An equivalent calculation method for mechanical parameters of composite panel assembly

Abstract

The present invention belongs to the field of composite material wall panel assembly and discloses a mechanical parameter equivalent calculation method for composite material wall panel assembly, which is used to quickly predict the assembly deformation, strain and stress of the wall panel after being subjected to external loads, as well as the distribution of residual assembly gaps. This method establishes a finite element equivalent model of composite material wall panel assembly based on the homogenization modeling method to reduce the number of model nodes and units, and uses commercial finite element software to extract the stiffness matrix. Based on the matrix characteristics, an efficient solution method is constructed, and the assembly process is abstracted as solving a quadratic programming function containing linear constraints and obtaining the wall panel assembly deformation. The wall panel strain and stress are obtained by combining homogenization decoupling and the finite element method. This method can greatly improve the computational efficiency of the numerical analysis of the composite material structure assembly process, realize real-time calculation in an assembly environment, or be used for optimization iterations that require repeated solutions.

Description

Technical Field

[0001] The present invention relates to the field of composite material wall panel assembly, and in particular to, but not limited to, a mechanical parameter equivalent calculation method for composite material wall panel assembly. Background Art

[0002] During the manufacturing process, composite structures can suffer from low geometric accuracy due to curing deformation, leading to gaps and interference during assembly. Because composites are anisotropic materials, their mechanical properties and failure modes are more complex than those of metals, making them susceptible to localized damage under stress during assembly. Therefore, it is necessary to regulate the deformation and internal stress of composite structures during assembly to reduce assembly stress and improve assembly coordination.

[0003] Currently, the control of composite structure assembly is generally analyzed and designed using the finite element method (FEM), which simulates the structure's assembly using finite element simulation software. In typical finite element modeling of composite structures, the prepreg layup sequence is followed, with the composite structure divided into units along its thickness and each layer assigned material orientation and properties. However, for large composite panel structures, which are widely used in aircraft structures, the large number of plies and the significant difference between the thickness of individual layers and the overall size result in an overly dense mesh in the thickness direction of the finite element equivalent model. Furthermore, due to their large size, the finite element mesh is refined as much as possible to ensure computational accuracy. This results in a very large number of mesh elements and nodes in the composite finite element equivalent model established using traditional methods. Furthermore, the contact between components involved in the assembly process makes conventional finite element calculation methods demanding on computer hardware and inefficient, which in turn affects the production cycle and lead time of aircraft products. Summary of the Invention

[0004] In view of this, an embodiment of the present invention provides an equivalent calculation method for mechanical parameters of composite material panel assembly, aiming to solve the problem of low efficiency when using traditional finite element simulation.

[0005] The technical solutions of the embodiments of the present invention are as follows:

[0006] An embodiment of the present invention provides a method for calculating equivalent mechanical parameters for composite material panel assembly, comprising:

[0007] Step S1: Based on the homogenization modeling method, the composite wall panel is divided into a preset number of sub-laminates in the thickness direction, each sub-laminate includes multiple adjacent single-layer panels, each sub-laminate is discretized using one unit in the thickness direction, and the homogenized material properties of the sub-laminate are calculated based on the single-layer properties;

[0008] Step S2: establishing a finite element equivalent model of the composite wall panel based on the definitions of the respective sub-laminates and their corresponding material properties, and extracting the stiffness matrix of the finite element equivalent model using finite element software; wherein the initial boundary conditions of the finite element equivalent model are set according to the assembly positioning method;

[0009] Step S3, defining key nodes in the finite element equivalent model according to the actual wall panel assembly situation;

[0010] Step S4, extracting node information and unit information from the finite element equivalent model, and constructing a quadratic programming function in combination with the stiffness matrix;

[0011] Step S5, constructing the load vectors of the key nodes according to the stress conditions of the composite panel assembly, solving the quadratic programming function to obtain the panel assembly deformation, and calculating the residual gaps between the composite panel and the front and rear spars after assembly;

[0012] Step S6: Based on the wall panel assembly deformation and the residual gap, the strain and stress of each sub-laminate are calculated using the finite element method, and the strain and stress of the sub-laminate are decoupled to calculate the strain and stress of the single-layer plate.

[0013] In some embodiments, the key nodes include load application nodes and displacement constraint nodes; the load application nodes are related nodes used to apply external loads on the finite element equivalent model during assembly; the displacement constraint nodes are nodes in the contact part of the wall panel and the skeleton in the finite element equivalent model, which are used to prevent penetration between the wall panel and the skeleton during assembly.

