Direct Static Simulation Method and System for 3D Mechanical Components Oriented to Boundary Representation

Abstract

The present invention discloses a direct static simulation method and system for three-dimensional mechanical components oriented to boundary representation, which is particularly applicable to stress and deformation analysis of aircraft and electronic products under load. The traditional finite element method requires complex conformal mesh generation for the model, and very dense elements are often needed in narrow / small feature regions, seriously affecting the calculation efficiency. The present invention embeds three-dimensional mechanical components in a regular Cartesian background grid. Through the topological structure analysis of each trimmed regular element, the unit integral calculation is converted into a high-order curved tetrahedral element integral based on templates and oriented to boundary representation. While avoiding cumbersome model conversion and mesh generation, it realizes efficient and robust static simulation calculation of mechanical products. A large number of numerical experiments have verified the accuracy, efficiency and robustness of the present invention, demonstrating great performance advantages in stress analysis of complex structures such as aircraft and electronic products.

Description

Technical Field

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

[0002] The finite element method is an important numerical analysis tool in structural mechanics, and is widely used in researching, optimizing and verifying various engineering and scientific problems, such as studying the behaviors of stress, strain, deformation and stability inside 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 structures by analyzing these physical quantities. Numerical integration is an important step in the finite element analysis method. For integrals that are difficult to calculate analytically, the numerical method uses discrete approximation to calculate the integral value. The theoretical basis of numerical integration is established on classical mathematical analysis, especially calculus theory and interpolation theory. Early numerical integration techniques include Simpson's formula, trapezoidal formula, Gaussian integration, etc. The finite element method needs to calculate integrals inside the element (such as stiffness matrix, mass matrix and load vector), and most of these integrals have no analytical solutions. Therefore, the Gaussian integration method in numerical integration is usually adopted. The integration region is transformed to the standard element, and Gaussian points and weights are used for calculation. Finally, the results of each element are summed up to obtain the final mechanical analysis result.

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

[0004] 1. Define the analysis objective: Determine the simulation task (such as vibration mode analysis, collision simulation), geometric model, material properties, boundary conditions and load conditions.

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

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

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

[0008] 5. Result post-processing: Visualize the analysis results, such as stress distribution, displacement field, etc.

[0009] In the above process, mesh generation is a key step but also the main bottleneck. CAD models of complex mechanical components (such as aircraft fuselages and wings) are usually composed of the boundary representation (BRep) method, that is, BRep class models, which need to be converted into STL models and then meshed. This process not only takes time but also may lead to loss of geometric accuracy. According to statistics, the time for mesh generation accounts for about 80% of the entire simulation process, seriously reducing the simulation efficiency.

[0010] When traditional finite element methods are used to process complex CAD models, the following problems exist:

[0011] 1. Low intermediate conversion efficiency: The CAD model needs to be converted into an STL model, resulting in additional computational overhead and accuracy loss.

[0012] 2. Complex mesh generation: Mesh generation for complex geometries (such as curved 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 efficiency, which are difficult to meet by traditional methods.

[0014] In recent years, researchers have proposed some optimization methods based on traditional finite elements, avoiding the intermediate conversion step. For example, the finite cell method directly immerses the CAD model into a simple geometric domain - such as a Cartesian background grid. After approximating the computational domain in the background grid with straight lines instead of curves, the Gaussian quadrature method is used to calculate mechanical variables. The non-uniform rational B-spline enhanced finite element method (NEFEM) directly meshes the CAD model and uses an optimized Gaussian quadrature method for sub-elements containing parametric surfaces.

[0015] However, when the finite cell method processes complex boundaries of CAD models, it relies on octree multi-level recursive processing to improve computational 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-elements suitable for its rules, and there is still no stable and efficient method in the industry to complete its meshing step.

