Adaptive subdivision grid topology optimization method and system based on balanced quadtree

Abstract

The present invention discloses an adaptive subdivision grid topology optimization method and system based on a balanced quadtree. The steps of the method include establishing a sparse grid model and defining loads and boundaries; establishing a data structure for storing unit and node information; initializing design variables, calculating the objective function and constraint function, and the sensitivity of the function to the design variables; calculating the subdivision factor of each unit and determining whether it is greater than a threshold; for grids greater than the subdivision factor, using a recursive method to decompose the grid units and update the unit and node data structures; establishing a stiffness matrix, a constraint matrix and a calculation matrix for the updated model, and updating the design variables; repeating the above steps until convergence. Based on the above method, the corresponding modules are constructed and a system is formed. The method of the present invention ensures high computational efficiency while achieving extremely high boundary accuracy, greatly broadening the scope of application of the adaptive topology optimization method.

Description

Technical Field

[0001] The present invention relates to the technical field of structural optimization design, and specifically designs an adaptive subdivision grid topology optimization method and system based on a balanced quadtree. Background Art

[0002] Structural topology optimization, as an efficient design method, can significantly reduce the weight of a structure while still meeting its performance requirements. With the gradual maturity of 3D printing technology, structural topology optimization is playing an increasingly important role in the field of structural engineering. To facilitate subsequent manufacturing, the optimized structure needs to have a high degree of boundary clarity. To achieve this, the traditional technical approach is to increase the number of meshes during the optimization process. For three-dimensional problems, to increase boundary clarity by 100%, the overall number of meshes needs to be increased by 800%, resulting in a significant decrease in optimization efficiency and unacceptable computational time.

[0003] Since the optimized configuration occupies a relatively low proportion of the initial design domain, a feasible way to solve this problem is to refine only the mesh of the area containing solid materials according to the optimization results during the optimization process, that is, adaptive mesh division. Existing adaptive mesh topology optimization methods mainly use two types of methods: (1) pre-setting the parent level and child level, storing them, and calling them during the optimization process. This method has fewer adaptive levels and can generally only achieve three-level mesh adaptive division. In many cases, it cannot meet the boundary accuracy requirements; (2) completely using the data structure method in the image discipline, using the "east, south, west and north" orientation to store adjacent unit information, and can only process rectangular design domains and rectangular mesh units such as standard images. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method and system for topology optimization of adaptive subdivision grids with high boundary accuracy and wide application range.

[0005] To solve the above technical problems, the present invention provides an adaptive subdivision grid topology optimization method based on a balanced quadtree, and the technical solution includes the following steps:

[0006] Step 1: For the two-dimensional structure to be optimized, establish a sparse finite element mesh model and define boundary conditions and loads;

[0007] Step 2: Read in the grid model, set the optimization parameters, and initialize the information of each unit;

[0008] Step 3: Record the unit information of each node, including the unit number and the current grid level of the unit;

[0009] Step 4: Initialize the design variables, calculate the stiffness matrix of each element, and based on this, calculate the node displacement under load, the objective function, and the sensitivity of the objective function to the design variables, and update the design variables;

[0010] Step 5: Calculate the i-th unit A i If f is greater than the threshold, proceed to the next step. If f is less than the threshold, determine the subdivision factors f of other units and repeat step 5.

[0011] Step 6: Use quadtree to store and recursively divide the unit grid. According to the data structure of units and nodes, find the current unit A. i There are adjacent cells with common edges. Traverse the adjacent cells. If the grid level of the adjacent cell is smaller than the current cell A i level, then define the adjacent unit as the current pre-grid subdivision unit, repeat step 6 until the final grid subdivision unit is obtained, and proceed to the next step. Otherwise, directly define unit A as the current pre-grid subdivision unit. i As the final mesh subdivision unit, proceed to the next step.

[0012] Step 7: Mesh the mesh subdivision elements, update the element and node data structures, and calculate the element stiffness matrix of the corresponding mesh;

[0013] Step 8: After traversing all elements, calculate the overall stiffness matrix of the element after adaptive meshing, establish the constraint matrix, and synthesize the solution matrix with the overall stiffness matrix; calculate the node displacement under the load; calculate the objective function and the sensitivity of the objective function to each design variable, and update the design variables;

[0014] Step 9: Repeat steps 5 to 8 until the convergence condition is met or the maximum number of iterations is reached.

