Design method for porous variable stiffness composite rib structures driven by principal stress traces

Abstract

This invention relates to the field of thin-walled stiffened structure design technology, and discloses a principal stress trajectory-driven design method for porous variable stiffness composite curved rib structures. The method includes the following steps: performing finite element analysis on the initial porous structure to extract the stress field and process it to generate a smooth and continuous principal stress direction field; tracing principal stress trajectories based on the principal stress direction field, and performing cluster analysis on the traced principal stress trajectory family to determine representative equivalent principal stress trajectories from the family, setting the equivalent principal stress trajectories as the non-uniform paths of the curved rib structure; describing the rib cross-sectional thickness distribution based on a piecewise cubic Hermite interpolation polynomial function; describing the curved fiber trajectory based on a linear function; and fusing the non-uniform rib path, the rib cross-sectional thickness distribution function, and the curved fiber trajectory function to generate a principal stress trajectory-driven porous variable stiffness composite curved rib structure. This fully explores the load-bearing potential of porous variable stiffness composite structures.

Description

Technical Field

[0001] This invention relates to the field of thin-walled stiffened structure design technology, and in particular, to a design method for porous variable stiffness composite material curved stiffener structures driven by principal stress traces. Background Technology

[0002] With the increasing demand for high-performance lightweight structures in aerospace and other fields, composite material structures are widely used due to their advantages such as high specific stiffness and high specific strength. In structural design, to meet the requirements of system integration or subsequent testing, it is often necessary to create holes in the main load-bearing structure. This inevitably causes stress concentration and local stiffness reduction, which in turn poses a challenge to the load-bearing efficiency and stability of the structure.

[0003] Variable stiffness composite material structure design is one of the effective ways to improve the performance of porous structures. Currently, research in this field mainly revolves around two directions: one is variable stiffness composite material design based on curved fiber trajectories, which adjusts the in-plane stiffness distribution by optimizing the fiber placement direction; the other is variable stiffness structure design based on curved stiffeners, which reconstructs the load transfer path by arranging curved stiffeners. Although both methods can theoretically effectively improve the performance of porous structures, they still face a common challenge in practical engineering design: how to efficiently and accurately determine the optimal curved layout scheme that matches the main load path.

[0004] Specifically, existing technologies present the following design challenges: First, for curved stiffening layouts, especially when the structure has openings, there is a lack of a systematic method that can automatically generate curved stiffening paths directly based on the structure's inherent mechanical properties. Current methods largely rely on the designer's experience or complex optimization algorithms, making it difficult to balance design efficiency with optimal solution performance. Second, in the design of variable stiffness composite material structures, curved fiber trajectory design and curved stiffening layout design are usually treated as two relatively independent steps, failing to fully utilize the potential of fibers and stiffeners in synergistic load-bearing and jointly optimizing structural stiffness distribution. Summary of the Invention

[0005] This invention provides a principal stress trajectory-driven design method for porous variable stiffness composite material curved reinforcement structures. It can automatically and rationally determine the curved reinforcement path based on the mechanical response of the structure, and realize the integrated collaborative design of the composite material curved fiber trajectory and curved reinforcement layout. This fully taps the load-bearing potential of porous variable stiffness composite material structures, thus solving the technical problems of existing design methods that rely on the designer's experience, are difficult to automatically determine the optimal curved reinforcement path, and fail to effectively realize the collaborative design of curved fiber trajectory and curved reinforcement layout.

[0006] This invention provides a principal stress trajectory-driven design method for porous variable stiffness composite rib structures, comprising the following steps: S100, performing finite element analysis on the initial porous structure, extracting the stress field and processing it to generate a smooth and continuous principal stress direction field; S200, tracing principal stress trajectories based on the principal stress direction field, and performing cluster analysis on the traced principal stress trajectory family to determine representative equivalent principal stress trajectories from the principal stress trajectory family, and setting the equivalent principal stress trajectories as non-uniform paths of the rib structure; S300, describing the rib section thickness distribution based on a piecewise cubic Hermite interpolation polynomial function; S400, describing the curved fiber trajectory based on a linear function; S500, fusing the non-uniform rib path determined in step S200, the rib section thickness distribution function determined in step S300, and the curved fiber trajectory function determined in step S400 to generate a principal stress trajectory-driven porous variable stiffness composite rib structure.

[0007] Further, step S100 specifically involves: conducting finite element analysis on the initial porous structure to obtain initial nodal stress field information, including the magnitude and direction of stress at the nodes; using finite element analysis to obtain the initial nodal stress field information, and solving for the magnitude and direction of principal stresses through eigenvalues ​​and eigenvectors to obtain a smooth and continuous principal stress direction field.

[0008] Furthermore, step S100 specifically includes:

[0009] S101: Given the initial design domain and boundary conditions of the porous structure, perform finite element analysis;

[0010] S102: Based on the finite element analysis results, obtain the stress field and extract the stress information at the nodes, including the magnitude and direction of the nodal stress. Taking a two-dimensional plane problem as an example, the stress matrix is ​​represented as follows:

[0011] ;

[0012] in, for x Principal stresses in the direction of for y Principal stresses in the direction of Shear stress on the plane;

[0013] S103: Calculate the magnitude and direction of the principal stresses at the nodes through eigenvalue and eigenvector decomposition. The principal stress values ​​and corresponding directions are expressed as follows:

[0014] ;

[0015] ;

[0016] in, and These are the maximum principal stress and the minimum principal stress, respectively; Indicates the direction angle of the principal stress; the corresponding direction vectors of the maximum and minimum principal stresses are respectively... and The magnitude and direction of the principal stresses at any point outside the nodes are obtained through interpolation. Therefore, for any point in the design space... Its direction vector is represented as and .

[0017] Further, step S200 specifically includes: S201, using the Euler method to trace the principal stress points, obtaining a series of principal stress points and forming corresponding principal stress trajectories; S202, selecting 2 principal stress points within the design domain. N S201 is used to obtain the corresponding principal stress traces and principal stress trajectories, and the maximum and minimum principal stress trajectories are constructed. S203: Based on the two principal stress trajectories obtained in step S202, namely the maximum principal stress trajectories and the minimum principal stress trajectories, hierarchical clustering is performed to divide similar principal stress trajectories into non-intersecting clusters. The cluster center in each cluster and the corresponding principal stress trajectories of each cluster center are selected to form the final equivalent principal stress trajectories. The non-uniform rib path layout is carried out according to the equivalent principal stress trajectories.

[0018] Furthermore, step S201 specifically includes:

[0019] S2011. Select an initial principal stress trace point. initial point The direction vector of the local principal stress at point is and ;

[0020] S2012: Using step size as... Perform iterative tracing to obtain the next principal stress point on the principal stress trajectory. The direction and magnitude of the principal stress at a given location are expressed as follows:

[0021] ;

[0022] in, Indicates starting from the initial point Perform bidirectional tracking, but at the starting point When located at the boundary, only one-way tracking is performed;

[0023] S2013: Repeat step S2012 to obtain a series of principal stress traces. When a new principal stress trace exceeds the design domain, the point where the principal stress direction intersects with the boundary is taken as the final principal stress trace. If the new principal stress trace satisfies the following formula, i.e., the new principal stress trace obtained by tracking falls into the opening area, then the tracking is terminated and the corresponding trace is marked as an invalid principal stress trace to ensure that such invalid traces are excluded when selecting the equivalent principal stress trace in the future. Finally, spline curves are used to connect all the trajectory points obtained by this tracking to form the principal stress trace.

