A 3D Structure Interactive Topology Optimization Method Based on Level Set

Abstract

The present invention discloses a three-dimensional structure interactive topology optimization method based on level set, which relates to the technical fields of computer-aided design, topology optimization, and interactive design. The method includes establishing a three-dimensional structure topology optimization design region; importing the level set field of the initial structure or a three-dimensional model file and generating an initial level set field; extracting a geometric structure from the level set field by using the Marching Cubes method, rendering and displaying the initial model; performing level set topology optimization on the structure, updating and real-time rendering and displaying the structure form; during the optimization process, the process can be paused at any time for interactive modification, and forced or non-forced intervention methods are adopted to increase or decrease the structure or refine the form through an interactive sphere, and the level set field is updated in real time to continue the optimization. Therefore, by adopting the above method, the topology optimization of complex initial models can be efficiently realized, the structure form can be dynamically adjusted, the cumbersome post-processing steps of traditional methods can be effectively reduced, and the structure design efficiency, accuracy, 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 in particular, 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 significantly reduce the material usage, and thus has been widely applied in many fields such as aerospace, mechanical engineering, biomedicine, and civil engineering. However, the topology configurations generated by the existing technologies often exhibit highly irregular geometric shapes, 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 designer's subjective preferences on the basis of the traditional bi-directional evolutionary structural optimization (BESO), enabling the designer 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, there are still several core problems to be solved urgently in the above methods. First, both of these two methods require the initial shape design of the structure to be completed before 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 further adjustment or fine decoration of the optimized structure is needed, it usually relies on cumbersome and complex post-processing steps, reducing the interactivity and efficiency of the optimization method. Second, the current methods lack the function of importing external model files. When topological optimization of a complex initial model is required, users must manually complete the modeling operation within 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, and often requires additional filtering or post-processing steps to generate an optimized structure with clear boundaries, further increasing the complexity of the process. Summary of the Invention

[0005] The object of the present invention is to provide an interactive topological optimization method for three-dimensional structures based on level sets, which can efficiently realize the topological optimization of complex initial models, dynamically adjust the structure form, and improve the structure design efficiency, accuracy and flexibility.

[0006] To achieve the above object, the present invention provides an interactive topological optimization method for three-dimensional structures based on level sets, including the following steps:

[0007] S1. Set the number of nodes in the X, Y, and Z directions, establish a three-dimensional structure topological optimization design area, define boundary conditions and configure parameters. The boundary conditions are structural loads and constraint conditions, and the configuration parameters are iteration parameters in the topological optimization process. The nodes are grid points in the design area;

[0008] S2. Import the level set field of the initial model into the design area , or calculate the SDF signed distance function of the 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 ;

[0009] S3. Use the level set field , and render and generate the display model of the initial structure in the design area by the Marching Cubes method;

[0010] S4. According to the configuration parameters, use the level set topological optimization to solve the design variables. The design variables include mathematical variables that describe the structure shape and topology in the level set topological optimization method;

[0011] S5. Observe the optimization status of the display model. 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.

[0012] S6. Select forced intervention or non-forced intervention. Forced intervention means that the modification of the structure will not change with the continuation of optimization, and non-forced intervention means that the modification of the structure will change with the continuation of optimization.

[0013] S7. Generate an interactive sphere, set the radius R of the interactive sphere to control the interaction accuracy, move the interactive sphere through an interaction device, and perform operations of deleting or adding structures to the display model in the movement trajectory of the interactive sphere. Real-time display the modified content and record the node positions Xc passed by the movement trajectory.

[0014] 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 an interaction device, perform fine modification of the surface shape, and record the positions Xd of the modified surface control points.

[0015] 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. ;

[0016] S10. Continue the optimization process, adopt the level set field interactive iterative optimization algorithm to iteratively update the adjusted level set field. , and use the Marching Cubes method to real-time render the display model.

[0017] 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.

[0018] Preferably, the mathematical model of the level set is as follows:

[0019] .

