A scaffolding expanded metal mesh construction method based on BIM

Abstract

The present application discloses a method for building a steel mesh for scaffolding based on BIM, which involves BIM modeling and includes: obtaining the characteristic parameters of the steel mesh for scaffolding; using the parametric modeling method to establish a three-dimensional solid model of the steel mesh for scaffolding according to the characteristic parameters; performing mesh division on the three-dimensional solid model by using an adaptive mesh division algorithm to obtain finite element meshes; using an adaptive mesh refinement algorithm to identify the stress concentration areas in the finite element meshes and performing mesh refinement on the stress concentration areas to obtain the refined finite element meshes; using a topology optimization algorithm to perform structural optimization on the refined finite element meshes to obtain an optimized three-dimensional solid model of the steel mesh for scaffolding; and using a discrete topology optimization algorithm to perform component layout optimization on the three-dimensional solid model after structural optimization to obtain the final BIM model of the steel mesh for scaffolding. Aiming at the large redundancy in the erection of the steel mesh for scaffolding in the prior art, the present application reduces redundant design.

Description

Technical Field

[0001] This application relates to the field of BIM modeling, and particularly to a method for building a steel mesh scaffold based on BIM. Background Art

[0002] Scaffolds are indispensable temporary engineering structures in building construction and are widely used in various engineering fields such as buildings and bridges. Most traditional scaffolds are erected using steel pipes, which have problems such as low erection efficiency and low reuse rate of components. In recent years, steel mesh has gradually become one of the main materials for scaffolds. It has advantages such as high strength, good stiffness, and convenient assembly. Therefore, scaffold systems based on steel mesh have been increasingly applied.

[0003] However, there are still some deficiencies in the design and erection of existing steel mesh scaffolds. One prominent problem is that there is a large amount of redundancy in the erection of scaffolds, with a large number of repeated and unnecessary components, resulting in serious material waste. For example, traditional two-dimensional construction drawings are difficult to comprehensively express the spatial structural relationship of scaffolds, and problems such as inaccurate component positioning and unreasonable node connections are likely to occur, leading to component redundancy or scrapping and waste during construction. Summary of the Invention

[0004] In view of the problem of large redundancy in the erection of steel mesh scaffolds in the prior art, this application provides a method for building a steel mesh scaffold based on BIM. By performing BIM modeling and topological optimization, and setting volume constraints, structural stiffness constraints, and surface stability constraints, etc., redundant design is reduced.

[0005] The purpose of this application is achieved through the following technical solutions.

[0006] This application provides a method for building a steel mesh scaffold based on BIM, including: obtaining the characteristic parameters of the steel mesh scaffold, where the characteristic parameters include the cross-sectional dimensions of the vertical poles, the cross-sectional dimensions of the horizontal bars, and the steel plate thickness; according to the characteristic parameters, using the parametric modeling method to establish a three-dimensional solid model of the steel mesh scaffold; using an adaptive mesh division algorithm to divide the three-dimensional solid model into grids to obtain finite element grids; using an adaptive mesh refinement algorithm to identify the stress concentration areas in the finite element grids and refine the grids in the stress concentration areas to obtain refined finite element grids; using a topological optimization algorithm to optimize the structure of the refined finite element grids to obtain an optimized three-dimensional solid model of the steel mesh scaffold; using a discrete topological optimization algorithm to optimize the component layout of the three-dimensional solid model after structural optimization to obtain the final BIM model of the steel mesh scaffold.

