Assembly deformation stress cooperative control-oriented aircraft rigid-flexible hybrid structure multi-level analysis method

Abstract

The invention relates to the technical field of solid mechanical modeling, and solves the technical problem that an existing unified mechanism modeling strategy neglects geometric nonlinear characteristics of local weak-rigidity parts of an assembly, so that the static response prediction precision of the assembly is not high. The assembly deformation stress cooperative control-oriented aircraft rigid-flexible hybrid structure multi-level analysis method comprises the following steps: carrying out linear and nonlinear response analysis on finite element models of rigid framework parts and weakly rigid thin-wall parts, and establishing a linear mapping model and a nonlinear explicit mapping model; combining the two models to obtain a deformation stress analysis model; and obtaining a clamp holding force-displacement stress mapping model for representing the mapping relationship between the multi-point holding force of the assembly and the node displacement and the node stress based on the deformation stress analysis model. According to the method, the problems of lack of explanation and few mechanisms of a variable stiffness structure model are solved, and efficient prediction and damage early warning of the internal stress of the component are realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of solid mechanics modeling, and particularly relates to a multi-level analysis method for rigid-flexible mixed structure of an airplane aiming at assembly deformation stress collaborative control. BACKGROUND

[0002] The high maneuverability, high stealth and long service life requirements of the new generation of fighter aircraft put strict standards on the strength performance and aerodynamic shape accuracy of the aircraft structure. Compared with traditional aircraft, the new generation of aircraft has the characteristics of complex shape and large number of composite thin-walled components. The composite components are prone to hidden delamination and cracking damage under improper stress, which greatly reduces the load-carrying capacity and fatigue strength of the structure, and brings safety hazards to the normal service of the aircraft. The multi-objective quality requirements of geometric accuracy and mechanical performance of the aircraft body pose challenges to the prediction and control of the assembly deformation and stress of the aircraft structure.

[0003] Around the problem of deformation stress analysis of aircraft assembly structure, from the early rebound deformation analysis model, to the later linear response statistical analysis strategy combining finite element model, influence coefficient method and Monte Carlo simulation, to the current various data-driven models, domestic and foreign scholars have carried out a lot of fruitful research work, but there is still room for improvement. On the one hand, the current mechanism modeling focuses on linear structures with small deformation. For variable stiffness structures with geometric nonlinearity, simply using data-driven ideas and regarding the input-output relationship as a black box, the mapping model lacks sufficient explanatory and mechanical mechanism support. On the other hand, the internal part of the aircraft component is a complex structure composed of rigid skeleton parts and weak rigid thin-walled parts. The existing modeling strategies mostly regard the assembly structure as a whole and process it uniformly according to the linear or nonlinear response characteristics, which limits the accuracy and efficiency of the deformation stress analysis. SUMMARY

[0004] In view of the deficiencies of the prior art, the present application provides a multi-level analysis method for rigid-flexible mixed structure of an airplane aiming at assembly deformation stress collaborative control, which solves the technical problem that the existing unified mechanism modeling strategy ignores the geometric nonlinear characteristics of the local weak rigid parts of the assembly, resulting in low prediction accuracy of the static response of the assembly.

[0005] The present application aims to solve the deficiencies of the above-mentioned existing assembly structure deformation stress analysis technology, provides a stress prediction target for aircraft components during the assembly process, proposes a multi-level modeling and analysis method for the deformation stress of rigid-flexible mixed assembly structure, solves the problem of lack of explanation and mechanism of variable stiffness structure model, and realizes efficient prediction and damage warning of the internal stress of the component. Based on this, the following technical solutions are provided: A multi-level analysis method for rigid-flexible mixed structure of an airplane aiming at assembly deformation stress collaborative control, the method comprising the following steps: The body assembly structure parts are classified into rigid skeleton parts and weak rigid thin-walled parts, independent finite element models of each part are respectively established, and the finite element model area is divided into three parts of connecting interface, fixture holding area and free area; The linear response analysis of the finite element model of the rigid skeleton part under small deformation is carried out, and a linear mapping model is established to represent the mapping relationship between the node force and the node displacement and the node stress of the rigid skeleton part; The nonlinear response analysis of the finite element model of the weak rigid thin-walled part under large deformation is carried out, and a nonlinear explicit mapping model is established to represent the mapping relationship between the node force and the node stress and the node stress of the weak rigid part; According to the connecting constraint relationship between the parts, the linear mapping model of the rigid skeleton part and the nonlinear explicit mapping model of the weak rigid thin-walled part are combined to establish a deformation stress analysis model for representing the mapping relationship between the node force and the node displacement and the node stress of the whole assembly structure; Based on the deformation stress analysis model, the constant node gravity load and the holding force applied by the fixture are separated according to the fixture layout position, and a fixture holding force-displacement stress mapping model is obtained to represent the mapping relationship between the multi-point fixture holding force and the node displacement and the node stress of the assembly; According to the fixture holding force-displacement stress mapping model, the multi-point fixture holding force for stress balancing and deformation control of the assembly is obtained f 1~ f c , and the multi-point fixture holding force is optimized by using an intelligent optimization algorithm f 1~ f c An optimal set of multi-point fixture holding forces is obtained by optimization.

[0006] The technical scheme divides the whole structure into rigid skeleton parts and weak rigid thin-walled parts, establishes the finite element models of each part, carries out linear finite element analysis on the rigid skeleton parts, obtains multiple sets of simulation data of node force and displacement stress, identifies the node force-node displacement and node force-node stress mapping matrix (i.e. flexibility matrix and stress matrix) of the rigid skeleton part by using the least square method, and establishes a linear mapping model between the load and displacement stress.