[0014] In some embodiments, in step S1, the elastic matrix of the sub-laminates divided in the composite wall panel in the global coordinate system is calculated by the following process:

[0015] The relationship between stress and strain for any single layer k in a sub-laminate s is:

[0016] Formula (1);

[0017] Formula (2);

[0018] in, is the elastic matrix of the single-layer plate k, i and j are row variables and column variables respectively, and are the stress and strain of the single-layer plate k in the material coordinate system of the current single layer;

[0019] Define a global coordinate system and transfer the strains and stresses of the single-layer plate from the material coordinate system to the global coordinate system:

[0020] Formula (3);

[0021] Formula (4);

[0022] in, is the coordinate transformation matrix, with m = cos(θ), n = sin(θ), where θ is the angle between the material coordinate system of the current single layer and the global coordinate system; and are the stress and strain of the single-layer plate k in the global coordinate system;

[0023] Elastic matrix of single-layer plate k In the global coordinate system It can be expressed as:

[0024] Formula (5);

[0025] in, is the coordinate transformation matrix The inverse matrix of

[0026] The elastic matrix of the sub-laminate s in the global coordinate system is in the form Expressed as:

[0027] Formula (6);

[0028] Formula (7);

[0029] Formula (8);

[0030] Formula (9);

[0031] Formula (10);

[0032] in, is the ratio of the thickness of the single layer k to the total thickness of the sub-laminate s to which it belongs, Single-layer board The ratio of the thickness of the laminate to the total thickness of the sub-laminate s to which it belongs, q is the total number of single layers contained in the sub-laminate s, is the elastic matrix of the single-layer plate k in the global coordinate system The amount in 、 、 、 The intermediate variables after processing, is the elastic matrix of the single-layer plate l in the global coordinate system The amount in 、 、 、 The intermediate variables after processing.

[0033] In some embodiments, in step S4, the stiffness matrix K of the finite element equivalent model is repartitioned according to the key nodes and the remaining nodes:

[0034] Formula (11);

[0035] in, To partition the matrix into blocks containing only key nodes, To block the matrix containing only the remaining nodes, and Both represent transition matrix blocks;

[0036] Solving matrix equations Solution And as the rest of the node displacement recovery matrix , further calculate the reduced stiffness matrix : ;

[0037] Define the displacement constraint vector based on the initial gap between the composite panel and the frame , and define the corresponding constraint coefficient matrix according to the global coordinate system ;

[0038] Set the load vector of key nodes according to the actual assembly process , and combined with the reduced stiffness matrix , displacement constraint vector , constraint coefficient matrix The quadratic programming function under the constraints is constructed as follows:

[0039] Formula (12);

[0040] in, is the minimum value of the quadratic programming function, is the displacement of the key node, for The transposed matrix of is the load vector of the key node The transposed matrix of .

[0041] In some embodiments, the panel assembly deformation is represented by the displacement of the key nodes and the displacement of the remaining nodes, and the quadratic programming function under the constraint condition is solved in step S5. The displacement of the key node corresponding to the minimum value , and calculate the displacements of the remaining nodes on the finite element equivalent model by the following formula : ;

[0042] Some nodes in the contact area between the wall panel and the frame are selected as displacement monitoring nodes, that is, the displacement monitoring nodes are part of the displacement constraint nodes. and initial gap , calculate the residual gap between the wall panel and the frame after assembly by the following formula for: .

[0043] In some embodiments, in step S6, the strains of all sub-laminates corresponding to the composite wall panel are calculated by combining the displacements of all nodes on the finite element equivalent model with the finite element method. and stress , and decouple, and calculate the strain of each single layer plate in the global coordinate system by the following formula and stress :

[0044] Formula (13);

[0045] Formula (14);

[0046] Formula (15);

[0047] Formula (16);

[0048] Then, the strain of each single-layer plate in the material coordinate system is obtained by converting formulas (3) and (4): and stress .

[0049] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0050] In an embodiment of the present invention, for composite wall panel assembly, a finite element equivalent model of composite wall panel assembly is established based on a homogenization modeling method to reduce the number of model nodes and units, and a commercial finite element software is used to extract the stiffness matrix. An efficient solution method is constructed based on the matrix characteristics, and the assembly process is abstracted as solving a quadratic programming function with linear constraints and obtaining the wall panel deformation. The wall panel strain and stress are obtained by combining homogenization decoupling and the finite element method. This method is used to quickly predict the assembly deformation, strain and stress of the wall panel after being subjected to external loads, as well as the distribution of residual assembly gaps. It can greatly improve the computational efficiency of the numerical analysis of the composite structure assembly process, realize real-time calculation in an assembly environment, or be used for optimization iterations that require repeated solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive work, among which:

