Free-form surface grid paving method and device based on mechanics principle

Abstract

The invention discloses a free-form surface grid paving method and device based on the mechanics principle, and the method comprises the steps: building a target curved surface, building an active surface and a passive surface corresponding to the target curved surface, and enabling the passive surface to be located on the active surface; further analyzing the target curved surface and the active surface to obtain a displacement load between the target curved surface and the active surface; further analyzing the passive surface, and setting a constraint relationship between the passive surface and the active surface; step-by-step iterative loading is carried out on the active surface based on the displacement load and the constraint relation so as to update the passive surface; and based on the target curved surface, further analyzing the passive surface, and optimizing the passive surface through a deviation reduction method. According to the method, the expected grid form can be automatically laid on the free-form surface through mechanical simulation based on the mechanics principle, the laying difficulty of the complex grid form is reduced, free laying of the complex grid is achieved, and the time cost is saved. The obtained grid form is natural and smooth and has mechanical properties, and additional improvement measures are not needed.

Description

Technical Field

[0001] This invention relates to the field of building structure technology, and more specifically, to a method and apparatus for laying free-form surface grids based on mechanical principles. Background Technology

[0002] With the rapid development of computer-aided design technology, freeform surface structures are increasingly being promoted and applied in architectural projects due to their natural and smooth visual expression and diversified architectural functions. To achieve the architectural form of a freeform surface, it is necessary to first find a supporting grid system that adapts to the building's skin shape. However, due to the free transformation and complexity of the surface, finding a suitable supporting grid system is extremely difficult. Currently, research on grid generation for freeform surface spatial structures is still in its early stages, and there is no mature and widely applicable grid generation theory or method. The most commonly used methods fall into two categories: direct segmentation, which directly segments the surface to form a grid, and direct segmentation is further divided into segmentation methods controlled by certain grid logic rules and finite element mesh generation methods. The other category is mapping, which typically involves forming the required grid on a plane and then mapping it onto the surface using mathematical methods.

[0003] However, direct segmentation methods based on certain mesh logic rules often involve complex logic rules, making mesh generation difficult. Furthermore, the meshes obtained by direct segmentation methods based on finite element mesh generation are usually monotonous and overly uniform in distribution, lacking variation and failing to meet specific design requirements. Mapping methods, on the other hand, suffer from mapping distortion when the surface curvature varies significantly, requiring additional processing that is cumbersome.

[0004] Therefore, it is necessary to design a freeform surface mesh laying method and device based on mechanical principles. This method should be able to automatically lay the desired mesh form onto a freeform surface based on mechanical principles and through mechanical simulation, reducing the difficulty of laying complex mesh forms, realizing the freedom of complex mesh laying, and saving time and costs. At the same time, the obtained mesh form should be natural and smooth and have mechanical properties, meeting specific design requirements without the need for additional improvement measures. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for laying freeform surface meshes based on mechanical principles, so as to solve the problems of existing mesh generation methods for freeform surface spatial structures, which have high difficulty in mesh generation, single form and lack of variation, and the need to improve the mapping distortion.

[0006] To achieve the above objectives, this invention provides a freeform surface mesh laying method based on mechanical principles, comprising the following steps:

[0007] A target surface is established, and corresponding active and passive surfaces are created, with the passive surface located on the active surface. The target surface and active surface are further analyzed to obtain the displacement load between them. The passive surface is further analyzed, and the constraint relationship between the passive surface and the active surface is set. Based on the displacement load and constraint relationship, the active surface is iteratively loaded in steps to update the passive surface. Finally, based on the target surface, the passive surface is further analyzed, and the passive surface is optimized using the deviation restoration method.

[0008] The freeform surface mesh laying method based on mechanical principles provided by this invention can automatically lay the desired mesh form onto a freeform surface based on mechanical principles and through mechanical simulation, reducing the difficulty of laying complex mesh forms, realizing the freedom of complex mesh laying, and saving time and costs. At the same time, the obtained mesh form is natural and smooth and has mechanical properties, which can meet specific design requirements without the need for additional improvement measures.

[0009] The above-mentioned freeform surface mesh laying method based on mechanical principles establishes the active and passive surfaces within the target surface.

[0010] The above-mentioned freeform surface mesh laying method based on mechanical principles has active and passive surfaces that are spherical, planar, or curved, and the active and passive surfaces have the same shape.

[0011] In the above-mentioned freeform surface mesh tiling method based on mechanical principles, if the active and passive surfaces are spherical or curved, the volume of the active and passive surfaces is half the volume of the target curved surface.

[0012] The aforementioned freeform surface mesh tiling method based on mechanical principles further includes the following steps for analyzing the target surface and the active surface to obtain the displacement load between the target surface and the active surface: establishing a mapping relationship between the target surface and the active surface; obtaining the first coordinate data of each node of the target surface according to the mapping relationship; obtaining the second coordinate data of each node on the active surface corresponding to the target surface; and obtaining the displacement load based on the first coordinate data and the second coordinate data.

[0013] The aforementioned method for tiling freeform surfaces based on mechanical principles, which involves obtaining the first coordinate data of each node on the target surface according to the mapping relationship, and obtaining the second coordinate data of each node on the active surface corresponding to the target surface, further includes: dividing the target surface and the active surface into meshes according to the mapping relationship to obtain the first coordinate data and the second coordinate data.

[0014] The above-mentioned freeform surface mesh tiling method based on mechanical principles uses automatic meshing, triangular meshing, or quadrilateral meshing as the meshing method.

[0015] The above-mentioned freeform surface mesh laying method based on mechanical principles has a radial-to-circular mapping relationship.

[0016] The aforementioned freeform surface meshing method based on mechanical principles further includes the steps of analyzing the passive surface and setting the constraint relationship between the passive and active surfaces, specifically: meshing the passive surface and setting contact constraints between the passive and active surfaces.

[0017] The aforementioned freeform surface mesh laying method based on mechanical principles uses sliding contact constraints as the contact constraint.

[0018] The aforementioned method for meshing freeform surfaces based on mechanical principles further includes the following steps for meshing a passive surface: setting the centroid of each mesh unit of the passive surface according to the mesh form of the passive surface; performing mesh triangulation on the mesh unit according to the centroid; and numbering the nodes and centroids of the mesh unit respectively.

[0019] In the aforementioned freeform surface mesh tiling method based on mechanical principles, the node numbers and centroid numbers are different.

[0020] The aforementioned freeform surface mesh tiling method based on mechanical principles, which involves iteratively loading the active surface to update the passive surface, further includes: setting an iterative displacement loading amount based on the displacement load; loading the active surface with the iterative displacement loading amount to obtain iterative active surfaces and iterative passive surfaces, and updating the active and passive surfaces based on the iterative active and passive surfaces; and updating the displacement load based on the displacement load and the iterative displacement loading amount, and repeating the step of updating the passive surface until the displacement load is 0.

[0021] The aforementioned freeform surface mesh tiling method based on mechanical principles, further includes the step of setting iterative displacement loading based on displacement load, which further comprises: preloading displacement load onto the active surface to obtain the maximum displacement loading; and setting iterative displacement loading based on the maximum displacement loading; wherein the iterative displacement loading is less than or equal to the maximum displacement loading.

[0022] The aforementioned freeform surface mesh tiling method based on mechanical principles, further includes the step of updating the displacement load based on the displacement load and the iterative displacement loading amount, which further comprises: updating the displacement load based on the difference between the displacement load and the iterative displacement loading amount.

[0023] The aforementioned freeform surface mesh laying method based on mechanical principles updates the passive surface by performing step-by-step iterative loading on the active surface using a geometric nonlinear calculation method, wherein the membrane stiffness of the passive surface is set to 10-100 MPa.