[0007] Nonlinear finite element analysis is carried out on the weak rigid thin-walled part, the loading process is discretized into multiple load steps, the flexibility matrix and the stress matrix of the weak rigid part at each load step are extracted, the flexibility matrix and the stress matrix of the weak rigid thin-walled part at each load step are interpolated by using the Gaussian kernel function, the mapping relationship between the node force vector and the two matrices is fitted, and a nonlinear explicit mapping model between the load and displacement stress of the thin-walled part is established; According to the connection constraint relationship between the parts, the linear model of the rigid skeleton part and the nonlinear model of the weak rigid thin-walled part are combined to establish the analysis model of the whole assembly structure, the mapping relationship between the holding force of the tool fixture and the deformation stress of the assembly body is represented, and the online sensing of the stress deformation is realized based on the fixture holding force feedback.

[0008] On this basis, an assembly body multi-point holding force optimization model is constructed for the stress distribution equalization and deformation control target, an optimal set of holding force sizes is solved through a particle swarm algorithm, and the shape and performance collaborative control of the stress distribution and key point displacement of the assembly body is realized.

[0009] Through the above technical scheme, the aircraft rigid-flexible mixed structure multi-level analysis method for assembly deformation stress collaborative control is provided, and at least the following beneficial effects are achieved: 1. The assembly structure multi-level analysis model based on rigid-flexible part division has higher analysis efficiency and scalability compared with the traditional linear or nonlinear analysis model of the whole assembly, effectively avoiding the problem that the existing unified modeling strategy ignores the geometric nonlinear characteristics of the local weak rigid part of the assembly body, resulting in low prediction accuracy of the static response of the assembly body. When the boundary conditions or the connection relationship of the internal parts of the assembly body change, the method of the present application does not need to re-divide the grid to establish the finite element analysis model of the single part, and has stronger scalability and applicability compared with the machine learning model.

[0010] 2. The present application proposes a nonlinear interpolation method for flexibility matrix and stress mapping matrix for weak rigid thin-walled parts, establishes a nonlinear explicit mapping model between the external load and displacement stress of the weak rigid component, solves the problem of efficient static response analysis of large deformation parts in the geometric nonlinear state, and realizes the fast prediction of displacement stress response based on node force.

[0011] 3. The present application proposes a multi-point holding force optimization method for the stress distribution equalization target of the assembly body, which can effectively avoid the damage of the assembly body caused by local stress concentration compared with the traditional optimization strategy with single geometric accuracy and deformation as control target, and improve the fatigue strength of the aircraft assembly structure. DETAILED DESCRIPTION

[0012] The drawings described herein are used to provide further understanding of the present application, and form a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application, and do not constitute an improper limitation on the present application. In the drawings: Figure 1 The flowchart of the aircraft rigid-flexible mixed structure multi-level analysis method in the present application; Figure 2 The connection interface, holding area and free area division example of the part and the finite element model unit type schematic diagram in the present application; Figure 3 This is a Gaussian kernel function image used for nonlinear interpolation of the compliance matrix and stress matrix of weakly rigid thin-walled components in this invention; Figure 4 This is a schematic diagram of coordinate registration of the finite element models of the two connectors and node matching of the connection interface in this invention; Figure 5 This is a schematic diagram of the multi-level connection process of the part model of the complex multi-body assembly structure in this invention; Figure 6 The above figures show the simulation cloud diagram of the large deformation of the weakly rigid aluminum fuselage side plate sample in this invention and the displacement stress calculation error results of the nonlinear explicit mapping model relative to the simulation software. Figure 7 This is a comparison of the displacement stress field of the fuselage assembly sample before and after the optimization of the nodal force in the holding region in this invention. Detailed Implementation

[0013] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0014] This embodiment addresses the nonlinear analysis problem of weakly rigid thin-walled parts. The proposed Gaussian kernel interpolation method for the compliance and stress matrices relies on the prior law that "structures under similar load distributions have similar displacement-stress fields." The established phenomenological mechanical model effectively matches the load-displacement-stress nonlinear mapping relationship, offering stronger interpretability compared to machine learning models and eliminating the need for massive sample data and training time. Furthermore, this embodiment employs a multi-level structural mechanics modeling strategy for assemblies based on rigid-flexible part partitioning. Compared to current methods that treat the assembly structure as a whole and establish a unified linear or nonlinear model, this strategy offers higher analytical efficiency and scalability. Based on this, this embodiment proposes a multi-level analysis method for aircraft rigid-flexible hybrid structures oriented towards the coordinated control of assembly deformation stress. This enables efficient analysis and online sensing of aircraft assembly deformation stress, improving the uniformity of stress distribution and the geometric accuracy of key areas in the assembly structure. Figure 1 As shown, the method includes the following steps: S1. Classify the body assembly structure parts into rigid skeleton parts and weakly rigid thin-walled parts. Use eight-node hexahedral elements and eight-node continuous shell elements to mesh them respectively, establish independent finite element models for each part, and divide the finite element model region of each part into three parts: connection interface, fixture holding region, and free region.

[0015] To ensure analysis efficiency and facilitate the connection and combination of multiple finite element models of parts, finite element models of rigid skeleton parts and weakly rigid thin-walled parts were established using eight-node hexahedral elements and eight-node continuous shell elements, respectively. Figure 2 As shown. The mesh for the connection interface and the fixture-held region is finer and denser, and the stiffness matrix of each element is calculated using the quadratic full integration method. In contrast, the mesh for the free region is coarser and sparser, and the element stiffness matrix is ​​calculated using the linear reduced integration method. The integration method used here is a mature algorithm from finite element analysis software, and therefore will not be elaborated upon.