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

[0017] The object of the present invention is to address the deficiencies in the structural mechanics simulation of key components or systems of aircraft, such as the fuselage, wings, landing gears, etc. The present invention proposes a direct static simulation method and system for three-dimensional mechanical components based on boundary representation without conformal mesh division. By directly processing the original CAD geometric model of the three-dimensional mechanical component, this method avoids the inefficient STL model conversion and manual mesh division problems in the traditional simulation process, and significantly improves the dynamic analysis efficiency and accuracy 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 mesh division, comprising the following steps:

[0020] 1) Construct a structural model for the three-dimensional mechanical component, embed the background mesh, and divide the mesh elements into internal elements and cutting elements according to the position relationship between the mesh and the model. The internal elements are the elements that completely belong to the interior of the model, and the cutting elements are the elements that do not completely belong to the interior of the model;

[0021] 2) For each cutting element, perform an intersection calculation with the boundary representation of the model to determine the internal structure of each mesh element and classify it into the basic template element;

[0022] 3) For each cutting element, perform a curved tetrahedron decomposition 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 elements, perform integration on each curved tetrahedron of the cutting elements, assemble the element stiffness matrix, solve the global equation, and obtain the static simulation result of the model.

[0024] In the above technical solution, further, in step 2), for the composed structural model, to calculate the exact geometric boundaries between the cutting unit and the model boundary, namely the intersection points and intersection lines, first, preprocess each surface of the structural model. Perform step-by-step sampling on the parameter domain where each surface is located, expand the bounding box where the parameter domain is located, and uniformly sample within the parametric surface according to the set sampling point spacing; sample according to the sampling distance of the parametric surface boundary derived from the Taylor expansion formula; triangulate the parameter domain of the parametric surface according to the sampling points and divide it into parameter triangles; map the parameter triangles to the triangles on the three-dimensional mechanical component structural model through the parametric surface expression to complete the triangulation of the structural model surface. For each edge of the cutting unit, find the triangles passing through it, use the parameter values corresponding to their intersection points as the starting points of Newton iteration, and the Newton iteration method can be used to find the true intersection points of each background grid and the model parametric surface, and then trace out the intersection lines using these intersection points.

[0025] Further, in step 2), the background grid intersecting with the model contains several surfaces. When the number of surfaces is 1, classify the elements according to the intersection situation between the element edge and the model and the internal and external relationships between the element vertices and the model, and they can be classified into 7 basic template elements; when the number of surfaces is greater than 1, if there are small surfaces inside that do not intersect any surface of the background grid, perform octree subdivision on this background grid until all the surfaces inside intersect with the surfaces of the background grid.

[0026] Further, in step 3), for each basic template element, decompose it into different types of sub-tetrahedrons. The specific decomposition method is as follows: judge 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 should be non-repetitive and non-omissive, and then connect the curved triangles with the vertices of the background grid to form curved tetrahedrons. These 7 basic template elements precisely define the above-mentioned edge connection relationships and topological forms. The curved edges / surfaces of the curved tetrahedrons are directly defined by boundary representation for subsequent exact integration.

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

[0028]

[0029] wherein is the parametric domain representation of the tetrahedral surface, is the vertex of the surface face. By performing Gaussian integration in the parametric domain, the integration points and integration weights of the curved tetrahedron are obtained, and accurate integration of the curved tetrahedron is performed; if it is a curved tetrahedron element containing a parametric edge, its parameterization is:

[0030]

[0031] wherein and the connected edge is a parametric curve, and the parametric equation of the parametric curve is , and the connected edges are all straight edges, is the formed face, is the parametric representation:

[0032]

[0033] By performing Gaussian integration in the parametric domain, the integration points and integration weights of the curved tetrahedron are obtained, and accurate integration of the curved tetrahedron is performed; the integration values of each sub-tetrahedron are assembled into the local stiffness matrix to form the element stiffness matrix of the basic template unit. The element stiffness matrices of each basic template unit are assembled according to the global node numbers to form the global stiffness matrix. Based on the global stiffness matrix, the external load vector (such as force, moment) and the boundary conditions (such as fixed constraints, displacement constraints), the global equilibrium equation is constructed, and the stress, strain distribution and other static mechanical performance indexes (such as vibration mode, fatigue life, etc.) of the model 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 one of the above.

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

[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 the method described in any one of the above.

[0038] A computer-readable storage medium stores computer-executable instructions, and the above instructions are used to implement the method described in any one of the above when executed.

