints. The maximum thickness of the ribs is 10 mm and the minimum thickness is 1 mm. The laminates are set with balanced ply constraints, symmetrical ply constraints, ply constraints with the number of consecutive plies of the same angle not exceeding 3, and ply constraints with the angle difference between two adjacent plies not exceeding 45°.

[0099] The initial rib layout in the optimization is set to a 6×6 grid layout, such as Figure 6 As shown in (a), after 390 iterations, the optimization results converged and the optimized laminate layout is [45 / 0 2 / -45 / 0 / -45 / 90 3 / 45] S , the rib layout is as follows Figure 6 As shown in (b), the total strain energy of the structure is 2.611 mJ, and the total volume of the optimized ribs is 9988.22 mm 3 , less than 10000mm 3 The optimized rib layout after removing the redundant and penalized thin ribs is shown in the figure below: Figure 6 As shown in (c), the total strain energy of the structure is 2.619mJ. It can be seen that the ribs below the lower limit of thickness are subject to stiffness penalty in the analysis, and their thickness is reduced to 0.001mm due to the effect of the Heaviside function. Therefore, deleting this part of the ribs has almost no effect on the overall structure, and the strain energy only increases by about 0.3%. The iterative curves of the objective function, rib volume, and penalized rib volume during the optimization process are shown in Figure 2. Figure 7 shown.

[0100] The optimization results are compared with the cyclic ply method [0 / (0 / 45 / 90 / -45)] which is commonly used in engineering and meets the constraint requirements. 2 / 90] S , the total volume of the ribs is 10000mm 3 And the rib arrangement is Figure 6 (a) is compared with the initial grid reinforcement layout structure (referred to as the comparison layout). Finite element analysis is performed in Abaqus. The calculated stress absolute value maximum value cloud diagram and displacement cloud diagram are shown in Figure 8 As shown, Figure 8 (a) is the maximum value cloud diagram of the absolute value of stress and the displacement cloud diagram of the comparison layout. Figure 8 (b) is the maximum value cloud diagram of the absolute value of stress and displacement of the collaborative optimization result. The total strain energy of the structure of the comparison layout is 3.500mJ, and the total strain energy of the structure of the optimization result is 2.619mJ. The strain energy of the optimized structure is reduced by 25.17% compared with the comparison layout.

[0101] right Figure 6 By analyzing the optimization results of (c), it can be seen that the total number of 0° layers and 90° layers in the laminate optimization results is 6, but the 0° layer is closer to the outside, and the laminate's ability to resist left and right bending is stronger than its ability to resist up and down bending; in the optimized rib layout, the longitudinal ribs are more than the transverse ribs, so the ability to resist up and down bending is stronger than the ability to resist left and right bending. Figure 5It can be seen from the working conditions that the bending moment of the plate under external force is the same in the vertical bending and the horizontal bending. Through the laminated plate reinforced structure obtained by collaborative optimization, the laminated plate and the reinforcement complement each other in resisting the external force bending and jointly resist the external force. Figure 8 It can be seen that, compared with the commonly used empirical design, the maximum stress of the collaborative optimization result is reduced from 20.35MPa to 15.49MPa, and the maximum displacement is reduced from 7.011e-2mm to 5.23e-2mm. The structure is significantly enhanced. It can be seen from the displacement cloud map of the optimization result that even if the laminate bottom plate is anisotropic, the collaborative optimization with the ribs can improve the stiffness and strength of the structure. At the same time, the displacement contour of the deformation of the optimization result is close to a circle, and a displacement state similar to that of the isotropic plate is obtained.

[0102] In order to verify the fundamental frequency optimization of the square laminate reinforced structure, this embodiment selects a square laminate with a side length of 200 mm, sets simply supported displacement constraints at four right angles to the plate, and sets a mass point of 0.5 tonne at the center of the plate, such as Fig. 9 shown.

[0103] In this embodiment, the total number of plies of the given square laminate is 20, the thickness of each layer is 0.2 mm, the rib height is 10 mm, and the total volume of the ribs is limited to 50000 mm. 3 . Set symmetric constraints on the ribs, with a maximum thickness of 10 mm and a minimum thickness of 1 mm. Set symmetric ply constraints on the laminate, set the number of consecutive plies with the same angle to no more than 3, and set the angle difference between two adjacent plies to no more than 45°. For material density, set the laminate density to 2.0e-9 tonne / mm 3 , the rib density is set to 2.7e-9tonne / mm 3 .