[0020] Preferably, in step S2, the display model file is a three-dimensional geometric structure file, including OBJ, STL, and PLY formats.

[0021] 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:

[0022] ;

[0023] ;

[0024] ;

[0025] In the formula, and 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.

[0026] Preferably, in step S5, a head-mounted display or a 3D display is used to observe the optimization of the model, and the viewing angle and position of the structure are controlled through an interaction device, and the changes of the structure are observed from multiple perspectives inside and outside the structure.

[0027] Preferably, in step S5, the surface control points are generated by a method based on B-spline surfaces.

[0028] Preferably, in step S10, the level set field interactive iterative optimization algorithm is as follows:

[0029]

[0030] When forced intervention is selected:

[0031]

[0032] When non-forced intervention is selected:

[0033]

[0034] In the formula, is the node position passed by the interaction sphere's movement trajectory; is the position of the surface control point after the model is modified; is the level set function evolution velocity field; is the iterative time step; is the non-forced intervention weight coefficient, which is adjusted in real time through a slider; n is the number of iterative steps when modifying the model.

[0035] 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.

[0036] 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.

[0037] Therefore, the present invention adopts the above-mentioned three-dimensional structure interactive topology optimization method based on level set, and has the following technical effects:

[0038] (1) The present invention adopts the level set method to accurately express the structure boundary with an implicit function, which can realize the accurate description and flexible adjustment of the structure boundary; moreover, during the optimization process, it has the functions of interactive pause and intervention, allowing designers to adjust the overall shape of the structure through the interactive sphere, optimize local details with the help of surface control points, and supports two modes of forced intervention and non-forced intervention, enabling designers 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 displayed model (the structural geometry of the optimization result), ensuring the accuracy and reliability of structural optimization.

[0039] (2) The present invention supports importing three-dimensional geometric files such as OBJ, STL, and PLY into the design domain, and efficiently constructs the level set field through the rapid calculation of the signed distance function (SDF), so as to directly process complex initial structure models. Different from the traditional topology optimization method that is 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.

[0040] (3) The present invention realizes the real-time visualization of the entire process of interactive operation, and provides operation record backtracking and collaborative design support. Based on the Marching Cubes method, the present invention can render the structural form update 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 three-dimensional 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.

[0041] The technical solution of the present invention will be further described in detail below with reference to the drawings and embodiments. Description of the Drawings

[0042] Figure 1 is a flowchart of a three-dimensional structure interactive topology optimization method based on level set;

[0043] 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;

[0044] Figure 3It is the initial optimization model of the structure drawn in the Rhino modeling software in an embodiment of a three-dimensional structure interactive topology optimization method based on the level set;

[0045] Figure 4 It is the initial optimization model of the structure rendered in Ue4.27 in an embodiment of a three-dimensional structure interactive topology optimization method based on the level set;

[0046] Figure 5 It is a schematic diagram of the rendering results of the optimized structures of two adjacent iteration steps in an embodiment of a three-dimensional structure interactive topology optimization method based on the level set in Ue4.27, 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;

[0047] Figure 6 It is a schematic diagram of the structure model rendered in Ue4.27 when the iterative optimization pauses in an embodiment of a three-dimensional structure interactive topology optimization method based on the level set, where (a) is the first view and (b) is the second view;

[0048] Figure 7 It is a schematic diagram of the Bezier surface control points in Ue4.27 in an embodiment of a three-dimensional structure interactive topology optimization method based on the level set;

[0049] Figure 8 It is a schematic diagram of the rendering results of the structure optimized by the interactive sphere in Ue4.27 in an embodiment of a three-dimensional structure interactive topology optimization method based on the level set. (a) is the optimized structure of step S7, and (b) is the optimized structure of step S8;

[0050] Figure 9 It is a schematic diagram of the rendering results of the optimized structure in Ue4.27 in an embodiment of a three-dimensional structure interactive topology optimization method based on the level set;

[0051] Figure 10 It is a schematic diagram of the rendering results of the structure designed by the existing method in Ue4.27 in an embodiment of a three-dimensional structure interactive topology optimization method based on the level set. Detailed implementation mode

[0052] The present invention can be more detailedly explained through 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.