[0024] The aforementioned freeform surface meshing method based on mechanical principles, which optimizes the passive surface through the deviation restoration method, further includes: establishing a mapping relationship between the target surface and the passive surface, optimizing the passive surface according to the mapping relationship, and updating the mesh form of the passive surface according to the nodes of the passive surface.

[0025] The aforementioned freeform surface mesh tiling method based on mechanical principles, further includes the following steps for optimizing the passive surface according to the mapping relationship: obtaining the third coordinate data of each node of the target surface according to the mapping relationship, and obtaining the fourth coordinate data of each node on the passive surface corresponding to the target surface; and, if the third coordinate data is not equal to the fourth coordinate data, updating the fourth coordinate data according to the third coordinate data to optimize the passive surface.

[0026] To better achieve the objectives of this invention, the present invention also provides a freeform surface mesh laying device based on mechanical principles, used to implement the above method, including: a modeling module for establishing a target surface and establishing an active surface and a passive surface corresponding to the target surface, with the passive surface located on the active surface; a displacement load analysis module for further analyzing the target surface and the active surface to obtain the displacement load between the target surface and the active surface; a constraint module for further analyzing the passive surface and setting the constraint relationship between the passive surface and the active surface; an iterative analysis module for performing step-by-step iterative loading on the active surface to update the passive surface based on the displacement load and constraint relationship; and a model optimization module for further analyzing the passive surface based on the target surface and optimizing the passive surface through a deviation restoration method.

[0027] To better achieve the objectives of this invention, this invention also provides a computer-readable storage medium having a computer program stored thereon, the computer program being configured to execute the freeform surface mesh tiling method based on mechanical principles as described above when running.

[0028] To better achieve the objectives of this invention, the present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to execute the freeform surface mesh tiling method based on the above mechanical principles.

[0029] To better achieve the objectives of this invention, this invention also provides a computer program product, including a computer program that, when executed by a processor, implements the freeform surface mesh tiling method based on mechanical principles as described above.

[0030] Furthermore, the freeform surface mesh laying device, computer-readable storage medium, electronic device, and computer program product based on mechanical principles provided by this invention have the same beneficial technical effects as the above-mentioned methods.

[0031] To provide a better understanding of the above and other aspects of the present invention, specific embodiments are described below in conjunction with the accompanying drawings, but these are not intended to limit the scope of protection of the present invention. Attached Figure Description

[0032] Figure 1 This is a flowchart illustrating the steps of a freeform surface mesh laying method based on mechanical principles, according to an embodiment of the present invention.

[0033] Figure 2 This is a cross-sectional view of the target surface, passive surface, and active surface according to an embodiment of the present invention.

[0034] Figure 3A This is a schematic diagram of an embodiment of the present invention, in which the active surface and the passive surface are spherical.

[0035] Figure 3B This is a schematic diagram of an embodiment of the present invention, in which the active and passive surfaces are planar.

[0036] Figure 3C This is a schematic diagram of an embodiment of the present invention where the active surface and the passive surface are curved surfaces.

[0037] Figure 4 This is a flowchart illustrating the steps for obtaining displacement load according to an embodiment of the present invention.

[0038] Figure 5A This is a schematic diagram of the mesh mapping of the target surface based on the radial-to-circular mapping relationship according to an embodiment of the present invention.

[0039] Figure 5B This is a schematic diagram of the mesh mapping of the active surface based on the radial-to-circular mapping relationship according to an embodiment of the present invention.

[0040] Figure 6A This is a schematic diagram of a passive surface in the form of a quadrilateral grid, according to an embodiment of the present invention.

[0041] Figure 6B This is a schematic diagram of the passive surface after mesh triangulation processing according to an embodiment of the present invention.

[0042] Figure 7A This is a schematic diagram of the nodes before active surface displacement according to an embodiment of the present invention.

[0043] Figure 7B This is a schematic diagram of a node after active surface displacement according to an embodiment of the present invention.

[0044] Figure 8 This is a flowchart illustrating the step-by-step iterative loading process according to an embodiment of the present invention.

[0045] Figure 9 This is a schematic diagram illustrating the setting of the iterative displacement loading amount according to an embodiment of the present invention.

[0046] Figures 10A to 10E This is a schematic diagram illustrating step-by-step iterative loading according to an embodiment of the present invention.

[0047] Figure 11 This is a flowchart illustrating the steps of a deviation restoration method according to an embodiment of the present invention.

[0048] Figure 12A This is a schematic diagram of a passive surface obtained by step-by-step iterative loading of an active surface according to an embodiment of the present invention.

[0049] Figure 12B This is a schematic diagram illustrating the deviation between the passive surface and the target surface in one embodiment of the present invention.

[0050] Figure 12C This is a schematic diagram of an optimized passive surface according to an embodiment of the present invention.

[0051] Figure 12D This is a schematic diagram of the updated passive surface mesh form according to an embodiment of the present invention.

[0052] Figure 13 This is a structural block diagram of a freeform surface mesh laying device based on mechanical principles, according to an embodiment of the present invention.

[0053] Figure 14 This is a structural block diagram of an electronic device according to an embodiment of the present invention.

[0054] In the attached figures, the following labels are used:

[0055] S1, S2, S21, S211, S3, S4, S41, S5, S51, S511: Steps of the freeform surface mesh laying method based on mechanical principles

[0056] 1, 1', 1”, 1”', 11, 12 – Target Surface

[0057] 2.21 – Active Side

[0058] 3, 3', 3”, 3”' – Passive side

[0059] 31, 31' – Passive Surface

[0060] 41, 41', 41”, 41”', 41”” – Passive side

[0061] 51, 51', 51” – Passive side

[0062] O – Center point of the target surface

[0063] O' – Center point of active surface

[0064] L, L' – Intersection

[0065] A, A' – Nodes

[0066] P1, P2, P1', P2' – Active surface boundary nodes

[0067] P3, P3' – Passive surface boundary nodes

[0068] G – Quadrilateral Mesh Cell

[0069] 100, 101, 102, 103 – Nodes of quadrilateral mesh cells

[0070] Centroid of 1000000-quadrilateral mesh element

[0071] D1, D2 – Iterative displacement loading amounts

[0072] 100A - Freeform Surface Mesh Laying Device Based on Mechanical Principles

[0073] 101A – Modeling Module

[0074] 102A – Displacement Load Analysis Module

[0075] 103A – Constraint Module

[0076] 104A – Iterative Analysis Module

[0077] 105A – Model Optimization Module

[0078] 200A – Electronic Equipment

[0079] 201A – Memory

[0080] 202A – Processor Detailed Implementation

[0081] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that references to "an embodiment," "embodiment," "example embodiment," etc., in the specification refer to embodiments that may include specific features, structures, or characteristics, but do not necessarily include these specific features, structures, or characteristics. Furthermore, such expressions do not refer to the same embodiment. Moreover, when describing specific features, structures, or characteristics in conjunction with embodiments, whether or not explicitly described, it indicates that incorporating such features, structures, or characteristics into other embodiments is within the knowledge scope of those skilled in the art.

[0082] It should be noted that in this specification, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Certain terms are used in the specification and subsequent claims to refer to specific modules, components, or parts. Those skilled in the art will understand that users or manufacturers may use different names or terms to refer to the same module, component, or part. This specification and subsequent claims do not distinguish modules, components, or parts by differences in name, but rather by differences in function. The terms "comprising" and "including" used throughout the specification and subsequent claims are open-ended and should be interpreted as "including but not limited to." Furthermore, the term "connection" here includes any direct and indirect electrical connection means. Indirect electrical connection means include connections via other means.