[0104] The initial rib layout in the optimization is set to a 6×6 grid layout, such as Fig.10 As shown in (a), after 99 iterations, the optimization results converged and the optimized laminate layout is [-45 / 0 / -45 / 90 / 45 / 90 / 45 2 / 0 / -45] S , the rib layout is as follows Fig.10 As shown in (b), the optimized rib layout after deleting the redundant and penalized thin ribs is as follows Fig.10 As shown in (c), the total volume of the ribs is 48870.8mm 3 , less than 50000mm 3 The iterative curves of the objective function, rib volume and penalized rib volume during the optimization process are shown in Fig.11 shown.

[0105] The optimization results are compared with the cyclic ply method [0 / (0 / 45 / 90 / -45)] which is commonly used in engineering and meets the constraint requirements. 2 / 90] S and volume is 50000mm 3 The laminated plate reinforced structure with the initial grid reinforcement layout is analyzed and compared in Abaqus. The vibration displacement cloud diagram is shown in Fig.12 As shown, Fig.12 (a) is the first-order vibration displacement cloud diagram of the comparison layout. Fig.12 (b) is the first-order vibration mode displacement cloud diagram of the collaborative optimization result. It can be seen that compared with the comparison layout, the first-order vibration mode of the optimized structure is closer to the vibration mode of the isotropic square plate, and the displacement contour in the vibration mode is closer to a circle. Compared with the commonly used empirical design, the first-order eigenvalue of the cyclic ply grid reinforced structure is 1857.4, the fundamental frequency is 6.8592Hz, and the first-order eigenvalue of the collaborative optimization result is 2538.9, the fundamental frequency is 8.0193Hz, and the fundamental frequency is increased by 16.91%.

[0106] In summary, the advantages of the composite wall panel structure ply-reinforcement collaborative optimization method proposed in this technical solution can be summarized as follows: (1) It can solve the problem of minimizing the flexibility of the laminated reinforced structure, and can improve the strength and stiffness of the structure from the side; (2) It can solve the problem of maximizing the fundamental frequency of the laminated reinforced structure and prevent the occurrence of adverse conditions such as resonance; (3) By considering the influence of the laminate design variables and the rib design variables at the same time, a global optimized configuration can be obtained, which can give full play to the role of the laminate and the ribs; (4) An efficient analytical sensitivity method is used for optimization, and analysis is performed based on shell units. Compared with the optimization analysis method of solid units, the number of finite elements is greatly reduced, the analysis time of finite elements is shortened, and the optimization efficiency is improved.

[0107] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims

1. A composite material wall panel structure layup-reinforcement collaborative optimization method, characterized in that: Including description methods of rib layout, description methods of laminate layup angles, composite wall structure layup-reinforcement collaborative optimization, flexibility minimization design and fundamental frequency maximization design of composite wall structure layup-reinforcement collaborative optimization; The description method of the rib layout adopts a reinforcement optimization design method based on the MMC method to explicitly describe the rib information and use it as a design variable to obtain the rib path; The method for describing the angle of the ply of the laminate adopts a parameterization method using a shape function with penalty to determine the orientation angle of the laminate; The ply-reinforcement collaborative optimization of composite wall structure requires the given thickness and quantity information of the laminate, and the ply angle of each layer is determined through optimization to obtain the most suitable orientation angle of each layer of the laminate. For the ribs, the upper limit of the mass constraint needs to be given, and the coordinates of the end points of each rib and the thickness of the rib are obtained through optimization. The flexibility minimization design of the composite panel structure ply-reinforcement collaborative optimization is to minimize the total strain energy of the reinforced panel structure; The fundamental frequency maximization design of collaborative optimization is to minimize the inverse of the first-order eigenvalue of the stiffened panel structure, which is equivalent to maximizing the first-order frequency of the structure.