[0052] Figure 1 A schematic flow chart of a method for calculating equivalent mechanical parameters for composite material panel assembly according to an embodiment of the present invention;

[0053] Figure 2 A diagram illustrating an example of assembling a composite material panel in a wing box according to an embodiment of the present invention;

[0054] Figure 3 A schematic diagram of the node for applying the initial hole perimeter load provided in an embodiment of the present invention;

[0055] Figure 4 A schematic diagram of the contact area and displacement constraint nodes on a composite material panel provided by an embodiment of the present invention;

[0056] Figure 5 A normal displacement cloud diagram of the composite material wall panel assembly provided by an embodiment of the present invention;

[0057] Figure 6 A distribution diagram of the residual gap between the composite material panel and the front and rear wing spars provided in an embodiment of the present invention;

[0058] Figure 7 A stress cloud diagram of the composite material wall panel assembly provided by an embodiment of the present invention;

[0059] Reference numerals:

[0060] 1-Front spar, 2-Wing rib, 3-Wall plate, 4-Rear spar. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments 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 part of the embodiments of the present invention, rather than all the embodiments. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention. 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.

[0062] In the following description, reference is made to “some embodiments”, which describes a subset of all possible embodiments, but it will be understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0063] It should be pointed out that the terms "first\second\third" involved in the embodiments of the present invention are only used to distinguish similar objects and do not represent a specific ordering of the objects. It can be understood that "first\second\third" can be interchanged with a specific order or sequence where permitted, so that the embodiments of the present invention described here can be implemented in an order other than that illustrated or described here.

[0064] Those skilled in the art will understand that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by those skilled in the art in the art to which the embodiments of the present invention pertain. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and, unless specifically defined as herein, should not be interpreted in an idealized or overly formal sense.

[0065] Figure 1 A schematic flow chart of a method for calculating equivalent mechanical parameters for composite material panel assembly provided by an embodiment of the present invention is shown in FIG. Figure 1 As shown, the method comprises at least the following steps:

[0066] Step S1: Based on the homogenization modeling method, the composite wall panel is divided into a preset number of sub-laminates in the thickness direction, each sub-laminate includes multiple adjacent single-layer panels, each sub-laminate is discretized using one unit in the thickness direction, and the homogenized material properties of the sub-laminate are calculated based on the single-layer properties;

[0067] Step S2: establishing a finite element equivalent model of the composite wall panel based on the definitions of the respective sub-laminates and their corresponding material properties, and extracting the stiffness matrix of the finite element equivalent model using finite element software; wherein the initial boundary conditions of the finite element equivalent model are set according to the assembly positioning method;

[0068] Step S3, defining key nodes in the finite element equivalent model according to the actual wall panel assembly situation;

[0069] Step S4, extracting node information and unit information from the finite element equivalent model, and constructing a quadratic programming function in combination with the stiffness matrix;

[0070] Step S5, constructing the load vectors of the key nodes according to the stress conditions of the composite panel assembly, solving the quadratic programming function to obtain the panel assembly deformation, and calculating the residual gaps between the composite panel and the front and rear spars after assembly;

[0071] Step S6: Based on the wall panel assembly deformation and the residual gap, the strain and stress of each sub-laminate are calculated using the finite element method, and the strain and stress of the sub-laminate are decoupled to calculate the strain and stress of the single-layer plate.

[0072] In this embodiment, step S1 is intended to simplify the structure of the complex composite wall panel and convert it into relatively simple sub-laminate units to facilitate subsequent analysis and calculation.

[0073] In this embodiment, the establishment of the finite element equivalent model in step S2 provides a basis for subsequent numerical analysis. The extraction of the stiffness matrix plays a key role in the subsequent solution of mechanical parameters. Reasonable initial boundary conditions can ensure that the simulation results are consistent with the actual assembly conditions.

[0074] In this embodiment, step S3 defines key nodes in the finite element equivalent model based on the actual wall panel assembly situation. These key nodes are often where stress is concentrated and has a significant impact on assembly accuracy. Identifying these nodes facilitates subsequent targeted analysis of the impact of assembly stress.

[0075] In this embodiment, the node information and unit information in step S4 include, but are not limited to, the node or unit number and coordinates. The constructed quadratic programming function can represent the minimization problem of the system's energy and other related mechanical properties under certain constraints, providing a mathematical model basis for the subsequent solution of parameters such as deformation.

[0076] In this embodiment, the load vectors at the key nodes in step S5 reflect the actual assembly stress conditions. Solving the quadratic programming function to obtain the panel assembly deformation results and calculating the residual gap can effectively evaluate the assembly quality. The panel assembly deformation results are represented by node displacements, including the displacements of key nodes and other nodes.