[0083] Furthermore, in the following description and claims, numerous terms will be referenced, which should be defined as having the following meanings. The singular forms “a” and “the” include plural referents, unless the context clearly specifies otherwise. “Optional” or “optionally” indicates that an event or situation subsequently described may or may not occur, and the description includes both the scenario where the event occurs and the scenario where the event does not occur.

[0084] The core of this invention lies in providing a method and apparatus for laying freeform surface meshes based on mechanical principles. This method automatically lays the desired mesh form onto a freeform surface based on mechanical principles and through mechanical simulation, reducing the difficulty of laying complex mesh forms, achieving freedom in complex mesh laying, and saving time and costs. Simultaneously, the obtained mesh form is natural and smooth, possessing mechanical properties, and can meet specific design requirements without requiring additional improvement measures.

[0085] It should be noted that this invention is implemented using one or more of the following: 3D modeling software (including AutoCAD, SketchUp, Rhino, Revit, 3ds Max or other software capable of modeling), finite element analysis software (including ABAQUS, ANSYS, OptiStruct, Nastran, Femap or other software capable of finite element analysis), and / or programming languages ​​(including Grasshopper and its battery pack function, Python or other programming languages ​​capable of linear and nonlinear design), but this invention is not limited thereto.

[0086] Please see Figure 1 , Figure 1The flowchart of a freeform surface mesh laying method based on mechanical principles according to an embodiment of the present invention includes the following steps:

[0087] S1: Create the target surface, and create an active surface and a passive surface corresponding to the target surface, with the passive surface located on top of the active surface.

[0088] In one specific embodiment, when using the freeform surface mesh tiling method based on mechanical principles provided by this invention, a target surface is established according to the shape of the freeform surface to be tiled. The target surface is the mesh form ultimately desired by this invention. The freeform surface is the building shape to be constructed or designed, which is an existing completed building model or data. The target surface is directly established by importing the existing model or data, or the target surface can be newly generated by the user in modeling software according to the building or design needs. This invention is not limited to this. Corresponding to the shape of the target surface, active surfaces and passive surfaces are established respectively. Specifically, the passive surface is located on the active surface and is attached to the active surface. The active surface is used to achieve uniform expansion to the target surface, and the passive surface attached to the active surface is pushed by the expansion of the active surface to finally tile onto the target surface to obtain the desired mesh form. The obtained passive surface is the support mesh system adapted to the target surface. Furthermore, the established passive surface is a polygonal mesh structure, which is established by importing existing meshes from the database or by creating them as needed, without the need for additional meshing processing. It should be noted that the polygonal mesh structure of the passive surface is in the form of a quadrilateral mesh, or it can be in other polygonal mesh forms, and this invention is not limited thereto.

[0089] Please see Figure 2 , Figure 2 This is a cross-sectional view of the target surface, passive surface, and active surface according to an embodiment of the present invention. In a preferred embodiment, the active surface 2 and passive surface 3 are established within the target surface 1. In a specific embodiment, to provide sufficient expansion and deformation space for the active surface 2 and passive surface 3, they are established within the target surface 1. Furthermore, depending on the shape of the target surface 1, i.e., the desired freeform architectural shape, parts of the passive surface 3 and active surface 2 may extend beyond the target surface 1, and the volumes of the active surface 2 and passive surface 3 may also be other sizes depending on the different shapes of the target surface 1; the present invention is not limited thereto.

[0090] Please refer to Figures 3A to 3C , Figure 3A This is a schematic diagram showing that the active surface and the passive surface are spherical according to an embodiment of the present invention. Figure 3B This is a schematic diagram illustrating that the active and passive surfaces are planar in one embodiment of the present invention. Figure 3C This is a schematic diagram of an embodiment of the present invention where the active surface and the passive surface are curved surfaces.

[0091] In a preferred embodiment, the active and passive surfaces are spherical, planar, or curved, and they have the same shape. In one specific embodiment, active and passive surfaces with shapes corresponding to the target curved surface can be created based on the different shapes of the target curved surface. For example... Figure 3A As shown, based on the shape of the target surface 1', the passive surface 3' is an ellipsoid, and a portion of the passive surface 3' extends beyond the range of the target surface 1'; for example... Figure 3B As shown, based on the shape of the target surface 1", the passive surface 3" is a plane and lies within the target surface 1"; as Figure 3C As shown, based on the shape of the target surface 1”', the passive surface 3”' is an irregular curved surface and is located within the target surface 1”'. Furthermore, if the active and passive surfaces 3’, 3”' are spherical or curved surfaces, their volumes are half the volume of the target surfaces 1’, 1”', so as to obtain a mesh form with a significant expansion-driven effect with high efficiency during the expansion process of the active and passive surfaces 3’, 3”'. It should be noted that the ratio of the volume of the active and passive surfaces 3’, 3”' to the volume of the target surfaces 1’, 1”' can also be other values, such as 30%-60%, but this invention is not limited to these values.

[0092] In this embodiment of the invention, by establishing active and passive surfaces, and by using the expansion of the active surface to push the passive surface to the target surface to obtain the desired mesh form, the tiling method of the present invention is applicable to freeform surfaces of different shapes, and has wide applicability and high adaptability, and is not limited to specific freeform surfaces.

[0093] Please see Figure 4 , Figure 4 This is a flowchart illustrating the steps for obtaining displacement load according to an embodiment of the present invention. The present invention provides a freeform surface mesh laying method based on mechanical principles, which further includes the following steps:

[0094] S2: Further analyze the target surface and the active surface to obtain the displacement load between the target surface and the active surface.

[0095] In a preferred embodiment, the step of further analyzing the target surface and the active surface to obtain the displacement load between the target surface and the active surface further includes:

[0096] S21: Establish the mapping relationship between the target surface and the active surface, obtain the first coordinate data of each node of the target surface according to the mapping relationship, and obtain the second coordinate data of each node of the active surface corresponding to the target surface. Obtain the displacement load according to the first coordinate data and the second coordinate data.

[0097] In one specific embodiment, to enable the active surface to expand and push the passive surface towards the target surface to obtain the desired mesh shape, it is necessary to further analyze the displacement load between the target surface and the active surface. Based on the target surface and the active surface established in step S1, a mapping relationship between the target surface and the active surface is established using one or more of 3D modeling software, finite element analysis software, and / or programming languages. That is, a one-to-one mapping relationship is established between points on the target surface and points on the active surface. This mapping relationship is a radial-to-circular mapping relationship, but the present invention is not limited thereto.

[0098] Please see Figure 5A and Figure 5B , Figure 5A This is a schematic diagram of the mesh mapping of a target surface based on radial-to-circular mapping relationship according to an embodiment of the present invention. Figure 5B This is a schematic diagram of the mesh mapping of an active surface based on a radial-to-circular mapping relationship according to an embodiment of the present invention. In a specific embodiment, a target surface 11 and a planar active surface 21 are established according to step S1, and a radial-to-circular mapping relationship is established between the target surface 11 and the active surface 21. Specifically, as... Figure 5A and Figure 5B As shown, the radial-to-circular mapping relationship is a parameterized correspondence expressed by the polar radius and rotation angle of the polar coordinate system. The center point O of the target surface 11 and the center point O' of the active surface 21 are taken as the origin. Vertical planes within the coordinate system are rotated around the origin at a certain angle to cut the target surface 11 and the active surface 21 respectively, forming two sets of intersection lines L and L'. These intersection lines L and L' are divided into the same number of segments, and the resulting segment points have a one-to-one paired mapping relationship. For example... Figure 5A and Figure 5B As shown, based on the radial-to-circular logical relationship, node A on the target surface 11 and node A' on the active surface 21 have a one-to-one pairing mapping relationship. It should be noted that the mapping relationship between the target surface 21 and the active surface 22 can also be other or set as needed, and the present invention is not limited thereto.