[0015] Furthermore, the unit data format in step 3 is a structure, which includes the node number, line number, parent unit number, child unit number, current grid level, unit center coordinates, and unit volume. The node data format is also a structure, which includes the unit number and corresponding unit level corresponding to the node.

[0016] Furthermore, the i-th unit A i The subdivision factor calculation formula is:

[0017] f = x i (1-x i )

[0018] Among them, x i is the design variable value of the i-th unit, i = 1, ..., m, m is the current number of design variables, and its value is greater than 0.001 and less than 1.

[0019] Furthermore, the network subdivision unit is meshed in the following way: along the midpoints of the four sides of the network subdivision unit, the unit is divided into four sub-units, the sub-units are numbered, the added node numbers and the numbers of the surrounding units of these nodes are recorded, and the four sub-unit numbers are added to the information of the network subdivision unit; and the unit number of the network subdivision unit is added to the parent unit information of the four sub-units, the unit level of the sub-unit is increased by 1 compared to the parent unit, and the position of the parent unit in the design variable is replaced by the sub-unit.

[0020] According to another aspect of the present invention, an adaptive subdivision grid topology optimization system based on a balanced quadtree is provided, and the technical solution is as follows:

[0021] The system includes a data reading and initialization module, a grid division module, an optimization module, a grid division adaptive decision module, and a convergence decision module.

[0022] The data reading and initialization module is used to read the sparse finite element mesh model, set the optimization parameters, initialize the information of each unit and store it; record the unit information to which each node belongs; and initialize the design variables;

[0023] The grid division adaptive decision module is used to decide the final grid subdivision unit, specifically: calculate the i-th unit A i The subdivision factor f, if f is greater than the threshold, is stored in a quadtree and the unit grid is divided recursively. First, each unit A is traversed. i If the grid level of the adjacent cell is greater than or equal to the current grid level, then the decision unit A is i For the final grid subdivision unit, otherwise repeat the traversal of each and unit A i Collinear adjacent units, according to the data structure of units and nodes, find the current unit A i There are adjacent cells with common edges. Traverse the adjacent cells. If the grid level of the adjacent cell is smaller than that of cell A, i level, the adjacent unit is defined as the current pre-grid subdivision unit, and the adjacent units are repeatedly traversed until the final grid subdivision unit is obtained; if f is less than the threshold, the grid division of other units is determined;

[0024] The grid division module performs grid division on the grid subdivision unit and updates the unit and node data structures;

[0025] The optimization module is used to calculate the stiffness matrix of each unit after meshing, or calculate the overall stiffness matrix after meshing all units, establish a constraint matrix, and synthesize the solution matrix with the overall stiffness matrix; calculate the node displacement under the action of load; calculate the objective function, the sensitivity of the objective function to each design variable, and update the design variables;

[0026] The convergence judgment module is used to judge whether the mesh division has traversed all units or completed the set number of optimization iteration steps. If not, the mesh division adaptive judgment module, the mesh division module and the optimization module are continued to be mobilized to perform adaptive mesh division. After traversing all units, it is used to judge whether the optimized structural configuration meets the convergence condition. If the convergence condition is met or the set number of optimization iteration steps is completed, the adaptive mesh division is terminated. Otherwise, the adaptive mesh division is continued until the convergence condition is met or the number of optimization iteration steps is completed.

[0027] Furthermore, the unit data format is a structure, which contains the node number, line number, parent unit number, child unit number, current grid level, unit center coordinates, and unit volume. The node data format is also a structure, which contains the unit number and corresponding unit level corresponding to the node.

[0028] Furthermore, Unit A i The subdivision factor calculation formula is:

[0029] f = x i (1-x i )

[0030] Among them, x i is the design variable value of the i-th unit, i = 1, ..., m, m is the current number of design variables, and its value is greater than 0.001 and less than 1.