[0077] In this embodiment, step S6 can deeply analyze the mechanical state of each sub-laminate and single-layer plate, providing a detailed basis for the subsequent evaluation of the mechanical properties of the composite wall panel after assembly and whether damage occurs. It is a key link in the entire method to achieve the transition from macro-model analysis to micro-structural mechanical property analysis.

[0078] In an embodiment of the present invention, a homogenization modeling method is first used to equate multiple adjacent single layers in the composite material to a sub-laminate (discrete with only one unit in the thickness direction), establish a finite element equivalent model, and divide the key areas; then, based on the composition of the key areas, relevant variables and quadratic programming functions are constructed and the deformation of the composite wall panel is calculated; finally, through homogenization decoupling, the strain and stress of the composite wall panel are calculated using the finite element method based on the node displacements in the model.

[0079] In some embodiments, the key nodes include load application nodes and displacement constraint nodes; the load application nodes are related nodes used to apply external loads on the finite element equivalent model during assembly; the displacement constraint nodes are nodes in the contact part of the wall panel and the skeleton in the finite element equivalent model, which are used to prevent penetration between the wall panel and the skeleton during assembly.

[0080] In this embodiment, load application nodes are used to apply external loads, and the following nodes are typically selected: connection nodes, i.e., the connection points between the wall panel and components such as the front and rear wing spars, as these points are often subjected to external loads during assembly, such as nodes at bolt or rivet connections; stress concentration areas, i.e., areas on the wall panel prone to stress concentration, such as the edges, openings, or near stiffeners of the wall panel, which may be subjected to localized loads during assembly; and key support points, i.e., the support points of the wall panel during assembly, which need to bear the weight of the wall panel or other external loads to ensure the stability and rigidity of the wall panel. Preferably, the areas around bolt holes (for applying bolt loads) and the contact portion between the wall panel and the outer clip (for clip clamping) are selected as load application nodes.

[0081] In this embodiment, displacement constraint nodes are used to prevent penetration between the wall panels and the skeleton, and the following nodes are usually selected: contact nodes, that is, nodes where the wall panels are in direct contact with skeleton components such as front and rear wing beams. The displacement of these nodes needs to be constrained to ensure the assembly accuracy between the wall panels and the skeleton; key boundary nodes, that is, nodes at the boundaries where the wall panels contact the skeleton. The displacement constraints of these nodes can prevent unreasonable displacement or deformation of the wall panels during the assembly process; supported nodes, that is, nodes where the wall panels are supported during the assembly process. The displacement constraints of these nodes can ensure the stability and stiffness of the wall panels.

[0082] In some embodiments, in step S1, the elastic matrix of the sub-laminates divided in the composite wall panel in the global coordinate system is calculated by the following process:

[0083] The relationship between stress and strain for any single layer k in a sub-laminate s is:

[0084] Formula (1);

[0085] Formula (2);

[0086] in, is the elastic matrix of the single-layer plate k, i and j are row variables and column variables respectively, and are the stress and strain of the single-layer plate k in the material coordinate system of the current single layer;

[0087] Define a global coordinate system and transfer the strains and stresses of the single-layer plate from the material coordinate system to the global coordinate system:

[0088] Formula (3);

[0089] Formula (4);

[0090] in, is the coordinate transformation matrix, with m = cos(θ), n = sin(θ), where θ is the angle between the material coordinate system of the current single layer and the global coordinate system; and are the stress and strain of the single-layer plate k in the global coordinate system;

[0091] Elastic matrix of single-layer plate k In the global coordinate system It can be expressed as:

[0092] Formula (5);

[0093] in, is the coordinate transformation matrix The inverse matrix of

[0094] The elastic matrix of the sub-laminate s in the global coordinate system is in the form Expressed as:

[0095] Formula (6);

[0096] Formula (7);

[0097] Formula (8);

[0098] Formula (9);

[0099] Formula (10);

[0100] in, is the ratio of the thickness of the single layer k to the total thickness of the sub-laminate s to which it belongs, Single-layer board The ratio of the thickness of the laminate to the total thickness of the sub-laminate s to which it belongs, q is the total number of single layers contained in the sub-laminate s, is the elastic matrix of the single-layer plate k in the global coordinate system The amount in 、 、 、 The intermediate variables after processing, For a single-layer plate in the global coordinate system Elasticity Matrix The amount in 、 、 、 The intermediate variables after processing.