[0024] ;

[0025] in, and This represents the coordinates of the current trace point. and The coordinates of the center of the hole are... Where is the opening radius, This is the tolerance parameter.

[0026] Further, step S202 specifically includes: S2021: Selecting 2 within the design domain according to design requirements. N 1 initial principal stress trace; S2022: based on the selected 2 N There are 1 initial principal stress trace points, among which N The initial point is generated according to the process in step S201 along the direction of the maximum principal stress. N Discrete maximum principal stress traces, in addition N The initial point is generated according to the process in step S201, along the direction of minimum principal stress. N These discrete minimum principal stress traces eventually form two families of principal stress traces: the maximum and the minimum.

[0027] Furthermore, step S203 specifically includes:

[0028] S2031. Perform uniform sampling for each principal stress trace, that is, uniformly discretize each principal stress trace into... A coordinate point, subsequently determined by A sample consisting of coordinate points is used to characterize the corresponding principal stress trace, i.e.:

[0029] ;

[0030] in, N The total number of principal stress traces in the current principal stress trace family is represented by . The total number of principal stress traces in the largest principal stress trace family is represented by . The total number of principal stress traces in the family of minimum principal stress traces is represented by . ;

[0031] S2032. Define the similarity between two clusters, dynamically optimize the clustering process, and realize intelligent clustering and grouping of principal stress trace families, specifically including:

[0032] The similarity between two clusters is defined using Ward's linkage criterion. Let there be similar clusters in the current principal stress trace family. and cluster Two clusters, with the number of principal stress traces in each cluster being respectively and Then the cluster centers of the two clusters are:

[0033] ;

[0034] The new cluster centers after the merger are:

[0035]

[0036] Based on the above definition, the principal stress trace family is intelligently clustered and grouped until the preset number of clusters is reached;

[0037] S2033. Obtain the corresponding clusters of the two types of principal stress trace families, find the cluster center of each cluster, and obtain a principal stress trace corresponding to each cluster center, which together form a complete equivalent principal stress trace. Finally, perform non-uniform rib path layout according to the equivalent principal stress trace, specifically including:

[0038] Construct from the family of maximum principal stress trajectories A cluster is constructed from the family of minimum principal stress trajectories. One cluster;

[0039] Based on the cluster center calculation formula in step S2032, the cluster center of each cluster and a principal stress trace corresponding to each cluster center are found. and The stripes together form a complete equivalent principal stress trace;

[0040] Based on the obtained equivalent principal stress trace, non-uniform rib paths are arranged along the equivalent principal stress trace.

[0041] Further, step 300 includes:

[0042] S301. Based on step S200, implement the non-uniform rib path layout setting driven by the principal stress trace;

[0043] S302: Construct an interpolation curve describing the thickness variation of the curved section using the PCHIP function. Specifically, it includes:

[0044] S3021, under normalization Select within the interval interpolation points

[0045] ;

[0046] The thickness curve should satisfy

[0047]

[0048] S3022, In order to obtain the principal stress trace driven by the first n The thickness of the curved rib is set as a variable. The value is 4, meaning four interpolation points are selected: To define the change in the cross-sectional thickness of the stiffener, the specific thickness of each stiffener can be calculated using this curve. For the first... n The thickness expression for a reinforcing bar is:

[0049] ;

[0050] in, For the first n The location of the root tendon.

[0051] Further, step 400 includes:

[0052] A linear function is used to describe the curved fiber trajectory for the fiber placement design of each layer in the laminate of a porous composite curved rib structure. The expression for the linearly changing fiber trajectory direction angle is:

[0053] ;

[0054] in, Indicates the length of the region. Indicates the trajectory of the curve in x The direction angle, and They are respectively and The direction of the location.

[0055] Further, step 500 specifically involves: constructing a pore-containing variable stiffness composite rib structure driven by principal stress traces based on the non-uniform rib path obtained in step S200, the rib section thickness set by the PCHIP function obtained in step S300, and the curved fiber trajectory of the laminate designed by the linear function obtained in step S400.

[0056] Furthermore, step 500 specifically includes:

[0057] S501. Each equivalent principal stress trace (i.e., non-uniform rib path) determined in step S200 is taken as a corresponding reference curve in three-dimensional space. It is the geometric center line of the stiffener, which establishes the accurate position and direction of the rib in space and constitutes the geometric skeleton of the entire rib structure.

[0058] S502. Based on the rib section thickness distribution function defined by the PCHIP function in step S300, assign a constant section thickness value to each rib. In 3D CAD or finite element preprocessing software, create a 3D solid model with a constant rectangular section (its width is determined by the output value of the PCHIP function corresponding to that rib) for each independent rib path. This step generates a 3D rib model, in which each rib has a constant thickness that remains unchanged along its entire length, but the thicknesses of different ribs can be different.

[0059] S503, the linear function defined in step S400 The described curved fiber trajectory is imparted to the composite laminate. According to The calculated fiber angle value defines the fiber direction of the composite layup at that point, and this direction is relative to the whole. xy In terms of coordinate system.

[0060] S504. Assemble and integrate the generated 3D solid model of the curved rib with variable thickness properties with the porous composite laminate with curved fiber properties. Finally, generate a complete, integrated digital model of a porous variable stiffness composite rib structure that is synergistically reinforced by the variable stiffness composite laminate and the variable stiffness curved rib.

[0061] The present invention has the following beneficial effects:

[0062] 1. It provides data-driven, automated, and intelligent rib path generation capabilities. The S200 step is based on the principal stress field obtained in the S100 step. Through an automated process of trace tracing and cluster analysis, it intelligently selects the equivalent principal stress traces representing the main load paths from the physical response of the structure as rib paths, solving the technical problems of relying on experience, strong subjectivity, and difficulty in obtaining the optimal path in traditional design.

[0063] 2. It achieves a high degree of matching between the stiffener path and the inherent load transfer path of the structure, improving the scientific nature and efficiency of the design from the source. Since the principal stress trajectory itself is the most important load transfer path inside the structure, using it as the stiffener path, the stiffeners are directly placed on the key load-bearing channels, enabling the stiffeners to participate in load transfer most effectively, avoiding the blindness of path placement, thus ensuring the superiority of the design scheme in principle and significantly improving design efficiency.

[0064] 3. It effectively avoids redundant stiffening design, achieving efficient material utilization and structural lightweighting. The clustering analysis step in S200 intelligently groups and filters the obtained principal stress trace families, identifying key force transmission paths that significantly contribute to the structural load-bearing capacity from a large number of initial traces as equivalent principal stress traces. This ensures that each stiffener ultimately arranged based on the equivalent principal stress traces corresponds to a major load path, thus avoiding unnecessary stiffeners on secondary or redundant force transmission paths. Precise material configuration is achieved from the layout source, ensuring structural performance while achieving the goal of lightweight design.

[0065] 4. Collaborative design and precise control of variable stiffness characteristics were achieved, fully leveraging the design potential of composite materials. Based on determining the optimal non-uniform stiffener path in step S200, step S300 sets different cross-sectional thicknesses for different stiffeners using a piecewise cubic Hermite interpolation polynomial (PCHIP) function, realizing customized design of stiffener cross-sectional properties (the same thickness for the same stiffener, different thicknesses for different stiffeners). Simultaneously, step S400 defines a curved fiber trajectory based on a linear function for the laminated plate in the porous composite stiffener structure, achieving collaborative optimization of the structural stiffness distribution and maximizing the performance potential of the composite material.

