A ply-stiffener collaborative optimization method for a composite material panel structure

Abstract

The present invention belongs to the technical fields of aerospace and topology optimization, and particularly relates to a method for collaborative optimization of ply-stiffener of a composite panel structure, including a description method for rib layout, a description method for ply angles of a laminated plate, collaborative optimization of ply-stiffener of a composite panel structure, minimum compliance design and maximum fundamental frequency design for collaborative optimization of ply-stiffener of a composite panel structure; the description method for rib layout uses a rib optimization design method based on the MMC method to explicitly describe rib information and takes it as a design variable to obtain the rib path. The present invention simultaneously considers the influences of design variables of the laminated plate and the rib, can obtain an optimized configuration globally, can give full play to the roles of the laminated plate and the rib more sufficiently, solves the problem of minimum compliance of the laminated plate stiffened structure, can improve the strength and stiffness of the structure from the side, solves the problem of maximum fundamental frequency of the laminated plate stiffened structure, and prevents the occurrence of adverse situations such as resonance.

Description

Technical Field

[0001] The present invention belongs to the technical fields of aerospace and topology optimization, and particularly relates to a method for collaborative optimization of ply-stiffener for composite panel structures. Background Art

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

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

[0004] Although there have been many studies on the optimization design of stiffeners and the optimization design of laminates, and significant results have been achieved, there are still some challenging problems that need to be further solved. First of all, in the existing research work, basically all focus on the optimization research of laminates alone or the optimization research of ribs alone. The two optimization methods of the laminate-stiffener structure are carried out separately, and the structure is optimized without comprehensive consideration, which often easily misses some globally optimal structures that are mutually coupled. Secondly, the commonly used implicit optimization methods often have problems such as many design variables, difficult to control explicit dimensions, and complicated post-processing. In the optimization of laminates, it is also often based on solid elements for analysis and calculation, with a long analysis time and a large amount of calculation. In addition, for the laminate structure commonly used in actual engineering, each single layer usually selects one of the angles from -45°, 0°, 45°, and 90°. Therefore, the design variables of the laminate structure are discrete, while the design variables of the ribs, such as the node coordinates at both ends of the ribs and the thickness of the ribs, etc., are within a specific value range, and its design variables are continuous design variables. It is also a difficulty in this work to realize the collaborative optimization of these two different types of design variables. Summary of the Invention

[0005] The object of the present invention is to provide a method for collaborative optimization of ply - stiffener in a composite panel structure. By considering the influence of both laminate design variables and stiffener design variables, a globally optimized configuration can be obtained, enabling the laminate and stiffener to play their roles more fully, solving the problem of minimizing the flexibility of the laminated - stiffened structure, enhancing the strength and stiffness of the structure from the side, solving the problem of maximizing the fundamental frequency of the laminated - stiffened structure, and preventing the occurrence of adverse situations such as resonance.

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

[0007] A method for collaborative optimization of ply - stiffener in a composite panel structure includes a description method of stiffener layout, a description method of laminate ply angles, collaborative optimization of ply - stiffener in a composite panel structure, flexibility - maximization design of ply - stiffener in a composite panel structure, and fundamental - frequency - maximization design of ply - stiffener in a composite panel structure;

[0008] The description method of the stiffener layout uses a stiffener optimization design method based on the MMC method to explicitly describe the stiffener information and take it as a design variable to obtain the stiffener path;

[0009] The description method of the laminate ply angles uses a parametric method with a penalized shape function to determine the laminate orientation angles;

[0010] For the collaborative optimization of ply - stiffener in a composite panel structure, the thickness and number information of the laminate need to be given. By optimization, the ply angle of each layer is determined to obtain the most suitable orientation angle of each laminate layer. For the stiffeners, an upper limit of mass constraint needs to be given, and the coordinates of the endpoints of each stiffener and the thickness of the stiffeners are obtained through optimization;

[0011] The flexibility - maximization design of ply - stiffener in a composite panel structure is to minimize the total strain energy of the stiffened panel structure;

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

[0013] The optimization formulation corresponding to the flexibility - maximization design of ply - stiffener in a composite panel structure is Equation (8):

[0014]

[0015] The optimization formulation corresponding to the fundamental - frequency - maximization design of the collaborative optimization is Equation (9):

[0016]

[0017]

[0018] Among them, P j is the coordinate of the j-th moving node describing the position of the rib, t i is the thickness of the i-th rib, R m , S m is the parameter describing the ply angle of the m-th ply of the laminate, n p is the total number of nodes controlling the rib position, ns is the total number of ribs, and nl is the total number of plies of the laminate.

