A method for CAD and CAE integration fast reanalysis based on volume subdivision

Abstract

The present application belongs to the technical field of CAD / CAE integrated design and structural reanalysis, and particularly relates to a CAD and CAE integrated fast reanalysis method based on volume subdivision, which deeply integrates volume subdivision technology and reanalysis technology, takes volume subdivision as a unified geometry-analysis representation framework of CAD / CAE, integrates local feature editing, discretization updating and finite element reanalysis in the same data structure, and constructs a fast reanalysis framework suitable for local feature addition and deletion, geometry deformation and topological change. The present application can efficiently process feature modification reanalysis scenarios of complex equipment, greatly improves the calculation efficiency while ensuring the analysis accuracy, completely solves the pain points of traditional methods, such as local feature modification triggering global reconstruction and high calculation cost, adapts to high-frequency feature iterative design requirements, and has extremely strong engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of CAD / CAE integrated design and structural reanalysis technology, specifically involving a rapid reanalysis method based on volume subdivision of CAD and CAE integration, which is suitable for rapid performance simulation analysis in scenarios of iterative modification (addition, deletion, geometric deformation, topology change) of structural features of complex engineering equipment. Background Technology

[0002] In the research and development of engineering equipment products such as automobiles, aerospace, and machinery, structural design and performance evaluation are highly dependent on frequent design iterations. Among these iterations, the local addition or deletion of structural features, geometric deformation, and topological changes are the most critical forms of iteration. Achieving efficient and high-precision numerical simulations after such feature modifications is key to shortening the development cycle and obtaining the optimal design solution.

[0003] The CAD / CAE integration technology aims to achieve seamless integration of design and simulation analysis, but it still faces bottlenecks in feature modification scenarios: On the one hand, there is an inherent heterogeneity between CAD geometric representation (B-Rep, NURBS, etc.) and CAE numerical discretization (finite element mesh). Preprocessing steps such as model conversion, mesh generation, and geometric repair are time-consuming and error-prone, especially for topological changes such as feature addition or deletion, where existing meshes may become invalid. On the other hand, existing reanalysis techniques are not deeply integrated with 3D volume subdivision techniques and cannot adapt to the characteristics of large support domains of volume subdivision basis functions. When feature modification causes local stiffness disturbances, problems such as basis vector correlation, unstable solutions, and insufficient accuracy are likely to occur, and it cannot efficiently handle common engineering modification scenarios such as feature addition or deletion and degree of freedom addition or deletion.

[0004] While traditional volume subdivision methods support unified modeling of 3D solids, they do not incorporate reanalysis techniques. Modification of local features can cause large-scale stiffness disturbances, making it impossible to reuse local meshes and historical analysis data. Existing integrated CAD / CAE methods (such as isogeometric analysis) can achieve a unified representation of geometry and analysis, but they are not compatible with topological modification scenarios such as feature addition and deletion. Furthermore, the reanalysis process still requires global solution, which cannot meet the needs of high-frequency feature iterative design. Summary of the Invention

[0005] This invention addresses the core deficiencies of existing technologies, builds upon existing research in reanalysis, and focuses on overcoming the bottleneck of deep integration between volume subdivision and reanalysis. It addresses scenarios involving structural feature modification (addition, deletion, geometric deformation, and topological changes), solving the following key technical problems:

[0006] 1. Solve the problems of heterogeneous discrete representation of CAD geometry and CAE analysis and loss of feature information transmission, realize the unified discrete representation of geometry and analysis, and fully retain feature information.

[0007] 2. To address the issue of local feature modifications triggering global reconstruction, we utilize the local editability of volume subdivision to update only the feature modification area, eliminating the need for global mesh redrawing.

[0008] 3. To address the high cost of repeated full-scale calculations after feature modification, an improved reanalysis algorithm is used to avoid repeated decomposition of the global stiffness matrix, thereby reducing computational costs.

