Three-dimensional structure interactive topological optimization method based on level set

Abstract

The invention discloses a three-dimensional structure interactive topological optimization method based on a level set, and relates to the technical field of computer aided design, topological optimization and interactive design, and the method comprises the steps: building a three-dimensional structure topological optimization design region; importing a level set field of an initial structure or a three-dimensional model file, and generating an initial level set field; a Marking Cubes method is adopted to extract a geometric structure from the level set field, and an initial model is rendered and displayed; performing level set topological optimization on the structure, and updating and rendering and displaying the structure form in real time; during optimization, the process can be paused at any time for interactive modification, a forced or non-forced intervention mode is adopted, structural increase and decrease or form refinement is performed through an interactive ball, and a level set field is updated in real time for continuous optimization. Therefore, by the adoption of the method, topological optimization of the complex initial model is efficiently achieved, the structural form is dynamically adjusted, tedious post-processing steps of a traditional method are effectively reduced, and the structural design efficiency, precision and flexibility are improved.

Description

Technical Field

[0001] The present invention relates to the technical fields of computer-aided design, topology optimization, and interactive design, and particularly relates to a three-dimensional structure interactive topology optimization method based on level sets. Background Art

[0002] Topology optimization is a technical method that iteratively evolves the material distribution within a given design space to improve the structural performance. This method can not only meet or enhance the mechanical properties but also greatly reduce the material usage, and thus has been widely applied in many fields such as aerospace, mechanical engineering, biomedical, and construction engineering. However, the topological configurations generated by existing technologies often exhibit highly irregular geometric morphologies, making it difficult to directly meet the process constraints of the structural geometric features in engineering manufacturing. Usually, it can only be used as a conceptual design scheme and requires a complex post-processing process to achieve engineering transformation.

[0003] Currently, in response to the above problems, some feasible methods have been proposed in the research. For example, the literature "Interactive 3D structural design in virtual reality using preference-based topology optimization" proposed a topology optimization method based on subjective preferences. This method introduces the subjective preferences of designers on the basis of traditional bi-directional evolutionary structural optimization (BESO), enabling designers to more intuitively control the structural optimization results. In addition, "An interactive playground for real-time immersed topology optimization" proposed an immersive topology optimization method combining augmented reality (AR) technology. This method allows users to define, manipulate, and solve topology optimization problems in real time in an AR environment, providing a more intuitive interaction mode.

[0004] However, the above methods still have several core problems that need to be solved. First, both methods require the initial shape design of the structure to be completed before the optimization starts. Once the optimization process starts, the optimization path tends to be fixed, and it is difficult to dynamically adjust the structure shape or optimization direction during the optimization process. If the optimized structure needs to be further adjusted or refined, it is usually necessary to rely on cumbersome and complex post-processing steps, which reduces the interactivity and efficiency of the optimization method. Second, the current method lacks the function of importing external model files. When it is necessary to perform topological optimization on a complex initial model, the user must manually complete the modeling operation in the software. This process is not only cumbersome and time-consuming, but also significantly reduces the convenience of user operation and design efficiency. Third, the above methods all use density-based implicit expressions to model and optimize the structure. This expression method is difficult to clearly and accurately describe the boundary contours of complex structures. It often requires additional filtering or post-processing steps to generate optimized structures with clear boundaries, which further increases the complexity of the process. Summary of the invention

[0005] The purpose of the present invention is to provide a three-dimensional structure interactive topology optimization method based on level sets, which can efficiently realize the topology optimization of complex initial models, dynamically adjust the structural morphology, and improve the efficiency, accuracy and flexibility of structural design.