[0031] Furthermore, the grid is divided into subdivision units as follows:

[0032] Divide the unit into 4 subunits along the midpoints of the four sides of the grid subdivision unit, and number the subunits. Record the added node numbers and the numbers of the surrounding units of these nodes, and add the 4 subunit numbers to the unit information of the grid subdivision unit. Add the unit number of the grid subdivision unit to the parent unit information of the 4 subunits. The unit level of the subunit is increased by 1 compared to the parent unit, and the position of the parent unit in the design variable is replaced by the subunit.

[0033] Compared with the prior art, the present invention has the following advantages:

[0034] (1) The present invention proposes a new data storage structure, which can theoretically realize unlimited automatic grid division, thereby achieving extremely high boundary accuracy.

[0035] (2) The method proposed in this invention can be used for adaptive meshing and topology optimization of non-rectangular design domains and grid cells, which greatly broadens the scope of application of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The accompanying drawings are included to provide a further understanding of the embodiments of the present invention, constitute a part of the specification, illustrate the embodiments of the present invention, and together with the description, explain the principles of the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and those skilled in the art can derive other drawings based on these drawings without inventive effort.

[0037] Figure 1 is a flow chart of an adaptive subdivision grid topology optimization method based on a balanced quadtree in an embodiment of the present invention;

[0038] Figure 2 This is an explanation of the unbalanced quadtree and the balanced quadtree in the embodiment of the present invention;

[0039] Figure 3 Schematic diagram of adaptive grid division and data structure before and after division according to an embodiment of the present invention;

[0040] Figure 4 Schematic diagram of the design domain, initial mesh division, boundary and load of an embodiment of the present invention;

[0041] Figure 5 The adaptive mesh division and optimized structure of the embodiment of the present invention when iterating 140 steps;

[0042] Figure 6 It is the adaptive mesh division situation and the final optimized structure at the end of iteration of the embodiment of the present invention. DETAILED DESCRIPTION

[0043] It should be noted that, in the absence of conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is in no way intended to limit the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0044] The present invention is further described below with reference to the accompanying drawings and specific embodiments. It is hereby stated that the enumerated embodiment is only an example application of the present invention, used to explain the present invention, and other applications within the framework of the principles of the present invention are all within the scope of protection of the present invention.

[0045] This embodiment describes an adaptive subdivision grid topology optimization method based on a balanced quadtree. Figure 1As shown, it includes the following steps:

[0046] Step 1: For the two-dimensional structure to be optimized, establish a sparse finite element mesh model, define boundary conditions, loads, etc., and export the mesh file stored in text format.

[0047] Step 2: Read in the mesh model and set the optimization parameters. Initialize and store the information of each unit. The unit information includes: (1) the node number of the unit; (2) the line number of the unit; (3) the parent unit number is set to 0; (4) the child unit number is set to 0; (5) the current mesh level is set to 0; (6) the unit center coordinates; and (7) the unit volume.

[0048] Step 3: Construct a node information structure to record the unit information of each node, including the unit number and the current grid level of the unit.

[0049] Step 4: Initialize the design variable x i , i=1,...,m, where m is the number of current design variables, x i is the design variable value for the i-th element, which should be greater than 0.001 and less than 1. Calculate the stiffness matrix for each element, and based on this, calculate the node displacements under load. Based on this, calculate the objective function and its sensitivity to the design variables, and filter the sensitivity. Update the design variables based on this sensitivity information.

[0050] Step 5: Calculate Cell A i Subdivision factor f. Assume that the design variable x i The corresponding unit number is A i , then the calculation formula of the unit subdivision factor is f = x i (1-x i If f is greater than the threshold, proceed to the next step. If f is less than the threshold, determine the subdivision factor f of other units and repeat step 5.

[0051] Step 6: Use quadtree to store and use recursive method to divide the unit grid to ensure the balance of the quadtree. Balanced and unbalanced quadtree grids are as follows Figure 2 Explanation, Figure 2 (a) The grid is an unbalanced quadtree grid because there are two dangling nodes on one edge of grid cell C (the bold edge in the figure). Figure 2 The grid in (b) is a balanced quadtree grid because there is at most one dangling node on any of the four edges of a cell.