[0007] Further, a three-dimensional solid model of the scaffolding expanded metal is established, including: according to the obtained cross-sectional dimensions of the vertical poles, cross-sectional dimensions of the horizontal bars, and thickness of the steel plate, a parametric geometric model of the scaffolding expanded metal is established by using a constraint-based solid modeling method; wherein, the parametric geometric model contains the geometric dimension information and relative position relationship of the vertical poles, horizontal bars, and steel plates; according to the parametric geometric model, combined with the preset scaffolding design specifications, a parametric-driven rule reasoning method is used to determine the number and arrangement spacing of the vertical poles and horizontal bars; wherein, the scaffolding design specifications include scaffolding structure design specifications, component arrangement rules, and component connection rules; according to the parametric geometric model, combined with the preset construction process requirements, a case-based knowledge reasoning method is used to determine the connection methods and joint structures between the vertical poles and the steel plates, and between the horizontal bars and the steel plates; wherein, the construction process requirements include scaffolding erection process and construction sequence; according to the determined number and arrangement spacing of the vertical poles and horizontal bars, and the determined connection methods and joint structures, entity merging and Boolean operations are used to generate a three-dimensional solid model of the scaffolding expanded metal.

[0008] Further, an adaptive mesh generation algorithm is used to mesh the three-dimensional solid model, including: using an octree space partitioning algorithm to recursively divide the bounding box of the three-dimensional solid model into eight sub-cubes until the preset mesh size is satisfied, generating initial mesh elements; calculating the average value of the coordinate differences between each node and its corresponding adjacent nodes in the initial mesh elements as the Laplacian coordinates of the nodes; according to the Laplacian coordinates of the mesh nodes, the global stiffness matrix K and the mass matrix M, a linear equation system of the mesh elements is established ; where x is the node coordinate quantity to be optimized, and f is the Laplacian coordinate of the node; setting the minimum size and the maximum size constraints as the inequality constraints of the node coordinate quantity to be optimized x ; combining the global stiffness matrix K, the mass matrix M, and the linear equation system after inequality constraints to obtain an overall linear equation system; using a conjugate gradient iteration algorithm to solve the overall linear equation system to obtain the position correction quantity of the node coordinate quantity to be optimized x, and using the position correction quantity to correct the node coordinate quantity to be optimized x; iteratively executing the node coordinate update step until the maximum displacement of the mesh nodes is less than the preset threshold to obtain the final finite element mesh.

[0009] Further, grid encryption is performed on the stress concentration area, including: according to the initial finite element grid, using the explicit finite element method to calculate the stress state of the scaffolding expanded metal under the preset load condition, and obtaining the stress tensor of each grid element; according to the stress tensor of each grid element, using the stress tensors of adjacent elements at the nodes of the grid element, fitting the stress field function of the corresponding node by the least square method, and taking the gradient of the stress field function to obtain the node stress gradient value; interpolating the node stress gradient value into the interior of the grid element to obtain the stress gradient field of the grid element; comparing the stress gradient field with the preset stress gradient threshold, and obtaining the grid elements with stress gradient greater than the stress gradient threshold as the stress concentration area; using the component classification method to divide the stress concentration area into a first area and a second area; the first area includes the stress concentration areas of the vertical poles and horizontal bars, and the second area includes the stress concentration area of the steel plate component; for the first area, the one-dimensional quadtree grid subdivision algorithm along the component axis is used for grid encryption; for the second area, the two-dimensional quadtree grid subdivision algorithm in the plane of the plate is used for grid encryption to obtain the encrypted finite element model.

[0010] Further, a topology optimization algorithm is used to optimize the structure of the encrypted finite element grid, including: taking the encrypted finite element grid as the design area of topology optimization, using the variable density algorithm to divide the design area into multiple sub-areas, and setting a relative density variable for each sub-area ; taking the minimum total strain energy of the scaffolding expanded metal structure as the optimization goal, taking the relative density variables of each sub-area as the optimization variables to establish a topology optimization model; solving the topology optimization model to obtain the optimal relative density of each sub-area ; according to the optimal relative density of each sub-area , updating the material properties of each sub-area to obtain the optimized three-dimensional solid model.