[0006] To achieve the above object, the present invention provides a three-dimensional structure interactive topology optimization method based on level sets, comprising the following steps: S1. Set the number of nodes in the three directions of XYZ, establish a three-dimensional structural topology optimization design area, define boundary conditions and configuration parameters, the boundary conditions are structural loads and constraints, the configuration parameters are iteration parameters in the topology optimization process, and the nodes are grid points in the design area; S2, import the level set field φ(X) of the initial model in the design area, or import the display model file and calculate the SDF signed distance function of the model, and then use the level set generation formula based on the SDF signed distance function to calculate the level set field φ(X); S3, using the level set field φ(X), a display model of the initial structure is generated by rendering in the design area through the Marching Cubes method; S4. Solving the design variables using the level set topology optimization according to the configuration parameters, wherein the design variables include mathematical variables describing the structure shape and topology in the level set topology optimization method; S5. Observe the optimization status of the displayed model, and when the optimization does not meet the design requirements, suspend the optimization process; the design requirements include aesthetic design, global optimal design, and avoiding stress concentration; S6. Select forced intervention or non-forced intervention. The forced intervention means that the modification of the structure will not change as the optimization continues, and the non-forced intervention means that the modification of the structure will change as the optimization continues; S7. Generate an interactive sphere, set the radius R of the interactive sphere to control the interaction accuracy, move the interactive sphere through the interaction device, and perform operations of deleting or adding structures to the display model in the movement trajectory of the interactive sphere, display the modified content in real time, and record the node positions Xc passed by the movement trajectory; S8. Change the size of the interactive sphere to determine the operation range, pick up the structural surface of the display model within the operation range of the interactive sphere, generate surface control points on this structural surface, select and drag-adjust the control points through the interaction device, perform fine modification on the surface shape, and record the positions Xd of the modified surface control points; S9. Calculate the SDF signed distance function of the modified display model, and use the level set generation formula based on SDF to calculate the updated level set field Φnew(X); S10. Continue the optimization process, use the level set field interactive iterative optimization algorithm to iteratively update the adjusted level set field Φnew(X), and use the Marching Cubes method to render the display model in real time; S11. Repeat steps S5 - S10 until the iteration converges, optimize to obtain a level set field that meets the design requirements, then import the level set field into software supporting implicit modeling, export the optimized structure, and complete the structural interactive design.

[0007] Preferably, the mathematical model of the level set is as follows: .

[0008] Preferably, in step S2, the display model file is a three-dimensional geometric structure file, including OBJ, STL, and PLY formats.

[0009] Preferably, the SDF signed distance function represents the shortest distance from any point in three-dimensional space to the object surface, and the level set generation formula based on the SDF signed distance function is: ; ; ; In the formula, , represent the minimum and maximum values of the SDF signed distance function values of all nodes in the design area, represents the gradient amplitude of the SDF field, represents the smoothing coefficient, represents the three-dimensional space coordinates.

[0010] Preferably, in step S5, a head-mounted display or a 3D display is used to observe the optimization of the model, and the interaction device is used to control the viewing angle and position of the structure, and the changes of the structure are observed from multiple perspectives inside and outside the structure.

[0011] Preferably, in step S5, the surface control points are generated by a method based on Bezier surface.

[0012] Preferably, in step S10, the level set field interactive iterative optimization algorithm is as follows: ; When forced intervention is selected: ; When non-forced intervention is selected: ;

[0013] In the formula, is the node position passed by the interaction sphere movement trajectory; is the position of the surface control point after the model is modified; is the evolution velocity field of the level set function; is the iterative time step; is the non-forced intervention weight coefficient, which is adjusted in real time by a slider; n is the number of iterative steps when modifying the model.

[0014] Preferably, in steps S7 and S8, the interaction operations of the interaction sphere are recorded to form a design history tree, which supports backtracking or redoing the modification operations of any step by sliding the time axis.

[0015] Preferably, in steps S5 to S11, with the help of multi-person real-time collaboration technology, the 3D model can be observed in the same environment and the structure can be modified in real time.

[0016] Therefore, the present invention adopts the above-mentioned three-dimensional structure interactive topology optimization method based on the level set, and has the following technical effects: (1) The present invention adopts the level set method to accurately express the structure boundary with an implicit function, and can realize the accurate description and flexible adjustment of the structure boundary; moreover, in the optimization process, it has an interactive pause and intervention function, allowing the designer to adjust the overall shape of the structure through the interaction sphere, and optimize the local details with the help of the surface control points, and supports both forced intervention and non-forced intervention modes, enabling the designer to freely adjust and design the structure. In addition, since no additional filtering operation is required, the present invention can effectively ensure the consistency between the implicitly expressed model (defined by the level set function) and the final display model (the structural geometry of the optimization result), and ensure the accuracy and reliability of the structure optimization.