[0019] Furthermore, the stiffened optimization design method based on the MMC method includes the following steps:

[0020] Use components to describe each rib inside the design domain. Each rib is connected by spatial nodes inside the design domain, so that the position of the rib changes as the nodes move, thereby changing the layout of the ribs. The positions of different spatial nodes determine the change in the rib shape;

[0021] During the optimization process, an adaptive base structure method driven by nodes is adopted to establish a rib model. The design variables are node coordinates and rib 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 stiffened layout.

[0022] Furthermore, during the optimization process, the lower limit of the value range of the rib thickness is t ε (t ε < t ), and the Heaviside function formula (1) is used to penalize it. Through the thickness penalty form of formula (2), that is, multiplying the thickness t i of the i-th rib by the Heaviside function to obtain the penalized thickness Take t ε =α = 0.001, ε = 0.1;

[0023]

[0024] Furthermore, the parametric method using a shape function with penalty writes the stiffness matrix of the k-th ply of the laminate as a weighted sum of the candidate material stiffness matrices:

[0025]

[0026] Among them, C (k) represents the elastic matrix of the k-th ply of the laminate, C 1 , C 2 , C 3 , C 4 represent the stiffness matrices corresponding to the fiber orientations 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 laminate, and the weight factor of the k-th layer laminate is determined by the design variables R (k) , S (k) represents, R (k) and S (k) vary between -1 and 1:

[0027]

[0028] Satisfy

[0029]

[0030] The weight factors need to satisfy equations (5) and (6) to obtain physically meaningful results; in the best case, the k-th layer should consist of one candidate layer with material properties C 1 , C 2 , C 3 or C 4 , so one of them should be equal to 1 and the others should be equal to 0; to obtain such a result, the intermediate values of the design variables need to be penalized, and an exponent p is applied to the shape function (SF), i.e., equation (4), to obtain a penalized shape function parameterization expression as shown in equation (7), which still satisfies equation (6), but does not satisfy equation (5) for the intermediate values of the design variables R (k) and S (k) , but satisfies it at the solution;

[0031]

[0032] In the SFP parameterization, when the design variables R (k) and S (k) corresponding to the k-th layer both take 1 or -1, the laminate orientation angle of this layer can be determined.

[0033] Furthermore, by optimization, the ply angles of each layer are determined to obtain the optimal orientation angle of each layer laminate, and the orientation angle is one of -45°, 0°, 45°, 90°.

[0034] The technical effects achieved by the present invention are:

[0035] (1) The ply-stiffener co-optimization method for a composite wall panel structure of the present invention can solve the problem of minimizing the flexibility of the laminated stiffened structure and can improve the strength and stiffness of the structure from the side.

[0036] (2) The ply-stiffener co-optimization method for the composite panel structure of the present invention can solve the problem of maximizing the fundamental frequency of the laminated stiffened structure and prevent the occurrence of adverse situations such as resonance.

[0037] (3) The ply-stiffener co-optimization method for the composite panel structure of the present invention simultaneously considers the influence of the design variables of the laminate and the stiffener, can obtain an optimized configuration globally, and can give full play to the roles of the laminate and the stiffener more fully.