[0052] According to the data structure of units and nodes, find the current unit A iFor adjacent cells with common edges, traverse the adjacent cells. If the grid level of the adjacent cell is smaller than the current grid level, define the adjacent cell as the cell of the current pre-grid subdivision. Repeat step 6 until the final grid subdivision cell A is obtained and proceed to the next step. Otherwise, directly convert cell A i As the final mesh subdivision, cell A proceeds to the next step.

[0053] Step 7: Divide the grid cell A into 4 sub-cells along the midpoints of the four sides. The sub-cells are numbered B1, B2, B3, and B4. Figure 3 As shown, Figure 3 (a) indicates that unit A is divided into 4 units B1, B2, B3, B4, Figure 3 (b) Data organization. Record the added node numbers and the element numbers surrounding these nodes. Add the four child element numbers to the element information of A. Add the element number of A to the parent element information of the four child elements. The element level of the child elements is increased by 1 compared to the parent element. Replace the parent element position in the design variable with the child element, and calculate the element stiffness matrix of the corresponding mesh.

[0054] Step 8: After traversing all elements, calculate the global stiffness matrix of the adaptively meshed elements. Due to the large number of hanging nodes, establish a constraint matrix and combine it with the global stiffness matrix to form a solution matrix. Calculate the node displacements under load. Calculate the objective function and the sensitivity of the objective function to each design variable, and update the design variables.

[0055] Step 9: Repeat steps 5 to 8 until the convergence condition is met or the maximum number of iterations is reached.

[0056] Based on the same concept, according to another aspect of the present invention, an adaptive subdivision mesh topology optimization system based on a balanced quadtree is provided.

[0057] The following describes the adaptive subdivision mesh topology optimization system based on a balanced quadtree provided by the present invention. The adaptive subdivision mesh topology optimization system based on a balanced quadtree described below and the adaptive subdivision mesh topology optimization method based on a balanced quadtree described above can refer to each other.

[0058] In an exemplary embodiment of the present invention, a balanced quadtree-based adaptive subdivision grid topology optimization system is provided, which includes a data reading and initialization module, a grid division module, an optimization module, a grid division adaptive decision module, and a convergence decision module.

[0059] The data reading and initialization module is used to read the sparse finite element mesh model, set the optimization parameters, initialize the information of each unit and store it; record the unit information to which each node belongs; initialize the design variable xi , i=1,...,m, where m is the number of current design variables, x i The design variable value for the i-th element is greater than 0.001 and less than 1. The element data format is a structure that contains the node number, line number, parent element number, child element number, current grid level, element center coordinates, and element volume. The node data format is also a structure that contains the element number and corresponding element level corresponding to the node.

[0060] The grid division adaptive decision module is used to determine the final grid subdivision unit, specifically: calculate the subdivision factor f of each unit, assuming that the design variable x i The corresponding unit number is A i , then the calculation formula of the unit subdivision factor is f = x i (1-x i ). If f is greater than the threshold, it is stored in a quadtree and the unit grid is divided recursively to ensure the balance of the quadtree. First, traverse each unit A. i If the grid level of the adjacent cell is greater than or equal to the current grid level, then the decision unit A is i For the final grid subdivision unit, otherwise repeat the traversal of each and unit A i Collinear adjacent units, according to the data structure of units and nodes, find the current unit A i There are adjacent cells with common edges. Traverse the adjacent cells. If the grid level of the adjacent cell is smaller than that of cell A, i level, the adjacent unit is defined as the unit of the current pre-grid subdivision, and the adjacent units are repeatedly traversed until the final grid subdivision unit A is obtained; if f is less than the threshold, the grid division of other units is determined.

[0061] The meshing module divides mesh subdivision unit A into four subdivision units along the midpoints of its four sides. The subdivision units are numbered. The added node numbers are recorded, along with the numbers of the surrounding units. The four subdivision unit numbers are added to the unit information of mesh subdivision unit A. The unit number of mesh subdivision unit A is then added to the parent unit information of the four subdivision units. The unit level of the subdivision units is increased by 1 compared to the parent unit, and the parent unit position in the design variable is replaced by the subdivision unit.

