Direct static simulation method and system for boundary representation-oriented three-dimensional mechanical part without conformal mesh generation

Abstract

The invention discloses a direct statics simulation method and system for a boundary-representation-oriented three-dimensional mechanical part without conformal mesh generation, and is particularly suitable for stress and deformation analysis of airplanes and electronic products under the action of loads. According to a traditional finite element method, complex conformal mesh generation needs to be carried out on a model, particularly dense units are often needed in a long and narrow / fine feature region, and the calculation efficiency is seriously affected. According to the method, the three-dimensional mechanical part is embedded in the regular Cartesian background grid, through topological structure analysis of each cutting rule unit, the conversion unit integral is calculated into the high-order curved tetrahedron unit integral based on the template and oriented to boundary representation, and the calculation efficiency is improved while tedious model conversion and grid subdivision are avoided. And efficient and robust statics simulation calculation of mechanical products is realized. A large number of numerical experiments verify the precision, efficiency and robustness of the method, and the method shows huge performance advantages in stress analysis of complex structures such as airplanes and electronic products.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural mechanics analysis, and relates to a direct statics simulation method and system for three-dimensional mechanical components with boundary-oriented representation without conformal meshing, which is mainly used in dynamic analysis in mechanical design, such as simulation and optimization of three-dimensional mechanical components such as aircraft fuselage structures or complex mechanical systems. Background Art

[0002] The finite element method is an important numerical analysis tool in structural mechanics. It is widely used to study, optimize and verify various engineering and scientific problems, such as studying the stress, strain, deformation and stability of structural objects (such as buildings, bridges, mechanical parts, etc.) under the action of external forces. The goal of structural mechanics is to ensure the safety and reliability of the structure by analyzing these physical quantities. Numerical integration is an important step in the finite element analysis method. For integrals that are difficult to calculate by analytical methods, numerical methods use discrete approximations to calculate the integral value. The theoretical basis of numerical integration is based on classical mathematical analysis, especially calculus theory and interpolation theory. Early numerical integration techniques include Simpson's formula, trapezoidal formula, Gaussian integral, etc. The finite element method requires the calculation of integrals inside the unit (such as stiffness matrix, mass matrix and load vector), and most of these integrals have no analytical solutions. Therefore, the Gaussian integral method in numerical integration is usually used to convert the integral area to a standard unit, use Gaussian points and weight calculations, and finally add the results of each unit to obtain the final mechanical analysis results.

[0003] Taking the dynamic analysis of aircraft fuselage structure as an example, the typical process of finite element simulation is as follows:

[0004] 1. Define the analysis objectives: determine the simulation tasks (such as vibration modal analysis, collision simulation), geometric models, material properties, boundary conditions, and load conditions.

[0005] 2. Import CAD models: Import CAD models (such as STEP, IGES files) from external CAD software (such as CATIA, SolidWorks).

[0006] 3. Meshing: Convert the model into an STL (mesh) model and perform meshing.

[0007] 4. Mechanical analysis: Perform static / dynamic analysis and calculate structural response.

[0008] 5. Post-processing of results: Visualization of analysis results, such as stress distribution, displacement field, etc.

[0009] In the above process, meshing is a key step, but also a major bottleneck. The CAD model of complex mechanical parts (such as aircraft fuselage wings) is usually composed of boundary representation (BRep) methods, that is, BRep-type models, which need to be converted into STL models and then meshed. This process is not only time-consuming, but may also lead to loss of geometric accuracy. According to statistics, the time of meshing accounts for about 80% of the entire simulation process, which seriously reduces the simulation efficiency.

[0010] The traditional finite element method has the following problems when processing complex CAD models:

[0011] 1. Low efficiency of intermediate conversion: CAD models need to be converted into STL models, resulting in additional computing overhead and loss of accuracy.

[0012] 2. Complex meshing: Meshing of complex geometries (such as surfaces and holes) requires manual intervention and is difficult to automate.

[0013] 3. High demand for dynamic analysis: Dynamic analysis of mechanical components (such as vibration and impact) requires high precision and high efficiency, which are difficult to meet with traditional methods.