[0011] Further, an initial topology optimization model is established, including: setting the volume constraint condition and the structural stiffness constraint condition of the scaffolding expanded metal; the expression of the volume constraint condition is as follows: , where is the actual material volume of the optimized structure represented by the SIMP interpolation method, is the initial volume of the design area, is the upper limit of the volume fraction; the expression of the structural stiffness constraint condition is as follows: , where is the total strain energy of the optimized structure under the construction condition, is the total strain energy of the initial design area under the same condition; through this constraint condition, it is ensured that the overall stiffness of the optimized structure is not lower than the initial design; setting the penalty factor λ, and constructing the optimization goal according to the constraint condition : O ( ρ ) = C ( ρ ) + λ [ V ( ρ ) − f v × V 0 ] , where λ is the penalty factor used to balance the relative importance of minimizing the total strain energy and satisfying the volume constraint. The larger the value of λ, the more conducive it is to satisfying the volume constraint, but it may reduce the optimization effect of the total strain energy. Establish the static equilibrium equation of the scaffolding expanded metal structure under the construction condition as the constraint condition for topology optimization: , where is the total stiffness matrix obtained by using the SIMP interpolation method, which is related to the relative density of each sub-region; U is the displacement vector of the structure under the construction load; F is the nodal load vector of the structure under the construction condition. Establish the buckling surface constraint condition of the scaffolding expanded metal: , where is the geometric stiffness matrix, which is related to the stress state of the structure; is the critical buckling load factor corresponding to the i-th buckling mode ; Through this constraint condition, the buckling stability and safety of the optimized structure are ensured. Establish the topology optimization model: Minimize: O ( ρ ) = C ( ρ ) + λ [ V ( ρ ) − f v × V 0 ] ; Constraint conditions: ; ; ; ; where is the lower limit of the relative density variable, usually taken as 0.001 to avoid singularity of the total stiffness matrix; n is the order of the buckling mode considered.

[0012] Furthermore, is the upper limit of the volume fraction, and its value range is 0.3 to 0.5.

[0013] Furthermore, solve the topology optimization model to obtain the optimal relative density of each sub-region, including: (1) Set the initial relative density field , and the initial iteration step t = 0; (2) Set the initial value of the Lagrange multiplier to 0, and let the iteration times k of be 0; (3) Calculate the objective function value , volume and structural stiffness under the current relative density field ; (4) Calculate the structural displacement field and stress field under the current relative density field ; By solving the following eigenvalue problem, obtain the critical buckling load factor : ; where is the total stiffness matrix obtained by using the SIMP interpolation method, is the geometric stiffness matrix, is the buckling mode; (5) Fix , update the relative density field through the following formula to obtain the updated relative density field : ; ρ e , t + 1 = max { ρ min ,min ρ e , t × B e , t η , 1 ] } , e = 1 , 2 ,....., N ; where, is the relative density of the e-th element at the t-th step, is the relative density of the e-th element at the (t + 1)-th step; is the relative change rate of the strain energy of the e-th element, is the numerical damping coefficient; N is the total number of elements divided in the design area;

[0014] (6) Judge whether the updated relative density field satisfies the volume constraint condition , if so, let , enter step (7); if not, then let , return to step (5); where, is the change step of Λ; (7) Judge whether is less than or equal to the set threshold , if so, let , enter step (9); if not, then let , return to step (5); (8) Judge whether the difference between the updated relative density field and the previous step is less than the set threshold , if so, output the optimal relative density , where, is the optimal relative density of the e-th element, terminate the optimization; if not, then return to step (3); (9) Use , return to step (5).

[0015] Furthermore, the expression is as follows: , where, is the partial derivative of the objective function with respect to the relative density of the e-th element, is the partial derivative of the volume with respect to the relative density of the e-th element.

[0016] Furthermore, η is the numerical damping coefficient, taking 0.3 - 0.5.

[0017] Compared with the prior art, the advantages of this application are:

[0018] An adaptive mesh encryption algorithm is adopted to identify the stress concentration area and refine the mesh through the stress gradient criterion and component classification, which can greatly improve the pertinence and efficiency of mesh encryption.