[0066] 5. A complete, systematic design methodology has been developed that can be directly used to guide manufacturing. From the reconstruction and smoothing of the principal stress field in step S100 to the intelligent curvature path generation in step S200, then to setting different cross-sectional thicknesses for different curvatures in step S300, and the design of the curved fiber trajectory of the laminate in step S400, and finally to the generation of the porous variable stiffness composite material curvature structure driven by the principal stress trajectory in step S500, the entire process is interconnected, forming a closed and repeatable design system. Its output is a parameterized digital model that can be recognized and executed by modern automated manufacturing equipment (such as automatic fiber placement machines), and has good engineering practical value.

[0067] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0068] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0069] Figure 1 This is a flowchart illustrating the design method for a porous variable stiffness composite material curved rib structure driven by principal stress traces according to a preferred embodiment of the present invention.

[0070] Figure 2 This is a flowchart of the principal stress trace family generation method based on the Euler method according to a preferred embodiment of the present invention;

[0071] Figure 3 This is a schematic diagram of principal stress trace tracking according to a preferred embodiment of the present invention, wherein... Figure 3 (a) is a diagram of the principal stress traces for unidirectional search. Figure 3 (b) is a diagram showing the principal stress traces for bidirectional search;

[0072] Figure 4 This is a schematic diagram of the termination condition for principal stress trace tracking in a preferred embodiment of the present invention;

[0073] Figure 5 This is a schematic diagram of a preferred embodiment of the present invention for obtaining equivalent principal stress trajectories based on hierarchical clustering, wherein... Figure 5 (a) is the clustering tree diagram corresponding to the family of maximum principal stress traces. Figure 5 (b) represents the family of maximum principal stress traces. Figure 5 (c) is the equivalent maximum principal stress trace diagram. Figure 5 (d) is the clustering tree diagram corresponding to the family of minimum principal stress traces. Figure 5 (e) is the family diagram of minimum principal stress traces. Figure 5 (f) is the equivalent minimum principal stress trace diagram. Figure 5 (g) is the complete equivalent principal stress trace diagram;

[0074] Figure 6 This is a schematic diagram of the stiffener section thickness setting based on the PCHIP function according to a preferred embodiment of the present invention;

[0075] Figure 7 This is a schematic diagram of a curved fiber trajectory described by a linear function according to a preferred embodiment of the present invention;

[0076] Figure 8 This is a schematic diagram of the geometric configuration and composition of a porous variable stiffness composite rib structure based on principal stress traces driven by a preferred embodiment of the present invention, wherein... Figure 8 (a) shows the linear function-type curved fiber trajectory and composite laminate layup design. Figure 8 (b) Layout diagram of the rib path driven by the principal stress trace. Figure 8 (c) is a curve of the cross-sectional thickness of the curved reinforcement. Detailed Implementation

[0077] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, the present invention can be implemented in many different ways as defined and covered below.

[0078] The principal stress trace-driven design method for porous variable stiffness composite rib structures in this embodiment includes the following steps:

[0079] S100. Perform finite element analysis on the initial porous structure, extract the stress field and process it to generate a smooth and continuous principal stress direction field.

[0080] S200. Based on the principal stress direction field, principal stress traces are traced, and cluster analysis is performed on the traced principal stress trace family to determine the representative equivalent principal stress trace from the principal stress trace family. The equivalent principal stress trace is set as the non-uniform path of the curved rib structure.

[0081] S300, based on piecewise cubic Hermite interpolation polynomial function to describe the thickness distribution of curved rib sections;

[0082] S400, describes the curve fiber trajectory based on a linear function;

[0083] S500, by combining the non-uniform rib path determined in step S200, the rib section thickness distribution function determined in step S300, and the curved fiber trajectory function determined in step S400, a pore-containing variable stiffness composite rib structure driven by principal stress traces is generated.

[0084] This invention presents a principal stress trace-driven design method for porous variable stiffness composite stiffener structures. Step S200, based on the principal stress field obtained in step S100, intelligently selects the equivalent principal stress traces representing the main load paths from the structure's physical response through an automated process of trace tracing and cluster analysis. This solves the technical problems of traditional design, which relies on experience, is highly subjective, and struggles to obtain the optimal path. Since the principal stress traces themselves are the most important load transfer paths within the structure, using them as stiffener paths allows stiffeners to be directly placed on the critical load-bearing channels, enabling them to participate in load transfer most effectively. This avoids the blind placement of paths, thus ensuring the superiority of the design scheme in principle and significantly improving design efficiency. The clustering analysis step in step S200 intelligently groups and filters the obtained principal stress traces, identifying the key force transmission paths that contribute most to the structural load-bearing capacity from a large number of initial traces as equivalent principal stress traces. This ensures that each rib arranged according to the equivalent principal stress trace corresponds to a major load path, thus avoiding unnecessary ribs on secondary or redundant force transmission paths. Precise material configuration is achieved from the layout source, ensuring structural performance while achieving lightweight design. Based on determining the optimal non-uniform rib path in step S200, step S300 sets different cross-sectional thicknesses for different ribs based on the piecewise cubic Hermite interpolation polynomial (PCHIP) function, realizing customized design of rib cross-sectional properties (the same thickness for the same rib, different thicknesses for different ribs). Simultaneously, step S400 defines a curved fiber trajectory based on a linear function for the laminate in the porous composite rib structure, achieving synergistic optimization of structural stiffness distribution and maximizing the performance potential of the composite material. From the reconstruction and smoothing of the principal stress field in step S100, to the intelligent path generation in step S200, then to setting different cross-sectional thicknesses for different curved ribs in step S300, and the design of the curved fiber trajectory of the laminate in step S400, and finally to the generation of the porous variable stiffness composite curved rib structure driven by the principal stress trace in step S500, the entire process is interconnected, forming a closed and repeatable design system. This invention's principal stress trace-driven design method for porous variable stiffness composite curved rib structures, through a combination of principal stress trace-driven design and intelligent screening using cluster analysis, successfully transforms the design of porous variable stiffness composite curved rib structures from experience-based to a data-driven, automated, and systematic modern design method. This ensures the scientific and optimal nature of the rib path, and through the coordinated variable stiffness design of the rib cross-sectional thickness and fiber trajectory, it achieves a significant improvement in structural load-bearing efficiency and a rational distribution of materials, providing reliable technical support for the design of high-performance lightweight composite material structures.

[0085] In this embodiment, step S100 specifically involves: performing finite element analysis on the initial porous structure to obtain initial nodal stress field information, including the magnitude and direction of stress at the nodes; using finite element analysis to obtain the initial nodal stress field information, and solving for the principal stress magnitude and direction through eigenvalues ​​and eigenvectors to obtain a smooth and continuous principal stress direction field. Through a standardized finite element analysis process, starting from the initial porous structure, the obtained nodal stress field information reflects the mechanical state of the structure under actual loads, ensuring that all subsequent design decisions are based on an accurate and smooth principal stress field, rather than arbitrary assumptions, thus guaranteeing the objectivity and scientific nature of the design scheme from the outset. By solving for eigenvalues ​​and eigenvectors, the nodal stress is decomposed into the magnitude and direction of the principal stress, where the principal stress direction clearly indicates the main load transmission direction at that point. The principal stress directions obtained directly from finite element nodes are discrete and may have abrupt changes. By processing them to make them smooth and continuous, a continuously changing vector field without singularities is formed in the structural domain. This ensures that when using numerical integration methods such as the Euler method for path tracing in the S200 step, the trace can extend smoothly and stably without failing to trace due to abrupt changes or interruptions in the direction field. This ensures the physical rationality and engineering usability of the finally generated rib path.