[0014] In recent years, researchers have proposed some optimization methods based on traditional finite elements, avoiding the intermediate conversion steps. For example, the finite cell method directly immerses the CAD model into a simple geometric domain, such as a Cartesian background grid, approximates the computational domain within the background grid by replacing the curve with a straight line, and then uses the Gaussian integral method to calculate the mechanical variables; the non-uniform rational B-spline enhanced finite element method (NEFEM) directly divides the CAD model and uses the optimized Gaussian integral method for sub-units containing parametric surfaces.

[0015] However, when dealing with complex boundaries of CAD models, the finite cell method relies on octree multi-layer recursive processing to improve calculation accuracy, which also leads to a decrease in efficiency. The premise of the non-uniform rational B-spline enhanced finite element method is to divide the CAD model into sub-units that suit its rules. Currently, the industry still does not have a stable and efficient method to complete its segmentation steps.

[0016] In order to solve the bottleneck of existing mechanical analysis algorithms, the present invention provides a direct static simulation method for three-dimensional mechanical components based on boundary representation without conformal meshing, which combines the advantages of the finite element method and the non-uniform rational B-spline enhanced finite element method, directly avoids inefficient STL model conversion and a large amount of precision loss, and can handle complex geometric features in aircraft fuselages, wings, and cabin structures (such as multi-segment splicing of curved surfaces, riveted hole groups, and wing rib reinforcement structures), meet the high-precision design requirements of the aviation industry, and provide high-confidence simulation results that meet airworthiness certification standards in tasks such as vibration modal analysis under aerodynamic loads, bird strike impact simulation, and fatigue life assessment of composite materials. Summary of the invention

[0017] The purpose of the present invention is to address the deficiencies of the prior art in the structural mechanics simulation of key aircraft components or systems such as aircraft fuselages, wings, and landing gears. The present invention proposes a direct statics simulation method and system for three-dimensional mechanical components that do not require conformal meshing and are oriented to boundary representation. This method directly processes the original CAD geometric model of the three-dimensional mechanical component, avoiding the inefficient STL model conversion and manual meshing problems in the traditional simulation process, and significantly improves the efficiency and accuracy of dynamic analysis of complex mechanical structures.

[0018] The technical solution adopted by the present invention is as follows:

[0019] A direct static simulation method for three-dimensional mechanical components based on boundary representation without conformal meshing comprises the following steps:

[0020] 1) Construct a structural model for the three-dimensional mechanical parts. The model is embedded in the background grid. The grid cells are divided into internal cells and cutting cells according to the positional relationship between the grid and the model. The internal cells are cells that are completely inside the model, and the cutting cells are cells that are not completely inside the model.

[0021] 2) For each cutting unit, the intersection calculation is performed with the boundary representation of the model to determine the internal structure of each grid unit and classify it into the basic template unit;

[0022] 3) For each cutting unit, the curved tetrahedron is decomposed according to the basic template, and the curved edges / surfaces of the tetrahedron are directly defined by the boundary representation;

[0023] 4) Perform standard Gaussian integration on the internal units, integrate each curved tetrahedron of the cutting unit, assemble the unit stiffness matrix, solve the overall equation, and obtain the static simulation results of the model.

[0024] In the above technical solution, further, the step 2) is to calculate the precise geometric boundaries of the cutting unit and the model boundary, i.e., the intersection and the intersection line, for the components of the structural model, and first pre-process each surface of the structural model. The parameter domain where each surface is located is sampled in steps, the bounding box where the parameter domain is located is expanded, and the sampling is uniformly performed in the parameter surface according to the set sampling point spacing; the sampling distance of the parameter surface boundary is derived according to the Taylor expansion formula for sampling; the parameter domain of the parameter surface is triangulated according to the sampling points, and it is divided into parameter triangles; the parameter triangles are mapped to triangles on the three-dimensional mechanical component structure model through the parameter surface expression, and the triangulation of the structural model surface is completed. For each edge of the cutting unit, find the triangle passing through it, and use the parameter value of their intersection as the starting point of Newton iteration. The Newton iteration method can be used to find the real intersection of each background grid and the model parameter surface, and then the intersection can be used to track the intersection line.

[0025] Furthermore, in the step 2), the background mesh intersecting with the model contains several surfaces. When the number of surfaces is 1, the unit is classified according to the intersection of the unit edge with the model and the internal and external relationship between the unit vertex and the model, and can be classified into 7 types of basic template units; when the number of surfaces is greater than 1, if it contains small surfaces that do not intersect with any surface of the background mesh, the background mesh is subdivided by octree until all the surfaces contained inside intersect with the surfaces of the background mesh.