[0019] In the topology optimization model, with the minimum total strain energy of the scaffolding expanded metal structure as the optimization goal and the relative material density as the optimization variable, the optimal material distribution is obtained through density field solution. On the premise of meeting the volume constraint and structural performance requirements, the theoretically optimal topological configuration can be obtained, giving full play to the efficiency of materials and reducing redundancy and waste.

[0020] In topology optimization, the actual volume constraint, overall stiffness constraint, and buckling stability constraint are comprehensively considered, and an optimization result that meets the engineering practice and is safe and reliable can be obtained. By combining the constraint conditions and the objective function through the penalty function method, complex constraint problems can be efficiently solved. Through critical buckling load analysis, the overall stability of the scaffolding structure can be further ensured.

[0021] In the iterative solution process of topology optimization, the optimization criterion is continuously updated through the Lagrange multiplier method, and a balance can be sought between the volume constraint and the optimal goal, meeting both the volume fraction requirement and the optimization effect of the total strain energy. Combining numerical damping and sensitivity filtering techniques can accelerate the optimization convergence speed and avoid the checkerboard phenomenon in the density field. Brief Description of the Drawings

[0022] This application will be further described in the form of exemplary embodiments, and these exemplary embodiments will be described in detail through the drawings. These embodiments are not restrictive. In these embodiments, the same numbers represent the same structures, where:

[0023] Figure 1 is an exemplary flowchart of a method for building a scaffolding expanded metal based on BIM according to some embodiments of this application;

[0024] Figure 2 is an exemplary flowchart of constructing a three-dimensional solid model of a scaffolding expanded metal according to some embodiments of this application;

[0025] Figure 3 is an exemplary flowchart of generating a finite element mesh according to some embodiments of this application;

[0026] Figure 4 is an exemplary flowchart of generating an encrypted finite element model according to some embodiments of this application. Detailed Description of the Specific Embodiments

[0027] The methods and systems provided in the embodiments of this application will be described in detail below with reference to the drawings.

[0028] AsFigure 1 As shown, obtain the characteristic parameters of the scaffolding steel mesh. The characteristic parameters include the cross-sectional dimensions of the vertical poles, the cross-sectional dimensions of the horizontal bars, and the steel plate thickness. According to the characteristic parameters, use the parametric modeling method to establish a three-dimensional solid model of the scaffolding steel mesh. Use the adaptive mesh generation algorithm to mesh the three-dimensional solid model to obtain the finite element mesh. Use the adaptive mesh refinement algorithm to identify the stress concentration areas in the finite element mesh and refine the mesh in the stress concentration areas to obtain the refined finite element mesh. Use the topology optimization algorithm to optimize the structure of the refined finite element mesh to obtain the optimized three-dimensional solid model of the scaffolding steel mesh. Use the discrete topology optimization algorithm to optimize the component layout of the three-dimensional solid model after structural optimization to obtain the final BIM model of the scaffolding steel mesh.

[0029] Specifically, to obtain the characteristic parameters of the scaffolding steel mesh, which include the cross-sectional dimensions of the vertical poles, the cross-sectional dimensions of the horizontal bars, and the steel plate thickness. Through the human-computer interaction interface, the user directly inputs the characteristic parameters such as the cross-sectional dimensions of the vertical poles, the cross-sectional dimensions of the horizontal bars, and the steel plate thickness. The system receives and stores these parameter values to form structured parameter data. Read the pre-input characteristic parameter values from an external data file (such as an Excel spreadsheet). The system parses the file format, extracts the data such as the cross-sectional dimensions of the vertical poles, the cross-sectional dimensions of the horizontal bars, and the steel plate thickness, and converts them into the internal data structure of the program. Extract the characteristic parameters from the BIM model or CAD graphic file. Use the geometric recognition algorithm to identify the vertical poles, horizontal bars, and steel plate components in the model, extract their cross-sectional dimensions and thickness information, and convert them into structured parameter data.