[0101] In this embodiment, the coordinate transformation matrix is ​​an orthogonal transformation matrix, and its elements are determined by the angle θ between the material coordinate system and the global coordinate system. It is worth noting that composite materials are orthotropic materials, and their mechanical properties are usually defined in the material coordinate system, such as the fiber direction (x1 direction), the transverse direction (x2 direction), and the thickness direction (x3 direction). In the establishment of the finite element model, the coordinates of all nodes are described in the global coordinate system. Therefore, the strain calculated directly based on the node displacement is described in the global coordinate system here, and the strain needs to be converted to the material coordinate system. For the sub-laminate s, the form of its elastic matrix in the global coordinate system can be calculated by weighted averaging the elastic matrices of all single-layer plates. Through the steps of this embodiment, the elastic matrix of each sub-laminate in the global coordinate system can be obtained. These elastic matrices will be used for subsequent finite element analysis and calculation of assembly deformation.

[0102] In some embodiments, in step S4, the stiffness matrix K of the finite element equivalent model is repartitioned according to the key nodes and the remaining nodes:

[0103] Formula (11);

[0104] in, To partition the matrix into blocks containing only key nodes, To block the matrix containing only the remaining nodes, and Both represent transition matrix blocks;

[0105] Solving matrix equations Solution And as the rest of the node displacement recovery matrix , further calculate the reduced stiffness matrix : ;

[0106] Define the displacement constraint vector based on the initial gap between the composite panel and the frame , and define the corresponding constraint coefficient matrix according to the global coordinate system ;

[0107] Set the load vector of key nodes according to the actual assembly process , and combined with the reduced stiffness matrix , displacement constraint vector , constraint coefficient matrix The quadratic programming function under the constraints is constructed as follows:

[0108] Formula (12);

[0109] in, is the minimum value of the quadratic programming function, is the displacement of the key node, for The transposed matrix of is the load vector of the key node The transposed matrix of .

[0110] In this embodiment, the stiffness matrix K is firstly re-divided into key nodes and other nodes, and then the displacement recovery matrix is ​​obtained by solving the matrix equation, and the original stiffness matrix K is projected into the key node space to obtain the reduced stiffness matrix .

[0111] In this embodiment, the displacement constraint vector It describes the relative displacement between the wall panel and the skeleton in the initial state; the constraint coefficient matrix A is used to describe the relationship between the constraint conditions and the displacement of key nodes.

[0112] In this embodiment, the quadratic programming function represents the elastic potential energy, represents the external potential energy, Represents the constraints that the displacements of key nodes must satisfy to ensure the assembly accuracy between the wall panels and the frame.

[0113] In some embodiments, the panel assembly deformation is represented by the displacement of the key nodes and the displacement of the remaining nodes, and the quadratic programming function under the constraint condition is solved in step S5. The displacement of the key node corresponding to the minimum value , and calculate the displacements of the remaining nodes on the finite element equivalent model by the following formula : ; Select some nodes in the contact area between the wall panel and the frame as displacement monitoring nodes, based on the normal displacement of the displacement monitoring nodes and initial gap , calculate the residual gap between the wall panel and the frame after assembly by the following formula for: .

[0114] In this embodiment, the displacement of the key node can be obtained by solving the quadratic programming problem. , which is the basis of the displacement field of the entire finite element equivalent model. Then the displacement recovery matrix is ​​used to recover the displacement of the remaining nodes. , ensuring that the displacement field of the entire model satisfies the constraints of the stiffness matrix. These displacement fields will be used to subsequently calculate the assembly deformation and residual gap. By comparing the initial gap and the normal displacement after assembly, the residual gap between the wall panel and the frame after assembly is calculated. , which is an important indicator for evaluating assembly quality. Through the above steps, we can fully understand the deformation and residual gap of the wall panel after assembly, providing a basis for subsequent strain and stress analysis.

[0115] In some embodiments, in step S6, the strains of all sub-laminates corresponding to the composite wall panel are calculated by combining the displacements of all nodes on the finite element equivalent model with the finite element method. and stress , and decouple, and calculate the strain of each single layer plate in the global coordinate system by the following formula and stress :

[0116] Formula (13);

[0117] Formula (14);

[0118] Formula (15);

[0119] Formula (16);

[0120] Then, the strain of each single-layer plate in the material coordinate system is obtained by converting formulas (3) and (4): and stress .

[0121] In this example, the finite element method (FEM) is used to calculate the strain of each element based on the nodal displacements. For each sub-laminate, the strain is calculated using the element's strain interpolation function and the nodal displacements. Stress is calculated based on the elastic matrix and strain of the sub-laminate. Through these steps, the strain and stress of each individual layer in the composite panel can be calculated in both the global and material coordinate systems. These results are crucial for evaluating the mechanical properties and potential damage of the panel after assembly.