[0009] 4. To address the issue of unusable historical analysis data before and after feature modification, a unified space of freedom is constructed to establish data relationships before and after feature modification, thereby enabling efficient reuse of historical information.

[0010] 5. To address the issue of poor adaptability of classic reanalysis methods to volume subdivision and feature modification scenarios, the reanalysis algorithm is optimized to improve solution stability and accuracy, and to adapt to core scenarios such as feature addition and deletion.

[0011] The specific technical solution of this invention is as follows:

[0012] A rapid reanalysis method integrating CAD and CAE based on volume subdivision is proposed. This method deeply integrates volume subdivision technology with reanalysis technology, using volume subdivision as a unified geometry-analysis representation framework for CAD / CAE. It integrates local feature editing, discretization updates, and finite element reanalysis into the same data structure, constructing a rapid reanalysis framework suitable for adding or deleting local features, geometric deformation, and topological changes. The specific technical solution is as follows:

[0013] Step 1: Construct a volume subdivision unified geometry-analysis discrete model

[0014] Based on a three-dimensional coarse control mesh (tetrahedral elements), a combination of Loop surface subdivision and midpoint volume subdivision is used to generate a smooth and continuous three-dimensional solid discrete model. Structural features (ribs, support columns, bosses, etc.) are integrated into the volume subdivision control mesh to achieve a unified geometric-analysis representation of the features.

[0015] The core advantages of this step are: volume subdivision retains strong local editability; feature geometry modifications only affect the finite support domain around the control points in the feature region, without disrupting the global mesh topology, and without requiring any modifications to non-feature regions; the implicit mesh generated by subdivision is directly used as the CAE analysis mesh, without additional geometric transformation and mesh repair, avoiding the loss of feature information during the transformation process; an adaptive subdivision strategy is adopted for the feature region, balancing feature analysis accuracy and overall computational efficiency, laying the foundation for subsequent local reanalysis.

[0016] Step 2: Establish a globally unified degree-of-freedom space and a local update mechanism for feature modifications

[0017] To adapt to various feature modification scenarios, a unified degree-of-freedom space is constructed. The node sets of the reference model (before feature modification) and the modified model (after feature modification) are projected onto the same global numbering system, enabling displacement, load, and stiffness increments to be represented within a unified indexing framework. The degree-of-freedom numbers, adjacency relationships, and most stiffness contributions of the unmodified region (non-feature region) can be directly reused; only the elements affected by the feature modification need to be updated, without global reconstruction.

[0018] For three typical feature modification scenarios in engineering, a dedicated local update strategy is designed:

[0019] 1. Feature deletion (such as rib deletion, support column removal): The corresponding element is deleted, and its stiffness contribution is removed from the global system. Only the element stiffness corresponding to the feature needs to be subtracted in the unified degree of freedom space, without affecting other regions.

[0020] 2. Feature geometric deformation (such as boss size adjustment, rib thickness change): The topology remains unchanged for the corresponding element geometric deformation. Only the node coordinates of the feature region need to be updated and the element stiffness of the region needs to be recalculated. There is no need to modify the mesh and stiffness of non-feature regions.

[0021] 3. Feature addition (e.g., adding a boss or rib): When the corresponding element is inserted, its stiffness is added as a local increment to the unified degree of freedom space. Only the local stiffness increment needs to be assembled in the feature addition area, without the need to reassemble the stiffness matrix globally.

[0022] The modified global stiffness matrix can be represented as the superposition of the reference stiffness matrix and the local stiffness changes in the feature modification region. This eliminates the need to reassemble the entire model, thus completely resolving the pain point of feature modification triggering global reconstruction.

[0023] Step 3: Establish a reference model and a unified node space

[0024] In the initial design phase, the global stiffness matrix, reference displacement vector, and reference load vector of the reference model (initial characteristic state) are obtained through complete finite element implicit analysis, and only the substructures corresponding to the unconstrained degrees of freedom are retained.