[0086] In this embodiment, step S100 specifically includes:

[0087] S101: Given the initial design domain and boundary conditions of the porous structure, perform finite element analysis;

[0088] S102: Based on the finite element analysis results, obtain the stress field and extract the stress information at the nodes, including the magnitude and direction of the nodal stress. Taking a two-dimensional plane problem as an example, the stress matrix is ​​represented as follows:

[0089] ;

[0090] in, for x Principal stresses in the direction of for y Principal stresses in the direction of Shear stress on the plane;

[0091] S103: Calculate the magnitude and direction of the principal stresses at the nodes through eigenvalue and eigenvector decomposition. The principal stress values ​​and corresponding directions are expressed as follows:

[0092] ;

[0093] ;

[0094] in, and These are the maximum principal stress and the minimum principal stress, respectively; Indicates the direction angle of the principal stress; the corresponding direction vectors of the maximum and minimum principal stresses are respectively... and The magnitude and direction of the principal stresses at any point outside the nodes are obtained through interpolation. Therefore, for any point in the design space... Its direction vector is represented as and .

[0095] Step S101 clarifies that the starting point is a given initial design domain and boundary conditions for the porous structure. It initiates the analysis for a specific engineering problem (porous structure) and specific working conditions (boundary conditions), ensuring that all subsequent analyses have clear engineering objectives and physical meaning, avoiding aimless analysis, and demonstrating its standardization and practicality as an engineering design method. Steps S102 and S103, by demonstrating the specific stress matrix and eigenvalue / eigenvector decomposition formulas, represent the plane stress state at each point (…). , , The stress is decomposed into two mutually perpendicular principal stress values ​​and directions, providing the most direct and scientific vector field basis for principal stress tracing in the S200 step. The principal stress direction at any point outside the node is obtained through interpolation, solving the problem that the finite element analysis result is a discrete field. It generates a smooth and continuous principal stress direction field covering the entire design domain (for any point, there is a corresponding principal stress direction vector). This continuous vector field is a prerequisite for using numerical integration methods such as the Euler method to perform continuous path tracing, ensuring that the final generated rib path is smooth and continuous, rather than being pieced together from discrete line segments.

[0096] In this embodiment, step S200 specifically includes:

[0097] S201. Use the Euler method to track principal stress points, obtain a series of principal stress points and form corresponding principal stress lines;

[0098] S202, Select 2 within the design domain N The initial principal stress traces are obtained, and the corresponding principal stress traces and principal stress trajectories are obtained by repeating step S201 to construct the maximum and minimum principal stress trajectories.

[0099] S203. Based on the two principal stress trace families obtained in step S202, namely the maximum principal stress trace family and the minimum principal stress trace family, hierarchical clustering is then performed to divide similar principal stress traces into non-intersecting clusters. The cluster center in each cluster and the corresponding principal stress trace of each cluster center are selected to form the final equivalent principal stress trace. Non-uniform rib path layout is then carried out according to the equivalent principal stress trace.

[0100] Step S201 employs the classic numerical integration method, the Euler method, to integrate and trace the continuous principal stress direction field generated in S100. This transforms the abstract, field-wide distributed vector directions into concrete geometric curves (principal stress traces) that characterize the load transfer path, thus automating the rib path design process. Step S202 involves selecting 2... N By establishing initial points and iteratively tracing, a family of maximum and minimum principal stress trajectories covering the entire design domain was constructed. This ensured that all potential and important load transfer paths were considered, providing a sufficient data foundation for subsequent optimization and selection. It avoided the risk of missing optimal paths due to improper initial point selection, and prevented material redundancy and excessive structural weight from directly using all principal stress trajectories for stiffening. Step S203 introduced hierarchical clustering, an unsupervised machine learning method, to automatically group trajectories based on their similarity, forming an intelligent selection process that could identify representative categories from a large number of similar redundant paths. After clustering, the principal stress trajectories corresponding to the cluster centers were selected as equivalent paths, which most effectively represented this type of load transfer behavior. This allowed for structural strengthening with the fewest possible stiffeners while ensuring load-bearing efficiency, achieving lightweight design.

[0101] In this embodiment, step S201 specifically includes:

[0102] S2011. Select an initial principal stress trace point. initial point The direction vector of the local principal stress at point is and ;

[0103] S2012: Using step size as... Perform iterative tracing to obtain the next principal stress point on the principal stress trajectory. The direction and magnitude of the principal stress at a given point are expressed as follows:

[0104] ;

[0105] in, Indicates starting from the initial point Perform bidirectional tracking, but at the starting point When located at the boundary, only one-way tracking is performed;

[0106] S2013: Repeat step S2012 to obtain a series of principal stress traces. When a new principal stress trace exceeds the design domain, the point where the principal stress direction intersects with the boundary is taken as the final principal stress trace. If the new principal stress trace satisfies the following formula, i.e., the new principal stress trace obtained by tracking falls into the opening area, then the tracking is terminated and the corresponding trace is marked as an invalid principal stress trace to ensure that such invalid traces are excluded when selecting the equivalent principal stress trace in the future. Finally, spline curves are used to connect all the trajectory points obtained by this tracking to form the principal stress trace.

[0107] ;

[0108] in, and This represents the coordinates of the current trace point. and The coordinates of the center of the hole are... Where is the opening radius, This is the tolerance parameter.

[0109] Step S201 clarifies the complete process from selecting an initial point and defining the direction vector to iterating with a fixed step size Δ. This step-by-step iterative numerical method (Eulerian method) transforms the physical concept of principal stress trajectories into a programmable and precisely executable algorithm, ensuring the repeatability and objectivity of the results. Employing a bidirectional tracking strategy, starting from any initial point, traces can be generated simultaneously along the principal stress direction and its opposite direction, thus obtaining a complete load path passing through that point. Clearly defined termination rules handle tracking to the vicinity of the opening area and to the boundary, ensuring that the generated traces completely cover the effective load-bearing area from boundary to boundary, avoiding incomplete paths. A clear judgment criterion was established: when a trace point falls into an opening area, tracking is terminated and the trace is marked as invalid. This mechanism has dual benefits: it automatically filters out interrupted load paths (such as paths entering holes), ensuring that the datasets processed by subsequent cluster analysis are all real and valid load transfer paths, guaranteeing the engineering significance of the final selected equivalent principal stress traces from the source; and it avoids unreasonable solutions such as incorrectly placing stiffener paths inside holes or outside the structure, directly ensuring the engineering feasibility of the design results. Using spline curves to connect discrete tracking points results in a smooth and continuous curve. Smooth paths avoid drastic changes in fiber direction, reduce manufacturing defects, and better meet the mechanical performance requirements of the structure.

[0110] In this embodiment, step S202 specifically includes:

[0111] S2021: Based on design requirements, select 2 within the design domain. N One initial principal stress trace point;

[0112] S2022: Based on selected 2 N There are 1 initial principal stress trace points, among which N The initial point is generated according to the process in step S201 along the direction of the maximum principal stress. N Discrete maximum principal stress traces, in addition N The initial point is generated according to the process in step S201, along the direction of minimum principal stress. N These discrete minimum principal stress traces eventually form two families of principal stress traces: the maximum and the minimum.