[0099] Furthermore, based on the mapping relationship between the target surface 11 and the active surface 21, the first coordinate data of each node on the target surface 11 and the second coordinate data of each node on the active surface 21 corresponding to the target surface 11 are obtained. Then, the displacement load is obtained based on the first and second coordinate data. The first coordinate data represents the three-dimensional coordinates of each node on the target surface 11, and the second coordinate data represents the three-dimensional coordinates of each node on the active surface 21 corresponding to the target surface 11. These coordinates are obtained using 3D modeling software, finite element analysis software, and / or programming languages; this invention is not limited to these methods. Based on the first and second coordinate data, the displacement difference between each node on the target surface 11 and its corresponding node on the active surface 21 is calculated, thus obtaining the displacement load of each node between the target surface 11 and the active surface 21.

[0100] In a preferred embodiment, the steps of obtaining the first coordinate data of each node of the target surface according to the mapping relationship, and obtaining the second coordinate data of each node on the active surface corresponding to the target surface, further include:

[0101] S211: Based on the mapping relationship, mesh the target surface and the active surface respectively to obtain the first coordinate data and the second coordinate data.

[0102] In one specific embodiment, after establishing the target surface and the active surface, the target surface and the active surface are meshed using the meshing function of 3D modeling software, finite element analysis software, and / or programming languages ​​to form individual nodes and obtain the first and second coordinate data of each node. In the engineering field, meshing is commonly used in finite element analysis to ensure computational accuracy and efficiency. The main purpose of surface meshing is to discretize a continuous surface into a series of discrete mesh elements for subsequent numerical calculations or simulation analysis; this process is called mesh generation or meshing. Meshing can transform complex continuous surface problems into discrete numerical problems that can be solved using computers, thereby obtaining more accurate computational or simulation results. Furthermore, the meshing methods can be automatic meshing, triangular meshing, or quadrilateral meshing. In one specific embodiment, since the active surface pushes the passive surface through expansion, the target surface and the active surface do not need to have an excessively high level of surface meshing fineness. Quadrilateral meshing is used to mesh the target surface and the active surface into a quadrilateral mesh structure, but this invention is not limited thereto.

[0103] In this embodiment of the invention, by establishing a mapping relationship between the target surface and the active surface, the displacement load required for the active surface to push the passive surface to be laid onto the target surface can be accurately obtained, further enabling the passive surface to be applied to different types of complex free-form surface structures and reducing the difficulty of laying.

[0104] Please refer to the following: Figure 1 The present invention provides a freeform surface mesh laying method based on mechanical principles, which further includes the following steps:

[0105] S3: Further analyze the passive surface and set the constraint relationship between the passive surface and the active surface.

[0106] In a preferred embodiment, the step of further analyzing the passive surface and setting the constraint relationship between the passive surface and the active surface further includes:

[0107] Mesh the passive surface and set contact constraints between the passive and active surfaces.

[0108] In a preferred embodiment, the step of meshing the passive surface further includes:

[0109] Based on the mesh form of the passive surface, the centroid of each mesh cell of the passive surface is set, and the mesh cells are triangulated based on the centroids; and the nodes and centroids of the mesh cells are numbered respectively.

[0110] Please see Figure 6A and Figure 6B , Figure 6A This is a schematic diagram of a passive surface in the form of a quadrilateral grid according to an embodiment of the present invention. Figure 6B This is a schematic diagram of the passive surface after mesh triangulation processing according to an embodiment of the present invention.

[0111] Similar to the purpose of meshing the target surface and the active surface in step S2, to facilitate subsequent numerical calculations and simulation analysis, the passive surface is meshed triangulated using the meshing functions of 3D modeling software, finite element analysis software, and / or programming languages. Furthermore, since the passive surface needs to be pushed by the expansion of the active surface to ultimately fit onto the complex target surface to obtain the desired mesh form, the passive surface requires a higher degree of mesh refinement than the active and target surfaces to ensure the accuracy and efficiency of subsequent simulation calculations. Please refer to [reference needed]. Figure 5A , 5B and Figure 6A In one specific embodiment, such as Figure 5A and 5B As shown, the target surface 11 and the active surface 21 are meshed using a quadrilateral meshing method, meaning that the target surface 11 and the active surface 21 are divided into multiple quadrilateral mesh structures. Please refer to [further details omitted]. Figure 6A In this embodiment of the invention, the mesh structure of the passive surface 31 is a quadrilateral polygonal mesh, but the invention is not limited thereto.

[0112] Since the mesh of the passive surface can be any polygon, and polygonal meshes are not conducive to finite element calculations, it is necessary to triangulate the polygonal mesh before calculation. In a specific embodiment, such as... Figure 6B As shown, the passive surface 31' is composed of multiple quadrilateral mesh elements G. The method for mesh triangulation involves setting the centroid 1000000 of the quadrilateral mesh element G and connecting the centroid 10000000 with nodes 100, 101, 102, and 103 of the quadrilateral mesh element G. This divides the quadrilateral mesh element G into four triangles. The same method is applied to other polygonal mesh elements G sequentially. This method is applicable to any polygonal mesh form and will not be elaborated further. After mesh triangulation, the passive surface 31' has a mesh form composed of multiple triangular mesh elements.

[0113] Furthermore, to facilitate subsequent calculations, the nodes and centroids of the quadrilateral mesh element G need to be numbered separately, with the node numbers and centroid numbers being different. In one specific embodiment, to distinguish between the node numbers and centroid numbers, the starting number of the centroid can be set to be greater than the total number of mesh nodes. For example... Figure 6B As shown, the nodes are numbered sequentially from 100, 101, 102, and 103, while the centroids are numbered starting from 1000000. Each quadrilateral mesh element G is composed of its corresponding numbered nodes. The node numbers remain unchanged during the calculation process. It should be noted that the data processing described above can be achieved using any software with data processing capabilities, not limited to Grasshopper.

[0114] Furthermore, to ensure the passive surface is pushed onto the target curved surface by the active surface, and simultaneously allows the passive surface to slide freely on the active surface and automatically adjust its position under the action of membrane stress, the constraint relationship between the passive and active surfaces is further set as a contact constraint. Specifically, the active surface is set as a shell element and the passive surface as a membrane element using 3D modeling software, finite element analysis software, and / or programming languages. The deformation of shell elements is mainly bending, and they can withstand in-plane tensile and bending stresses. Using shell elements for simulation can save computation time and increase solution accuracy. Membrane elements, on the other hand, can only withstand in-plane tensile (or tension) loads, providing strength on the element plane but lacking bending stiffness. Therefore, the active and passive surfaces are set as sliding contact constraints, allowing the passive surface to deform with the deformation of the active surface while maintaining slidability between them. In one specific embodiment, the sliding contact constraint on the active and passive surfaces is implemented using ABAQUS software. It is implemented using the node-to-surface and surface-to-surface functions in the Discretization Method of contact, or using the finite sliding and small sliding functions in the Tracking Method of contact, as well as the corresponding path-based and state-based tracking algorithms. This invention is not limited to these methods.