[0026] Furthermore, in step 3), for each basic template unit, it is decomposed into different types of sub-tetrahedrons. The specific decomposition method is: determine the topological form of the parameter domain of the parameter surface of the model located inside the background grid. If it is a curved triangle, no further division is required; if it is a curved quadrilateral, two opposite vertices of the curved quadrilateral are connected on the parameter domain; if it is a curved pentagon, two internal straight edges are added to divide it into three triangles; if it is a curved hexagon, three internal straight edges are added to divide it into four curved triangles. The divided curved triangles must be non-repetitive and non-omitted, and then the curved triangles are connected to the vertices of the background grid to form a curved tetrahedron. These 7 types of basic template units accurately define the above-mentioned edge connection relationship and topological form. The curved edges / surfaces of the curved tetrahedron are directly defined by the boundary representation for subsequent precise integration.

[0027] Furthermore, in step 4), the standard Gaussian integral is performed on the internal unit; for each curved tetrahedron of the cutting unit, the non-uniform rational B-spline enhanced finite element method NEFEM is used to construct the precise parameterization of the curved tetrahedron according to the definition of the curved edge / surface. If it is a curved tetrahedron unit containing a parametric surface, its parameterization for:

[0028]

[0029] in is the parametric domain representation of the tetrahedral surface, is the vertex of the curved surface. Gaussian integration is performed in the parameter domain to obtain the integration points and integration weights of the curved tetrahedron, and accurate integration of the curved tetrahedron is performed; if it is a curved tetrahedron unit with a parameter edge, its parameterization for:

[0030]

[0031] in and The connected edge is a parametric curved edge, and the parameter formula of the parametric curved edge is , and The connected edges are all straight edges. for The surface composed of yes The parameterized representation of is:

[0032]

[0033] By Gaussian integration is performed on the parameter domain to obtain the integration points and integration weights of the curved tetrahedron, and accurate integration of the curved tetrahedron is performed; the integral values ​​of each sub-tetrahedron are assembled into the local stiffness matrix to form the unit stiffness matrix of the basic template unit. The unit stiffness matrix of each basic template unit is assembled according to the global node number to form an overall stiffness matrix. Based on the overall stiffness matrix, external load vectors (such as force, torque) and boundary conditions (such as fixed constraints, displacement constraints), the overall equilibrium equation is constructed, and the stress, strain distribution and other static performance indicators of the model (such as vibration mode, fatigue life, etc.) can be calculated. The present invention also provides a mechanical analysis system for three-dimensional mechanical components oriented to boundary representation, which is used to implement the method described in any of the above items.

[0034] The present invention also provides an electronic device, comprising:

[0035] one or more processors;

[0036] A memory for storing one or more programs;

[0037] When the one or more programs are executed by the one or more processors, the one or more processors implement any of the methods described above.

[0038] A computer-readable storage medium stores computer-executable instructions, wherein the instructions are used to implement any of the above methods when executed.

[0039] The beneficial effects of the present invention are:

[0040] 1) Aiming at the common curved surfaces and holes in three-dimensional mechanical parts, the method of the present invention avoids the inefficient STL model conversion and manual meshing process in the traditional finite element method. The component model is divided by adopting the Cartesian background grid, and a set of templates for decomposing the cutting units generated by the background grid is designed, while retaining the integrity of the original design geometry to ensure the accurate capture of stress concentration areas (such as the local stress distribution at the wing connection in aircraft structure simulation).

[0041] 2) CAD models of three-dimensional mechanical parts often contain a variety of trimmed surfaces (such as aircraft fuselage covers and casting surfaces of engine components), and their parameter domains are mostly irregular polygons. When solving the intersections and intersections between such trimmed surfaces and meshes, traditional methods cannot quickly and accurately find the initial points used for the Newton iteration method to accurately solve the intersections and intersections. The present invention combines the parameter domain triangulation method to generate high-quality parameter triangular meshes, which can cover any type of trimmed surfaces, thereby obtaining the precise geometric boundaries of the cutting unit, and providing a more accurate geometric model for subsequent decomposition and simulation. Taking the cooling hole analysis of aircraft engine blades as an example, this method can adaptively divide the parameter domain with complex boundaries, ensure the efficiency and stability of the surface integral, and avoid the numerical divergence problem caused by the irregularity of the parameter domain in traditional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic diagram of the overall process of the method of the present invention;