[0016] S2. Perform linear response analysis on the finite element model of the rigid skeleton part under small deformation to establish a linear mapping model to characterize the mapping relationship between nodal forces, nodal displacements, and nodal stresses of the rigid skeleton part. This embodiment obtains multiple sets of nodal force and displacement stress analysis data by performing linear finite element analysis on the rigid skeleton part. The least squares method is used to identify each element in the nodal force-nodal displacement mapping matrix (i.e., the compliance matrix) and the nodal force-nodal stress mapping matrix (i.e., the stress matrix) of the rigid skeleton part (hereinafter referred to as the compliance matrix and stress matrix, respectively). A linear analysis model of the deformation stress of the rigid skeleton part is established, that is, a linear mapping model between nodal forces, nodal displacements, and nodal stresses. The specific process includes: Let the total number of element nodes in the finite element model of any rigid skeleton part be... n Then, under the zero displacement constraint condition of the nodes in the clamp holding region, based on N Group( N ≥ n Sample data of nodal force vectors and corresponding nodal displacement stress vectors were used to identify the compliance matrix using the least squares method. D and stress matrix S The formula is: ; In the formula (•) + For the Moore-Penrose generalized inverse operator of a matrix; F t , d t , σ t They are respectively from N The matrix is ​​constructed from the sample data of nodal forces, displacements, and stress vectors, i.e.: ; Among them, matrix F t In f ij For the first i During the second loading, the finite element model of the rigid skeleton part...j A three-dimensional load vector applied to each node along the coordinate direction; matrix d t and σ t In d ij and σ ij The first i During the second loading, the finite element analysis software output the first... j The three-dimensional displacement vector and six-dimensional stress vector of each node along the coordinate direction.

[0017] Based on the identified compliance matrix D and stress matrix S External force vectors at nodes of a rigid skeleton part finite element model f p With displacement vector d p and stress vector σ p The mapping relationships can be expressed as follows: ; ; Wherein, displacement vector d p In d i and stress vector σ p In σ i ( i =1~ n ) represent the finite element models of the currently output parts. i Displacement and stress vectors of each node; external force vector f p In f j ( j =1~ n ) represents the current input number. j The load vector applied to each node. The above two equations represent the external force vector at each node of a single rigid frame component. f p to displacement vector d p and stress vector σ p The linear mapping model.

[0018] This embodiment applies multiple sets of different loads along the coordinate direction at each node, while applying zero displacement constraints at the nodes in the clamp holding area. The displacement stress data of each node is obtained through finite element analysis software. Based on multiple sets of node load and displacement stress samples, the least squares method is used to identify each element in the compliance matrix and stress matrix, and a linear mapping model between the node force and node displacement stress of the rigid part is established.

[0019] S3. A nonlinear response analysis under large deformation is performed on the finite element model of a weakly rigid thin-walled part to establish a nonlinear explicit mapping model characterizing the mapping relationship between nodal forces, nodal stresses, and nodal stresses in the weakly rigid part. In this embodiment, nonlinear finite element analysis is performed on the weakly rigid thin-walled part. The loading process is discretized into multiple load steps, and the nodal force and displacement stress data are obtained for each load step. The stiffness matrix, strain matrix, and constitutive matrix of the weakly rigid part under each load step are extracted. The nodal force-displacement stress mapping matrix under each load step is calculated. A Gaussian kernel function is used to interpolate the nodal force-displacement stress mapping matrix under each load step to fit the complex nonlinear mapping relationship between nodal forces, nodal displacements, and nodal stresses of the weakly rigid part, thus obtaining a nonlinear explicit mapping model between nodal forces, nodal displacements, and nodal stresses.

[0020] The stiffness matrix of a weakly rigid thin-walled member under each load step is obtained by iterative calculation based on the nodal displacements of the previous load step. The iterative update process of the stiffness matrix of a weakly rigid thin-walled member under multiple load steps is as follows: First, calculate the element stiffness matrix of each shell element in the finite element model of the weakly rigid thin-walled member, that is, the element stiffness matrix of the shell element in the first finite element model. i Under the load step, the first j The stiffness matrix expression for a shell element is: ; In the formula, V j For the first j The spatial domain encompassed by each unit body; These are the local coordinate variables of the unit cell; C It is the constitutive matrix that characterizes the stress-strain relationship of a material; it is a constant matrix that is independent of coordinate variables. For the first j The unit cell in the first i The strain matrix under each load step represents the partial differential relationship between the nodal strain and displacement of the element. Let be the partial derivative mapping matrix of the shape function, representing the th i Under the load step, the first j The interpolation shape function of the nodal displacements of each element with respect to the global coordinate variables x , y , z Partial derivatives to their local coordinate variables of the element The mapping relationship of partial derivatives. Wherein, , , The expressions for the three matrices are as follows: ; ; ; In the formula, E and These are Young's modulus and Poisson's ratio of the material, respectively. N j1 ~ N j8 The first j Displacement interpolation shape function for 8 nodes of a continuous shell element; , , The first i The first load step j The global coordinates of each element with 8 nodes are obtained by adding the initial node coordinates of the undeformed finite element model to the coordinates of the previous nodes. i The cumulative displacement over -1 load step is obtained. Shape function N j1 ~ N j8 Regarding the local coordinates of the unit The expression is: ; The shape function can be easily obtained from the above formula. N j1 ~ N j8 Regarding the local coordinates of the unit The first-order partial derivative at any point within the unit cell: They are related to shape functions N j1 ~ N j8 Regarding global coordinates x , y , z First-order partial derivative , , , ..., , , The following relationship exists between them: ; Based on the above formula, the shape function can be... N j1 ~ N j8Transform the partial derivative with respect to local coordinates at any point within the element to the global coordinate system, and substitute it into the strain matrix above. The expression for this is used to derive the strain matrix. The element value corresponding to the coordinates of that point within the cell, combined with the constitutive matrix. C and partial derivative mapping matrix The determinant value, using the previous stiffness matrix The expression is obtained by numerical integration. i The first load step j Stiffness matrix of a continuous shell element As described above regarding the specific measures of step S1, the numerical integration algorithm employs either quadratic full integration or linear reduced integration, depending on the region where the element is located. Given that these are mature algorithms, they will not be elaborated upon here.