[0062] The optimization module is used to calculate the stiffness matrix of each unit after meshing, or calculate the overall stiffness matrix after traversing all units for meshing, establish a constraint matrix, and synthesize the solution matrix with the overall stiffness matrix; calculate the node displacement under the action of load; calculate the objective function, the sensitivity of the objective function to each design variable, and update the design variables.

[0063] The convergence judgment module is used to judge whether the mesh division has traversed all units or completed the set number of optimization iteration steps. If not, the mesh division adaptive judgment module, the mesh division module and the optimization module are continued to be mobilized to perform adaptive mesh division. After traversing all units, it is used to judge whether the optimized structural configuration meets the convergence condition. If the convergence condition is met or the set number of optimization iteration steps is completed, the adaptive mesh division is terminated. Otherwise, the adaptive mesh division is continued until the convergence condition is met or the number of optimization iteration steps is completed.

[0064] It should be noted that parts of the present invention that are not described in detail are well known to those skilled in the art.

[0065] The application effect of the present invention is further explained in conjunction with an embodiment. The specific description of the embodiment is as follows: the design domain size, the sparse grid division corresponding to the design domain, the constraint boundary and the load are as follows: Figure 4 As shown in the figure, the initial sparse grid contains 48 grid elements and 65 nodes. The design domain is non-rectangular, and the grid is non-rectangular. The plate thickness corresponding to the design domain is 1 mm, the load is 1000 N, and the material used in the design domain has a modulus of E = 70 GPa, a Poisson's ratio of υ = 0.3, and a density of ρ = 2.7 kg / m 3 The objective function of the topology optimization design is to minimize the compliance of the structure, the constraint is that the optimized material mass is no more than 30% of the initial design mass, and the threshold of the mesh subdivision factor is 0.16.

[0066] At the 140th optimization iteration, the mesh division of the design domain and the optimized structural configuration are as follows: Figure 5 As shown, Figure 5 (a) is the adaptive mesh division under the current iteration step, Figure 5 (b) is the optimized configuration at the current iteration step, which contains a total of four mesh levels. At this time, because the mesh is still relatively coarse, the boundaries are visible and appear "jagged" and not very clear.

[0067] At the end of the iteration, the meshing of the design domain and the optimized structural configuration are as follows: Figure 6 As shown, Figure 6 (a) is the adaptive mesh division under the current iteration step, Figure 6 (b) shows the optimized configuration at the current iteration, which contains a total of 6 mesh levels. It can be seen that the boundary transitions of the optimized configuration are smooth and clear, making it easy to process.

[0068] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. An adaptive subdivision grid topology optimization method based on a balanced quadtree, characterized in that: The method comprises the following steps: Step 1: For the two-dimensional structure to be optimized, establish a sparse finite element mesh model and define boundary conditions and loads; Step 2: Read in the grid model, set the optimization parameters, and initialize the information of each unit; Step 3: Record the unit information of each node, including the unit number and the current grid level of the unit; Step 4: Initialize the design variables, calculate the stiffness matrix of each element, and based on this, calculate the node displacement under load, the objective function, and the sensitivity of the objective function to the design variables, and update the design variables; Step 5: Calculate the i-th unit A i If f is greater than the threshold, proceed to the next step. If f is less than the threshold, determine the subdivision factors f of other units and repeat step 5. Step 6: Use quadtree to store and recursively divide the unit grid. According to the data structure of units and nodes, find the current unit A. i There are adjacent cells with common edges. Traverse the adjacent cells. If the grid level of the adjacent cell is smaller than the current cell A i level, then define the adjacent unit as the current pre-grid subdivision unit, repeat step 6 until the final grid subdivision unit is obtained, and proceed to the next step. Otherwise, directly define unit A as the current pre-grid subdivision unit. i As the final grid subdivision unit, proceed to the next step; Step 7: Mesh the mesh subdivision elements, update the element and node data structures, and calculate the element stiffness matrix of the corresponding mesh; Step 8: After traversing all elements, calculate the overall stiffness matrix of the element after adaptive meshing, establish the constraint matrix, and synthesize the solution matrix with the overall stiffness matrix; calculate the node displacement under the load; Calculate the objective function, the sensitivity of the objective function to each design variable, and update the design variables; Step 9: Repeat steps 5 to 8 until the convergence condition is met or the maximum number of iterations is reached. i The subdivision factor calculation formula is: f=x i (1-x i ) Among them, x i Design variable values for the i-th unit, i = 1, ..., m, where m is the current number of design variables and its value is greater than 0.001 and less than 1. Grid division is performed on the network subdivision unit by dividing the unit into four subunits along the midpoints of the four sides of the network subdivision unit, numbering the subunits, recording the added node numbers and the numbers of the surrounding units of these nodes, and adding the four subunit numbers to the information of the network subdivision unit; and adding the unit number of the network subdivision unit to the parent unit information of the four subunits, increasing the unit level of the subunit by 1 compared to the parent unit, and replacing the position of the parent unit in the design variable with the subunit.