[0017] (2) The present invention supports importing 3D geometric files such as OBJ, STL, and PLY into the design domain, and efficiently constructs a level set field through the rapid calculation of the signed distance function (SDF), so as to be able to directly process complex initial structure models. Different from traditional topology optimization methods that are only applicable to regular or simplified models, the technical solution of the present invention can be compatible with the topology optimization requirements of complex shapes, heterogeneous structures, or porous structures, greatly expanding the application scope of this method in the industrial and scientific research fields.

[0018] (3) The present invention realizes the real-time visualization of the entire process of interactive operation, and provides support for operation record backtracking and collaborative design. Based on the Marching Cubes method, the present invention can render the updated situation of the structural form in real time during the optimization iteration process, and with the help of interactive devices and multi-view display, enable designers to instantly observe the structural changes in the VR / AR / XR or 3D display environment. At the same time, the interactive operation process automatically generates a modification history record, supporting backtracking and redoing by sliding the time axis. In addition, the present invention also has the function of multi-person real-time collaboration, significantly improving the efficiency of complex project team collaboration and the traceability of the design process.

[0019] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0020] Figure 1 is a flowchart of a three-dimensional structure interactive topology optimization method based on level set; Figure 2 is a schematic diagram of the design area and boundary conditions in an embodiment of a three-dimensional structure interactive topology optimization method based on level set; Figure 3 is an initial optimization model of the structure drawn in Rhino modeling software in an embodiment of a three-dimensional structure interactive topology optimization method based on level set; Figure 4 is an initial optimization model of the structure rendered in Ue4.27 in an embodiment of a three-dimensional structure interactive topology optimization method based on level set; Figure 5 is a schematic diagram of the rendering results of the optimized structures at two adjacent iteration steps in an embodiment of a three-dimensional structure interactive topology optimization method based on level set, where (a) is the external view of the structure at the nth iteration step, (b) is the internal view of the structure at the nth iteration step, (c) is the external view of the structure at the (n + 1)th iteration step, and (d) is the internal view of the structure at the (n + 1)th iteration step; Figure 6Schematic diagram of a structural model rendered in Ue4.27 when iterative optimization pauses in an embodiment of a level-set-based three-dimensional structural interactive topology optimization method, where (a) is the first perspective and (b) is the second perspective; Figure 7 Schematic diagram of Bezier surface control points in Ue4.27 in an embodiment of a level-set-based three-dimensional structural interactive topology optimization method; Figure 8 Schematic diagram of the result of rendering the structure optimized by an interactive sphere in Ue4.27 in an embodiment of a level-set-based three-dimensional structural interactive topology optimization method, where (a) is the optimized structure of step S7 and (b) is the optimized structure of step S8; Figure 9 Schematic diagram of the result of rendering the optimized structure in Ue4.27 in an embodiment of a level-set-based three-dimensional structural interactive topology optimization method; Figure 10 Schematic diagram of the rendering result of the structure designed by the existing method in Ue4.27 in an embodiment of a level-set-based three-dimensional structural interactive topology optimization method. Detailed implementation manners

[0021] The present invention can be more specifically explained by the following embodiments. The purpose of disclosing the present invention is to protect all changes and improvements within the scope of the present invention. The present invention is not limited to the following embodiments.

[0022] Please refer to Figure 1 , the present invention provides a level-set-based three-dimensional structural interactive topology optimization method, aiming to avoid the drawbacks of a large amount of post-processing required after optimization in traditional methods, enabling designers to dynamically adjust the structure in real time during the optimization process, thereby effectively avoiding subsequent cumbersome manual modifications and repeated calculations. It also allows designers to conveniently add constraints according to actual engineering manufacturing constraints, greatly improving the efficiency of structural optimization and design modification, and meeting the needs of engineering practice. The specific steps are as follows: S1. According to the design space range required in practice, set the number of nodes in the X, Y, and Z directions, and establish a three-dimensional structural topology optimization design area; at the same time, according to the optimization model and optimization goal required in practice, define boundary conditions and configure parameters. Among them, the boundary conditions include structural loads and constraint conditions, and the configured parameters include iterative parameters during the topology optimization process. The nodes are grid points of the design area.