[0021] In the i Based on the stiffness and strain matrices of each shell element under each load step, the stiffness matrix of each element is... and strain matrix By combining the individual components, we can obtain the overall stiffness matrix that characterizes the mapping relationship between nodal forces and nodal displacements in the entire model under this load step. K (i) and the global strain matrix characterizing the relationship between nodal displacement and strain. B (i) Furthermore, a zero constraint condition for the nodal displacements in the fixed region is introduced, and the overall stiffness matrix is ​​adjusted accordingly. K (i) The corresponding flexibility matrix is ​​obtained by performing the inversion operation. To obtain a continuous mapping model of the compliance matrix as a function of applied load, the assumption of "load similarity" is proposed: under external loads at similar nodes, the deformation and stress fields of weakly rigid thin-walled components are similar, thus their compliance matrices are similar, and the similarity of the compliance matrices is positively correlated with the similarity of the external loads. Based on this assumption, a Gaussian kernel function is used to interpolate the compliance matrix at each load step to obtain the compliance matrix of the weakly rigid thin-walled component. D Regarding external loads f p Explicit expression: ; In the formula, exp(•) is an exponential function with the natural constant e as its base, i.e., the Gaussian kernel function; f p These are the nodal force vectors of the finite element model; f i This is the first step in the nonlinear response analysis of weakly rigid thin-walled components. i The nodal force vectors applied in each load step; ω It is an adjustable parameter; lThis represents the total number of load steps. This expression can be viewed as a weighted sum of the compliance matrices for each load step, where... Corresponding to the first i The weighting coefficients of the load step compliance are shown in the following graph: Figure 3 As shown, the function value is non-negative and... The inverse correlation characteristic makes it a good measure of the compliance matrix of weakly rigid thin-walled members under the current applied load, and its relationship with the first... i Correlation between the compliance matrices of each load step.

[0022] In the compliance matrix D Regarding external loading f p Based on the interpolation expression, combined with the overall strain matrix B (i) constitutive matrix of materials C The stress matrix can be further obtained. S Regarding external loads f p Interpolation expression: ; Based on the compliance matrix of weakly rigid thin-walled components D and stress matrix S It can establish nodal force vectors for finite element models of weakly rigid thin-walled components. f p displacement vector to the node d p and stress vector σ p The nonlinear explicit mapping model, namely: ; ; This embodiment utilizes the finite element model of a weakly rigid thin-walled component established in S1 to conduct nonlinear response analysis. A maximum target load is set for each node, and zero displacement constraints are applied to the nodes in the clamping region. Starting from zero, nodal forces are applied stepwise along three coordinate directions at each node until the maximum target load is reached. The stiffness matrix representing the mapping relationship between nodal forces and nodal displacements under each load step is extracted from the finite element analysis software. The corresponding compliance matrix is ​​obtained through inverse operation of the stiffness matrix. Simultaneously, the corresponding stress matrix is ​​calculated based on the material constitutive matrix and the stiffness matrix. The compliance matrix and stress matrix under each load step are interpolated using a Gaussian kernel function to characterize the mapping relationship between the nodal force vector and the two matrices, thereby establishing a nonlinear explicit mapping model between nodal forces, nodal displacements, and nodal stresses for the weakly rigid thin-walled component under large deformation.

[0023] S4. Based on the connection constraints between parts, combine the linear mapping model of rigid skeleton parts and the nonlinear explicit mapping model of weakly rigid thin-walled parts to establish a deformation stress analysis model to characterize the mapping relationship between nodal forces, nodal displacements, and nodal stresses of the overall assembly structure. Building upon the linear mapping model established in step S2 and the nonlinear explicit mapping model established in step S3, register the coordinate systems of each part model according to the pairwise connection constraints and the geometric pose relationships between parts. Further utilize the force-position constraints at the connection interfaces to combine the nodal force-nodal displacement stress mapping models (i.e., compliance matrix and stress matrix) of each part, obtaining the external load and deformation stress mapping relationship of the overall assembly structure. Specifically: 1. Coordinate registration and connection interface node pairing of multiple part finite element models.

[0024] First, based on the mating relationship between the parts, establish the constraint relationships of the nodal forces and displacements in the connection region of the finite element model of the parts. Consider the finite element models of two mating parts A and B in different coordinate systems, and assume their... m The direction vectors of the normals of the connecting holes in their respective coordinate systems are as follows: n a1 , n a2 , ..., n am and n b1 , n b2 , ..., n bm The position vectors of the center of the hole end face in their respective coordinate systems are respectively p a1 , p a2 , ..., p am and p b1 , p b2 , ..., p bm .

[0025] Using the coordinate system of part A as a reference, the coordinates of the nodes in the finite element model of part B are transformed, and the corresponding rotation matrix is ​​adjusted. R Translation vector t The following least-squares optimization model is established with the objectives of aligning the connection hole positions and axial alignment: ; In the formula, n am , n bm These are parts A and B respectively.m The direction vectors of the normals of each connecting hole in their respective coordinate systems; p am , p bm These are parts A and B respectively. m The position vector of the center of each hole end face in its respective coordinate system; m This represents the total number of connecting holes in the finite element models of parts A and B in different coordinate systems.

[0026] Rotation matrix that satisfies the optimization objective of the above equation R Translation vector t The expression is: ; In the formula V and U It is an orthogonal matrix and satisfies: ; The orthogonal matrix can be solved using the singular value decomposition algorithm based on the above formula. U and V Singular value decomposition (SVD) is a mature numerical algorithm for solving matrix eigenvalues ​​and eigenvectors, which will not be elaborated here.

[0027] Using rotation matrix R Translation vector t Transform the nodal coordinates of the finite element model of part B to the model coordinate system of part A to complete the registration between the two model coordinate systems, that is: ; In the formula, p bi This is the finite element model of part B. i The original coordinates of each node; These are its transformed coordinates.