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

[0040] 1) For the common curved surfaces and holes in three-dimensional mechanical components, the method of the present invention avoids the inefficient STL model conversion and manual mesh generation processes in the traditional finite element method. By using the Cartesian background mesh to divide the component model, a set of templates for decomposing the cutting elements generated from the background mesh is designed, while maintaining 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) The CAD models of three-dimensional mechanical components often contain various trimmed surfaces (such as the covering parts of the aircraft fuselage and the casting surfaces of engine components), and their parameter domains are mostly irregular polygons. When solving the intersection points and intersection lines of such trimmed surfaces and meshes, the traditional method cannot quickly and accurately find the initial points for the Newton iteration method to accurately solve the intersection points and intersection lines. The present invention combines the parameter domain triangulation method to generate high-quality parameter triangular meshes, which can cover any type of trimmed surface, so as to obtain the accurate geometric boundaries of the cutting elements, and can provide 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 to ensure the efficiency and stability of surface integral, and avoid the numerical divergence problem caused by the irregularity of the parameter domain in the traditional method. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0043] Figure 2 is a schematic diagram of the detailed flow of the method of the present invention;

[0044] Figure 3 is a schematic diagram of the structural model immersed in the Cartesian background mesh;

[0045] Figure 4 is a schematic diagram for determining the inside and outside of the background mesh;

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

[0047] Figure 6 is a schematic diagram for classifying cutting elements based on topological rules;

[0048] Figures 7 - 13 is a schematic diagram of the tetrahedron decomposition rules for 7 basic templates of cutting elements;

[0049] Figure 14 is a schematic diagram of obtaining integration points by tetrahedralizing a single cutting element. DETAILED DESCRIPTION OF THE INVENTION

[0050] The present invention will be 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 components oriented to boundary representation without conformal mesh generation, which is particularly suitable for mechanical simulation of complex mechanical systems such as aircraft fuselage structures. By immersing the CAD model of the mechanical component into a Cartesian background mesh and adaptively optimizing the integration process, the efficiency and accuracy of dynamic analysis are significantly improved.

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

[0053] Immerse the CAD model into a Cartesian background mesh domain. The immersed domain is a Cartesian background mesh of the same size, so that the mesh generation of the model can be avoided, and the integration calculation is limited to each unit mesh. Therefore, the immersed domain needs to completely cover the model, and the size of the unit mesh needs to be adaptively adjusted according to the actual model size. Subsequently, the internal and external determination of the background mesh vertices is performed. If the background mesh does not intersect with the CAD model, that is, all eight vertices are outside the model, the calculation process can ignore it; if the background mesh is completely inside the CAD model, that is, all eight vertices are inside the model, its integration method can fully use the standard Gaussian integration without further processing; when there are both vertices inside and outside the model in the background mesh, it is the unit that needs to be processed in the next step.

[0054] To determine the intersection mode 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 edges of the background mesh can be abstracted as a straight line parallel to the coordinate axis. If the intersection points of each surface of the CAD model with this straight line are directly solved, it is necessary to solve a system of nonlinear equations multiple times, resulting in reduced efficiency. Therefore, an axisymmetric bounding box (AABB) is established for each parametric surface of the CAD model, and the intersection judgment is made with the background mesh, and only the parametric surfaces with intersections of the bounding box are left.

[0055] The non - linear equations for the intersection of parametric surfaces and lines are generally solved using the Newton - Raphson iteration method to calculate the intersection points. The Newton - Raphson iteration method highly depends on the choice of the initial value. If the guessed initial point is far from the true result, it may lead to the failure to solve for the true point. Therefore, the parametric domain of the parametric surface is discretely segmented. Since parametric surfaces are mostly trimmed surfaces, that is, the parametric domain is not a regular two - dimensional rectangle and may be an irregular curved polygon composed of multiple parametric curves. Then, the AABB bounding box of the two - dimensional region where the parametric domain is located is found, and sampling points are evenly placed. The internal and external determination is performed on all sampling points, and only the sampling points located inside the parametric domain are left. Then, the parametric curves forming the boundary of the parametric domain are sampled, and thus all the vertices for triangulating the surface parametric domain are obtained. These vertices are input into the Delaunay triangulation algorithm to triangulate the entire surface parametric domain.