[0023] In one embodiment, the design space is a cuboid, and in other embodiments, it can also be designed in different shapes. In this embodiment, a cuboid with the number of nodes in three directions being X = 31, Y = 11, and Z = 11 is used as the design space, and the number of nodes can be adjusted according to actual requirements. The configuration parameters are set as the number of iterations nloop = 500, the target volume fraction volfrac = 0.3, the elastic modulus E0 = 1, the Poisson's ratio nu = 0.3, and the iteration time step dt = 0.5. In other embodiments, the configuration parameters can be adjusted according to the optimization objectives. The boundary conditions of this embodiment are set as a cantilever beam with a fixed constraint at the left end, and a unit force vertically downward is applied to the central node at the right end. Please refer to Figure 2 the red part of

[0024] S2. Import the level set field φ(X) of the initial model into the design area; or calculate the SDF signed distance function of the display model after importing the display model file, and then use the level set generation formula based on the SDF signed distance function to calculate the level set field φ(X). Among them, the level set field φ(X) refers to implicitly defining the distribution and topology of materials in the design domain through a continuous scalar function, and X is the spatial coordinate. The level set generation formula based on the SDF signed distance function is: ; ; ; In the formula, the SDF signed distance function is a mathematical tool widely used in geometric processing and 3D modeling, which represents the shortest distance from any point in the three-dimensional space to the surface of the object, and distinguishes whether the point is outside (positive value) or inside (negative value) the object through the sign; SDFmin represents the minimum value of the SDF signed distance function values of all nodes in the design area; SDFmax represents the maximum value of the SDF signed distance function values of all nodes in the design area; dmax is the global maximum absolute value of SDF; is the gradient magnitude (local change intensity) of the SDF field; is the smoothing coefficient, which controls the influence of the gradient on the normalization. In this embodiment, the value is 0.1dmax, and it can be adjusted according to the requirements for the smoothness of the model during design.

[0025] In one embodiment of the present invention, the initial optimization model of the structure is drawn through Rhino modeling software (please refer to Figure 3 ), and after exporting its OBJ file, the SDF signed distance function of the model is calculated using the ray marching method. In other embodiments, the SDF signed distance function can also be obtained through other common calculation methods in computer graphics such as the fast marching method and octree search.

[0026] S3. Use the level set field φ(X) to render and generate a display model of the initial structure in the design area through the Marching Cubes method. Among them, the Marching Cubes method is a common surface reconstruction method for extracting explicit geometric boundaries from the level set field φ(X).

[0027] In one embodiment of the present invention, the Ue4.27 game engine is used to render the display model of the optimized structure. Please refer to Figure 4 .

[0028] S4. According to the configuration parameters, perform level set topology optimization on the design variables to solve, update the level set field φ(X), and then use the Marching Cubes method to render the display model in real time. Among them, the design variables include the mathematical variables that describe the structure shape and topology in the level set topology optimization method.

[0029] In one embodiment of the present invention, the Ue4.27 game engine is used to display and render the structure and interactively modify the structure. Please refer to Figure 5 , (a) and (b) are the optimized models at the nth iteration step, (a) is the external view of the structure, and (b) is the internal view of the structure; (c) and (d) are the optimized models at the (n + 1)th iteration step, (c) is the external view of the structure, and (d) is the internal view of the structure.

[0030] S5. Please refer to Figure 6 , observe the optimization of the display model. When the optimization does not meet the design requirements, pause the optimization process and execute step S6. Among them, the design requirements include aesthetic design, global optimal design, avoiding stress concentration, etc.