[0113] Step S202: Based on design requirements, select 2 in a planned manner. N Starting from a single initial point, and clearly distinguishing between the directions of the maximum and minimum principal stresses for tracing, ensures that the constructed trace family comprehensively and systematically covers all possible major load transfer paths within the design domain. This avoids path omissions due to the randomness of the initial point selection and provides an unbiased and complete data foundation for subsequent screening. The maximum and minimum principal stress traces together completely characterize the plane stress state within the structure. Step S202 explicitly constructs them as independent trace families, providing richer path choices for subsequent design. Designers can flexibly select the most suitable path from the combination of the two as the rib path according to specific performance objectives. This capture of the complete stress state and differentiation of paths enhances the flexibility and relevance of the design method in dealing with complex load conditions. Cluster analysis is a data-driven technique whose effectiveness heavily depends on the quantity and quality of input data. Step S202 generates a sufficient number of discrete traces representing different paths, providing the clustering algorithm with statistically significant data samples necessary for pattern recognition and automatic grouping.

[0114] In this embodiment, step S203 specifically includes:

[0115] S2031. Perform uniform sampling for each principal stress trace, that is, uniformly discretize each principal stress trace into... A coordinate point, subsequently determined by A sample consisting of coordinate points is used to characterize the corresponding principal stress trace, i.e.:

[0116] ;

[0117] in, N The total number of principal stress traces in the current principal stress trace family is represented by . The total number of principal stress traces in the largest principal stress trace family is represented by . The total number of principal stress traces in the family of minimum principal stress traces is represented by . ;

[0118] S2032. Define the similarity between two clusters, dynamically optimize the clustering process, and realize intelligent clustering and grouping of principal stress trace families, specifically including:

[0119] The similarity between two clusters is defined using Ward's linkage criterion. Let there be similar clusters in the current principal stress trace family. and cluster Two clusters, with the number of principal stress traces in each cluster being respectively and Then the cluster centers of the two clusters are:

[0120] ;

[0121] The new cluster centers after the merger are:

[0122]

[0123] Based on the above definition, the principal stress trace family is intelligently clustered and grouped until the preset number of clusters is reached;

[0124] S2033. Obtain the corresponding clusters of the two types of principal stress trace families, find the cluster center of each cluster, and obtain a principal stress trace corresponding to each cluster center, which together form a complete equivalent principal stress trace. Finally, perform non-uniform rib path layout according to the equivalent principal stress trace, specifically including:

[0125] Construct from the family of maximum principal stress trajectories A cluster is constructed from the family of minimum principal stress trajectories. One cluster;

[0126] Based on the cluster center calculation formula in step S2032, the cluster center of each cluster and a principal stress trace corresponding to each cluster center are found. and The stripes together form a complete equivalent principal stress trace;

[0127] Based on the obtained equivalent principal stress trace, non-uniform rib paths are arranged along the equivalent principal stress trace.

[0128] Sub-step S2031 of step S203 discretizes each continuous principal stress trace into a single point by uniform sampling. N pA standardized dataset composed of coordinate points transforms curves of varying shapes into structured data (coordinate point sets) that can be directly processed by computer algorithms, making subsequent cluster analysis based on numerical calculations possible and realizing the transformation from geometric form to data model. Sub-step S2032 adopts Ward's linkage criterion with a clear mathematical definition, aiming to minimize the variance increment within the merged clusters. Similar principal stress trajectories are divided into non-intersecting clusters. This process is entirely based on the objective laws of the data itself, eliminating human subjectivity in the design and ensuring the scientific and optimal nature of the grouping results. In sub-step S2033, the cluster center is determined and its corresponding actual trajectory is selected as the equivalent trajectory. This equivalent trajectory is geometrically the center of the entire cluster and best represents the common load-bearing characteristics of the trajectories in the corresponding cluster. Based on this, a single reinforcing rib is arranged, which can equivalently replace the reinforcement effect of all similar trajectories in the cluster. Thus, while ensuring structural performance, the number of ribs is minimized, fundamentally avoiding material redundancy and directly achieving the effect of structural lightweighting. Steps S2031 to S2033 form a complete closed loop of "data preparation → intelligent analysis → decision output", which can automatically select the most representative key paths from hundreds or thousands of possible load paths for rib design, freeing designers from the heavy manual comparison and selection work, and providing an efficient, reliable and optimal automated layout scheme generation method.

[0129] In this embodiment, step 300 includes:

[0130] S301. Based on step S200, implement the non-uniform rib path layout setting driven by the principal stress trace;

[0131] S302: Construct an interpolation curve describing the thickness variation of the curved section using the PCHIP function. Specifically, it includes:

[0132] S3021, under normalization Select within the interval interpolation points

[0133] ;

[0134] The thickness curve should satisfy

[0135]

[0136] S3022, In order to obtain the principal stress trace driven by the first n The thickness of the curved rib is set as a variable. The value is 4, meaning four interpolation points are selected. To define the change in the cross-sectional thickness of the stiffener, the specific thickness of each stiffener can be calculated using this curve. For the first... n The thickness expression for a reinforcing bar is:

[0137] ;

[0138] in, For the first n The location of the root tendon.

[0139] Step 300 involves fine-tuning the thickness of the curved rib section by introducing a parametric mathematical model. The PCHIP (piecewise cubic Hermite interpolation polynomial) function is used to construct the curved rib section thickness curve. The mathematical properties of this function determine that its interpolation results can not only accurately pass through preset thickness control points (such as...) t 1 , t 2 , t 3 , t 4) This ensures the continuity of the first derivative of the curve, resulting in a smooth, abrupt thickness distribution and avoiding new stress concentrations caused by sudden changes in thickness. The stiffener paths are uniformly mapped to... The normalized interval is used to express the thickness as a position. function t n =T(x n ) This is a highly parametric design method. This method adjusts the parameters of a few control points (…). t 1 to t 4) This allows for flexible and efficient definition of the cross-sectional thickness values ​​for different stiffeners, greatly improving the versatility and portability of the design scheme. In this embodiment, four interpolation points are preferentially used ( =4) defines the thickness value of each curved stiffener section, reflecting the design philosophy of controlling more with fewer points. The PCHIP function, determined by these four control points, inputs its normalized coordinates when calculating the thickness of any stiffener. The thickness curve function will then output the corresponding constant thickness value. t n With minimal design variables (four thickness values), the thickness of each stiffener can be assigned, avoiding excessive redundancy in design parameters while ensuring a smooth and continuous transition in thickness distribution between different stiffeners through the PCHIP function. This achieves an excellent balance between design efficiency and performance control. Since the thickness of each stiffener is explicitly expressed as a control point thickness value (…),… t 1 , t 2 , t 3 , t4) These thickness values ​​naturally become design variables for subsequent dimensional optimization; for example, buckling load or structural weight can be used as targets to automatically optimize these thickness control parameters, thereby further exploring the structural performance potential. This parameterization lays a solid foundation for higher-level performance optimization.

[0140] In this embodiment, step 400 includes:

[0141] A linear function is used to describe the curved fiber trajectory for the fiber placement design of each layer in the laminate of a porous composite curved rib structure. The expression for the linearly changing fiber trajectory direction angle is:

[0142] ;

[0143] in, Indicates the length of the region. Indicates the trajectory of the curve in any x The direction angle at that location, and They are respectively and The direction of the location.