[0115] Furthermore, during the process of the active surface pushing the passive surface to move and tile onto the target surface, if the passive and active surfaces are set to sliding contact constraints, the boundaries of the passive surface and the active surface can be further configured to move in a coordinated manner. Specifically, the boundaries of the active and passive surfaces are defined based on two adjacent nodes on the meshed active surface and the arc length. Please refer to [link to relevant documentation]. Figure 7A and Figure 7B , Figure 7A This is a schematic diagram of a node before active surface displacement according to an embodiment of the present invention. Figure 7B This is a schematic diagram of the nodes after displacement of the active surface according to an embodiment of the present invention. In a specific embodiment, the passive surface is located above and in contact with the active surface. The meshed boundary nodes P1 and P2 of the active surface and the boundary node P3 of the passive surface connected to the active surface are shown below. Figure 7A As shown. When the active surface undergoes displacement, the boundary nodes P1' and P2' of the active surface are the positions of the nodes after displacement, while the boundary node P3' of the passive surface is the position of the node after displacement due to the push of the active surface. The coordinated displacement of the passive surface boundary node P3' with the boundary of the active surface is limited by the following formula:

[0116] P3′ i =P2′i +l P2P3 / l P1P2 (P1′ i -P2′ i )

[0117] Among them, P3′ i Let P3 represent the new coordinates of point P3 in the i(x,y,z) direction, and P2′ represent the new coordinates of point P3 in the i(x,y,z) direction. i Let P2 represent the new coordinates of point P2 in the direction i(x,y,z), and let P1′ be the coordinates of point P2. i Let l represent the new coordinates of point P1 in the i(x,y,z) direction. P2P3 The length of the arc between points P2 and P3 is represented by l. P1P2 This represents the arc length between points P1 and P2. The active surface boundary nodes P1, P2, P1', and P2' are two adjacent nodes on the active surface boundary after meshing, and the passive surface boundary nodes P3 and P3' are nodes connected to the arc between these two adjacent nodes. This invention is not limited to these boundaries. When the passive surface experiences excessive distortion during displacement, the boundary constraints can be partially relaxed, and the correspondence between the active and passive surfaces' coordinated displacements can be omitted, with only the sliding contact constraint between the active and passive surfaces as described above. In one specific embodiment, if the active and passive surfaces are planes, the nodes at the boundary can be restricted only in their Z-direction displacement, thereby achieving free sliding of the passive surface boundary at the active surface boundary. However, this invention is not limited to these boundaries. Furthermore, depending on the shape and structure requirements of the target surface and the passive surface, the constraint relationship between the passive surface boundary and the target surface boundary can be further set. Specifically, the nodes where the boundary of the passive surface connects to the bottom boundary of the target surface are constrained to the bottom boundary of the target surface and do not shift with the push of the active surface, so as to form a four-point constrained surface or a six-point constrained surface in which four or six nodes on the boundary of the passive surface are constrained to the bottom boundary of the target surface, but the present invention is not limited thereto.

[0118] In this embodiment of the invention, by setting a constraint relationship between the active surface and the passive surface, the passive surface is able to slide freely on the active surface, and can automatically adjust its position during the expansion and pushing process of the active surface, so that the final passive surface has the characteristics of uniform distribution, natural transition, well-proportioned density and tension.

[0119] Please see Figure 8 , Figure 8 This is a flowchart illustrating the step-by-step iterative loading process according to an embodiment of the present invention. The present invention provides a freeform surface mesh laying method based on mechanical principles, which further includes the following steps:

[0120] S4: Based on the relationship between displacement load and constraint, the active surface is iteratively loaded in stages to update the passive surface.

[0121] In a preferred embodiment, the step of performing step-by-step iterative loading on the active surface to update the passive surface further includes:

[0122] S41: Set the iterative displacement loading amount based on the displacement load;

[0123] Apply iterative displacement loading to the active surface to obtain the iterative active surface and the iterative passive surface, and update the active surface and the passive surface based on the iterative active surface and the iterative passive surface; and,

[0124] The displacement load is updated based on the displacement load and the iterative displacement loading amount, and the step of updating the passive surface is repeated until the displacement load is 0.

[0125] After establishing, analyzing, and setting the target surface, active surface, and passive surface through steps S1 to S3, the active surface is further iteratively loaded stepwise according to displacement loads and constraint relationships to push the passive surface to the target surface to obtain the desired mesh form. Since the deformation of the passive surface during its approach to the target surface is enormous, such a large deformation will cause mesh distortion, leading to divergent calculation results and preventing successful loading in one go. Therefore, this invention uses a stepwise iterative loading method to achieve the approach and tiling of the passive surface to the target surface. The approximation of the passive surface by the active surface is controlled by displacement loading, dividing the total displacement load into multiple steps, thus achieving the effect of stepwise approach and tiling to the target surface. In actual operation, the result of the previous step in the stepwise iterative loading process becomes the initial state for the next step, continuously updating the model's geometric features, and iterating in this way to obtain the final active and passive surfaces.

[0126] In one specific embodiment, the displacement load and constraint relationship are obtained according to steps S2 and S3. The iterative displacement loading amount for each step in the step-by-step iterative loading process is further set based on the displacement load. The active surface is subjected to iterative displacement loading amounts using 3D modeling software, finite element analysis software, and / or programming languages ​​for simulation analysis and calculation. After the active surface is loaded with iterative displacement loading amounts, it expands and pushes the passive surface closer to the target surface. Because the active surface deforms and shifts to new spatial coordinates after the iterative displacement loading amount is applied, and the passive surface also deforms and shifts to new spatial coordinates due to the sliding contact constraint relationship with the active surface, new active and passive surfaces can be obtained after one iterative displacement loading amount is completed. These new active and passive surfaces are then used as iterative active and passive surfaces. The spatial coordinate data of the iterative active and passive surfaces are used to update the active and passive surfaces. Based on the active and passive surfaces obtained after one iterative displacement loading amount is completed, the above steps are repeated for the next iterative loading. Since the total displacement load required to push the passive surface to the target surface is the displacement load obtained in step S2, after each iteration of loading is completed, the iterative displacement load loaded in this step is removed from the displacement load, the remaining displacement load is updated to the displacement load of the next iteration of loading, and a new iterative displacement load is set according to the new displacement load in the next step, until all displacement loads are loaded, so that after the last iteration of loading is completed, the remaining displacement load after deducting the iterative displacement load loaded in this step from the displacement load is 0.

[0127] In a preferred embodiment, the step of setting the iterative displacement loading amount based on the displacement load further includes:

[0128] Preload the active surface with a displacement load and obtain the maximum displacement load; and,

[0129] The iterative displacement loading is set based on the maximum displacement loading; wherein the iterative displacement loading is less than or equal to the maximum displacement loading.

[0130] Furthermore, the step of updating the displacement load based on the displacement load and the iterative displacement loading amount further includes:

[0131] The displacement load is updated based on the difference between the displacement load and the iterative displacement loading amount.