[0031] In one embodiment of the present invention, the designer needs to consider drawing a letter "A" at the center of the cantilever beam to consider aesthetic design and make detailed adjustments to the structure. In other embodiments, the designer can also consider design issues such as global optimality and avoiding stress concentration according to his own experience.

[0032] S6. Select forced intervention or non-forced intervention: Forced intervention means that the modification of the structure will not change with the continuation of the optimization, and non-forced intervention means that the modification of the structure will change with the continuation of the optimization.

[0033] When forced intervention is selected: ; When non-forced intervention is selected: ; In the formula, is the node position passed by the movement trajectory of the interactive sphere; is the position of the surface control point after the model is modified; is the evolution velocity field of the level set function; is the iteration step size; is the non-compulsory intervention weight coefficient, which is adjusted in real time through a slider and takes the value of 0.3 in this embodiment; is the number of iteration steps when modifying the model.

[0034] In one embodiment of the present invention, forced intervention is adopted for the drawing of the letter "A", and non-compulsory intervention is adopted for the adjustment of other areas of the model.

[0035] S7. Generate an interactive sphere and set the radius R of the interactive sphere to control the interaction accuracy; move the interactive sphere through an interactive device, and perform operations of deleting and adding structures to the displayed model in its movement trajectory, display the modified content in real time, and record the node positions X passed by the movement trajectory c .

[0036] In one embodiment of the present invention, the designer used the interactive sphere to draw a letter "A" at the center of the cantilever beam through operations of deleting and adding structures, and made aesthetic design adjustments to other areas of the model.

[0037] S8. Change the size of the interactive sphere to determine the operation range, pick up the structural surface of the displayed model within the operation range of the interactive sphere, and generate surface control points on this structural surface; select and drag the control points through an interactive device to finely modify the surface shape, and record the positions X of the modified surface control points d . Please refer to Figure 7 , the surface control points are generated by the method based on Bezier surface, and the green small balls in the figure are interactive spheres.

[0038] In one embodiment of the present invention, the designer finely adjusted the shape of the letter "A" by adjusting the positions of the surface control points, and made aesthetic design adjustments to other areas of the model. Please refer to Figure 8 .

[0039] S9. Calculate the SDF (Signed Distance Function) of the modified model, and then use the level set generation formula based on SDF to calculate the updated level set field Φnew(X).

[0040] S10. Continue the optimization process, adopt the level set field interactive iterative optimization algorithm to iteratively update the adjusted level set field Φnew(X), and use the Marching Cubes method to render and display the model in real time. Among them, the level set field interactive iterative optimization algorithm is: .

[0041] S11. Repeat steps S5 - S10 until the design requirements are met and the iteration converges, obtaining the level set field Φ(X) that meets the design requirements, and importing the level set field Φ(X) into software supporting implicit modeling to export the optimized structure, thus completing the interactive design of the structure.

[0042] During the iteration process, for the rendering result of the display model of the optimized structure in Ue4.27, please refer to Figure 9 . For the rendering display of the design structure without using the method of the present invention in Ue4.27, please refer to Figure 10 .

[0043] The three - dimensional structure interactive topology optimization method based on level set described in the present invention is developed and used in mainstream game engines such as Unreal eigen and Unity 3D, and is applied in scenarios such as VR, AR, XR, and 3D displays.

[0044] Therefore, by adopting the above - mentioned three - dimensional structure interactive topology optimization method based on level set, designers can effectively introduce subjective design intentions into the algorithm model without directly modifying complex mathematical formulas, and can adjust structure parameters in real time during the optimization calculation process, so that the structure performance can better meet the specific requirements of actual engineering applications.