[0144] The fiber orientation angle is defined using a piecewise linear function expression. Depending on location x The variation law of the stiffness field creates a continuous and smoothly varying stiffness field within the composite laminate. This variable stiffness characteristic can more effectively redistribute and transfer loads, and is particularly beneficial for mitigating stress concentration problems caused by discontinuous areas such as openings. The function in... x ≥0 or x <0 within the central axis ( x =0) is mirror symmetric, making the fiber trajectory laying highly regular and predictable. The entire complex curved fiber trajectory is determined only by the region length. Central angle and boundary angle With all three parameters completely determined, this highly parameterized approach allows designers or optimization algorithms to globally control the fiber orientation of the entire region by adjusting only a very small number of variables. This simplifies the design space and greatly facilitates further searching for the optimal fiber trajectory through numerical optimization methods, achieving a highly efficient balance between design efficiency and design freedom. Step S400, parallel to the variable thickness of stiffeners in S300, is a specific solution for variable stiffness in composite materials. It transforms the concept of curved fiber trajectory into a precise mathematical model that can be embedded in the overall design process. This allows the curved stiffener path based on the principal stress trajectory and the linearly changing fiber trajectory in the composite laminate to be collaboratively designed and integrated within a unified parameterized framework, jointly contributing to the improvement of the overall structural performance.

[0145] In this embodiment, step 500 specifically involves: constructing a porous variable stiffness composite material curved rib structure based on the non-uniform rib path obtained in step S200, the rib cross-sectional thickness set by the PCHIP function obtained in step S300, and the curved fiber trajectory of the laminate designed by the linear function obtained in step S400. S200 (rib path), S300 (rib cross-sectional thickness), and S400 (fiber trajectory) are collectively constructed into a unified digital structural model. The final generated structural model simultaneously possesses the rib path driven by the principal stress trace, the rib cross-sectional thickness based on the PCHIP function, and the linear function fiber trajectory, enabling active and precise control of the structure's stiffness distribution. The output is a digital model of a porous variable stiffness composite material curved rib structure driven by parameterized principal stress traces, containing complete geometric information (such as the rib path, rib cross-sectional thickness distribution, and curved fibers). Since the final model is directly constructed based on the aforementioned parameters with clear mathematical and physical meaning (principal stress field, equivalent principal stress trace, PCHIP function, and linear function), the distortion in the information transmission process is minimized. The final structural model accurately reflects the core design intent driven by the principal stress field and optimized by clustering, ensuring that the theoretical superiority of the design scheme can be transferred to the manufacturable product model without loss.

[0146] Step 500 specifically includes:

[0147] S501. Each equivalent principal stress trace (i.e., non-uniform rib path) determined in step S200 is taken as a corresponding reference curve in three-dimensional space. It is the geometric center line of the stiffener, which establishes the accurate position and direction of the rib in space and constitutes the geometric skeleton of the entire rib structure.

[0148] S502. Based on the rib section thickness distribution function defined by the PCHIP function in step S300, assign a constant section thickness value to each rib. In 3D CAD or finite element preprocessing software, create a 3D solid model with a constant rectangular section (its width is determined by the output value of the PCHIP function corresponding to the rib) for each independent rib path. This step generates a 3D rib model in which each rib has a constant thickness along its entire length, but the thicknesses of different ribs can be different, thus realizing the "variable stiffness" of the rib itself.

[0149] S503, the linear function defined in step S400 The described curved fiber trajectory is imparted to the composite laminate. According to The calculated fiber angle value defines the fiber direction of the composite layup at that point, and this direction is relative to the whole. xy In terms of coordinate system.

[0150] S504. Assemble and integrate the generated 3D solid model of the curved rib with variable thickness properties with the porous composite laminate model with curved fiber properties. Finally, generate a complete and integrated digital model of a porous variable stiffness composite rib structure that is synergistically reinforced by a variable stiffness composite laminate and a variable stiffness curved rib.

[0151] In practice, a design method for a porous variable stiffness composite stiffener structure driven by principal stress traces is provided. This structure is a variable stiffness composite material structure that integrates linear function-type curved fiber trajectories and principal stress trace-driven stiffener paths. The method includes: performing finite element analysis of the initial porous structure, extracting the magnitude and direction of nodal stresses, and constructing a smooth and continuous principal stress direction field; selecting initial principal stress traces within the design domain, tracing the principal stress traces using the Euler method, and obtaining two families of principal stress traces: the largest and smallest; combining hierarchical clustering technology to achieve intelligent clustering and grouping of principal stress trace families, and finding corresponding cluster centers and principal stress traces to form equivalent principal stress traces, based on which non-uniform stiffener path layout is set; further, describing the stiffener cross-sectional thickness distribution based on a piecewise cubic Hermite interpolating polynomial (PCHIP) function, and describing the curved fiber trajectory based on a linear function; thus, constructing a porous variable stiffness composite material stiffened structure that integrates linear function-type curved fiber trajectories and principal stress trace-driven stiffener paths. This invention can improve the buckling load capacity of the structure while ensuring the lightweight requirements of the reinforced structure with porous variable stiffness composite material.

[0152] Figure 1 A method for designing a porous variable stiffness composite rib structure driven by principal stress traces, as provided in this embodiment of the invention, includes the following steps:

[0153] S1: To obtain the maximum and minimum principal stress trace families of the structure, finite element analysis is first performed on the initial porous structure to obtain the stress magnitude and direction at the nodes. Then, the principal stress magnitude and direction are obtained through eigenvalue decomposition, thereby constructing a smooth and continuous principal stress field. Finally, two principal stresses are selected within the design domain. N Initial principal stress points are identified, and principal stress traces are tracked using the Euler method. Continuous and smooth principal stress trajectories are generated by fitting these discrete principal stress points, ultimately obtaining two families of principal stress trajectories: the largest and the smallest. The overall process is as follows: Figure 2 This includes the following sub-steps:

[0154] S11: Based on the finite element analysis results of the initial porous structure, a smooth and continuous principal stress field is constructed. S11 specifically includes:

[0155] S111: Given the initial design domain and boundary conditions of the porous structure, perform finite element analysis;

[0156] S112: Based on the finite element analysis results, obtain the stress field and extract the stress information at the nodes, including the magnitude and direction of the nodal stress. Taking a two-dimensional plane problem as an example, the stress matrix can be represented as:

[0157] ;

[0158] in, for x Principal stresses in the direction of for y Principal stresses in the direction of Shear stress on the plane;

[0159] S113: Calculate the magnitude and direction of the principal stresses at the nodes through eigenvalue and eigenvector decomposition. The principal stress values ​​and corresponding directions are expressed as follows:

[0160] ;

[0161] ;

[0162] in, and These are the maximum principal stress and the minimum principal stress, respectively; Indicates the direction angle of the principal stress; the corresponding direction vectors of the maximum and minimum principal stresses are respectively... and The magnitude and direction of the principal stresses at any point outside the nodes are obtained through interpolation. Therefore, for any point in the design space... Its direction vector is represented as and ;

[0163] S12: Following S11, the Euler method is used to trace the principal stress points, forming the corresponding principal stress traces, such as... Figure 3 S12 specifically includes:

[0164] S121: Select an initial principal stress trace point initial point The direction vector of the local principal stress at point is and ;

[0165] S122: Using step size as... Perform iterative tracing to obtain the next principal stress point on the principal stress trajectory. The direction and magnitude of the principal stress at a given point are expressed as follows:

[0166] ;

[0167] in, Indicates starting from the initial point Perform bidirectional tracking, but at the starting point When located at the boundary, only one-way tracking is performed;

[0168] S123: Repeat S122 to obtain a series of principal stress traces. When a new principal stress trace exceeds the design domain, the point where the principal stress direction intersects the boundary is taken as the final principal stress trace. If the new principal stress trace satisfies the following formula, i.e., the newly obtained principal stress trace falls into the opening area, then the tracking is terminated. Figure 4 The corresponding traces are marked as invalid principal stress traces to ensure that such invalid traces are excluded when selecting equivalent principal stress traces in the future. Finally, spline curves are used to connect all the trajectory points obtained in this tracking to form principal stress traces.