[0122] The equivalent calculation method of mechanical parameters for composite material wall panel assembly is described below with reference to a specific embodiment. However, it should be noted that this specific embodiment is only for better illustrating the present invention and does not constitute an improper limitation to the present invention.

[0123] This specific embodiment considers the assembly process of a composite panel in a wing box, such as Figure 2 As shown, a uniform gap of 0.6 mm is left between the composite panel and the front and rear wing spars. The assembly process is to install bolts with a preload of 300 N in the initial holes numbered [2, 5, 8, 11, 13, 16, 17, 20, 21, 24]. The dimensions of the composite panel are 500 mm × 400 mm × 3.2 mm, and the ply orientation is [+45 / 90 / -45 / 0 / 90 / 0 / -45 / 90 / +45 / -45 / -45 / +45 / 90 / -45 / 0 / 90 / 0 / -45 / 90 / +45]. There are 20 layers in total, and the nominal thickness of a single layer is 0.16 mm. The composite panel contains 24 initial holes for installing bolts, and the initial hole diameter is 5 mm. The following operations are performed in sequence according to the steps proposed by the present invention:

[0124] Step 1: Equivalently divide the composite wall panel into several layers of sub-laminates and homogenize the composite wall panel. Each sub-laminate contains several adjacent single layers. The number of sub-laminates is allocated according to the specific situation of the analyzed problem, and the material properties of each sub-laminate are calculated separately.

[0125] The composite wall panel's plies are symmetrical about its midplane. In this specific embodiment, the midplane is used as the boundary for the sub-laminates, which are divided into upper and lower sub-laminates. The homogenization process in step 1 indicates that the material properties after homogenization are independent of the ply layup order within the sub-laminates. The ply layup angles in the upper and lower sub-laminates are consistent, resulting in consistent material properties for the upper and lower sub-laminates after homogenization. The material properties of the sub-laminates are calculated using the relevant formulas in step 1.

[0126] Step 2: Based on the definitions of each sub-laminate and its material properties in step 1, establish a finite element equivalent model corresponding to the composite wall panel, assign corresponding material properties to each sub-laminate, set boundary conditions according to the assembly positioning method, and output the stiffness matrix of the finite element equivalent model.

[0127] This specific embodiment uses Abaqus as the finite element modeling software. A finite element equivalent model of the composite wall panel is established in the software. The finite element equivalent model is established in a solid form, and the grid uses C3D8R units. The finite element equivalent model is divided into grids with a specification of 10 mm in the length and width directions, and divided into two layers in the thickness direction, representing the upper and lower sub-laminates respectively. According to the material properties of the sub-laminates calculated in step 1, the upper and lower sub-laminates of the finite element equivalent model are assigned. The finite element equivalent model contains a total of 4688 units and 4977 nodes. According to the bottom edge positioning and side ear positioning methods, constraints in corresponding directions are set on the bottom and side surfaces of the finite element equivalent model to simulate the positioning of the composite wall panel during assembly.

[0128] Step 3: Based on the actual panel assembly situation, define key nodes in the finite element equivalent model of the composite panel, mainly including load application nodes and displacement constraint nodes.

[0129] On the basis of establishing the finite element equivalent model, the key node set is defined, which mainly includes the following contents:

[0130] 1) Load application nodes: Load application nodes are the nodes on the finite element equivalent model of the wall panel used to apply external loads during assembly, such as the area around the bolt holes (used to apply bolt loads) and the contact area between the wall panel and the outer bracket (used for bracket clamping).

[0131] In this specific embodiment, the wall panels are assembled by installing bolts at the initial holes of the composite wall panels. Therefore, the load application nodes in this specific embodiment are the nodes around all the initial holes outside the finite element equivalent model, such as Figure 3 As shown in the figure, 32 nodes were selected around each primary hole to account for the head size of the connecting bolts. During bolt installation, the bolt load was evenly distributed among the 32 nodes around the corresponding primary hole. This means that the same concentrated force was applied to each node, simulating the bolt load during assembly. The composite panel has 24 primary holes, resulting in a total of 768 load-applying nodes.

[0132] 2) Displacement constraint nodes: Displacement constraint nodes are the nodes where the composite panels contact the frame in the assembly model. They are used to prevent penetration between the composite panels and the frame during assembly and include all possible contact areas between the composite panels and the frame.

[0133] In this embodiment, possible contact areas on the composite panel are as follows: Figure 4 As shown, the contact area represents the portion of the wall panel that will come into contact with the frame during assembly, so the displacement constraint nodes in this specific embodiment are selected in this area. In this area, a node is selected at an average interval of 20 mm, for a total of 96 nodes.

[0134] According to the above operations, there are 837 key nodes in this specific embodiment.