[0038] (4) The ply-stiffener co-optimization method for the composite panel structure of the present invention uses an efficient analytical sensitivity method for optimization and is analyzed based on shell elements. Compared with the optimization analysis method using solid elements, the number of finite elements is greatly reduced, the finite element analysis time is shortened, and thus the optimization efficiency is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a schematic diagram of the node-driven adaptive basic structure method of the present invention;

[0040] Figure 2 is the principle of the SFP parameterization of the present invention;

[0041] Figure 3 is the co-optimization design content of the present invention;

[0042] Figure 4 is the optimization flow chart of the present invention;

[0043] Figure 5 is a schematic diagram of the flexibility optimization example of the square plate of the present invention;

[0044] Figure 6 is the rib layout of the flexibility optimization of the simply supported square plate of the present invention;

[0045] Figure 7 is the optimization iteration curve of the objective function, rib volume, and penalized rib volume in the flexibility optimization of the square plate of the present invention;

[0046] Figure 8 is the stress nephogram and displacement nephogram of the comparison layout and the optimized layout of the present invention;

[0047] Figure 9 is a schematic diagram of the fundamental frequency optimization example of the square plate of the present invention;

[0048] Figure 10 is the rib layout of the fundamental frequency optimization of the simply supported square plate of the present invention;

[0049] Figure 11 is the optimization iteration curve of the objective function, rib volume, and penalized rib volume in the fundamental frequency optimization of the square plate of the present invention;

[0050] Figure 12 These are the mode shape nephograms of the comparative layout and the optimized layout of the present invention. Specific Embodiments

[0051] In order to make the objectives and advantages of the present invention clearer and more understandable, the present invention will be specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific implementation manners of the present invention, and does not strictly limit the scope of protection specifically claimed by the present invention.

[0052] This technical solution proposes a method for collaborative optimization of ply - stiffener for composite panel structures. Through the collaborative optimization of the ply angles of the laminate and the stiffener layout, the maximum flexibility design and the maximum fundamental frequency design of the composite laminate stiffened structure are realized; the optimization content includes the ply angles of the laminate, the stiffening paths of the rectangular stiffeners, and the thicknesses of the ribs.

[0053] Moreover, through constraint settings, the optimization results can meet the manufacturing constraints in engineering, including the maximum and minimum thickness constraints of the ribs, the symmetric distribution constraint of the ribs, and the balanced ply constraint (the same number of ±45° plies), the symmetric ply constraint, the maximum repeated ply number constraint for adjacent plies with the same angle, and the constraint that the adjacent plies do not exceed 45° in the ply settings of the laminate, so that the optimized structure can be directly applied to actual production and manufacturing.

[0054] Different from the prior art, this technical solution realizes the sensitivity analysis of ply - stiffener collaborative optimization for the first time, has strict sensitivity derivation, can perform ply - stiffener optimization on thin - wall structures of any shape, and verifies the accuracy of the analytical sensitivity through differential sensitivity, ensuring fast and accurate sensitivity analysis. The gradient optimization algorithm such as the Moving Asymptotic Method (MMA) can be directly used for optimization, and the optimization speed is fast. In addition, the sensitivity analysis can be carried out using shell elements. Compared with the topology optimization method of solid elements, it greatly reduces the finite - element calculation time and improves the calculation efficiency. The optimization uses the Moving Morphable Component (MMC) method with explicit description characteristics to describe the rib information, so that the optimization results consist of a group of components with clear geometric parameters, which greatly simplifies the post - processing and improves the accuracy of the analysis.

[0055] Embodiment 1:

[0056] As Figures 1-12 shown, a method for collaborative optimization of ply - stiffener for composite panel structures includes a description method of rib layout, a description method of ply angles of the laminate, collaborative optimization of ply - stiffener for composite panel structures, maximum flexibility design and maximum fundamental frequency design of collaborative optimization of ply - stiffener for composite panel structures;

[0057] Among them, please refer toFigure 1 As shown in Figure 1 , the description method of the rib layout adopts a ribbed optimization design method based on the MMC method. The ribbed optimization design method based on the MMC method can explicitly describe rib information and use it as a design variable. This method can obtain a clear and accurate rib path without any post-processing.