[0169] ;

[0170] in, and This represents the coordinates of the current trace point. and The coordinates of the center of the hole are... Where is the opening radius, This is the tolerance parameter.

[0171] S13: Following S12, select 2 within the design domain. N An initial principal stress trace is obtained, and the corresponding principal stress trace and principal stress line are obtained by repeating S12. Two families of principal stress lines, the largest and the smallest, are constructed. S13 specifically includes:

[0172] S131: Based on design requirements, select 2 within the design domain. N One initial principal stress trace point;

[0173] S132: Based on selected 2 N There are 1 initial principal stress trace points, among which The initial point is generated according to the S12 process along the direction of the maximum principal stress. Discrete maximum principal stress traces, in addition The initial point is generated according to the S12 process along the direction of minimum principal stress. The discrete minimum principal stress traces are used to construct two families of principal stress traces: the maximum and the minimum.

[0174] S2: Based on the two principal stress trace families obtained in S1, namely the maximum principal stress trace family and the minimum principal stress trace family, hierarchical clustering is performed to divide similar principal stress traces into non-overlapping clusters. The cluster center in each cluster and the corresponding principal stress trace of each cluster center are selected to form a complete equivalent principal stress trace. The non-uniform rib path layout is then designed according to the equivalent principal stress trace, including the following sub-steps:

[0175] S21: Perform uniform sampling for each principal stress trace, that is, uniformly discretize each principal stress trace into... A coordinate point, subsequently determined by A sample consisting of coordinate points is used to characterize the corresponding principal stress trace, i.e.:

[0176] ;

[0177] in, N The total number of principal stress traces in the current principal stress trace family is represented by . The total number of principal stress traces in the largest principal stress trace family is represented by . The total number of principal stress traces in the family of minimum principal stress traces is represented by . ;

[0178] S22: Following S21, define the similarity between the two clusters, dynamically optimize the clustering process, realize intelligent clustering and grouping of principal stress trace families, and obtain the clustering trees corresponding to the largest and smallest principal stress trace families, such as... Figure 5 (a) and Figure 5 (d) forming corresponding clusters, such as Figure 5 (b) and Figure 5 (e) Then, the cluster centers in each cluster are found, and the principal stress trajectories corresponding to the cluster centers are obtained, such as... Figure 5 (c) and Figure 5 (f) S22 specifically includes:

[0179] S221: Define the similarity between two clusters using Ward's linkage criterion, assuming there are similar clusters in the current principal stress trace family. and cluster Two clusters, with the number of principal stress traces in each cluster being respectively and Then the cluster centers of the two clusters are:

[0180]

[0181] S222: The new cluster centers after the merger are:

[0182] ;

[0183] Based on the above definition, the principal stress trace family is intelligently clustered and grouped until the preset number of clusters is reached;

[0184] S23: Following S22, obtain the corresponding clusters of the two types of principal stress trace families, find the cluster center of each cluster, and obtain a principal stress trace corresponding to each cluster center to form a complete equivalent principal stress trace. Finally, perform non-uniform rib path layout design according to the equivalent principal stress trace. S23 specifically includes:

[0185] S231: Construct from the family of maximum principal stress trajectories A cluster is constructed from the family of minimum principal stress trajectories. One cluster;

[0186] S232: Based on the cluster center calculation formula described in S222, find the cluster center of each cluster and a principal stress trace corresponding to each cluster center, such as... Figure 5 (c) and Figure 5 (f), and The stripes together form a complete equivalent principal stress trace, such as Figure 5 (g);

[0187] S233: Based on the equivalent principal stress trace obtained in S232, design a non-uniform rib path layout along the equivalent principal stress trace;

[0188] S3: Based on the non-uniform rib path layout obtained in S2, the rib section thickness is set using the PCHIP function, such as... Figure 6 The curved fiber trajectory of composite laminates is designed based on linear functions, such as... Figure 7 This leads to the construction of porous variable stiffness composite material rib structures, such as... Figure 8 Specifically, it includes the following sub-steps:

[0189] S31: Based on the method described in S2, implement the design of non-uniform rib path layout driven by principal stress traces, such as... Figure 8 (b);

[0190] S32: Construct an interpolation curve describing the thickness variation of the curved section using the PCHIP function. ,like Figure 8 (c), where variables are set It is determined by four parameters, namely, the selection of four interpolation points. To define the change in the cross-sectional thickness of the stiffener, the specific thickness of each stiffener can be calculated using this curve. For the first... n The thickness expression for a reinforcing bar is:

[0191] ;

[0192] in, For the first n The location of the root tendon.

[0193] S33: A linear function is used to describe the curved fiber trajectory, such as... Figure 7 To conduct the layup design of laminated plates in porous variable stiffness composite curved rib structures, such as... Figure 8 (a) The expression for the linearly changing fiber trajectory direction angle is:

[0194] ;

[0195] in, Indicates the length of the region. Indicates the trajectory of the curve in any x The direction angle at that location, and They are respectively and The direction of the location.

[0196] The present invention provides a principal stress trace-driven design method for porous variable stiffness composite material curved rib structures, which has the following advantages:

[0197] 1. Based on the principal stress direction field and hierarchical clustering, the equivalent principal stress trace was obtained. Then, based on the equivalent principal stress trace, the non-uniform rib path layout was designed. Compared with the traditional stiffened structure, the rib layout driven by the principal stress trace is closer to the optimal layout design. At the same time, the thickness distribution of the rib section was designed based on the PCHIP function, and the curved fiber trajectory was designed based on the linear function.

[0198] 2. Based on this design method, the coordinated design of curved fiber trajectory and curved stiffener layout and size can be realized. Compared with the traditional single variable stiffness composite material structure, the porous variable stiffness composite material curved rib structure driven by principal stress trajectory can give full play to the buckling resistance of variable stiffness composite material structure.

[0199] 3. This invention provides a new method for designing porous composite material structures in engineering structures.

[0200] Matters not covered in this invention are common knowledge.

[0201] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0202] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