[0135] Step 4: Extract the node, unit and other information in the composite material finite element equivalent model, construct relevant variables and the quadratic programming function for solving the wall panel assembly deformation.

[0136] This specific embodiment uses MATLAB software to process the data of this step.

[0137] The 837 key nodes are taken as the key node set, and the remaining 4140 nodes are taken as the remaining node set. The reconstruction stiffness matrix K is constructed and the displacement recovery matrix of the remaining nodes is calculated. and the reduced stiffness matrix .

[0138] There are 837 key nodes, each of which contains 3 degrees of freedom in space. Therefore, a 2511×2511 identity matrix and a 2511×1 zero vector are created. The following operations are performed on the identity matrix and the zero vector respectively:

[0139] 1) Since the deformation direction of the wall panel during assembly is mainly in the negative direction of the Z axis, in the unit matrix, the value representing the Z direction corresponding to each displacement constraint node on the diagonal is set to -1 to form the constraint coefficient matrix ;

[0140] 2) There is a uniform gap of 0.6mm between the wall panel and the front and rear wing spars. The value representing the Z direction corresponding to each displacement constraint node in the zero vector is set to 0.6 to form the displacement constraint vector .

[0141] Step 5: Define the key node load vector, solve the quadratic programming function, and calculate the panel assembly deformation and residual gap.

[0142] The assembly step is to install bolts with a preload of 300N in the primary holes numbered [2, 5, 8, 11, 13, 16, 17, 20, 21, 24]. A 2511×1 zero vector is constructed, and the Z-direction positions of the key nodes corresponding to these holes in the vector are set to -9.375, indicating that a concentrated force of -9.375N is applied to each node along the negative direction of the Z axis. For each hole, the resultant force is 300N. This operation completes the load vector of the key node. Definition of .

[0143] In MATLAB, use the "quadprog" function to connect the variables constructed in step 4 with the load vector of the key node. As input to the function and run it to obtain the displacement of the key node and the remaining node displacements , the normal displacement of the composite panel is as follows Figure 5 As shown in Figure 2, the monitoring nodes are 24×2 nodes on the composite panel that are in contact with the front and rear wing spars. The displacements of these 48 nodes are extracted from the displacements of the key nodes to calculate the residual gap between the composite panel and the front and rear wing spars after assembly. The residual gap distribution is shown in Figure 2. Figure 6 shown.

[0144] Step 6: Use the finite element method to calculate the strain and stress of the sub-laminate, then homogenize and decouple the sub-laminate to calculate the strain and stress of each layer.

[0145] The strain and stress of the unit are calculated by the finite element method through the displacement of each node on the finite element equivalent model, and the strain and stress of each layer are obtained by the corresponding decoupling method. The stress cloud diagram is as follows: Figure 7 shown.

[0146] In summary, the above is one of the application examples listed in the present invention. The example only introduces the overall process of the implementation of the present invention, and some of the operational details are not described in detail.

[0147] The equivalent mechanical modeling method for composite panel assembly provided by the embodiments of this invention can also be applied to other simplified mechanical modeling involving elastic deformation, not just panel assembly. Furthermore, because this equivalent modeling method improves computational efficiency, it can also be applied to optimization iterations for specific environments. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application shall be included within the scope of protection of this application.

[0148] It should be understood that "one embodiment" or "an embodiment" mentioned throughout the specification means that the specific features, structures or characteristics related to the embodiment are included in at least one embodiment of the present invention. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. In addition, these specific features, structures or characteristics can be combined in one or more embodiments in any suitable manner. It should be understood that in various embodiments of the present invention, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present invention. The serial numbers of the above-mentioned embodiments of the present invention are for description only and do not represent the advantages and disadvantages of the embodiments.

[0149] It should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus comprising the element.

[0150] In the several embodiments provided herein, it should be understood that the disclosed methods can be implemented in other ways. The methods disclosed in the several method embodiments provided herein can be combined arbitrarily, unless they conflict, to produce new method embodiments. The features disclosed in the several method embodiments provided herein can be combined arbitrarily, unless they conflict, to produce new method embodiments.