2. The composite material wall panel structure layup-reinforcement collaborative optimization method according to claim 1, characterized in that: The reinforcement optimization design method based on the MMC method comprises the following steps: Use components to describe each rib in the design domain. Each rib is connected through a spatial node in the design domain, so that the position of the rib changes with the movement of the node, thereby changing the layout of the rib. The position of different spatial nodes determines the change of the rib shape. During the optimization process, the node-driven adaptive base structure method is used to establish the reinforcement model. The design variables are the node coordinates and the reinforcement thickness. An efficient shape sensitivity analysis method is used to iteratively update the entire structure by moving a series of driving nodes and changing some dimensional parameters of the components until convergence to obtain the optimal reinforcement layout.

3. The composite material wall panel structure layup-reinforcement collaborative optimization method according to claim 2, characterized in that: During the optimization process, the lower limit of the rib thickness range is t ε (t ε < t ), the Heaviside function (1) is used to penalize it, and the thickness penalty form of formula (2) is used to penalize the thickness of the i-th rib t i Multiply by the Heaviside function to get the thickness after penalty Take t ε =α=0.001,ε=0.1; The formula (1) and formula (2) are as follows:

4. The composite material wall panel structure layup-reinforcement collaborative optimization method according to claim 1, characterized in that: The stiffness matrix of the kth ply of the laminate is written as the weighted sum of the candidate material stiffness matrices using the parameterized method of the penalized shape function: Among them, C (k) represents the elastic matrix of the k-th layer of the laminate, C1, C2, C3, and C4 represent the stiffness matrix corresponding to the fiber orientation of -45°, 0°, 45°, and 90°, respectively, and their weight factors are represents the weight of the i-th orientation angle in the k-th layer of the laminate. The weight factor of the k-th layer of the laminate is obtained by the design variable R (k) , S (k) Indicates that R (k) and S (k) The value of varies between -1 and 1: satisfy The weight factors need to satisfy equations (5) and (6) to obtain physically meaningful results; in the best case, the kth layer should consist of one candidate layer with material properties C1, C2, C3 or C4, so one of them needs to be is equal to 1 and the others =0; In order to obtain this result, it is necessary to penalize the intermediate values ​​of the design variables, and impose an exponent p on the shape function (SF), i.e., equation (4), to obtain the penalized shape function parameterized expression as shown in equation (7). This expression still satisfies equation (6), but for the design variable R (k) and S (k) The intermediate value of does not satisfy equation (5), but it does at the solution; In SFP parameterization, when the parameter R corresponding to the kth layer (k) and S (k) When both are 1 or -1, the orientation angle of the laminate of that layer can be determined.

5. The composite material wall panel structure layup-reinforcement collaborative optimization method according to claim 1, characterized in that: The ply angle of each layer is determined by optimization, and the most suitable orientation angle of each layer of the laminate is obtained, and the orientation angle is one of -45°, 0°, 45°, and 90°.

6. The composite material wall panel structure layup-reinforcement collaborative optimization method according to claim 1, characterized in that: The optimization formula corresponding to the flexibility minimization design of the composite panel structure ply-reinforcement collaborative optimization is formula (8): Among them, P i is the coordinate of the i-th moving node describing the position of the rib, t i is the thickness of the i-th rib, R i ,S i is the parameter describing the ply angle of the i-th layer of the laminate, np is the total number of nodes controlling the position of the ribs, ns is the total number of ribs, and nl is the total number of layers of the laminate.

7. The composite material wall panel structure layup-reinforcement collaborative optimization method according to claim 1, characterized in that: The optimization formula corresponding to the collaborative optimization fundamental frequency maximization design is formula (9): Among them, P i is the coordinate of the i-th moving node describing the position of the rib, t i is the thickness of the i-th rib, R i ,S i is the parameter describing the ply angle of the i-th layer of the laminate, np is the total number of nodes controlling the position of the ribs, ns is the total number of ribs, and nl is the total number of layers of the laminate.

8. The composite material wall panel structure layup-reinforcement collaborative optimization method according to claim 1, characterized in that: The rib mass constraints include a maximum thickness constraint, a minimum thickness constraint, a rib layout and thickness being symmetrical in a certain rectangular coordinate system, or being symmetrical in a certain rectangular coordinate system.

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