[0043] Figure 2 Detailed schematic diagram of the method of the present invention;

[0044] Figure 3 Schematic diagram of the structural model immersed in a Cartesian background grid;

[0045] Figure 4 It is a schematic diagram for judging the inside and outside of the background grid;

[0046] Figure 5 It is a triangulated schematic diagram of the Face13 parameter domain of the structural model;

[0047] Figure 6 A schematic diagram of the classification of cutting units based on topological rules;

[0048] Figure 7-Figure 13 Schematic diagram of tetrahedral decomposition rules for 7 basic templates of cutting units;

[0049] Fig.14 Schematic diagram of finding integration points for tetrahedralization of a single cut cell. DETAILED DESCRIPTION

[0050] The present invention is further described below in conjunction with the accompanying drawings and specific examples.

[0051] The present invention proposes a direct static simulation method for three-dimensional mechanical parts with boundary-oriented representation without conformal meshing, which is particularly suitable for mechanical simulation of complex mechanical systems such as aircraft fuselage structures. This method significantly improves the efficiency and accuracy of dynamic analysis by immersing the CAD model of the mechanical part into a Cartesian background grid and adaptively optimizing the integration process.

[0052] like Figure 1 and Figure 2 As shown, the core idea of ​​the present invention is as follows:

[0053] The CAD model is immersed in a Cartesian background grid domain. The immersed domain is a Cartesian background grid of the same size, so that the meshing of the model can be avoided, and the integral calculation is limited to each unit grid. Therefore, the immersed domain needs to completely cover the model, and the unit grid size needs to be adaptively adjusted according to the actual model size. Then the background grid vertices are judged inside and outside. If the background grid has no intersection with the CAD model, that is, all eight vertices are outside the model, it can be ignored in the calculation process; if the background grid is completely inside the CAD model, that is, all eight vertices are inside the model, then its integration method can completely use the standard Gaussian integral, and no further processing is required; when the vertices of the background grid are both inside and outside the model, they are units that need to be processed in the next step.

[0054] In order to determine the intersection pattern between the model and the background mesh, it is necessary to calculate the intersection of each edge of the background mesh with the model. Most CAD models used in industry are composed of NURBS (Non-Uniform Rational B-spline) parametric surfaces, and the edge of the background mesh can be abstracted as a straight line parallel to the coordinate axis. If the intersection of each surface of the CAD model and the straight line is directly solved, it is necessary to solve multiple nonlinear equations, which reduces efficiency. Therefore, an axisymmetric bounding box (AABB) is established for each parametric surface of the CAD model, and the intersection with the background mesh is judged, leaving only the parametric surfaces that intersect with the bounding box.

[0055] The nonlinear equations for the intersection of a parametric surface and a straight line generally use the Newton iteration method to calculate the intersection point. The Newton iteration method is extremely dependent on the selection of initial values. If the guessed initial point is far from the actual result, it may not be possible to solve the actual point. Therefore, the parameter domain of the parametric surface is discretely segmented. Since most parametric surfaces are clipped surfaces, that is, the parameter domain is not a regular two-dimensional rectangle, it may be an irregular polygon composed of multiple segments of parametric curves. Then find its AABB bounding box for the two-dimensional area where the parameter domain is located, and evenly place the sampling points. Perform internal and external judgments on all sampling points, leaving only the sampling points inside the parameter domain. Then sample the parameter curves that constitute the parameter domain boundary of the parameter domain, so that all the vertices for triangulating the surface parameter domain are obtained. Inputting these vertices into the Delaunay triangulation algorithm can triangulate the entire surface parameter domain.

[0056] After the surface parameter domain is triangulated, the parameter triangle is mapped to the physical domain of the three-dimensional mechanical component. Next, it is necessary to find which physical triangle the edge of the background mesh unit will pass through, find the intersection point of the edge and the intersecting triangle, map it back to the parameter domain to obtain its parameter point, and use this parameter point as the starting point of the Newton iteration. Finally, the real intersection point is found based on the nonlinear equations of the parametric surface and the background mesh edge.