[0151] The above description is merely an embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A mechanical parameter equivalent calculation method for composite panel assembly, characterized in that: include: Step S1: Based on the homogenization modeling method, the composite wall panel is divided into a preset number of sub-laminates in the thickness direction, each sub-laminate includes multiple adjacent single-layer panels, each sub-laminate is discretized using one unit in the thickness direction, and the homogenized material properties of the sub-laminate are calculated based on the single-layer properties; Step S2: establishing a finite element equivalent model of the composite wall panel based on the definitions of the respective sub-laminates and their corresponding material properties, and extracting the stiffness matrix of the finite element equivalent model using finite element software; wherein the initial boundary conditions of the finite element equivalent model are set according to the assembly positioning method; Step S3, defining key nodes in the finite element equivalent model according to the actual wall panel assembly situation; Step S4, extracting node information and unit information from the finite element equivalent model, and constructing a quadratic programming function in combination with the stiffness matrix; Step S5, constructing the load vectors of the key nodes according to the stress conditions of the composite panel assembly, solving the quadratic programming function to obtain the panel assembly deformation, and calculating the residual gaps between the composite panel and the front and rear spars after assembly; Step S6: Based on the wall panel assembly deformation and the residual gap, the strain and stress of each sub-laminate are calculated using the finite element method, and the strain and stress of the sub-laminate are decoupled to calculate the strain and stress of the single-layer plate.

2. The method according to claim 1, characterized in that The key nodes include load application nodes and displacement constraint nodes; The load application node is a related node on the finite element equivalent model during assembly for applying external loads; the displacement constraint node is a node in the contact part between the wall panel and the frame in the finite element equivalent model, which is used to prevent penetration between the wall panel and the frame during assembly.

3. The method according to claim 1 or 2, characterized in that In step S1, the elastic matrix of the sub-laminates divided in the composite wall panel in the global coordinate system is calculated by the following process: The relationship between stress and strain for any single layer k in a sub-laminate s is: Formula (1); Formula (2); in, is the elastic matrix of the single-layer plate k, i and j are row variables and column variables respectively, and are the stress and strain of the single-layer plate k in the material coordinate system of the current single layer; Define a global coordinate system and transfer the strains and stresses of the single-layer plate from the material coordinate system to the global coordinate system: Formula (3); Formula (4); in, is the coordinate transformation matrix, with m = cos(θ), n = sin(θ), where θ is the angle between the material coordinate system of the current single layer and the global coordinate system; and are the stress and strain of the single-layer plate k in the global coordinate system; Elastic matrix of single-layer plate k In the global coordinate system It can be expressed as: Formula (5); in, is the coordinate transformation matrix The inverse matrix of The elastic matrix of the sub-laminate s in the global coordinate system is in the form Expressed as: Formula (6): Formula (7): Formula (8): Formula (9): Formula (10); in, is the ratio of the thickness of the single layer k to the total thickness of the sub-laminate s to which it belongs, Single-layer board The ratio of the thickness of the laminate to the total thickness of the sub-laminate s to which it belongs, q is the total number of single layers contained in the sub-laminate s, is the elastic matrix of the single-layer plate k in the global coordinate system The amount in 、 、 、 The intermediate variables after processing, is the elastic matrix of the single-layer plate l in the global coordinate system The amount in 、 、 、 The intermediate variables after processing.

4. The method according to claim 3, characterized in that In step S4, the stiffness matrix K of the finite element equivalent model is repartitioned according to the key nodes and the remaining nodes: Formula (11); in, To partition the matrix into blocks containing only key nodes, To block the matrix containing only the remaining nodes, and Both represent transition matrix blocks; Solving matrix equations Solution And as the rest of the node displacement recovery matrix , further calculate the reduced stiffness matrix : ; Define the displacement constraint vector based on the initial gap between the composite panel and the frame , and define the corresponding constraint coefficient matrix according to the global coordinate system ; Set the load vector of key nodes according to the actual assembly process , and combined with the reduced stiffness matrix , displacement constraint vector , constraint coefficient matrix The quadratic programming function under the constraints is constructed as follows: Formula (12); in, is the minimum value of the quadratic programming function, is the displacement of the key node, for The transposed matrix of is the load vector of the key node The transposed matrix of .

5. The method according to claim 4, characterized in that The panel assembly deformation is represented by the displacement of the key nodes and the displacement of the remaining nodes. In step S5, the quadratic programming function under the constraint condition is solved. The displacement of the key node corresponding to the minimum value , and calculate the displacements of the remaining nodes on the finite element equivalent model by the following formula : ; Some nodes in the contact area between the wall panel and the frame are selected as displacement monitoring nodes. and initial gap , calculate the residual gap between the wall panel and the frame after assembly by the following formula for: .

6. The method according to claim 5, characterized in that In step S6, the strain of all sub-laminates corresponding to the composite wall panel is calculated by combining the displacement of all nodes on the finite element equivalent model with the finite element method. and stress , and decouple, and calculate the strain of each single layer plate in the global coordinate system by the following formula and stress : Formula (13); Formula (14); Formula (15); Formula (16); Then, the strain of each single-layer plate in the material coordinate system is obtained by converting formulas (3) and (4): and stress .

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