[0028] After coordinate registration was completed, the connecting holes and interfaces of parts A and B were closely fitted, as shown below. Figure 4 As shown, the mesh nodes on the connection interface of part B are traversed. For each node of part B, the spatial distance from each node on the connection interface of part A to that node is calculated. The node with the closest distance is used as the matching point pair and the degree of freedom coupling constraint is applied.

[0029] 2. Establishment of the nodal force-nodal displacement stress mapping model (i.e., deformation stress analysis model) of the assembly.

[0030] Based on the independent nodal force-nodal displacement-stress mapping models of the two parts, a displacement-stress analysis model for the assembly formed by them is established by applying degree-of-freedom coupling constraints to the matching nodes at the interface of the two parts. Here, it is assumed that the connection interface remains in close contact in the normal direction and does not experience tangential slippage. Therefore, the displacements of the matching nodes at the interface of the two parts are made equal along the three coordinate directions, and the external forces are equal in magnitude and opposite in direction. Let the first part be the mating region of part A. i ~ i + l The nodes are respectively related to the first node of part B. j~j + l Each node is a matching pair. The nodal force-nodal displacement stress mapping models for parts A and B are as follows: ; ; In the formula, d a,1 ~ d a,n , σ a,1 ~ σ a,n and f a,1 ~ f a,n Finite element models of part A are shown below. n Displacement, stress, and external force vectors of each node; d b,1 ~ d b,n , σ b,1 ~ σ b,n and f b,1 ~ f b,m Finite element models of part B are shown below. m The displacement, stress, and external force vectors of each node. The degrees of freedom and force constraint relationships of the matching nodes at the connection interface between parts A and B can be expressed as: ; In the formula, d a,i ~ d a,i+l and f a,i ~ f a,i+l These are the nodal displacements and nodal forces at the connection interfaces on part A, respectively. d b,j ~ d b,j+l andf b,j ~ f b,j+l These are the nodal displacements and nodal forces at the connection interface on part B, respectively. Substituting the constraint relationship above into the nodal force-nodal displacement equations of parts A and B and simplifying, we can obtain the mapping relationship between the nodal forces at the connection interface and the nodal forces outside the interface as follows: ; ; In the vectors on the right side of the equation above, f a,1 ~ f a,i-1 , f a,i+l+1 ~ f a,n These are the nodal forces located outside the connection interface in the finite element model of part A; f b,1 ~ f b,j-1 , f b,j+l+1 ~ f b,m These are the nodal forces located outside the connection interface in the finite element model of part B. From the above equation, the nodal forces on the connection interface can be expressed as nodal forces outside the interface: ; Let matrix M and N for: ; ; Then all ( ) of the finite element models of the two parts m + n ) nodal force vectors f a,1 ~ f a,n , f b,1 ~ f b,m You can use connections outside the interface ( m + n -2 l -2) nodal force vectors are represented as: ; Substituting the above equation into the mapping equations for nodal force-displacement and nodal force-stress of parts A and B, the mapping relationship between nodal force and displacement-stress of the assembly connecting the two parts can be expressed as: ; ; The vector on the left side of the equation above represents the assembly formed by combining parts A and B. m + n - l -1) displacements of nodes and all ( m + n The stress vector of each node; due to the coupling relationship of the displacement degrees of freedom of the nodes at the connection interface, the displacement vector retains the displacement of the nodes on part A located at the connection interface. d a,i ~ d a,i+l And those parts B with the same connection interface were excluded. l +1 node displacement d b,j ~ d b,j+l The vector on the right side of the equals sign represents all the external forces at the nodes outside the assembly's connection interface.

[0031] The above describes the process of obtaining the overall external force and displacement-stress mapping relationship of the assembly formed by connecting the nodes of two independent finite element model nodes of the two parts, based on the displacement and force transmission relationship of the connecting interface nodes. This process requires matrix... M Perform the inverse operation. M This matrix contains mapping information of nodal contact forces and displacements at the interface between two parts. When parts A and B are both rigid parts, their flexibility and stiffness do not change with external loads. M Since it remains unchanged, its inverse can be obtained through offline pre-calculation, thus not affecting the efficiency of online solution of structural deformation stress; however, when one of the two parts is a weakly rigid variable stiffness part, M -1 Online solutions are needed based on the external forces at the nodes, but because M It is ( l This is a matrix of order +1, meaning its order is equal to the number of matching node pairs at the interface between the two parts. Its size is much smaller than the overall stiffness and flexibility matrices of parts A and B respectively. Therefore, its inverse operation takes significantly less time than inverting the overall stiffness matrix when performing finite element static analysis on a single part. M -1 The calculation still has a relatively small impact on the online solution efficiency of the deformation stress of the assembly.

[0032] For more complex multi-body connection structures, the structure can be decomposed level by level into several independent parts. Based on the mapping relationship between external forces and displacement stresses at the nodes of the finite element model of each part established in step S2, the above process is repeated several times using the pairwise connection relationships between the parts, finally obtaining the overall external force and displacement stress mapping model of the assembly. Here is an example of multi-level modeling of an assembly, such as... Figure 5 As shown. First, according to step S2, establish independent finite element nodal force-nodal displacement stress mapping models for parts A1, B1, C1, and D1 respectively; then, according to step S4, combine and connect the models of parts A1, B1, C1, and D1 respectively to obtain the nodal force-nodal displacement stress mapping models of sub-assemblies A2 formed by connecting A1 and B1 and sub-assemblies B2 formed by connecting C1 and D1; finally, according to step S3, combine the analysis models of sub-assemblies A2 and B2 again to obtain the load-displacement stress mapping relationship of the final assembly A3.

[0033] S5. Based on the deformation stress analysis model, the steady nodal gravity load and the holding force applied by the fixture are separated according to the fixture layout position. The fixture holding force-displacement stress mapping model, i.e. static analysis model, is obtained to characterize the mapping relationship between the multi-point holding force of the assembly and the nodal displacement and nodal stress.