2. The method for adaptive subdivision mesh topology optimization based on balanced quadtree according to claim 1, characterized in that: The unit data format in step 3 is a structure, which includes the node number, line number, parent unit number, child unit number, current grid level, unit center coordinates, and unit volume. The node data format is also a structure, which includes the unit number and corresponding unit level corresponding to the node.

3. The adaptive subdivision grid topology optimization system based on balanced quadtree is characterized by: Including data reading and initialization module, grid division module, optimization module, grid division adaptive decision module, convergence decision module, The data reading and initialization module is used to read the sparse finite element mesh model, set the optimization parameters, initialize the information of each unit and store it; record the unit information to which each node belongs; and initialize the design variables; The grid division adaptive decision module is used to decide the final grid subdivision unit, specifically: calculate the i-th unit A i The subdivision factor f, if f is greater than the threshold, is stored in a quadtree and the unit grid is divided recursively. First, each unit A is traversed. i If the grid level of the adjacent cell is greater than or equal to the current grid level, then the decision unit A is i For the final grid subdivision unit, otherwise repeat the traversal of each and unit A i Collinear adjacent units, according to the data structure of units and nodes, find the current unit A i There are adjacent cells with common edges. Traverse the adjacent cells. If the grid level of the adjacent cell is smaller than that of cell A, i level, then define the adjacent unit as the current pre-grid subdivision unit, and repeatedly traverse the adjacent units until the final grid subdivision unit is obtained; If f is less than the threshold, the grid division of other units is determined; The grid division module is used to perform grid division on the grid subdivision unit and update the unit and node data structure; The optimization module is used to calculate the stiffness matrix of each unit after meshing, or to calculate the overall stiffness matrix after meshing all units, establish a constraint matrix, and synthesize the solution matrix with the overall stiffness matrix; calculate the node displacement under load; Calculate the objective function, the sensitivity of the objective function to each design variable, and update the design variables; The convergence judgment module is used to judge whether the grid division has traversed all units or completed the set number of optimization steps. If not, the grid division adaptive judgment module, grid division module and optimization module are continued to be mobilized to perform adaptive grid division. After traversing all units, it is used to judge whether the optimized structural configuration meets the convergence condition. If the convergence condition is met or the set number of optimization steps is completed, the adaptive grid division is terminated. Otherwise, the adaptive grid division is continued until the convergence condition is met or the set number of optimization steps is completed. Unit A i The subdivision factor calculation formula is: f=x i (1-x i ) Among them, x i For the design variable value of the i-th unit, i = 1, ..., m, m is the number of current design variables, the value is greater than 0.001 and less than 1, the grid subdivision unit is divided as follows: Divide the unit into 4 subunits along the midpoints of the four sides of the grid subdivision unit, and number the subunits. Record the added node numbers and the numbers of the surrounding units of these nodes, and add the 4 subunit numbers to the unit information of the grid subdivision unit. Add the unit number of the grid subdivision unit to the parent unit information of the 4 subunits. The unit level of the subunit is increased by 1 compared to the parent unit, and the position of the parent unit in the design variable is replaced by the subunit.

4. The balanced quadtree-based adaptive subdivision grid topology optimization system according to claim 3, characterized in that: The unit data format is a structure, which contains the node number, line number, parent unit number, child unit number, current grid level, unit center coordinates, and unit volume. The node data format is also a structure, which contains the unit number and corresponding unit level corresponding to the node.

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