[0053] Please refer to Figure 1, the present invention provides a three-dimensional structure interactive topology optimization method based on level set, 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, thus 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 structure optimization and design modification, and meeting the requirements of engineering practice. The specific steps are as follows:

[0054] S1. According to the design space range of actual requirements, set the number of nodes in the X, Y, and Z directions, and establish a three-dimensional structure topology optimization design area; at the same time, according to the optimization model and optimization objectives of actual requirements, define boundary conditions and configuration parameters. Among them, the boundary conditions include structural loads and constraint conditions, and the configuration parameters include iteration parameters in the topology optimization process. The nodes are grid points of the design area.

[0055] 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 the three directions being X = 31, Y = 11, and Z = 11 is used as the design space, and this 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 in this embodiment are set as a cantilever beam with a fixed constraint at the left end and a unit force vertically downward applied at the central node at the right end. Please refer to Figure 2 the red part.

[0056] S2. Import the level set field 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 . Among them, the level set field refers to implicitly defining the distribution and topology of materials in the design domain through a continuous scalar function, where X is the spatial coordinate. The level set generation formula based on the SDF signed distance function is:

[0057] ;

[0058] ;

[0059] ;

[0060] In the formula, the SDF (Signed Distance Function) is a mathematical tool widely used in geometric processing and 3D modeling, representing the shortest distance from any point in three-dimensional space to the surface of an object, and distinguishing whether the point is outside (positive value) or inside (negative value) the object by a sign; SDFmin represents the minimum value of the SDF values of all nodes in the design area; SDFmax represents the maximum value of the SDF values of all nodes in the design area; dmax is the global maximum absolute value of the 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 requirement for the smoothness of the model during design.

[0061] In one embodiment of the present invention, an initial optimized model of the structure is drawn through Rhino modeling software (please refer to Figure 3 ), and after exporting its OBJ file, the SDF of the model is calculated using the ray marching method. In other embodiments, the SDF can also be obtained through other common calculation methods in computer graphics such as the fast marching method and octree search.

[0062] S3. Utilize the level set field 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 .

[0063] 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 .

[0064] S4. According to the configuration parameters, perform level set topology optimization on the design variables to solve, update the level set field , 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 shape and topology of the structure in the level set topology optimization method.

[0065] 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.

[0066] 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.

[0067] In one embodiment of the present invention, the designer needs to consider drawing a letter "A" at the center of the cantilever beam for aesthetic design and making detailed adjustments to the structure. In other embodiments, the designer can also consider design issues such as global optimization and avoiding stress concentration according to their own experience.

[0068] S6. Select forced intervention or non-forced intervention: Forced intervention means that the modification of the structure will not change with the continuation of optimization, and non-forced intervention means that the modification of the structure will change with the continuation of optimization.

[0069] When selecting forced intervention:

[0070] ;

[0071] When selecting non-forced intervention:

[0072] ;

[0073] 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 modification; is the evolution velocity field of the level set function; is the iteration step size; is the non-forced intervention weight coefficient, which is adjusted in real time through a slider and takes a value of 0.3 in this embodiment; is the number of iteration steps when modifying the model.

[0074] In one embodiment of the present invention, forced intervention is adopted for the drawing of the letter "A", and non-forced intervention is adopted for the adjustment of other areas of the model.

[0075] S7. Generate an interactive sphere and set the radius R of the interactive sphere to control the interaction accuracy; through the interaction device, move the interactive sphere, and perform operations of deleting and adding structures to the display model in its movement trajectory, display the modified content in real time, and record the node position X passed by the movement trajectory c .

[0076] In one embodiment of the present invention, the designer uses the interactive sphere to draw a letter "A" at the center of the cantilever beam through operations of deleting and adding structures, and makes aesthetic design adjustments to other areas of the model.