[0034] Based on the overall nodal force and nodal displacement stress mapping model of the assembly, the steady nodal gravity load and the holding force applied by the fixture are further separated according to the fixture layout, resulting in the mapping relationship between multi-point holding force and displacement stress of the assembly. Let the holding force vectors applied by the fixture to each element node within the holding region of the assembly be as follows: f 1~ f c The gravity vectors are respectively f g1 ~ f gc The displacement vectors are respectively d 1~ d c The stress vectors are respectively σ 1~ σ c The gravity vectors of the nodes in the remaining regions of the assembly are respectively f g,c+1 ~ f g,c+r The displacement vectors are respectively d c+1 ~ d c+r The stress vector is σ c+1 ~ σ c+rBased on the division of fixed and non-fixed regions, the nodal force vectors, nodal displacement-stress vectors, compliance matrix, and stress matrix of the assembly are divided into blocks. The nodal force-nodal displacement and nodal force-nodal stress mapping equations of the entire assembly are expressed as follows: ; ; Based on the above formula, the clamp holding force vector can be separated. f 1~ f c Thus, the clamp holding force and nodal displacement vector are obtained. d and stress vector σ The mapping model between them, namely: ; ; The above formula represents the optimization of fixture holding force in step S5, which aims to achieve stress equilibrium and deformation control of the assembly. f 1~ f c The foundation, among which, c Indicates the first c The nodal force exerted by a fixed node, r It is the position vector from the fixture holding area to the center of mass of the assembly.

[0035] S6. Obtain the multi-point clamping force based on the clamping force-displacement stress mapping model, aiming at stress equilibrium and deformation control of the assembly. f 1~ f c And an intelligent optimization algorithm is used to adjust the holding force of multi-point clamps. f 1~ f c The optimal set of multi-point clamping forces is obtained by performing optimization. f 1~ f c It is the tooling holding area of ​​the assembly. c The nodal forces applied at each node. Specifically, by constructing stress balance and deformation deviation indices for the assembly, an optimization model for clamp holding force is established to minimize stress distribution variance and deformation deviation. Then, the optimal holding force is solved using the particle swarm optimization algorithm.

[0036] This invention abandons the unified modeling strategy for deformation stress in large and complex aircraft assembly structures found in existing technologies. Instead, it divides the assembly structure into rigid skeleton parts with small deformations and weakly rigid thin-walled parts with large deformations. Linear constant stiffness analysis models and nonlinear variable stiffness analysis models are constructed for each part, respectively, to characterize the explicit mapping relationship between external forces and displacement stresses at the finite element model nodes of each part. Combined with the connection constraints between parts, a mapping from external forces to displacement stresses at the nodes of the entire assembly is established. This effectively avoids the problem of low accuracy in static response prediction of the assembly caused by neglecting the geometric nonlinear characteristics of locally weakly rigid parts in existing unified mechanism modeling strategies. When the boundary conditions of the assembly or the connection relationships of internal parts change, the method of this invention does not require re-meshing to establish finite element analysis models for individual parts, exhibiting stronger scalability and applicability compared to machine learning models.

[0037] This embodiment provides corresponding simulation experiments for the above method. First, a simulation verification of the nonlinear explicit mapping model of deformation stress for weakly rigid thin-walled aircraft parts is performed: To verify the accuracy of the nonlinear explicit mapping model based on Gaussian kernel function interpolation in step S3 for calculating the displacement stress field, a thin-walled side plate of an aluminum alloy fuselage was used as a sample. A set of nodal loads was given, and the displacement stress analysis results from the finite element software were compared with the analysis results from the nonlinear explicit mapping model established in this invention. Using the software results as a benchmark, the displacement stress analysis error of the mapping model was calculated. The simulation contour plot of the sample in the software is shown below. Figure 6 As shown in (a), the displacement stress analysis results of the software and the nonlinear explicit mapping model on 12 key nodes of the sample are compared. Figure 6 As shown in (b), the analytical data of the two at each node are in good agreement.

[0038] Secondly, simulation verification of the fixture holding force optimization effect for stress balancing and deformation control of the assembly: To verify the effect of multi-point holding force optimization in step S5 on stress distribution uniformity and key point displacement control, a fuselage assembly composed of an aluminum alloy side plate and a titanium alloy frame was used as a sample. A total of 12 regions on the assembly were designated as tooling holding areas. Loads were applied to each node in the holding areas based on the random initial values ​​before and the final results after optimization of the holding force vector. The stress and displacement distribution cloud diagrams of the assembly under the two sets of loads are shown below. Figure 7 As shown in (a) and 7(b), the comparison revealed that the stress and displacement were significantly lower after the holding force optimization than before the optimization.

[0039] In summary, the multi-level modeling and analysis method for aircraft rigid-flexible hybrid assembly structures proposed in this invention can be used for static response analysis of other mechanical assembly products or complex multi-body connection structures, and has broad potential application value.

[0040] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0041] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. Since the above embodiments are substantially similar to the method embodiments, their descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0042] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A multi-level analysis method for aircraft rigid-flexible hybrid structures oriented towards coordinated control of assembly deformation stress, characterized in that, The method includes the following steps: The assembly structure parts of the body are classified into rigid frame parts and weakly rigid thin-walled parts. Independent finite element models are established for each part, and the finite element model region is divided into three parts: connection interface, fixture holding region and free region. Linear response analysis under small deformation was carried out on the finite element model of the rigid skeleton part, and a linear mapping model was established to characterize the mapping relationship between nodal forces, nodal displacements and nodal stresses of the rigid skeleton part. Nonlinear response analysis under large deformation was carried out on the finite element model of weakly rigid thin-walled parts, and a nonlinear explicit mapping model was established to characterize the mapping relationship between nodal forces and nodal stresses in weakly rigid parts. Based on the connection constraint relationship between parts, a linear mapping model and a nonlinear explicit mapping model are combined to establish a deformation stress analysis model to characterize the mapping relationship between the overall nodal force of the assembly structure and the nodal displacement and nodal stress. Based on the deformation stress analysis model, the steady nodal gravity load and the holding force applied by the fixture are separated according to the fixture layout position, and a static analysis model is obtained to characterize the mapping relationship between the multi-point holding force of the assembly and the nodal displacement and nodal stress respectively. The multi-point clamping force is obtained based on the static analysis model to achieve the goals of stress equilibrium and deformation control of the assembly.