[0056] After triangulating the surface parametric domain, the parametric triangles are mapped into the physical domain of the three - dimensional mechanical component. Next, it is necessary to find which physical triangle the edge of the background mesh cell passes through, find the intersection point of this edge and the intersecting triangle, map it back to the parametric domain to obtain its parametric point, and use this parametric point as the starting point of the Newton iteration. Finally, the true intersection point is found according to the non - linear equations of the parametric surface and the background mesh edge.

[0057] Based on the intersection situation between the edge of the above - mentioned background mesh cell and the model, the topological structure of the intersection between the background mesh and the CAD model is inferred. Determine how many surfaces are contained in the background mesh that intersects the model. When the number of surfaces is 1, according to the intersection situation of each edge of the background mesh cell with the model and the internal and external relationships of each vertex of the background mesh cell with the model, it is classified into 7 basic templates; when the number of surfaces is greater than 1, if there are small surfaces inside that do not intersect any face of the background mesh, the background mesh is subdivided by an octree until all the surfaces contained inside intersect the faces of the background mesh.

[0058] For each basic template unit, it is decomposed into sub-tetrahedra of different categories. 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, then connect two opposite vertices of the curved quadrilateral in 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 should be non-repetitive and non-omissive. Then, connect the curved triangles with the vertices of the background grid to form curved tetrahedra. These 7 types of basic template units precisely define the above-mentioned edge connection relationship and topological form. Among them, for the sub-tetrahedra with parametric boundaries, the non-uniform rational B-spline enhanced finite element integration method is used to calculate the integration points, and for the sub-tetrahedra without parametric boundaries, the standard finite element integration method is used to calculate their element stiffness matrices. The local stiffness matrices of each sub-tetrahedron are combined to form the element stiffness matrix of the basic template unit. The element stiffness matrices of each basic template unit are assembled according to the global node numbers to form the global stiffness matrix. Based on the global stiffness matrix, external load vectors (such as forces, torques) and boundary conditions (such as fixed constraints, displacement constraints), the global equilibrium equation is constructed, and the stress, strain distributions and other mechanical property indicators (such as vibration modes, fatigue life, etc.) of the model can be calculated. The method of the present invention can be well applied to the mechanical analysis of three-dimensional mechanical components. For example, for the actual needs of aircraft structure design and simulation, there are:

[0059] In the dynamic simulation of aircraft structures, the geometric model usually contains a large number of complex features such as curved surfaces, holes and connectors. Traditional methods need to convert the CAD model into an STL mesh for finite element analysis. This process is not only time-consuming (accounting for more than 80% of the simulation cycle), but also may lead to accuracy loss of geometric details. The present invention proposes to directly immerse the aircraft CAD model into the Cartesian background grid domain. In addition, the element 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 size of the grid element can be dynamically optimized according to the wing surface curvature and local details). Through vertex inside / outside classification, the background grid elements intersecting with the aircraft structure are quickly screened out, and only the intersecting elements are processed subsequently, greatly reducing the ineffective calculation.

[0060] The CAD model of an aircraft structure is usually composed of NURBS surfaces, and its parameter domain is mostly an irregular region after trimming. To improve the calculation efficiency of the intersection line between the parametric surface and the background grid edge, the present invention adopts a parameter domain division method based on triangulation (usually Delaunay triangulation). Taking the surface of the fuselage as an example, first, the parameter domain is sampled by an AABB bounding box, the valid parameter points are retained, and the parameter 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 grid edge are further calculated to ensure the solution stability and efficiency.