[0077] S8. Change the size of the interaction sphere to determine the operation range, pick up the structural surface of the model displayed within the operation range of the interaction sphere, and generate surface control points on this structural surface; select and drag-adjust the control points through the interaction device to finely modify the surface shape, and record the position X of the modified surface control points d . Please refer to Figure 7 , and the surface control points are generated by the method based on the Bezier surface. The green small ball in the figure is the interaction sphere.

[0078] 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 .

[0079] 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 .

[0080] S10. Continue the optimization process, and use the level set field interactive iterative optimization algorithm to iteratively update the adjusted level set field , 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 as follows:

[0081] .

[0082] S11. Repeat steps S5 - S10 until the design requirements are met and the iteration converges to obtain a level set field that meets the design requirements , and import the level set field into software that supports implicit modeling to export the optimized structure and complete the interactive design of the structure.

[0083] During the iteration process, for the rendering result of the display model of the optimized structure in Ue4.27, please refer to Figure 9 . And for the rendering display of the design structure without using the method of the present invention in Ue4.27, please refer to Figure 10 .

[0084] A 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.

[0085] Therefore, the present invention adopts 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 structural parameters in real time during the optimization calculation process, so that the structural performance can better meet the specific requirements of actual engineering applications.

[0086] 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 or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot 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 set, characterized in that It includes the following steps: S1. Set the number of nodes in the X, Y, and Z directions, establish a three-dimensional structural topology optimization design area, define boundary conditions and configuration parameters. The boundary conditions are structural loads and constraint conditions, and the configuration parameters are iterative parameters in the topology optimization process. The nodes are grid points in the design area; 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 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); S3. Use the level set field φ(X) in step S2 to render in the design area through the Marching Cubes method to generate a display model of the initial structure; S4. According to the configuration parameters, use the level set topology optimization method to solve the design variables. The design variables include mathematical variables that describe the structure shape and topology in the level set topology optimization method; S5. Observe the optimization situation of the display model. When the optimization does not meet the design requirements, pause the optimization process. The design requirements include aesthetic design, global optimal design, and avoiding stress concentration; 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; S7. Generate an interactive sphere, set the radius R of the interactive sphere to control the interaction precision, 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 X passed by the movement trajectory c ; S8. Change the size of the interactive sphere to determine the operation range, pick up the structural surface of the model displayed 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 interactive device, make fine modifications to the surface shape, and record the position X of the modified surface control points d ; 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; The level set field interactive iterative optimization algorithm is as follows: ； 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 modification; is the evolution velocity field of 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 iteration step when modifying the model; S11. Repeat steps S5 to 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 that supports implicit modeling, export the optimized structure, and complete the structural interactive design.

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

4. A 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 an arbitrary point in three-dimensional space to the surface of an object. The level set generation formula based on the SDF (Signed Distance Function) is as follows: is: ； ； ； In the formula, , represent the minimum and maximum values of the SDF symbol 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.

5. A three-dimensional structure interactive topology optimization method based on level set according to claim 1, characterized in that, In step S5, use a head-mounted display or a 3D display to observe the optimization situation of the model, control the viewing angle and position of the structure through an interaction device, and observe the changes of the structure from multiple perspectives inside and outside the structure.

6. A three-dimensional structure interactive topology optimization method based on level set according to claim 1, characterized in that In step S8, the surface control points are generated by the method based on Bezier surface.

7. A three-dimensional structure interactive topology optimization method based on level set according to claim 1, characterized in that, In steps S7 and S8, record the interaction operations of the interaction sphere to form a design history tree, which supports backtracking or redoing the modification operations of any step by sliding the time axis.

8. A three-dimensional structure interactive topology optimization method based on level set according to claim 1, characterized in that In steps S5 to S11, with the help of multi-person real-time collaboration technology, observe the 3D model in the same environment and modify the structure in real time.

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