2. The multi-level analysis method for aircraft rigid-flexible hybrid structures according to claim 1, characterized in that, The establishment of the linear mapping model includes: Let the total number of element nodes in the finite element model of any rigid skeleton part be... n Then, under the zero displacement constraint condition of the nodes in the clamp holding region, based on N ≥ n The compliance matrix was identified using the least squares method from sample data of nodal force vectors and corresponding nodal displacement stress vectors. D and stress matrix S The formula is: ； In the formula (•) + For the Moore-Penrose generalized inverse operator of a matrix; F t , d t , σ t They are respectively from N The matrix is ​​constructed from sample data of nodal forces, displacements, and stress vectors. Based on the identified compliance matrix D and stress matrix S External force vectors at nodes of a rigid skeleton part finite element model f p With displacement vector d p and stress vector σ p The mapping relationships can be expressed as follows: ； ； Wherein, displacement vector d p In d i and stress vector σ p In σ i These represent the finite element models of the currently output parts. i Displacement and stress vectors of each node, i =1~ n External force vector f p In f j Indicates the current input number. j The load vector applied at each node, j =1~ n ; D nn and S nn These are the compliance matrices. D and stress matrix S The elements in.

3. The multi-level analysis method for aircraft rigid-flexible hybrid structures according to claim 1, characterized in that, The establishment of the nonlinear explicit mapping model includes: Nonlinear response analysis was performed on the finite element model of the weakly rigid thin-walled component. The maximum target load was set for each node. Zero displacement constraints were applied to the nodes in the clamp holding area. Starting from zero, nodal forces were applied stepwise at each node along the three coordinate directions until the maximum target load was reached. The stiffness matrix representing the mapping relationship between nodal forces and nodal displacements under each load step is extracted from the finite element analysis software. The corresponding flexibility matrix is ​​obtained through inverse operation of the stiffness matrix. At the same time, the corresponding stress matrix is ​​calculated based on the material constitutive matrix and stiffness matrix. The Gaussian kernel function is used to interpolate the compliance matrix and stress matrix under each load step to characterize the mapping relationship between the nodal force vector and the two matrices, and then a nonlinear explicit mapping model between nodal force, nodal displacement and nodal stress is established for weak rigid thin-walled members under large deformation.

4. The multi-level analysis method for aircraft rigid-flexible hybrid structures according to claim 3, characterized in that, The specific process of establishing the nonlinear explicit mapping model includes: the iterative update process of the stiffness matrix of the weakly rigid thin-walled member under multiple load steps, and the establishment of the nonlinear explicit mapping model between nodal forces, nodal displacements, and nodal stresses of the weakly rigid thin-walled member, namely: First, calculate the element stiffness matrix of each shell element in the finite element model of the weakly rigid thin-walled member, that is, the element stiffness matrix of the shell element in the first finite element model. i The first load step j Stiffness matrix of a continuous shell element The expression is: ； In the formula, V j For the first j The spatial domain encompassed by each unit body; These are the local coordinate variables of the unit cell; C It is the constitutive matrix that characterizes the stress-strain relationship of a material; it is a constant matrix that is independent of coordinate variables. For the first j The unit cell in the first i The strain matrix under each load step represents the partial differential relationship between the nodal strain and displacement of the element. Let be the partial derivative mapping matrix of the shape function, representing the th i Under the load step, the first j The interpolation shape function of the nodal displacements of each element with respect to the global coordinate variables x , y , z Partial derivatives to their local coordinate variables of the element Mapping relationship of partial derivatives; The stiffness matrix of each element and strain matrix By combining these components, we obtain the overall stiffness matrix that characterizes the mapping relationship between nodal forces and nodal displacements in the entire model under this load step. and the global strain matrix characterizing the relationship between nodal displacement and strain. ; Introducing zero-constraint conditions for nodal displacements in the fixed region, the overall stiffness matrix is... The corresponding flexibility matrix is ​​obtained by performing the inversion operation. ; The compliance matrix of a weakly rigid thin-walled component is obtained by interpolating the compliance matrix under each load step using a Gaussian kernel function. D Regarding external loads f p Explicit expression: ； In the formula, exp(•) is an exponential function with the natural constant e as its base, i.e., the Gaussian kernel function; f p These are the nodal force vectors of the finite element model; f i This is the first step in the nonlinear response analysis of weakly rigid thin-walled components. i The nodal force vectors applied in each load step; ω It is an adjustable parameter; l This is the total number of load steps; In the compliance matrix D Regarding external loading f p Based on the interpolation expression, combined with the overall strain matrix constitutive matrix of materials C The stress matrix is ​​obtained. S Regarding external loads f p Interpolation expression: ； Based on the compliance matrix of weakly rigid thin-walled components D and stress matrix S Establish nodal force vectors for a finite element model of a weakly rigid thin-walled component. f p displacement vector to the node d p and stress vector σ p The nonlinear explicit mapping model, namely: ； 。 5. The multi-level analysis method for aircraft rigid-flexible hybrid structures according to claim 1, characterized in that, The establishment of the deformation stress analysis model includes: coordinate registration of multiple part finite element models and pairing of connection interface nodes, as well as the establishment of the overall deformation stress analysis model of the assembly, namely: Using the coordinate system of part A as a reference, the coordinates of the nodes in the finite element model of part B are transformed, and the corresponding rotation matrix is ​​adjusted. R Translation vector t The following least-squares optimization model is established with the objectives of aligning the connection hole positions and axial alignment: ； In the formula, n am , n bm These are parts A and B respectively. m The direction vectors of the normals of each connecting hole in their respective coordinate systems; p am , p bm These are parts A and B respectively. m The position vector of the center of each hole end face in its respective coordinate system; m This represents the total number of connecting holes in the finite element models of parts A and B in different coordinate systems. Determine the rotation matrix that satisfies the optimization objective of the least squares optimization model. R Translation vector t The expression is: ； ； In the formula, V and U It is an orthogonal matrix; p ai , p bi The finite element models of parts A and B are respectively... i The original coordinates of each node; Using rotation matrix R Translation vector t Transform the nodal coordinates of the finite element model of part B to the model coordinate system of part A to complete the registration between the two model coordinate systems, that is: ； In the formula, These are its transformed coordinates; Traverse the mesh nodes on the connection interface of part B. For each node of part B, calculate the spatial distance from each node on the connection interface of part A to that node. Use the node with the closest distance as the matching point pair and apply degree of freedom coupling constraints.