[0061] In the collision simulation scenario, 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 by octree subdivision. For example, when the nose of the aircraft collides with an obstacle, the background grid cells in the intersecting area will be recursively subdivided until the accuracy requirements are met. The cells that do not need to be subdivided are classified into basic template cells according to the internal and external conditions of each vertex of the cell and the intersection conditions of each edge. Analyze the topological form of the parameter domain of the surface contained in the template cell, divide it into curved triangles by connecting edges, and then connect edges with the vertices in the background grid to form sub-tetrahedrons (possibly including sub-tetrahedrons with parametric curved edges / surfaces). For the sub-tetrahedrons with parametric boundaries, the non-uniform rational B-spline enhanced finite element integration method is used to calculate the integration points, and for the sub-tetrahedrons without parametric boundaries, the standard finite element integration method is used to calculate the element stiffness matrix of each sub-tetrahedron. The local stiffness matrices of each sub-tetrahedron are combined to form the element stiffness matrix of the basic template cell. The element stiffness matrices of each basic template cell are assembled according to the global node numbers to form the global stiffness matrix. Based on the global stiffness matrix, the external load vector (such as force, moment) and the boundary conditions (such as fixed constraints, displacement constraints), the global equilibrium equation is constructed, and the stress, strain distribution and other mechanical performance indexes (such as vibration mode, fatigue life, etc.) of the model can be calculated. This hybrid 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. Illustrated by an example, the direct static simulation method of three-dimensional mechanical components based on boundary representation without conformal mesh dissection of the present invention includes:

[0062] 1. Construct a Cartesian background grid in the space where the complex component is located

[0063] Obtain 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 required for complex models to obtain more accurate integration results. Immerse the model into the immersion domain composed of equal-sized background grids, as Figure 3 shown (only part of the grid area is shown in the figure).

[0064] 2. Sample the parameter domain of each surface of the complex component and solve the geometric boundaries of the cutting elements

[0065] Such as Figure 5 shows the parameter domain sampling results of the 13th surface of the complex component. Obtain the bounding box of the parameter domain of each surface , in order to make the distribution of sampling points more reasonable, expand the bounding box by a small constant size , where is the expanded bounding box is the lower left corner of the original bounding box is the upper right corner of the original bounding box is the expanded constant user-specified domain sampling point spacing, assumed to be , then evenly place domain sampling points with a spacing of in the plane where the two-dimensional parameter domain is located; since the surface boundary is a parametric curve, in order to make the sampling points on the parametric curve also evenly distributed, use the following formula to derive the parameter point distribution

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

[0067]

[0068] From the Taylor expansion formula, we get

[0069]

[0070] Substitute (2) into (1) to get

[0071]

[0072] That is

[0073]

[0074] The spacing of parameter points during parameter boundary sampling can be obtained

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

[0076] Preprocessing process: Traverse the discrete triangles after triangulating the parametric surfaces that make up the CAD model. If an intersection point between a certain triangle and the edge of the cutting element is found, let it be . Then further solution can be carried out. Assume the parametric expression of the line where the edge of the cutting element is located is , and the expression of the parametric surface is , the system of simultaneous equations is as follows: , the solution by Newton's method is as follows:

[0077]

[0078]

[0079] is the Jacobian matrix of this iterative formula, is the function taking the partial derivative with respect to the parameter u, and the same applies to the others. The iterative process is as follows. Substitute the starting point calculated above to obtain the recurrence parameter at each step :

[0080]

[0081] until and the distance between them is less than 1e-6, which means that the two iterations are very close. At this time, can be regarded as the intersection point of the finally obtained structural model and the edge of the cutting unit, and the intersection line can be traced out using this point by the tracing method.

[0082] 4. Classify and tetrahedronize the cutting unit according to its internal topology

[0083] After calculating the intersection points (if any) of each edge of the cutting unit with the model, at the same time, according to the internal and external relationships of the 8 vertices of the background grid (such as Figure 4 example), and the intersection relationships of the edges, it is divided into 7 categories, such as Figure 6 shown, and these 7 categories are basic template units. Figures 7 - 13 shows that the specific decomposition method of each type of basic template unit is as follows: judge the topological form of the parameter domain of the internal surface of 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 in the parameter domain to divide it into two curved triangles; if it is a curved pentagon, add two internal straight edges (connect a vertex to the two vertices of its opposite face) to divide it into three triangles; if it is a curved hexagon, add three internal straight edges (formed by connecting two adjacent vertices to the two adjacent vertices of their opposite faces) to divide it into four curved triangles. The divided curved triangles should be non-repetitive and non-omissive, and then connect the edges of the curved triangles with the vertices of the background grid to form a curved tetrahedron. If it does not conform to the basic template category and only contains one internal surface, it is subdivided by octree; if it does not conform to the basic template category and contains multiple internal surfaces, it is decomposed by the Delaunay tetrahedralization process.