[0057] The topological structure of the background mesh and the CAD model is inferred based on the intersection of the background mesh unit edge and the model. The background mesh that intersects the model contains several surfaces. When the number of surfaces is 1, it is classified according to the intersection of each edge of the background mesh unit with the model, and the internal and external relationship of each vertex of the background mesh unit with the model, and 7 basic templates are classified; when the number of surfaces is greater than 1, if it contains small surfaces that do not intersect with any surface of the background mesh, the background mesh is subdivided into octrees until all the surfaces contained in it intersect with the surfaces of the background mesh.

[0058] For each basic template unit, it is decomposed into different types of sub-tetrahedrons. The specific decomposition method is as follows: determine the topological form of the parameter domain of the parametric surface of the model located inside the background grid. If it is a curved triangle, no further division is required; if it is a curved quadrilateral, connect two opposite vertices of the curved quadrilateral on the parameter domain; if it is a curved pentagon, add two internal straight edges to divide it into three triangles; if it is a curved hexagon, add three internal straight edges to divide it into four curved triangles. The divided curved triangles must be non-repetitive and non-omission, and then the curved triangles are connected to the vertices of the background grid to form a curved tetrahedron. These 7 types of basic template units accurately define the above-mentioned edge connection relationship and topological form. Among them, the non-uniform rational B-spline enhanced finite element integration method is used to calculate the integration points for the sub-tetrahedrons with parameter boundaries, and the standard finite element integration method is used for the sub-tetrahedrons without parameter boundaries. The unit stiffness matrix is ​​calculated, and the local stiffness matrix of each sub-tetrahedron is combined to form the unit stiffness matrix of the basic template unit. The unit stiffness matrix of each basic template unit is assembled according to the global node number to form an overall stiffness matrix. Based on the overall stiffness matrix, external load vectors (such as force, torque) and boundary conditions (such as fixed constraints, displacement constraints), the overall equilibrium equation is constructed to calculate the stress, strain distribution and other mechanical performance indicators of the model (such as vibration mode, fatigue life, etc.). The method of the present invention can be well applied to the mechanical analysis of three-dimensional mechanical parts, such as the actual needs of aircraft structure design and simulation, including:

[0059] In the dynamic simulation of aircraft structures, geometric models usually contain a large number of complex features such as curved surfaces, holes and connectors. The traditional method requires converting the CAD model into an STL mesh for finite element analysis. This process is not only time-consuming (occupying more than 80% of the simulation cycle), but may also result in loss of accuracy of geometric details. The present invention proposes to directly immerse the aircraft CAD model in the Cartesian background grid domain. In addition, the cell size of the background grid can be adaptively adjusted according to the geometric complexity of the aircraft. For example, when analyzing the vibration mode of the wing, the background grid can cover the entire model geometry (based on the present invention, it can be further set so that the grid cell size can be dynamically optimized according to the curvature of the wing surface and local details). By classifying the vertices inside and outside, the background grid cells that intersect with the aircraft structure are quickly screened out, and only the intersecting cells are subsequently processed, which greatly reduces invalid calculations.

[0060] The CAD model of the aircraft structure is usually composed of NURBS surfaces, and its parameter domain is mostly an irregular area after clipping. In order to improve the efficiency of the intersection calculation between the parameter surface and the background mesh edge, the present invention adopts a parameter domain partitioning method based on triangulation (usually Delaunay triangulation). Taking the surface of the fuselage as an example, the parameter domain is first sampled by AABB bounding box, valid parameter points are retained, and a parametric triangular mesh is generated by Delaunay triangulation. After the triangulated parameter domain is mapped to the physical domain, the precise intersection points and intersection lines with the background mesh edge are further calculated to ensure the stability and efficiency of the solution.