[0045] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements do not make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A three-dimensional structure interactive topology optimization method based on level sets, characterized in that: The following steps are involved: S1. Set the number of nodes in the three directions of XYZ, establish a three-dimensional structural topology optimization design area, define boundary conditions and configuration parameters, the boundary conditions are structural loads and constraints, the configuration parameters are iteration parameters in the topology optimization process, and the nodes are grid points in the design area; S2, import the level set field φ(X) of the initial model in the design area, or import the display model file and calculate the SDF signed distance function of the model, and then use the level set generation formula based on the SDF signed distance function to calculate the level set field φ(X); S3, using the level set field φ(X) in step S2, rendering in the design area through the Marching Cubes method to generate a display model of the initial structure; S4. Solving the design variables using the level set topology optimization according to the configuration parameters, wherein the design variables include mathematical variables describing the structure shape and topology in the level set topology optimization method; S5. Observe the optimization status of the displayed model, and when the optimization does not meet the design requirements, suspend the optimization process; the design requirements include aesthetic design, global optimal design, and avoiding stress concentration; S6. Select mandatory intervention or non-mandatory intervention, wherein the mandatory intervention means that the modification to the structure will not change as the optimization continues, and the non-mandatory intervention means that the modification to the structure will change as the optimization continues; S7. Generate an interactive sphere, set the radius R of the interactive sphere to control the interactive accuracy, move the interactive sphere through the interactive device, delete or add structures to the display model in the motion trajectory of the interactive sphere, display the modified content in real time, and record the node position X passed by the motion trajectory c ; S8. Change the size of the interactive ball to determine the operation range, pick up the structural surface of the model displayed within the interactive ball operation range, generate surface control points on the structural surface, select and drag the control points through the interactive device, make fine modifications to the surface shape, and record the modified surface control point position X d ; S9, calculating the SDF signed distance function of the modified display model, and using the SDF-based level set generation formula to calculate the updated level set field Φnew(X); S10, continue the optimization process, use the level set field interactive iterative optimization algorithm, iteratively update the adjusted level set field Φnew (X), and use the Marching Cubes method to render and display the model in real time; S11. Repeat steps S5 to S10 until the iteration converges and the level set field that meets the design requirements is optimized. The level set field is then imported into software that supports implicit modeling, the optimized structure is exported, and the interactive structural design is completed.

2. The three-dimensional structure interactive topology optimization method based on level set according to claim 1, characterized in that: The mathematical model of the level set is as follows: 。 3. The three-dimensional structure interactive topology optimization method based on level set according to claim 1, characterized in that: In step S2, the model file is displayed as a three-dimensional geometric structure file, including OBJ, STL, and PLY formats.

4. The three-dimensional structure interactive topology optimization method based on level set according to claim 1, characterized in that: The SDF signed distance function represents the shortest distance from any point in three-dimensional space to the surface of an object. The level set generation formula based on the SDF signed distance function for: ； ； ； In the formula, , Indicates the minimum and maximum values ​​of the SDF signed distance function values ​​of all nodes in the design area. represents the gradient amplitude of the SDF field, represents the smoothing coefficient, Represents three-dimensional space coordinates.

5. The three-dimensional structure interactive topology optimization method based on level set according to claim 1, characterized in that: In step S5, a head mounted display or a 3D display is used to observe the optimization of the model, and the observation angle and position of the structure are controlled by an interactive device, so that changes in the structure can be observed from multiple perspectives inside and outside the structure.

6. The three-dimensional structure interactive topology optimization method based on level set according to claim 1, characterized in that: In step S5, the surface control points are generated using a Bezier surface-based method.

7. The three-dimensional structure interactive topology optimization method based on level set according to claim 1, characterized in that: In step S10, the level set field interactive iterative optimization algorithm is as follows: ； When you choose Forced Intervention: ； When choosing non-coercive intervention: ； In the formula, is the node position that the interactive ball motion trajectory passes through; Modify the position of the surface control points of the model; is the velocity field evolved by the level set function; is the iteration time step; is the non-mandatory intervention weight coefficient, which is adjusted in real time through the slider; n is the number of iterations when modifying the model.

8. The three-dimensional structure interactive topology optimization method based on level set according to claim 1, characterized in that: In step S7 and step S8, the interactive operation records of the interactive ball are formed into a design history tree, which supports backtracking or redoing the modification operation of any step by sliding the timeline.

9. The three-dimensional structure interactive topology optimization method based on level set according to claim 1, characterized in that: In step S5 to step S11, with the help of multi-person real-time collaboration technology, the 3D model is observed in the same environment and the structure is modified in real time.

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