[0058] The ribbed optimization design method based on the MMC method includes the following steps:

[0059] Use components to describe each rib inside the design domain. Each rib is connected by spatial nodes inside the design domain, so that the rib changes its position as the nodes move, thereby changing the rib layout. The positions of different spatial nodes determine the change in the rib shape.

[0060] During the optimization process, the node-driven adaptive basis structure method is used to establish a rib model. The design variables are the node coordinates and the rib thickness. An efficient shape sensitivity analysis method is adopted 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 ribbed layout.

[0061] Specifically, during the optimization process, due to the existence of volume constraints, there are often some thin ribs with a thickness less than the lower limit of the manufacturable thickness (denoted as t ). These ribs may contribute less to the stiffness at their current positions, so their thickness is small, but they cannot be directly deleted because during the optimization, as the layout changes, the contribution of these ribs to the stiffness may increase and their thickness will increase.

[0062] To ensure that the ribs with a thickness less than the thickness lower limit t can be deleted in the final structure, this technical solution sets the lower limit of the thickness value range of the ribs during the optimization process to be t ε (t ε < t ), and the Heaviside function formula (1) is used to punish it. Through the thickness penalty form of formula (2), that is, multiplying the thickness t i of the i-th rib by the Heaviside function to obtain the punished thickness In this work, t ε = α = 0.001, ε = 0.1. Through this penalty method, the number of ribs with a thickness in can be effectively reduced, and when the thickness reaches the lower limit t ε , due to the extremely small thickness, it hardly contributes to the stiffness of the structure, and it can be removed from the result to obtain a ribbed layout with a simple form.

[0063]

[0064] Please refer toFigure 2 As shown, for the description method of the ply angles of a constant stiffness laminate, the parameterization method using the shape function with penalty (SFP) proposed by M. Bruyneel et al. is adopted. In this method, the stiffness matrix of the k-th ply of the laminate is written as a weighted sum of the candidate material stiffness matrices:

[0065]

[0066] where, C (k) represents the elastic matrix of the k-th ply of the laminate, and C 1 , C 2 , C 3 , C 4 represent the stiffness matrices corresponding to the fiber orientations of -45°, 0°, 45°, and 90° respectively, and their weight factors are which represents the weight of the i-th orientation angle in the k-th ply of the laminate. The weight factor of the k-th ply of the laminate is represented by the design variables R (k) , S (k) . R (k) and S (k) vary between -1 and 1:

[0067]

[0068] satisfies

[0069]

[0070] The weight factors need to satisfy Eqs. (5) and (6) to obtain physically meaningful results. In the best case, the k-th ply should consist of one candidate ply with material properties C 1 , C 2 , C 3 or C 4 . Therefore, at its solution, one of them should be equal to 1 and the others should be equal to 0. To obtain such a result, the intermediate values of the design variables are penalized, and an exponent p is applied to penalize the shape function (SF), i.e., Eq. (4), to obtain the parameterized expression of the shape function with penalty (SFP) as shown in Eq. (7). This expression still satisfies Eq. (6), but does not satisfy Eq. (5) for the intermediate values of the design variables R (k) and S (k) , but satisfies it at the solution. Numerical tests show that this is allowed.

[0071]

[0072] In the SFP parameterization, the relationship between the parameter values and the corresponding orientation angles is as Figure 2 shown. When the design variable R corresponding to the k-th ply (k)and S (k) When both take 1 or -1, the ply orientation angle of this layer can be determined.

[0073] In the ply-stiffener co-optimization of composite panel structures, for the laminate bottom plate, the thickness and quantity information of the laminate need to be given, and the ply angle of each layer is determined through optimization. As shown in Figure 3 (a), the purpose of optimization is to obtain the most suitable orientation angle for each layer of laminate, and its value is one of the angles -45°, 0°, 45°, 90°. For the stiffeners, the upper limit of mass constraint needs to be given, and the coordinates of the endpoints of each stiffener and the thickness of the stiffeners are obtained through optimization. As shown in Figure 3 (b).