[0030] As Figure 2 shown, according to the characteristic parameters, use the parametric modeling method to establish a three-dimensional solid model of the scaffolding steel mesh. Take the cross-sectional dimensions of the vertical poles, the cross-sectional dimensions of the horizontal bars, and the steel plate thickness as parameter variables to establish a parametric cross-sectional profile sketch. Use the sketch constraint tools provided by the parametric modeling software, such as vertical, horizontal, collinear, etc., to define the geometric constraint relationships of the cross-sectional profile. Based on the parametric cross-sectional profile, use solid modeling commands such as extrusion and rotation to generate the three-dimensional solid models of the vertical poles, horizontal bars, and steel plates. During the modeling process, associate the dimensional parameters such as the length, width, and height of the components with the corresponding characteristic parameters to form a parameter-driven solid model. Define the relative position relationships of the vertical poles, horizontal bars, and steel plates in space through geometric constraints such as corresponding points and corresponding edges. Use the assembly constraint tools, such as parallel, perpendicular, and coincident, to establish the assembly constraints between the components to form a parametric assembly model.

[0031] According to the parametric geometric model, combined with the scaffolding design specifications, a parametric-driven rule reasoning method is adopted to determine the quantity and layout spacing of vertical poles and horizontal bars. Specifically, the scaffolding design specifications are formally represented as a series of parametric rules, such as "the spacing of vertical poles should not be greater than 1.2m" and "the spacing of horizontal bars should not be greater than 1.5m". Each rule contains attributes such as rule number, rule description, associated parameters, and constraint conditions. According to the size parameters of vertical poles and horizontal bars in the parametric geometric model, the corresponding design specification rules are matched. Using forward reasoning or backward reasoning methods, the rules that meet the constraint conditions are automatically identified, and the spacing parameters therein are extracted. Driven by the inferred spacing parameters, vertical pole and horizontal bar components are automatically inserted into the parametric geometric model. Through the programming interface, component instances are copied at the specified positions and directions, and the constraint relationships between components are updated to generate a complete scaffolding elevation.

[0032] According to the parametric geometric model, combined with the construction technology requirements, a case-based knowledge reasoning method is adopted to determine the connection methods and joint structures between vertical poles and steel plates, and between horizontal bars and steel plates. Specifically, a scaffolding construction technology case library is established in the database. Each case contains the following attributes: Scaffolding type: such as portal scaffolding, bowl-coupled scaffolding, etc.; Component type: such as vertical poles, horizontal bars, steel plates, etc.; Connection method: such as welding, bolt connection, pin connection, etc.; Joint structure: such as gusset plate, flange plate, connecting piece, etc.; 3D model data: The geometric information of the case is stored in the form of a BIM model or a CAD model. These attributes can be stored in a structured manner through fields for subsequent retrieval and analysis. The 3D model data can be associated with the attribute fields to achieve the integrated management of geometric information and process information. By collecting and organizing historical engineering cases, the case library is continuously enriched and improved to form a process knowledge base covering different types of scaffolding.

[0033] Based on similarity-based case retrieval, according to the characteristic parameters of the parametric geometric model, a similarity calculation method is adopted to retrieve several historical cases in the case library that are most similar to the current model. The similarity calculation considers the following factors: Scaffolding type: Cases of the same type as the current model are preferentially retrieved; Span: Cases with a span close to that of the current model are preferentially retrieved; Height: Cases with a height close to that of the current model are preferentially retrieved; Load: Cases with load conditions similar to those of the current model are preferentially retrieved. Methods such as weighted Euclidean distance can be used to calculate the similarity of the current model and each case in the case library in the above factors to obtain a similarity score. According to the similarity score, several cases with the highest scores are selected as similar cases. The number of similar cases can be set according to the scale of the case library and engineering requirements. Generally, 3 to 5 similar cases are selected for analysis.