[0203] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for the design of a composite tendon structure with a hole stiffness comprising a principal stress trajectory drive, characterized in that, The method comprises the following steps: S100, performing finite element analysis on the initial hole-containing structure, extracting a stress field and processing to generate a smooth and continuous principal stress direction field; S200, performing principal stress trace tracking based on the principal stress direction field, and performing cluster analysis on the principal stress trace family obtained by tracking to determine a representative equivalent principal stress trace from the principal stress trace family, and setting the equivalent principal stress trace as a non-uniform path of the curved tendon structure; Step S200 specifically comprises: S201, performing principal stress trace point tracking using the Euler method to obtain a series of principal stress trace points and form corresponding principal stress traces; S202, selecting 2N initial principal stress trace points in the design domain, and obtaining corresponding principal stress trace points and principal stress traces by repeating step S201 to construct maximum and minimum principal stress trace families; S203, based on the two types of principal stress trace families obtained in step S202, i.e., the maximum principal stress trace family and the minimum principal stress trace family, then performing hierarchical clustering, dividing similar principal stress traces into non-intersecting cluster clusters, selecting the cluster center in each cluster cluster, and the principal stress trace corresponding to each cluster center, to form the final equivalent principal stress trace, and performing non-uniform curved tendon path layout according to the equivalent principal stress trace; Step S203 specifically comprises: S2031、Uniformly sampling for each principal stress trajectory, that is, uniformly dispersing each principal stress trajectory into coordinate points, and then representing the corresponding principal stress trajectory by a sample composed of coordinate points, that is, wherein N is the total number of principal stress trajectories in the current principal stress trajectory family, the total number of principal stress trajectories in the maximum principal stress trajectory family is denoted by is the total number of principal stress trajectories in the minimum principal stress trajectory family ; S2032, defining the similarity between the two cluster clusters, dynamically optimizing the clustering process, and realizing intelligent clustering grouping of the principal stress trace family, specifically comprising: The similarity between two clusters is defined by Ward's linkage criterion, let the current principal stress trajectory family have similar clusters and cluster Two clusters, the number of principal stress trajectories in the two clusters are and The clustering centers of the two clusters are: The new cluster center after merging is: Based on the above definition, the principal stress trace family is intelligently clustered and grouped until the preset number of cluster clusters is reached; S2033, obtaining the corresponding cluster clusters of the two types of principal stress trace families, finding the cluster center of each cluster cluster, and obtaining a principal stress trace corresponding to each cluster center to form a complete equivalent principal stress trace, and finally performing non-uniform curved tendon path layout according to the equivalent principal stress trace, specifically comprising: from the family of maximum principal stress trajectories from the family of minimum principal stress trajectories clusters are constructed Based on the cluster center calculation formula of step S2032, the cluster center of each cluster is found, and a principal stress trajectory corresponding to each cluster center, and The bar trajectories together constitute a complete equivalent principal stress trajectory. Based on the obtained equivalent principal stress trace, the non-uniform curved tendon path is arranged along the equivalent principal stress trace; S300, describing the curved tendon cross-section thickness distribution based on a piecewise cubic Hermite interpolation polynomial function; S400, describing the curved fiber trajectory based on a linear function; S500, fusing the non-uniform curved tendon path determined in step S200, the curved tendon cross-section thickness distribution function determined in step S300, and the curved fiber trajectory function determined in step S400 to generate a principal stress trace driven hole-containing variable stiffness composite curved tendon structure.

2. The principal stress trajectory driven, hole-containing, variable stiffness composite tendon structure design method of claim 1, wherein, Step S100 specifically comprises: Performing finite element analysis on the initial hole-containing structure to obtain initial node stress field information, including stress size and direction at the node; Using finite element analysis to obtain initial node stress field information, obtaining principal stress size and direction through eigenvalue and eigenvector solution, thereby obtaining a smooth and continuous principal stress direction field.

3. The principal stress trajectory driven, hole-containing, variable stiffness composite tendon structure design method of claim 2, wherein, Step S100 specifically comprises: S101: Given the initial hole-containing structure design domain and boundary conditions, perform finite element analysis; S102: Based on the finite element analysis results, obtain the stress field, extract the stress information at the node, including the stress size and direction at the node, and taking a two-dimensional plane problem as an example, the stress matrix is represented as: wherein is x the principal stress in the direction is y the principal stress in the direction is the shear stress in the plane S103: Calculate the principal stress size and direction by eigenvalue and eigenvector decomposition, the principal stress value and the corresponding direction are expressed as: where, and are the maximum and minimum principal stresses, respectively; denotes the principal stress direction angle; the corresponding direction vectors of the maximum and minimum principal stresses are and The principal stress magnitude and direction at any point outside the nodes are obtained by interpolation, so for any point in the design space its direction vector is represented as and .

4. The principal stress trajectory driven, hole-containing, variable stiffness composite tendon structure design method of claim 1, wherein, Step S201 specifically includes: S2011. Select an initial principal stress point , the local principal stress direction vector at the initial point is and ; S2012: take a step of iterative tracking to obtain the next principal stress trajectory point on the principal stress trajectory the principal stress direction and size at the point, and its expression is: wherein, represents a bidirectional trace from the initial point but when the starting point is located at the border, only a unidirectional trace is performed; S2013: Repeat step S2012 to obtain a series of principal stress points, when the new principal stress point exceeds the design domain, the point where the principal stress direction intersects with the boundary is obtained as the final principal stress point; If the new principal stress point satisfies the following formula, that is, the new principal stress point obtained by tracking falls into the opening region, then terminate this tracking, and mark the corresponding trajectory as an invalid principal stress trajectory, ensure that such invalid trajectories are excluded when selecting equivalent principal stress trajectories, finally use spline curve to connect all the trajectory points obtained by this tracking to form the principal stress trajectory; wherein, and denotes the coordinate value of the current trace point, and denotes the coordinate value of the center of the opening circle, denotes the radius of the opening circle, denotes the tolerance parameter.

5. The principal stress trajectory driven, hole-containing, variable stiffness composite tendon structure design method of claim 4, wherein, Step S202 specifically includes: S2021: Select 2 initial principal stress points in the design domain according to design requirements N ​ S2022: generating a plurality of discrete maximum principal stress trajectories based on the selected 2 N initial principal stress points, wherein N the 2 N initial points are along the maximum principal stress direction according to the procedure of step S201, and additionally N the 2 N initial points are along the minimum principal stress direction according to the procedure of step S201, finally forming the maximum and minimum principal stress trajectory families.

6. The principal stress trajectory driven, hole-containing, variable stiffness composite tendon structure design method of claim 5, wherein, Step 300 includes: S301, based on step S200, realize the non-uniform curved tendon path layout driven by the principal stress trajectory; S302: An interpolation curve describing the change of the cross-sectional thickness of the curved tendon is constructed using the PCHIP function , and specifically comprises: S3021、In the normalization Selecting an interpolation point within the interval points ， Then the thickness curve should satisfy: S3022、to obtain the main stress trace driven by the first n The thickness of the strip curve, set variable 4, that is, select four interpolation points for To define the thickness of the curve muscle section changes, then the specific thickness of each reinforcing bar can be calculated by the curve, for the first n The thickness expression of the strip is: wherein is the n position of the root muscle strip.

7. The principal stress trajectory driven, hole-containing, variable stiffness composite tendon structure design method of claim 6, wherein, Step 400 includes: The linear function is used to describe the curve fiber trajectory, and each layer of the laminated plate in the curved tendon structure of the composite material with holes is designed, and the direction angle expression of the linearly changed fiber trajectory is: wherein, denotes the length of the region, denotes the direction angle of the curve trajectory at an arbitrary x point, and are the directions at and respectively.

8. The principal stress trajectory driven, hole-containing, variable stiffness composite tendon structure design method of claim 7, wherein, Step 500 specifically includes: S501, each equivalent principal stress trajectory determined in step S200 is regarded as a corresponding reference curve in three-dimensional space, the accurate position and direction of the curved tendon in space are established, and the geometric skeleton of the entire curved tendon structure is constituted; S502, based on the curved tendon cross-section thickness distribution function defined by the PCHIP function in step S300, a constant cross-section thickness value is given to each curved tendon; In three-dimensional CAD or finite element pre-processing software, a three-dimensional solid model with constant rectangular cross-section is created for each independent curved tendon path; S503, the linear function defined in step S400 is applied to the fiber angle value calculated in step S502 The described curvilinear fiber trajectory imparts to the composite laminate, according to The calculated fiber angle value defines the fiber direction of the composite ply at that point; S504, the three-dimensional solid model of the curved tendon generated above, which has the variable thickness attribute, is assembled and integrated with the composite material laminated plate with holes which has been given the curve fiber attribute; Finally, a complete and integrated digital model of the variable stiffness composite material curved tendon structure with holes is generated, which is reinforced by the variable stiffness composite material laminated plate and the variable stiffness curved tendon.

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