6. The multi-level analysis method for aircraft rigid-flexible hybrid structures according to claim 1 or 5, characterized in that, The establishment of the overall deformation stress analysis model of the assembly includes: Let the mating region of part A be the first i ~ i + l The nodes are respectively related to the first node of part B. j~j + l Each node is a matching pair. The nodal force-nodal displacement stress mapping models for parts A and B are as follows: ； ； In the formula, d a,1 ~ d a,n , σ a,1 ~ σ a,n and f a,1 ~ f a,n Finite element models of part A are shown below. n Displacement, stress, and external force vectors of each node; d b,1 ~ d b,n , σ b,1 ~ σ b,n and f b,1 ~ f b,m Finite element models of part B are shown below. m Displacement, stress, and external force vectors of each node; The degrees of freedom and force constraint relationships of the matching nodes at the connection interface between parts A and B are expressed as follows: ； In the formula, d a,i ~ d a,i+l and f a,i ~ f a,i+l These are the nodal displacements and nodal forces at the connection interfaces on part A, respectively. d b,j ~ d b,j+l and f b,j ~ f b,j+l These are the nodal displacement and nodal force at the connection interface on part B, respectively. Substituting the constraint relationship above into the nodal force-nodal displacement equations of the two parts A and B, and rearranging, we obtain the mapping relationship between the nodal forces at the connection interface and the nodal forces outside the interface as follows: ； In the vectors on the right side of the equation above, f a,1 ~ f a,i-1 , f a,i+l+1 ~ f a,n These are the nodal forces located outside the connection interface in the finite element model of part A; f b,1 ~ f b,j-1 , f b,j+l+1 ~ f b,m These are the nodal forces located outside the connection interface in the finite element model of part B; The above equation can be used to represent the nodal forces on the connection interface in terms of the nodal forces outside the interface as follows: ； Let matrix M and N for: ； ； Then all ( ) of the finite element models of the two parts m + n ) nodal force vectors f a,1 ~ f a,n , f b,1 ~ f b,m Use the connection outside the interface ( m + n -2 l -2) nodal force vectors are represented as: ； Substituting the above equation into the mapping equations for nodal force-displacement and nodal force-stress of parts A and B, the mapping relationship between nodal force and displacement-stress of the assembly connecting the two parts is expressed as follows: ； ； The vector on the left side of the equation above represents the assembly formed by combining parts A and B. m + n - l -1) displacements of nodes and all ( m + n The stress vector of each node; due to the coupling relationship of the displacement degrees of freedom of the nodes at the connection interface, the displacement vector retains the displacement of the nodes on part A located at the connection interface. d a,i ~ d a,i+l And those parts B with the same connection interface were excluded. l +1 node displacement d b,j ~ d b,j+l The vector on the right side of the equals sign represents all the external forces at the nodes outside the assembly's connection interface.

7. The multi-level analysis method for aircraft rigid-flexible hybrid structures according to claim 1, characterized in that, The process of obtaining the static analysis model includes: Suppose that within the holding region of the assembly, the holding force vectors applied by the fixture to each element node are respectively... f 1~ f c The gravity vectors are respectively f g1 ~ f gc The displacement vectors are respectively d 1~ d c The stress vectors are respectively σ 1~ σ c The gravity vectors of the nodes in the remaining regions of the assembly are respectively f g,c+1 ~ f g,c+r The displacement vectors are respectively d c+1 ~ d c+r The stress vector is σ c+1 ~ σ c+r ; Based on the division of the fixture-held region and the free region, the nodal force vector, nodal displacement-stress vector, compliance matrix, and stress matrix of the assembly are divided into blocks. The nodal force-nodal displacement and nodal force-nodal stress mapping equations of the entire assembly are expressed as follows: ； ； Based on the above formula, the clamp holding force vector can be separated. f 1~ f c The clamp holding force and nodal displacement vectors are obtained. d and stress vector σ The mapping model between them, namely: ； ； In the formula, , , , All are flexibility matrices D and stress matrix S The known elements in.

8. The multi-level analysis method for aircraft rigid-flexible hybrid structures according to claim 1, characterized in that, The establishment of finite element models for rigid skeleton parts and weakly rigid thin-walled parts includes: The mesh was generated using eight-node hexahedral elements and eight-node continuum shell elements respectively, and independent finite element models of each part were established. In the connection interface and the fixture holding region, the mesh is fine and the nodes are dense, and the stiffness matrix of each element is calculated using the quadratic full integration method; while in the free region, the mesh is coarse and the nodes are sparse, and the element stiffness matrix is ​​calculated using the linear reduced integration method.

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