[0132] In one specific embodiment, to more accurately apply the displacement load using a step-by-step iterative loading method, avoid mesh distortion, and obtain good calculation results, a pre-loading method is used to obtain and set the iterative displacement loading amount in each step of the iterative loading process. Specifically, before formally performing the step-by-step iterative loading on the active surface, the active surface is first pre-loaded with displacement loads. Since the displacement load is large, the calculation results may not converge during the calculation process, making it impossible to complete the loading calculation of all displacement loads at once. Therefore, the maximum displacement loading amount of the active surface when the calculation results do not converge is obtained, and the iterative displacement loading amount for this step is set based on this maximum displacement loading amount, wherein the iterative displacement loading amount is less than or equal to the maximum displacement loading amount. Please refer to [link to relevant documentation]. Figure 9 , Figure 9 This is a schematic diagram illustrating the setting of the iterative displacement loading amount according to an embodiment of the present invention. In a specific embodiment, the displacement load obtained through step S2 is 1 unit. Therefore, before performing the first iterative loading step, a displacement load of 1 unit is used to preload the active surface. Since the active surface cannot complete the displacement load calculation in one go, the calculation fails to converge and terminates when the displacement load reaches 0.311 units. Therefore, 0.311 units is the maximum displacement loading amount for the active surface. Then, during the formal iterative loading, the iterative displacement loading amount is set to 0.3 units to obtain new active and passive surfaces, ensuring that the active surface can successfully complete one iterative loading calculation. Since the loading calculation of 0.3 units has been completed, the remaining required displacement load is 0.7 units. Before the second iterative loading step, a displacement load of 0.7 units is applied to the new active surface for preloading. If the calculation fails to converge and terminates when the displacement load reaches 0.233 units, then 0.233 units represents the maximum displacement load on the active surface in this step. Subsequently, during the formal iterative loading, the iterative displacement load is set to 0.2 units to obtain the new active and passive surfaces. This method is used to continue the iterative loading calculations for subsequent steps until the displacement load after the final iterative loading is zero. It should be noted that, in addition to setting the iterative displacement load using the above method, the same iterative displacement load can also be set in each iterative loading step based on historical data or as needed, such as... Figure 9 The iterative displacement loading amount D2 is shown in the figure, but the present invention is not limited thereto.

[0133] Please refer to the following: Figures 10A to 10E , Figures 10A to 10E This is a schematic diagram of step-by-step iterative loading according to an embodiment of the present invention. In a specific embodiment, as shown... Figures 10A to 10EAs shown, passive surfaces 41, 41', 41”, 41”', and 41”” undergo iterative loading in five steps. Passive surface 41”” is obtained by pushing the active surface closer to the target surface through iterative loading calculation. Furthermore, the process of updating the passive surface by iteratively loading the active surface step by step is achieved using a geometric nonlinear calculation method. This method simulates the elastic stiffness of the passive surface membrane, which is elastic and can slide with the deformation of the active surface. However, under large geometric deformations, the passive surface membrane generates very large internal forces, making convergence difficult. Therefore, it is necessary to simultaneously set the membrane stiffness. Insufficient membrane stiffness cannot reproduce the elasticity of the passive surface and the sliding of the mesh; excessive membrane stiffness will generate large stresses with slight deformation, leading to non-convergence. Therefore, the membrane stiffness setting should ensure that the iterative displacement loading in each step proceeds normally, allowing the passive surface to remain taut and smoothly complete one step of the loading calculation. In a preferred embodiment, the membrane stiffness of the passive surface is set to 10-100 MPa.

[0134] In this embodiment of the invention, the active surface pushes the passive surface to the target surface by adopting a step-by-step iterative loading method. The loading calculation that cannot be completed in one go is divided into multiple steps, so as to realize the movement of the active surface to the target surface more accurately by step loading, thereby reducing the generation and calculation difficulty of complex meshes and reducing the difficulty of tiling.

[0135] Please see Figure 11 , Figure 11 This is a flowchart illustrating the steps of a deviation restoration method according to an embodiment of the present invention. The present invention provides a freeform surface mesh laying method based on mechanical principles, which further includes the following steps:

[0136] S5: Based on the target surface, further analyze the passive surface and optimize the passive surface through the deviation restoration method.

[0137] In a preferred embodiment, the step of optimizing the passive surface using the deviation restoration method further includes:

[0138] S51: Establish the mapping relationship between the target surface and the passive surface, optimize the passive surface based on the mapping relationship, and update the mesh form of the passive surface based on the nodes of the passive surface. The step of optimizing the passive surface based on the mapping relationship further includes:

[0139] S511: Obtain the third coordinate data of each node of the target surface according to the mapping relationship, and obtain the fourth coordinate data of each node on the passive surface corresponding to the target surface; and, if the third coordinate data is not equal to the fourth coordinate data, update the fourth coordinate data according to the third coordinate data to optimize the passive surface.

[0140] To avoid discrepancies between the calculated results of the passive surface and the target surface obtained after applying displacement load to the active surface in step S4 and performing simulation calculations, this invention further optimizes the passive surface using a deviation restoration method, so that the passive surface is more accurately laid onto the target surface to obtain the desired mesh form.

[0141] Please refer to the following: Figures 12A to 12D , Figure 12A This is a schematic diagram of a passive surface obtained by performing step-by-step iterative loading on an active surface according to an embodiment of the present invention. Figure 12B This is a schematic diagram illustrating a deviation between the passive surface and the target surface according to an embodiment of the present invention. Figure 12C This is a schematic diagram of an optimized passive surface according to an embodiment of the present invention. Figure 12D This is a schematic diagram of the updated passive surface mesh form according to an embodiment of the present invention.

[0142] In one specific embodiment, the passive surface 51 that is pushed onto the target curved surface is obtained through the above step S4, and it is as follows: Figure 12A The grid calculation results are shown below. Please refer to [link / reference]. Figure 12B There is a deviation between the passive surface 51 obtained through simulation calculation and the target surface 12. Therefore, the passive surface 51 needs to be optimized to more accurately align with the target surface 12. Specifically, as described in step S2, a mapping relationship between the target surface 12 and the passive surface 51 is established using one or more of 3D modeling software, finite element analysis software, and / or programming languages. That is, a one-to-one mapping relationship is established between points on the target surface 12 and points on the passive surface 51. The mapping relationship can be a radial-to-circular mapping relationship, or other relationships can be established as needed; this invention is not limited to this. Based on the mapping relationship between the target surface 12 and the passive surface 51, the third coordinate data of each node on the target surface 12 and the fourth coordinate data of each node on the passive surface 51 corresponding to the target surface 12 are obtained. If the third coordinate data is not equal to the fourth coordinate data, the fourth coordinate data is updated based on the third coordinate data to optimize the passive surface 51. That is, for nodes on the passive surface 51 that deviate from the target surface 12, the coordinate data of those nodes is optimized to match the coordinate data of their corresponding nodes on the target surface 12. The third coordinate data consists of the three-dimensional coordinates of each node on the target surface 12, and the fourth coordinate data consists of the three-dimensional coordinates of each node on the passive surface 51 corresponding to the target surface 12. These coordinates are obtained using 3D modeling software, finite element analysis software, and / or programming languages; however, this invention is not limited to these methods. The passive surface 51' obtained after optimization based on the third and fourth coordinate data is shown below. Figure 12C As shown, the deviation between it and the target surface 12 has been optimized and eliminated.

[0143] Since the optimized passive surface 51' is the final desired mesh form, no further simulation calculations are needed. To facilitate subsequent processing of the passive surface 51' or the construction of other models as needed for modeling, the mesh form of the passive surface 51' needs further optimization, restoring its mesh shape to a polygonal mesh form with a quadrilateral mesh structure, i.e., restoring it to the original topology, such as... Figure 12D The passive surface 51” is shown. Therefore, after all calculations are completed, the centroid numbers of the mesh elements on the passive surface are ignored, and the nodes of each mesh element are reconnected only according to their node numbers. Since the node numbers of the mesh elements do not change during the calculation process, the updated passive surface mesh is the original mesh form of the passive surface before mesh triangulation. It should be noted that the data processing described above can be implemented by any software with data processing capabilities, not limited to Grasshopper, and this invention is not limited thereto.

[0144] In this embodiment of the invention, the passive surface obtained by simulation calculation is optimized by the deviation restoration method to eliminate the deviation between it and the target surface, so that the optimized passive surface can be more accurately laid on the target surface, ensuring that the obtained passive surface is the desired mesh form.