[0034] Process knowledge extraction and optimization: Analyze and optimize the retrieved similar cases, and extract the connection methods and node structure knowledge from them. The specific steps include: statistically analyzing the connection methods of similar cases to obtain the applicable frequencies and evaluation indicators of different connection methods (such as construction difficulty, cost, reliability, etc.); optimizing the connection methods according to the characteristics and requirements of the current model to obtain recommended connection methods; summarizing and inducing the node structures of similar cases to extract key node structure knowledge (such as node force characteristics, construction key points, etc.); optimizing and combining the node structure knowledge to obtain a node structure scheme applicable to the current model; during the analysis and optimization process, data mining and statistical analysis techniques can be used to discover the laws and correlations in the case data, improving the efficiency and accuracy of knowledge extraction.

[0035] Adopt knowledge fusion and transfer learning techniques to apply the extracted and optimized connection methods and node structure knowledge to the current parametric model, and generate a matching connection and node structure scheme. Match the extracted connection method knowledge with the characteristic parameters of the current model to generate an applicable connection method scheme, and fuse the extracted node structure knowledge with the geometric information of the current model to generate a three-dimensional model of the node structure; use transfer learning techniques to adapt the node models of similar cases to the current model to achieve the rapid generation of the node structure scheme; check and optimize the generated connection and node structure scheme to ensure that it meets the process requirements and constraint conditions of the current model; through knowledge fusion and transfer learning, the empirical knowledge of historical cases can be fully utilized to improve the generation efficiency and quality of the current model's process scheme, and avoid repeated design and trial-and-error.

[0036] According to the determined number and layout spacing of vertical poles and horizontal bars, as well as the determined connection methods and node structures, use entity merging and Boolean operations to generate a three-dimensional solid model of the scaffolding steel mesh. Specifically, according to the number and layout spacing of vertical poles, calculate the three-dimensional coordinate positions of the vertical pole instances to form a spatial array of vertical pole instances. According to the number and layout spacing of horizontal bars, calculate the three-dimensional coordinate positions of the horizontal bar instances to form a spatial array of horizontal bar instances. Through array replication and coordinate transformation, batch generate the required vertical pole and horizontal bar component instances. During the array generation process, parametric modeling techniques can be used to parameterize the geometric dimensions, quantities, spacing, etc. of the vertical poles and horizontal bars to achieve the rapid generation and modification of component instances. At the same time, spatial indexing techniques, such as octrees, KD-trees, etc., can be used to index and manage the spatial coordinates of component instances to improve the calculation efficiency of subsequent operations.

[0037] According to the type and parameters of the connection method, corresponding connector entities, such as bolts, nuts, connection plates, etc., are generated at the intersection positions of the vertical poles and horizontal bars; according to the joint structure plan, joint component entities, such as stiffening plates, connecting angle pieces, etc., are generated around the connectors; an entity merging operation is adopted to combine the connectors with the vertical poles and horizontal bars to form an integrated connection joint; during the joint structure process, parametric modeling technology can be used to parameterize the geometric dimensions, quantities, positions, etc. of the connectors and joint components to achieve the rapid generation and modification of the joint structure. At the same time, collision detection technology can be used to check whether there are interferences and collisions between the connectors and joint components and the vertical poles and horizontal bars, and perform automatic adjustment and optimization to ensure the rationality and feasibility of the joint structure. The three-dimensional solid model of the steel plate is spatially superimposed with the instance array of the vertical poles and horizontal bars to form the initial model of the steel plate mesh. The Boolean difference operation is adopted, with the vertical pole and horizontal bar entities as the subtrahends and the steel plate entity as the minuend, to remove the parts where the steel plate intersects with the vertical poles or horizontal bars, and generate the three-dimensional solid model of the assembled scaffolding steel plate mesh. During the assembly process, spatial partitioning technologies, such as octree, BSP tree, etc., can be used to partition and index the spatial position relationships of the steel plates and component instances to improve the calculation efficiency of the Boolean operation. At the same time, multi-threaded parallel computing technology can be used to distribute the Boolean operation tasks to multiple processors or cores for parallel execution to further improve the computing performance. The generated three-dimensional solid model is topologically checked to judge the integrity and validity of the model. A topological rule checking algorithm is used to check whether there are errors such as hanging edges and non-manifold surfaces in the model, and perform automatic repair or manual correction. In this application, parametric modeling and instance array technology are adopted to achieve the rapid batch generation and layout of scaffolding components; entity merging and Boolean operation technology are adopted to achieve the automatic construction of connection joints and the assembly of steel plate meshes; topological rule checking and automatic repair technology are adopted to achieve the inspection and maintenance of model integrity; spatial indexing, parallel computing and other technologies are adopted to improve the calculation efficiency of model generation and operation.