[0061] In the collision simulation scene, the contact area between the aircraft and the obstacle often requires local high-precision analysis. The present invention adaptively divides the complex intersecting background grid through octree subdivision. For example, when the nose of the aircraft collides with an obstacle, the background grid unit in the intersection area will be recursively subdivided until the accuracy requirements are met. The units that do not need to be subdivided are classified into basic template units according to the internal and external conditions of each vertex of the unit and the intersection of each edge. The topological morphology of the parameter domain of the surface contained in the template unit is analyzed, and it is divided into curved triangles by connecting the edges, and then connected with the vertices in the background grid to form a sub-tetrahedron (which may contain a sub-tetrahedron with a parameter curved edge / surface). The sub-tetrahedron with parameter boundaries is calculated using the non-uniform rational B-spline enhanced finite element integration method, and the sub-tetrahedron without parameter boundaries is calculated using the standard finite element integration method. The unit stiffness matrix is ​​calculated, and the local stiffness matrix of each sub-tetrahedron is combined to form the unit stiffness matrix of the basic template unit. The unit stiffness matrix of each basic template unit is assembled according to the global node number to form an overall stiffness matrix. Based on the overall stiffness matrix, external load vectors (such as force, moment) and boundary conditions (such as fixed constraints, displacement constraints), the overall equilibrium equation is constructed to calculate the stress, strain distribution and other mechanical performance indicators of the model (such as vibration mode, fatigue life, etc.). This mixed integration strategy avoids redundant calculations while ensuring accuracy, and is particularly suitable for stress analysis of thin-walled parts (such as wing skins) and stiffeners in aircraft structures. Using a graphical example to illustrate, the direct static simulation method of a three-dimensional mechanical component for boundary representation without conformal meshing of the present invention includes:

[0062] 1. Construct a Cartesian background grid for the space where the complex components are located

[0063] Get the bounding box of the mechanical component model. The user can specify the resolution of the background grid (10*10 is used in the example). A higher resolution is used for complex models to obtain more accurate integration results. Immerse the model in an immersion domain composed of background grids of equal size, such as Figure 3 As shown (only part of the grid area is shown in the figure).

[0064] 2. Sample the parameter domain of each surface that makes up the complex component and solve the cutting unit geometric boundary

[0065] like Figure 5 The parameter domain sampling results of the 13th surface of the complex component are shown. Get the bounding box of each surface parameter domain , in order to make the sampling point distribution more reasonable, the bounding box is expanded by a small constant size, ,in, is the enlarged bounding box, is the lower left corner of the original bounding box, is the upper right corner of the original bounding box, The user-specified domain sampling point spacing for the enlarged constant is assumed to be , then the spacing is evenly placed on the plane where the two-dimensional parameter domain is located. Domain sampling points; Since the surface boundary is a parametric curve, in order to make the sampling points on the parametric curve evenly distributed, the following formula is used to derive the distribution of parameter points:

[0066] Assuming a parametric curve The current parameter point is , the next parameter point to be determined is , for and The distance between

[0067]

[0068] From the Taylor expansion formula we get:

[0069]

[0070] Substituting (2) into (1), we obtain:

[0071]

[0072] Right now:

[0073]

[0074] The spacing of parameter points when sampling parameter boundaries can be obtained.

[0075] 3. Find the intersection points and intersection lines between each surface of the complex component and the cutting unit

[0076] Preprocessing: Traverse the discrete triangles of the triangulated parametric surface that constitute the CAD model. If a triangle is found to have an intersection with the edge of the cutting unit, set it as . Then further solution can be performed. Assume that the parameter expression of the line where the edge of the cutting unit is located is , the expression of the parametric surface is , the simultaneous equations are: , Newton's method is solved as follows:

[0077]

[0078]

[0079] is the Jacobian matrix of the iterative formula, For function The partial derivative of parameter u is calculated, and the rest is the same. The iterative process is as follows, substituting the starting point calculated in the previous article You can get the recursive parameters for each step :

[0080]

[0081] until and If the distance between them is less than 1e-6, it means that the two iterations are very close, and then It is regarded as the intersection point of the final structural model and the cutting unit edge, and the intersection line can be traced out using the tracking method using this point.

[0082] 4. Classify and tetrahedronize the cutting units according to their internal topology

[0083] After calculating the intersection of each edge of the cutting unit and the model (if any), according to the internal and external relationship of the 8 vertices of the background mesh (such as Figure 4 Example), and the intersection relationship of the edges is divided into 7 categories, such as Figure 6 As shown, these 7 categories are basic template units. Figure 7-Figure 13 The specific decomposition method of each type of basic template unit is shown as follows: determine the topological form of the parameter domain of the surface in the unit. If it is a curved triangle, no further division is required; if it is a curved quadrilateral, connect two opposite vertices of the curved quadrilateral on the parameter domain to divide it into two curved triangles; if it is a curved pentagon, add two internal straight edges (take a vertex to connect the two vertices opposite it) to divide it into three triangles; if it is a curved hexagon, add three internal straight edges (take two adjacent vertices to connect the two adjacent vertices opposite it) to divide it into four curved triangles. The divided curved triangles must be non-repetitive and non-omitted, and then connect the curved triangles with the background mesh vertices to form a curved tetrahedron. If it does not meet the basic template category and contains only one curved surface inside, it will be subdivided by octree; if it does not meet the basic template category and contains multiple curved surfaces inside, it will be decomposed using the Delaunay tetrahedronization process.