[0145] This invention provides a freeform surface meshing method based on mechanical principles. It employs mechanical simulation to lay meshes on complex freeform surfaces. By establishing a target surface, active surface, and passive surface, mechanical simulation calculations are performed to obtain the displacement load between the target surface and the active surface, and constraint relationships are set between the passive surface and the active surface. Then, through step-by-step iterative loading, the active surface pushes the passive surface to lay the mesh onto the target surface. Finally, the passive surface is further optimized to obtain the desired mesh form. In contrast, existing freeform surface spatial structure meshing methods suffer from problems such as high mesh generation difficulty, limited form and lack of variation, and the need to improve mapping distortion, making it impossible to accurately lay the mesh onto the target surface to obtain the desired mesh form. Therefore, the freeform surface meshing method based on mechanical principles provided by this invention can automatically lay the desired mesh form onto the freeform surface based on mechanical principles and through mechanical simulation, reducing the difficulty of laying complex mesh forms, achieving freedom in complex mesh laying, and saving time and costs. Simultaneously, the obtained mesh form is natural and smooth, possessing mechanical properties, meeting specific design requirements without the need for additional improvement measures.

[0146] Please refer to the following: Figure 13 , Figure 13This is a structural block diagram of a freeform surface mesh laying device based on mechanical principles according to an embodiment of the present invention. The freeform surface mesh laying device 100A based on mechanical principles provided by the present invention is used to implement the methods in steps S1 to S5 above. The device 100A includes the following modules:

[0147] Modeling module 101A is used to create the target surface and corresponding active and passive surfaces, with the passive surface located on top of the active surface.

[0148] In a preferred embodiment, in the modeling module 101A, the active surface and the passive surface are established inside the target surface.

[0149] In a preferred embodiment, in the modeling module 101A, the active surface and the passive surface are spherical, planar, or curved, and the active surface and the passive surface have the same shape.

[0150] In a preferred embodiment, in the modeling module 101A, if the active surface and the passive surface are spherical or curved, the volume of the active surface and the passive surface is half the volume of the target curved surface.

[0151] The specific implementation method and beneficial technical effects of the modeling module 101A are the same as those described in step S1, and will not be repeated here.

[0152] The freeform surface mesh laying device 100A based on mechanical principles provided by this invention also includes:

[0153] The displacement load analysis module 102A is used to further analyze the target surface and the active surface to obtain the displacement load between the target surface and the active surface.

[0154] In a preferred embodiment, the step of further analyzing the target surface and the active surface in the displacement load analysis module 102A to obtain the displacement load between the target surface and the active surface further includes: establishing a mapping relationship between the target surface and the active surface, obtaining the first coordinate data of each node of the target surface according to the mapping relationship, obtaining the second coordinate data of each node on the active surface corresponding to the target surface, and obtaining the displacement load according to the first coordinate data and the second coordinate data.

[0155] In a preferred embodiment, the steps of obtaining the first coordinate data of each node of the target surface and the second coordinate data of each node on the active surface corresponding to the target surface in the displacement load analysis module 102A according to the mapping relationship further include: dividing the target surface and the active surface into meshes according to the mapping relationship to obtain the first coordinate data and the second coordinate data.

[0156] In a preferred embodiment, the mesh generation method in the displacement load analysis module 102A is automatic mesh generation, triangular mesh generation, or quadrilateral mesh generation, and the mapping relationship is radial-to-circular mapping relationship.

[0157] The specific implementation method and beneficial technical effects of the displacement load analysis module 102A are the same as those described in step S2, and will not be repeated here.

[0158] The constraint module 103A is used to further analyze the passive surface and set the constraint relationship between the passive surface and the active surface.

[0159] In a preferred embodiment, the step of further analyzing the passive surface and setting the constraint relationship between the passive surface and the active surface in the constraint module 103A further includes: meshing the passive surface and setting contact constraints between the passive surface and the active surface.

[0160] In a preferred embodiment, the contact constraint in the constraint module 103A is a sliding contact constraint.

[0161] In a preferred embodiment, the step of meshing the passive surface in the constraint module 103A further includes:

[0162] Based on the mesh form of the passive surface, the centroid of each mesh cell of the passive surface is set, and the mesh cells are triangulated based on the centroids; and the nodes and centroids of the mesh cells are numbered respectively.

[0163] In a preferred embodiment, the node numbering and the centroid numbering are different in the constraint module 103A.

[0164] The specific implementation method and beneficial technical effects of the constraint module 103A are the same as those described in step S3, and will not be repeated here.

[0165] The iterative analysis module 104A is used to update the passive surface by performing step-by-step iterative loading on the active surface based on the displacement load and constraint relationship.

[0166] In a preferred embodiment, the step of performing step-by-step iterative loading on the active surface to update the passive surface in the iterative analysis module 104A further includes: setting an iterative displacement loading amount according to the displacement load; loading the iterative displacement loading amount onto the active surface to obtain the iterative active surface and the iterative passive surface, and updating the active surface and the passive surface according to the iterative active surface and the iterative passive surface; and updating the displacement load according to the displacement load and the iterative displacement loading amount, and repeating the step of updating the passive surface until the displacement load is 0.

[0167] In a preferred embodiment, the step of setting the iterative displacement loading amount according to the displacement load in the iterative analysis module 104A further includes: preloading the displacement load on the active surface to obtain the maximum displacement loading amount; and setting the iterative displacement loading amount based on the maximum displacement loading amount; wherein the iterative displacement loading amount is less than or equal to the maximum displacement loading amount.

[0168] In a preferred embodiment, the step of updating the displacement load based on the displacement load and the iterative displacement loading amount in the iterative analysis module 104A further includes: updating the displacement load based on the difference between the displacement load and the iterative displacement loading amount.

[0169] In a preferred embodiment, in the iterative analysis module 104A, the active surface is iteratively loaded stepwise using a geometric nonlinear calculation method to update the passive surface, wherein the membrane stiffness of the passive surface is set to 10-100 MPa.

[0170] The specific implementation method and beneficial technical effects of the iterative analysis module 104A are the same as those described in step S4, and will not be repeated here.

[0171] The model optimization module 105A is used to further analyze the passive surface based on the target surface and optimize the passive surface through the deviation restoration method.

[0172] In a preferred embodiment, the step of optimizing the passive surface by means of the deviation restoration method in the model optimization module 105A further includes: establishing a mapping relationship between the target surface and the passive surface, optimizing the passive surface according to the mapping relationship; and updating the mesh form of the passive surface according to the nodes of the passive surface.

[0173] In a preferred embodiment, the step of optimizing the passive surface according to the mapping relationship in the model optimization module 105A further includes: obtaining the third coordinate data of each node of the target surface according to the mapping relationship, and obtaining the fourth coordinate data of each node on the passive surface corresponding to the target surface; and, if the third coordinate data is not equal to the fourth coordinate data, updating the fourth coordinate data according to the third coordinate data to optimize the passive surface.

[0174] The specific implementation method and beneficial technical effects of the model optimization module 105A are the same as those described in step S5, and will not be repeated here.

[0175] Since the embodiments of the apparatus and the embodiments of the method correspond to each other, please refer to the description of the embodiments of the method for details on the apparatus and its beneficial technical effects, which will not be repeated here. It should be noted that the apparatus proposed above can also be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative, and the division of the modules described above is merely a logical functional division. In actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another apparatus, or some features may be ignored or not executed. This invention is not limited thereto.