[0074] In the maximum flexibility design of the ply-stiffener co-optimization of composite panel structures, the optimization goal is to minimize the total strain energy of the stiffened panel structure. The corresponding optimization formula is shown in Equation (8), where P j is the coordinate of the j-th moving node describing the position of the stiffener, t i is the thickness of the i-th stiffener, R m , S m is the parameter describing the ply angle of the m-th layer of the laminate. np is the total number of nodes controlling the position of the stiffeners, ns is the total number of stiffeners, and nl is the total number of layers of the laminate.

[0075]

[0076] The corresponding optimization formula for the maximum fundamental frequency design of co-optimization is shown in Equation (9). The optimization goal is to minimize the negative value of the first eigenvalue of the stiffened panel structure, which is equivalent to maximizing the first-order frequency of the structure.

[0077]

[0078] In this technical solution, in order to make the optimization results meet the manufacturing requirements or engineering constraints, in collaborative optimization, by setting constraint functions, the results can meet the required constraints. For example, in ribs, due to manufacturing process limitations, there are limitations on the maximum and minimum rib thicknesses. During the optimization process, for ribs that are too thin, we use the Heaviside function to impose penalties on density and stiffness, so that ribs below the thickness requirement can be removed from the optimization results, making the results meet the manufacturing requirement of the minimum thickness. Additionally, a symmetric rib layout can be set to make the optimization results meet some symmetry requirements in terms of quality. In the case of laminates, in order to prevent excessive local stress between laminate layers and avoid the influence of effects such as bending-torsion coupling and tension-shear coupling, there are some constraints on ply layup rules in engineering, such as the maximum and minimum proportions of each ply angle, balanced ply layup, symmetric ply layup, maximum continuous same ply limit, and the limit that the angle difference between adjacent two layers does not exceed 45°. Corresponding constraint functions are proposed as limitations to make the results meet the required constraints. The currently implemented constraints are summarized as follows.

[0079] Rib constraints:

[0080] 1. Maximum thickness constraint, minimum thickness constraint

[0081] 2. The rib layout and thickness are symmetric up and down or left and right in a certain rectangular coordinate system

[0082] 3. The rib layout and thickness are symmetric both up and down and left and right in a certain rectangular coordinate system

[0083] Ply layup constraints:

[0084] (1) Maximum and minimum volume proportions of each angle

[0085] (2) Balanced ply layup (the number of 45° plies is equal to the number of -45° plies)

[0086] (3) Symmetric ply layup

[0087] (4) The number of consecutive plies with the same angle does not exceed n, where n can take any value

[0088] (5) The angle difference between adjacent two layers does not exceed 45°

[0089] Among them, the optimization design process of the ply layup - stiffener collaborative optimization of the composite panel structure is as Figure 4As shown in the figure. At the beginning of the optimization, different optimization results can be obtained by arranging different numbers of stiffening components in the design domain. After the given initial design variables, due to the advantage of the MMC method in explicitly describing components, automatic parametric modeling, finite element analysis, extraction of field output results can be directly carried out in the commercial finite element analysis software Abaqus through Python scripts with the given initial design variables, and the analytical sensitivity can be calculated in Python. The design variables are updated through the MMA solver, and the updated model data is obtained to automatically carry out the next step of modeling and analysis. The entire iterative process requires no manual operation. Only by giving the initial information, the loop steps in the optimization process can be automatically carried out in the Python script. Only by inputting the initial parameters, one can wait for the optimization results to be generated, and the optimized results can be exported without post-processing, saving labor costs.

[0090] Example 2:

[0091] In this example, a simply supported example at the four corners of a square plate will be demonstrated. By performing flexibility optimization design and fundamental frequency optimization design on the stiffened structure of the square laminated plate, the effectiveness of this method is verified. The material properties selected in the optimization are set in Abaqus according to Table 1.

[0092] Table 1 Material properties of ribs and laminated plates

[0093]

[0094] To verify the flexibility optimization of the stiffened structure of the square laminated plate, the side length of the square laminated plate in this example is taken as 100 mm. Simply supported displacement constraints are set at the four right-angle positions of the plate, and a concentrated force load of 100 N acting vertically downward is applied at the center of the plate, as Figure 5 shown.