[0025] A unified node set is introduced, consisting of the union of the node sets of the reference model and the modified model. This set stores the coordinates of the unified nodes. After deducting boundary constraint nodes, the total number of unified degrees of freedom is calculated (each tetrahedral element node has three translational degrees of freedom). A one-to-one mapping relationship is established between the unified nodes and the nodes of the modified model, focusing on the node mapping of the feature modification region. This ensures accurate projection and restoration of displacement, stiffness, and other data before and after feature modification, enabling the reuse of historical analysis data.

[0026] Step 4: Unified modeling and assembly of three types of local modifications

[0027] Within a unified degree-of-freedom space, the modified global stiffness matrix is ​​the sum of the reference stiffness matrix and the stiffness increment of the feature modification region. For the three types of feature modification scenarios, a type identifier is assigned to each modified unit to achieve unified modeling.

[0028] 1. The element corresponding to the feature deletion: its stiffness is 0 after modification, and the stiffness increment is the negative value of the reference stiffness. Only the negative stiffness value needs to be added to the corresponding row block and column block, without affecting other areas of the global area.

[0029] 2. Elements corresponding to characteristic geometric deformation: The topology remains unchanged, only the node coordinates change, and the stiffness increment is the difference between the modified stiffness and the reference stiffness. Only the stiffness increment of the characteristic deformation region is updated.

[0030] 3. Add corresponding elements to the feature: its reference stiffness is 0, and the stiffness increment is the modified stiffness. Only the positive stiffness value needs to be added to the corresponding row and column blocks in the feature addition area. No global reassembly is required.

[0031] To address the issue of degree-of-freedom expansion caused by feature addition, an extended reference stiffness matrix is ​​constructed. A stiffness regularization term of a very small magnitude is introduced into the newly added degree-of-freedom sub-blocks to ensure the invertibility of the extended reference stiffness matrix without affecting the overall analysis accuracy. This solves the problem that existing reanalysis methods cannot adapt to feature addition.

[0032] Step 5: Construct an improved combinatorial approximate reanalysis algorithm that adapts to feature modifications.

[0033] For the optimization combinatorial approximation (CA) method in the scenario of volume subdivision and feature modification, a dimension-reduced basis vector is constructed for reanalysis, which solves the problems of basis vector correlation and unstable solution in the traditional CA method under the large support domain of volume subdivision.

[0034] Using the reference displacement solution as the initial basis vector, subsequent basis vectors are constructed recursively. This eliminates the need for explicit calculation of the inverse stiffness matrix; recursion is achieved solely through sparse matrix-vector multiplication and linear system solutions. A Schmidt orthogonalization method is employed to orthogonalize and normalize the basis vectors, improving numerical stability, avoiding linear dependence of basis vectors, adapting to stiffness perturbation scenarios caused by feature modifications, and enhancing the accuracy and stability of reanalysis.

[0035] Step 6: Construction and rapid solution of reduced-order equilibrium equations

[0036] The displacement vector is approximated as a linear combination of reduced-dimensional basis vectors and reduced-order coordinates. After substituting these into the equilibrium equations, the Galerkin projection method is used to construct the reduced-order equilibrium equations. The dimension of the reduced-order equations is much smaller than that of a fully free system, significantly reducing computational costs. The reduced-order equations are solved directly to obtain the reduced-order coordinates, thereby recovering the approximate displacement solution in a unified degree-of-freedom space.

[0037] By mapping nodes, the displacement solution is restored to the node order of the modified model, and the structural mechanical response of the modified feature region is output in a key way, which makes it easier for designers to optimize the feature structure in a targeted manner.

[0038] Step 7: Displacement result mapping recovery and iterative data reuse

[0039] 1. By unifying the node mapping relationship, the displacement solution in the unified degree-of-freedom space is restored to the node order of the modified model, and the structural mechanical response of the feature modification region is output as the main feature.