[0084] 5. Integrate the sub-tetrahedron volumes inside the unit and assemble them into the global stiffness matrix to obtain the mechanical analysis results

[0085] For each curved tetrahedron of the cutting unit, referring to the non-uniform rational B-spline enhanced finite element method, an exact parameterization of the curved tetrahedron is constructed according to the definition of the curved edge / surface. If it is a curved tetrahedron element containing a parametric surface, its parameterization is as follows:

[0086]

[0087] where is the parametric domain representation of the tetrahedron surface, are the vertices of the curved face. By performing Gaussian integration in the parametric domain, the integration points and integration weights of the curved tetrahedron are obtained, and the exact integration of the curved tetrahedron is carried out. Its integral formula is:

[0088]

[0089] where is the determinant of the Jacobian matrix of the mapping .

[0090] If it is a curved tetrahedron element containing a parametric edge, its parameterization is as follows:

[0091]

[0092] where and the connected edge is a parametric curve, and the parametric equation of this parametric curve is , and the connected edges are all straight edges, is the formed face, is the parametric representation of:

[0093]

[0094] By performing Gaussian integration in the parametric domain, the integration points and integration weights of the curved tetrahedron are obtained, and the exact integration of the curved tetrahedron is carried out. Its integral formula is:

[0095]

[0096] where is the determinant of the Jacobian matrix of the mapping .

[0097] Figure 14Shows one of the background grid tetrahedralizations and integration results (the colored dots in the figure are the integration points of the sub-tetrahedrons). After parameterization, Gaussian integration points can be selected within the parameter domain of the sub-elements, and through surface mapping and linear interpolation, they can be mapped into the actual model. Each integration point contributes a local stiffness matrix, and these local stiffness matrices 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 of the structure (resistance to deformation). Finally, based on the results of these local responses, the global mechanical response of the system is solved, that is, the static simulation solution result.

[0098] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) that contain computer-usable program code.

[0099] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows 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 the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0100] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0101] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, so that the instructions executed on the computer or other programmable device provide means for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1Steps of the functions specified in one or more boxes.

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

Claims

1. A direct statics simulation method for three-dimensional mechanical components based on boundary representation, 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, the intersection calculation is performed with the boundary representation of the model and classified as a basic template unit; for each cutting unit, the Newton method is used to iteratively calculate the intersection point with the model, and the geometric intersection line between the cutting unit surface and the model is tracked using the intersection point; 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 intersection point between the triangular surface mesh and the cutting unit corresponding to the point on the parameter domain is used as the initial point of the Newton iteration method; For each cutting unit, a curved tetrahedron is decomposed according to the basic template unit type to which it is classified, and the curved edge / surface of the tetrahedron is directly defined by the boundary representation; wherein, 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 judged, 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, two vertices opposite to a vertex are connected to form two internal straight edges to divide it into three triangles; if it is a curved hexagon, two adjacent vertices are 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 background mesh vertices to form curved tetrahedrons; the basic template unit accurately defines the above-mentioned edge connection relationship and topological form, and the curved edge / surface of the curved tetrahedron is directly defined by the boundary representation for subsequent precise integration; 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 components based on boundary representation 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 components based on boundary representation according to claim 1, 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.

4. The direct statics simulation method for three-dimensional mechanical components based on boundary representation according to claim 1, 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.

5. The direct statics simulation method for three-dimensional mechanical components based on boundary representation 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.

6. The direct statics simulation method for three-dimensional mechanical components based on boundary representation 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.

7. A direct statics simulation system for three-dimensional mechanical components based on boundary representation, characterized in that: Used to implement the method according to any one of claims 1 to 6.

8. 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 6 when executed.

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