[0095] In this example, the total number of plies of the square laminated plate is given as 20, the thickness of each ply is 0.2 mm, the height of the ribs is 5 mm, and the upper limit of the total volume of the ribs is 10000 mm 3 . Symmetric constraints are set for the ribs in the up-down and left-right directions. The maximum thickness of the ribs is 10 mm, and the minimum thickness is 1 mm. For the laminated plate, balanced ply constraints, symmetric ply constraints, the number of consecutive plies with the same angle does not exceed 3, and the ply constraint that the angle difference between adjacent two plies does not exceed 45° are set.

[0096] In the optimization, the initial rib layout is set as a 6×6 grid layout, as Figure 6 (a) shown. After 390 steps of iteration, the optimization results converge. The optimized laminated plate layout is [45 / 0 2 / -45 / 0 / -45 / 90 3 / 45] S , and the rib layout is asFigure 6 As shown in (b), the total structural strain energy is 2.611 mJ, and the total volume of the optimized ribs is 9988.22 mm 3 , meeting the upper limit constraint requirement of the total rib volume being less than 10000 mm 3 . The optimized rib layout after deleting the redundant penalized thin ribs is as shown in Figure 6 (c). The total structural strain energy is 2.619 mJ. It can be seen that the ribs below the thickness lower limit have been penalized in stiffness during the analysis, and their thickness has been reduced to 0.001 mm due to the Heaviside function. Therefore, deleting this part of the ribs has little impact 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 as shown in Figure 7 .

[0097] Compare the optimization results with the commonly used and constraint - meeting circular ply lay - up method [0 / (0 / 45 / 90 / -45) 2 / 90] S in engineering, with a total rib volume of 10000 mm 3 and the rib arrangement in the form of Figure 6 (a) of the initial grid - type stiffened layout structure (referred to as the comparison layout). Conduct a finite - element analysis in Abaqus, and the maximum absolute value stress contour and displacement contour are as shown in Figure 8 . Figure 8 (a) shows the maximum absolute value stress contour and displacement contour of the comparison layout, Figure 8 (b) shows the maximum absolute value stress contour and displacement contour of the collaborative optimization result. The total structural strain energy of the comparison layout is 3.500 mJ, and the total structural strain energy of the optimization result is 2.619 mJ. The strain energy of the optimized structure is reduced by 25.17% compared with the comparison layout.

[0098] Analyze the optimization result of Figure 6 (c). It can be seen that the total number of 0° layers and 90° layers in the optimized laminate result is 6 layers each, but the 0° layers are closer to the outside. The laminate's ability to resist left - right bending is stronger than its ability to resist up - down bending; in the optimized rib layout, the longitudinal ribs are more than the transverse ribs, so the ability to resist up - down bending is stronger than the ability to resist left - right bending. And through the Figure 5 working condition, it can be seen that the bending moment of the external force on the plate is the same for up - down bending and left - right bending. For the laminated plate stiffened structure obtained by collaborative optimization, the laminate and the stiffeners complement each other in resisting external force bending and jointly resist the external force. From Figure 8It can be seen that, compared with the commonly used empirical design, the maximum stress of the result of collaborative optimization decreases from 20.35 MPa to 15.49 MPa, and the maximum displacement decreases from 7.011e-2 mm to 5.23e-2 mm. The structure is significantly enhanced. Moreover, it can be seen from the displacement nephogram of the optimization result that even though the bottom plate of the laminated plate is anisotropic, through the collaborative optimization with the ribs, while the stiffness and strength of the structure are improved, the displacement contour lines of the optimized result deformation are close to circular, and a displacement state similar to that of an isotropic plate is obtained.

[0099] To verify the fundamental frequency optimization of the stiffened square laminated plate structure, in this embodiment, the side length of the square laminated plate is taken as 200 mm, simple support displacement constraints are set at the four right-angle positions of the plate, and a mass point of 0.5 tonne is set at the center of the plate, as Figure 9 shown.