[0040] 2. Store the analysis data (stiffness matrix, displacement vector, basis vector, etc.) of the currently modified model as a new reference state for the next local feature modification iteration, supporting rapid reanalysis of multiple consecutive local feature modifications and improving the efficiency of high-frequency feature iteration.

[0041] This invention deeply integrates volumetric subdivision and reanalysis, along with a dedicated adaptation for feature modification scenarios, distinguishing it from existing reanalysis papers (which do not incorporate volumetric subdivision and do not adapt to feature addition / deletion scenarios). Specifically, it includes:

[0042] 1. Taking volume subdivision as the core, a unified geometry-analysis discrete representation framework for CAD / CAE is constructed, integrating structural features into the volume subdivision control mesh to achieve unified representation and local editability of features;

[0043] 2. Construct a unified degree-of-freedom space and node mapping method for the reference model and the modified model, focusing on implementing node mapping in the feature modification region to support the reuse of historical data;

[0044] 3. Achieve unified modeling and assembly of stiffness increments for three types of modifications: feature deletion, geometric deformation, and feature addition, enabling localized processing of feature modifications and avoiding global reconstruction;

[0045] 4. To address the degree of freedom expansion caused by feature addition, a weak regularization method for the extended reference stiffness matrix is ​​proposed to solve the problem of non-invertibility of the stiffness matrix and adapt to feature addition scenarios.

[0046] 5. An improved combined approximation order reduction reanalysis algorithm that integrates Schmidt orthogonalization is used to adapt to stiffness disturbances caused by the characteristics of large support domains in volume subdivision and feature modifications, thereby improving the stability and accuracy of reanalysis.

[0047] The beneficial effects of the technical solution of this invention are as follows:

[0048] 1. Avoids repetitive mesh generation and adapts to feature modifications: Volume subdivision unifies the discrete representation of geometry and analysis, and local feature modifications only update the affected area, completely avoiding the traditional re-meshing process and significantly reducing preprocessing time;

[0049] 2. Significantly improved solution efficiency: By reusing historical analysis data and avoiding repeated decomposition of the global stiffness matrix, the computational efficiency of reanalysis is expected to be 2-3 times higher than that of global analysis, meeting the needs of high-frequency feature iterative design;

[0050] 3. High solution accuracy: For representative engineering models, the relative error of displacement and other responses does not exceed 5%, and the error in most engineering scenarios is close to 0, which is highly consistent with the full finite element analysis results, ensuring the reliability of characteristic region analysis;

[0051] 4. High adaptability: It uniformly handles three types of modifications: feature deletion, geometric deformation, and feature addition, supports topological changes and the addition and deletion of degrees of freedom, and covers all feature modification scenarios;

[0052] 5. Good numerical stability: By using basis vector orthogonalization and weak regularization, the problems of non-invertibility of extended stiffness matrix and basis vector correlation are solved, making it suitable for volume subdivision and feature modification scenarios;

[0053] 6. Wide engineering applicability: Applicable to the high-frequency feature iterative design of complex equipment such as motor brackets, forklift frames, and high-speed train bogies, meeting actual engineering needs;

[0054] 7. Integrate existing reanalysis foundations: Based on optimization of relevant reanalysis papers, expand the application scenarios and improve the performance of reanalysis technology, thus forming a technological barrier. Detailed Implementation

[0055] The technical solution of the present invention will be described in detail below with reference to specific engineering examples, so as to further verify the effectiveness and practicality of the present invention.

[0056] Example 1: Iterative Modification and Reanalysis of Motor Bracket Features

[0057] As a typical mechanical structure, the motor bracket's ribs, mounting bosses, and other features require frequent iterative modifications to meet assembly and strength requirements. The method of this invention is used for reanalysis, and the specific steps are as follows:

[0058] 1. Construct a unified volume subdivision model: Based on the three-dimensional coarse control mesh (tetrahedral element) of the motor bracket, a discrete model is generated by midpoint volume subdivision. Features such as ribs and mounting bosses are integrated into the control mesh, and the feature regions are adaptively subdivided to improve the analysis accuracy.