[0084] 5. Integrate the internal tetrahedron of the unit and assemble it into the overall stiffness matrix to obtain the mechanical analysis results

[0085] For each curved tetrahedron of the cutting unit, the non-uniform rational B-spline enhanced finite element method is used to construct the precise parameterization of the curved tetrahedron according to the definition of the curved edge / surface. If it is a curved tetrahedron unit containing a parametric surface, its parameterization for:

[0086]

[0087] in is the parametric domain representation of the tetrahedral surface, is the vertex of the curved surface. Gaussian integration is performed in the parameter domain to obtain the integration points and integration weights of the curved tetrahedron, and the precise integration of the curved tetrahedron is performed, and the integral formula is:

[0088]

[0089] in For mapping The determinant of the Jacobian matrix of .

[0090] If it is a curved tetrahedral element with a parametric edge, its parameterization for:

[0091]

[0092] in and The connected edge is a parametric curved edge, and the parameter formula of the parametric curved edge is , and The connected edges are all straight edges. for The surface composed of yes The parameterized representation of is:

[0093]

[0094] By Gaussian integration is performed in the parameter domain to obtain the integration points and integration weights of the curved tetrahedron, and the precise integration of the curved tetrahedron is performed, and the integral formula is:

[0095]

[0096] in For mapping The determinant of the Jacobian matrix of .

[0097] Fig.14The tetrahedralization and integration results of one of the background meshes are shown (the colored dots in the figure are the integration points of the sub-tetrahedron). The parameterized sub-units can select Gaussian integration points in the parameter domain, and can be mapped to the actual model through surface mapping and linear interpolation. Each integration point contributes a local stiffness matrix, which are finally combined into the global stiffness matrix of the entire structure. The stiffness matrix determines the response of the structure and reflects the rigidity (deformation resistance) of the structure. Finally, based on the results of these local responses, the global mechanical response of the system is solved, that is, the static simulation solution.

[0098] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0099] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0100] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0101] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1The steps for the functions specified in one or more boxes.

[0102] The above are only some of the preferred solutions of the present invention, but they are not intended to limit the present invention. Ordinary technicians in the relevant technical field can make various changes and modifications without departing from the spirit and scope of the present invention, and expand to corresponding electromagnetics, fluid simulation, etc. Therefore, all technical solutions obtained by equivalent replacement or equivalent transformation fall within the protection scope of the present invention.

Claims

1. A direct static simulation method for three-dimensional mechanical components based on boundary representation without conformal meshing, characterized in that: The steps include: Build a model of a three-dimensional mechanical component, embed it in a regular Cartesian background grid, and divide the grid cells into internal cells and cutting cells; For each cutting unit, an intersection calculation is performed with the boundary representation of the model and the unit is classified as a basic template unit; For each cutting unit, a curved tetrahedron decomposition is performed according to the basic template unit type to which it is classified, and the curved edges / surfaces of the tetrahedron are directly defined by the boundary representation; Perform standard Gaussian integration on the internal elements. At the same time, re-parameterize and define each curved tetrahedron of the cutting element and integrate it over the new parameter domain to obtain the element stiffness matrix on the cutting element. The unit stiffness matrix is ​​assembled and solved to obtain the mechanical analysis results of the three-dimensional mechanical component.

2. The direct statics simulation method for three-dimensional mechanical parts based on boundary representation without conformal meshing according to claim 1, characterized in that: 3D mechanical component model Embedded in a regular Cartesian background grid ,in is the number of grid cells, and the grid cells It is divided into units that are completely inside the model, namely , and some cutting elements inside the model, i.e. and ; Elements that are completely outside the model do not contribute to the simulation and are ignored.