[0100] In this embodiment, the total number of plies of the square laminated plate is given as 20, the thickness of each ply is 0.2 mm, the height of the ribs is 10 mm, and the upper limit of the total volume of the ribs is 50000 mm 3 . Symmetric constraints are set on the upper and lower sides of the ribs, and symmetric constraints are set on the left and right sides. The maximum thickness of the ribs is 10 mm, and the minimum thickness is 1 mm. Symmetric ply constraints are set on the laminated plate, the number of consecutive plies with the same angle does not exceed 3, and the ply constraint that the angle difference between adjacent two plies does not exceed 45° is set. For the material density, the density of the laminated plate is set as 2.0e-9 tonne / mm 3 , and the density of the ribs is set as 2.7e-9 tonne / mm 3 .

[0101] In the optimization, the initial rib layout is set as a 6×6 grid layout, as Figure 10 (a) shown. After 99 steps of iteration, the optimization result converges. The optimized laminated plate layout is [-45 / 0 / -45 / 90 / 45 / 90 / 45 2 / 0 / -45] S , and the rib layout is as Figure 10 (b) shown. The optimized rib layout after deleting the redundant and penalized thin ribs is as Figure 10 (c) shown. The total volume of the ribs is 48870.8 mm 3 , meeting the requirement of the upper limit constraint of the total rib volume less than 50000 mm 3 . The iteration curves of the objective function, rib volume, and penalized rib volume during the optimization process are as Figure 11 shown.

[0102] Compare the optimization result with the commonly used and constraint - meeting circular ply method [0 / (0 / 45 / 90 / -45) 2 / 90] Sand a laminated stiffened structure with an initial grid-type stiffening layout having a volume of 50000 mm 3 is subjected to finite element analysis and comparison in Abaqus. The vibration mode displacement nephogram is as shown in Figure 12 . Figure 12 (a) is the first vibration mode displacement nephogram of the comparison layout, Figure 12 (b) is the first vibration mode displacement nephogram of the collaborative optimization result. It can be seen that compared with the comparison layout, the first vibration mode of the optimized structure is closer to that of an isotropic square plate, and the contour lines of the displacement in the vibration mode are closer to a circle. Compared with the commonly used empirical design, the first eigenvalue of the circularly laminated grid stiffened structure is 1857.4, and the fundamental frequency is 6.8592 Hz. The first eigenvalue of the collaborative optimization result is 2538.9, and the fundamental frequency is 8.0193 Hz, with the fundamental frequency increased by 16.91%.

[0103] In summary, the advantages of the ply-stiffener collaborative optimization method for the composite panel structure proposed in this technical solution can be summarized as follows: (1) It can solve the problem of minimizing the flexibility of the laminated stiffened 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 stiffened structure and prevent the occurrence of adverse situations such as resonance; (3) By considering the influence of both the design variables of the laminate and the stiffeners simultaneously, a globally optimized configuration can be obtained, and the functions of the laminate and the stiffeners can be exerted more fully; (4) It uses an efficient analytical sensitivity method for optimization and is analyzed based on shell elements. Compared with the optimization analysis method using solid elements, the number of finite elements is greatly reduced, the finite element analysis time is shortened, and thus the optimization efficiency is improved.

[0104] The above is only the preferred implementation manner of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. The structures, devices, and operation methods not specifically described and explained in the present invention are implemented according to the conventional means in the art without special instructions and limitations.

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 maximization 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 maximization 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 wall structure, which is equivalent to maximizing the first-order frequency of the structure. The optimization formula corresponding to the flexibility maximization design of the composite panel structure ply-reinforcement collaborative optimization is formula (8): The optimization formula corresponding to the collaborative optimization fundamental frequency maximization design is formula (9): Among them, P j is the coordinate of the jth moving node describing the position of the rib, t i is the thickness of the i-th rib, R m ,S m is the parameter describing the layup angle of the mth 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.

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 (4) to penalize it. The parameterized expression of the shape function with penalty is obtained as shown in (7). This expression still satisfies (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 design variable 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°.

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