[0059] 2. Establish a reference model and a unified degree-of-freedom space: Perform a complete finite element analysis on the initial design of the motor support model to obtain the reference stiffness matrix and reference displacement vector, construct a unified node set, and establish the node mapping relationship between the reference model and the subsequently modified model.

[0060] 3. Feature Modification and Stiffness Increment Assembly: For three typical modification scenarios, namely "deleting a rib", "adjusting the size of the mounting boss", and "adding a reinforcing boss", stiffness increment calculation and assembly are performed respectively. Only the stiffness of the feature modification area is updated, without the need for global reconstruction.

[0061] 4. Improved combined approximation reanalysis solution: Construct a dimension-reduced basis vector and perform orthogonal normalization, establish a reduced-order equilibrium equation and solve it to quickly obtain the modified displacement response.

[0062] 5. Result verification and iterative reuse: The reanalysis results are compared with the full finite element analysis results. The relative displacement error is ≤1.8%, and the calculation efficiency is improved by 2.3 times. The analysis data of the currently modified model is stored for reference in the next feature iteration modification.

[0063] Example 2: Reanalysis of High-Speed ​​Train Bogie Feature Modification

[0064] The bogie structure of high-speed trains is complex, and modifications to its support structure, connecting bosses, and other features directly affect operational safety. This invention's method is used for reanalysis.

[0065] 1. Unified Model Construction for Volume Subdivision: A three-dimensional discrete model of the bogie is constructed by combining Loop surface subdivision and midpoint volume subdivision. Core features such as support structures and connecting bosses are integrated into the control mesh to achieve a unified representation of geometry and analysis.

[0066] 2. Establishment of Unified Degree of Freedom Space and Reference Model: Complete the full finite element analysis of the initial bogie model, construct a unified degree of freedom space, establish node mapping relationships, and store the reference stiffness matrix, displacement vector, and matrix decomposition results.

[0067] 3. Multi-type feature modification processing: For three types of modifications to the bogie support structure, namely geometric deformation, deletion of connecting bosses, and addition of reinforcing ribs, the stiffness increment is calculated separately, and weak regularization is used to process the stiffness sub-blocks corresponding to the newly added degrees of freedom to ensure solution stability.

[0068] 4. Reduced-order reanalysis solution: By constructing reduced-dimensional basis vectors through an improved combinatorial approximation method, the reduced-order equilibrium equations are solved to quickly obtain the modified structural response.

[0069] 5. Result verification: Compared with the full finite element analysis results, the displacement relative error is ≤2.5%, the calculation efficiency is improved by 2.5 times, and the high-frequency feature iterative design requirements are met.

[0070] The two engineering examples above demonstrate that the method of the present invention can efficiently handle the scenario of feature modification and reanalysis of complex equipment. While ensuring the accuracy of analysis, it can significantly improve the computational efficiency, completely solve the pain points of local feature modification triggering global reconstruction and high computational cost in traditional methods, adapt to the needs of high-frequency feature iteration design, and has extremely strong engineering application value.