3. The direct statics simulation method for three-dimensional mechanical parts based on boundary representation without conformal meshing according to claim 1, characterized in that: For each cutting unit, the Newton method is used to iteratively calculate its intersection with the model, and the intersection is used to track the geometric intersection line between the cutting unit surface and the model; in order to ensure the accuracy and iteration efficiency of the Newton method, the parametric surface of the model is first triangulated and preprocessed, and the point corresponding to the intersection of the triangular surface mesh and the cutting unit on the parameter domain is used as the initial point of the Newton iteration method.

4. The direct statics simulation method for three-dimensional mechanical parts based on boundary representation without conformal meshing according to claim 3, characterized in that: The triangulation preprocessing process is as follows: the parameter domain of the parametric surface patch of the model is sampled step by step, and the sampling is uniformly performed within the parametric surface according to the set sampling point spacing; the sampling distance of the parametric surface boundary is derived according to the Taylor expansion formula for sampling, and the sampling points are connected to form a parametric triangle based on the Delaunay triangulation method, and the parametric triangle is mapped to a triangle on the three-dimensional mechanical component structure model through a parametric surface expression, completing the triangulation of a single surface of the structural model, and obtaining the triangular surface mesh of the parametric surface on the three-dimensional mechanical component structure model.

5. The direct statics simulation method for three-dimensional mechanical components based on boundary representation without conformal meshing according to claim 3, characterized in that: The process of solving the intersection points and intersection lines of each cutting unit with the three-dimensional mechanical component model is as follows: for each edge of the cutting unit, find the triangle on the structural model that passes through the edge, use the intersection point of the edge and the triangle as the initial point, use Newton's iteration method to find the true intersection point of the mechanical component and the cutting unit edge, and based on the intersection point, use the tracking method to find the geometric intersection line of the mechanical component and the cutting unit surface.

6. The direct statics simulation method for three-dimensional mechanical components based on boundary representation without conformal meshing according to claim 1, characterized in that: Determine the number of model surfaces in the cutting unit; when the number of surfaces is 1, classify the cutting unit into different types of basic template units according to the intersection of the cutting unit edge and the model, and the internal and external relationship between the cutting unit vertex and the model; each type of basic template unit has its own tetrahedron decomposition rule; when the number of surfaces is greater than 1, if it contains surfaces that do not intersect with any face of the cutting unit, the cutting unit is subdivided into octrees until all the surfaces it contains intersect with the faces of the cutting unit, and then Delaunay tetrahedron decomposition is performed.

7. The direct statics simulation method for three-dimensional mechanical components based on boundary representation without conformal meshing according to claim 1, characterized in that: The curved tetrahedron is decomposed according to the basic template unit of the cutting unit: the topological form of the parameter domain of the curved surface in the unit is determined. If it is a curved triangle, no further division is required. If it is a curved quadrilateral, two opposite vertices of the curved quadrilateral are connected on the parameter domain to divide it into two curved triangles. If it is a curved pentagon, one vertex is taken and connected to the two vertices opposite to it to form two internal straight edges to divide it into three triangles. If it is a curved hexagon, two adjacent vertices are taken and connected to the two adjacent vertices opposite to it to form three internal straight edges to divide it into four curved triangles. The divided curved triangles must be without duplication or omission, and then the curved triangles are connected to the vertices of the background mesh to form a curved tetrahedron. The basic template unit accurately defines the above-mentioned edge connection relationship and topological form, and the curved edges / surfaces of the curved tetrahedron are directly defined by the boundary representation for subsequent precise integration.

8. The direct statics simulation method for three-dimensional mechanical components based on boundary representation without conformal meshing according to claim 1, characterized in that: For each curved tetrahedron of the cutting unit, the non-uniform rational B-spline enhanced finite element method is used to construct the exact parameterization of the curved tetrahedron according to the curved edge / surface definition. The integration points and integration weights of the curved tetrahedron are obtained by Gaussian integration in the parameter domain, and the exact integration of the curved tetrahedron is performed. The integral value of each curved tetrahedron is assembled into the unit stiffness matrix.

9. A direct statics simulation system for three-dimensional mechanical components without conformal meshing and boundary-oriented representation, characterized in that: Used to implement the method according to any one of claims 1 to 8.

10. A computer-readable storage medium storing computer-executable instructions, wherein the instructions are used to implement the method according to any one of claims 1 to 8 when executed.

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