[0176] An embodiment of the present invention also provides a computer-readable storage medium having a computer program stored thereon, the computer program being configured to execute the freeform surface mesh tiling method based on mechanical principles as described above when running, which will not be repeated here.

[0177] Please see Figure 14 , Figure 14 This is a structural block diagram of an electronic device according to an embodiment of the present invention. Another embodiment of the present invention provides an electronic device 200A, including a memory 201A and a processor 202A. The memory 201A stores a computer program, and the processor 202A is configured to run the computer program to execute the freeform surface mesh tiling method based on mechanical principles as described above.

[0178] An embodiment of the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the freeform surface mesh tiling method based on mechanical principles as described above.

[0179] The foregoing has provided a detailed description of the freeform surface mesh laying method, apparatus, computer-readable storage medium, electronic device, and computer program product based on mechanical principles provided by this invention. The various embodiments in the specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus, computer-readable storage medium, electronic device, and computer program product disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to in the method section.

[0180] Obviously, those skilled in the art should understand that the modules or steps of this application described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device, or fabricating them separately as individual integrated circuit modules, or fabricating multiple modules or steps into a single integrated circuit module. Thus, this application is not limited to any specific hardware and software combination.

[0181] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for laying freeform surface meshes based on mechanical principles, characterized in that, Includes the following steps: A target surface is established, and an active surface and a passive surface are established corresponding to the target surface, with the passive surface located on the active surface; Further analysis of the target surface and the active surface is conducted to obtain the displacement load between the target surface and the active surface; Further analysis of the passive surface reveals the establishment of constraint relationships between the passive surface and the active surface. Based on the displacement load and the constraint relationship, the active surface is iteratively loaded in stages to update the passive surface; and... Based on the target surface, the passive surface is further analyzed, and the passive surface is optimized using the deviation restoration method.

2. The freeform surface mesh laying method based on mechanical principles according to claim 1, characterized in that, The active surface and the passive surface are established inside the target surface.

3. The method for laying freeform surface mesh based on mechanical principles according to claim 2, characterized in that, The active surface and the passive surface are spherical, planar, or curved, and the active surface and the passive surface have the same shape.

4. The freeform surface mesh laying method based on mechanical principles according to claim 3, characterized in that, If the active surface and the passive surface are spherical or curved, the volume of the active surface and the passive surface is half the volume of the target curved surface.

5. The method for laying freeform surface mesh based on mechanical principles according to claim 1, characterized in that, The step of further analyzing the target surface and the active surface to obtain the displacement load between the target surface and the active surface further includes: Establish a mapping relationship between the target surface and the active surface, obtain the first coordinate data of each node of the target surface according to the mapping relationship, and obtain the second coordinate data of each node of the active surface corresponding to the target surface, and obtain the displacement load according to the first coordinate data and the second coordinate data.

6. The method for laying freeform surface mesh based on mechanical principles according to claim 5, characterized in that, The steps of obtaining the first coordinate data of each node of the target surface according to the mapping relationship, and obtaining the second coordinate data of each node on the active surface corresponding to the target surface, further include: Based on the mapping relationship, the target surface and the active surface are respectively divided into meshes to obtain the first coordinate data and the second coordinate data.

7. The method for laying freeform surface mesh based on mechanical principles according to claim 6, characterized in that, The method for mesh generation is automatic mesh generation, triangular mesh generation, or quadrilateral mesh generation.

8. A method for laying freeform surface mesh based on mechanical principles according to claim 5, 6, or 7, characterized in that, The mapping relationship is a radial-to-circular mapping relationship.

9. The method for laying freeform surface mesh based on mechanical principles according to claim 1, characterized in that, Further analysis of the passive surface, and the step of setting the constraint relationship between the passive surface and the active surface, further includes: The passive surface is meshed, and contact constraints are set between the passive surface and the active surface.

10. A method for laying freeform surface mesh based on mechanical principles according to claim 9, characterized in that, The contact constraint is a sliding contact constraint.

11. A method for laying freeform surface meshes based on mechanical principles according to claim 9 or 10, characterized in that, The step of meshing the passive surface further includes: Based on the mesh form of the passive surface, the centroid of each mesh cell of the passive surface is set, and the mesh cells are triangulated based on the centroids; and, The nodes and centroids of the grid cells are numbered respectively.

12. The method for laying freeform surface mesh based on mechanical principles according to claim 11, characterized in that, The node number is different from the centroid number.

13. The method for laying freeform surface mesh based on mechanical principles according to claim 1, characterized in that, The step of iteratively loading the active surface to update the passive surface further includes: The iterative displacement loading amount is set according to the displacement load; The iterative displacement is applied to the active surface to obtain an iterative active surface and an iterative passive surface, and the active surface and the passive surface are updated based on the iterative active surface and the iterative passive surface; and, The displacement load is updated based on the displacement load and the iterative displacement loading amount, and the step of updating the passive surface is repeated until the displacement load is 0.

14. The method for laying freeform surface mesh based on mechanical principles according to claim 13, characterized in that, The step of setting the iterative displacement loading amount according to the displacement load further includes: The displacement load is preloaded onto the active surface to obtain the maximum displacement load; and, The iterative displacement loading amount is set based on the maximum displacement loading amount; wherein the iterative displacement loading amount is less than or equal to the maximum displacement loading amount.

15. A method for laying freeform surface meshes based on mechanical principles according to claim 13 or 14, characterized in that, The step of updating the displacement load based on the displacement load and the iterative displacement loading amount further includes: The displacement load is updated based on the difference between the displacement load and the iterative displacement loading amount.

16. A method for laying freeform surface meshes based on mechanical principles according to claim 13 or 14, characterized in that, The passive surface is updated by step-by-step iterative loading of the active surface using a geometric nonlinear calculation method, wherein the membrane stiffness of the passive surface is set to 10-100 MPa.

17. The method for laying freeform surface mesh based on mechanical principles according to claim 1, characterized in that, The step of optimizing the passive surface using the deviation restoration method further includes: Establish a mapping relationship between the target surface and the passive surface, and optimize the passive surface based on the mapping relationship; and, The mesh form of the passive surface is updated based on the nodes of the passive surface.

18. A method for laying freeform surface mesh based on mechanical principles according to claim 17, characterized in that, The step of optimizing the passive surface based on the mapping relationship further includes: According to the mapping relationship, obtain the third coordinate data of each node of the target surface, and obtain the fourth coordinate data of each node on the passive surface corresponding to the target surface; and, If the third coordinate data is not equal to the fourth coordinate data, the fourth coordinate data is updated based on the third coordinate data to optimize the passive surface.

19. A free-form surface mesh laying device based on mechanical principles, used to implement the method as described in any one of claims 1-18, characterized in that, include: The modeling module is used to create a target surface, and to create an active surface and a passive surface corresponding to the target surface, wherein the passive surface is located on the active surface; The displacement load analysis module is used to further analyze the target surface and the active surface to obtain the displacement load between the target surface and the active surface; The constraint module is used to further analyze the passive surface and set the constraint relationship between the passive surface and the active surface. The iterative analysis module is used to perform step-by-step iterative loading on the active surface to update the passive surface based on the displacement load and the constraint relationship; and, The model optimization module is used to further analyze the passive surface based on the target surface and optimize the passive surface through the deviation restoration method.

20. A computer-readable storage medium having a computer program stored thereon, characterized in that, The computer program is configured to execute the freeform surface mesh laying method based on mechanical principles as described in any one of claims 1-18.

21. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and the processor is configured to run the computer program to perform the freeform surface mesh tiling method based on mechanical principles as described in any one of claims 1-18.

22. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the freeform surface mesh laying method based on mechanical principles as described in any one of claims 1-18.

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