Claims

1. A rapid reanalysis method integrating CAD and CAE based on volume subdivision, characterized in that, This paper deeply integrates volume subdivision technology with reanalysis technology, using volume subdivision as a unified geometry-analysis representation framework for CAD / CAE. It integrates local feature editing, discretization updates, and finite element reanalysis into the same data structure, constructing a fast reanalysis framework suitable for adding or deleting local features, geometric deformation, and topological changes. Specifically, it includes the following steps: Step 1: Construct a volume subdivision unified geometric-analysis discrete model; Based on a three-dimensional coarse control mesh, a combination of Loop surface subdivision and midpoint volume subdivision is used to generate a smooth and continuous three-dimensional solid discrete model. Structural features are integrated into the volume subdivision control mesh to achieve a unified geometric-analysis representation of the features. Step 2: Establish a globally unified degree-of-freedom space and a local update mechanism for feature modifications; To adapt to various feature modification scenarios, a globally unified degree-of-freedom space is constructed, and the node sets of the reference model and the modified model are projected onto the same global numbering system, so that displacement, load and stiffness increments can all be represented within a unified indexing framework. Step 3: Establish a reference model and a unified node space; In the initial design phase, the global stiffness matrix, reference displacement vector, and reference load vector of the reference model are obtained through complete finite element implicit analysis, and only the substructures corresponding to the unconstrained degrees of freedom are retained. A unified node set is introduced to establish a one-to-one mapping relationship between the unified node and the modified model node; Step 4: Unified modeling and assembly of the three types of local modifications; Within the globally unified degree-of-freedom space, the modified global stiffness matrix is ​​the sum of the reference stiffness matrix and the stiffness increment of the feature modification region; Step 5: Construct an improved combinatorial approximate reanalysis algorithm that adapts to feature modifications; For scenarios involving volume subdivision and feature modification, we optimize the combined approximation method and construct dimensionality-reduced basis vectors for reanalysis. Using the reference displacement solution as the initial basis vector, subsequent basis vectors are constructed recursively. The recursion is achieved through sparse matrix-vector multiplication and linear system solution. The basis vectors are orthogonally normalized using the Schmitt orthogonalization method. Step 6: Construction and rapid solution of the reduced-order equilibrium equations; The displacement vector is approximated as a linear combination of the reduced-dimensional basis vector and the reduced-order coordinates. After substituting it into the equilibrium equation, the reduced-order equilibrium equation is constructed using the Galerkin projection method. Step 7: Displacement result mapping recovery and iterative data reuse; the specific method is as follows: (1) By unifying the node mapping relationship, the displacement solution of the global unified degree of freedom space is restored to the node order of the modified model, and the structural mechanical response of the feature modification region is output as the main feature. (2) Store the analysis data of the current modified model as a new reference state for the next local feature modification iteration, so as to realize the rapid reanalysis of multiple consecutive local feature modifications and improve the efficiency of high-frequency feature iteration.

2. The rapid reanalysis method for CAD and CAE integration based on volume subdivision according to claim 1, characterized in that, In step 2, specific local update strategies are designed for three typical feature modification scenarios in the project: (1) Feature deletion: The corresponding element is deleted, and its stiffness contribution is removed from the global system. Only the element stiffness corresponding to the feature needs to be subtracted in the global unified degree of freedom space, without affecting other regions; (2) Feature geometry deformation: The topology remains unchanged for the corresponding element geometry deformation. Only the node coordinates of the feature region need to be updated and the element stiffness of the region needs to be recalculated. There is no need to modify the mesh and stiffness of the non-feature region. (3) Feature addition: When the corresponding element is inserted, its stiffness is added as a local increment to the global unified degree of freedom space. Only the local stiffness increment needs to be assembled in the feature addition area, and there is no need to reassemble the stiffness matrix globally.

3. The rapid reanalysis method for CAD and CAE integration based on volume subdivision according to claim 1, characterized in that, In step 4, for the three types of feature modification scenarios, a type identifier is assigned to each modified unit to achieve unified modeling: (1) The element corresponding to the feature deletion: its stiffness is 0 after modification, and the stiffness increment is the negative value of the reference stiffness. Only the negative stiffness value needs to be added to the corresponding row block and column block, which does not affect other areas of the whole. (2) Element corresponding to the feature geometric deformation: The topology remains unchanged, only the node coordinates change, the stiffness increment is the difference between the modified stiffness and the reference stiffness, and only the stiffness increment of the feature deformation region is updated. (3) Add the corresponding unit for the feature: its reference stiffness is 0, and the stiffness increment is the modified stiffness. Only the positive stiffness value needs to be added to the corresponding row block and column block in the feature addition area. There is no need for global reassembly.