[0038] such as Figure 3As shown in the figure, an adaptive mesh generation algorithm is used to mesh the three-dimensional solid model to obtain a finite element mesh. The octree space partitioning algorithm is adopted to recursively divide the bounding box of the three-dimensional solid model into eight sub-cubes until the preset mesh size is satisfied to generate initial mesh elements. Specifically, the bounding box of the geometric boundary of the three-dimensional solid model is calculated to obtain the minimum axis-aligned bounding box (AABB) of the model, that is, the smallest cuboid region that can completely contain the model. Taking the bounding box as the root node, recursively perform octree partitioning on it. The bounding box is evenly divided into two parts in the x, y, and z directions to obtain 8 sub-bounding boxes as the child nodes of the current node. Determine whether each sub-bounding box intersects with the three-dimensional solid model. If it intersects, add the sub-bounding box to the next layer of the octree and continue the recursive partitioning; if it does not intersect, discard the sub-bounding box. During the recursive partitioning process, continuously determine whether the size of the current bounding box meets the preset mesh size threshold. If it meets, mark the bounding box as a leaf node and stop the recursion; if it does not meet, continue the partitioning. Traverse all the leaf nodes of the octree and use them as initial mesh elements. Each initial mesh element contains the geometric information and topological relationship of its bounding box.

[0039] Calculate the average value of the coordinate differences between each node in the initial mesh element and its corresponding adjacent nodes as the Laplacian coordinates of the nodes. Specifically, for each initial mesh element, extract its 8 vertices as mesh nodes and establish a node index table. Traverse each mesh node and find its adjacent nodes according to its index in the node index table. For each node, calculate the average value of the coordinate differences between it and its adjacent nodes to obtain the Laplacian coordinates of the node : , , where is the set of adjacent nodes of node i, is the number of adjacent nodes, and are the coordinate vectors of adjacent node j and current node i respectively. Store the calculated Laplacian coordinates as node attributes and form the complete data structure of the nodes together with the node coordinates. According to the Laplacian coordinates of the mesh nodes, construct the global stiffness matrix K and mass matrix M, and establish the linear equations of the mesh elements ; where x is the quantity to be optimized of the node coordinates, and f is the Laplacian coordinates of the nodes. Initialize the global stiffness matrix and mass matrix , and determine the dimension of the matrix according to the number of mesh elements. K is a sparse symmetric positive definite matrix, and M is a diagonal matrix. Traverse each mesh element and calculate its local stiffness matrix and mass matrix . According to the geometric information and material properties of the elements, numerical integration methods (such as Gaussian integration) are used to calculate and . Assemble the local stiffness matrix and the mass matrix into the global stiffness matrix K and the mass matrix M, and determine the positions of the matrix elements according to the global numbers of the nodes. Construct the linear equations of the mesh elements . Among them, x is the quantity to be optimized of the node coordinates, that is, a column vector containing the coordinates to be optimized of all nodes; f is the column vector composed of the Laplacian coordinates of the nodes.

[0040] Set the minimum size and the maximum size constraints of the mesh elements as the inequality constraints of the quantity to be optimized x of the node coordinates . According to the requirements of mesh generation and the characteristics of the geometric model, set the minimum size and the maximum size of the mesh elements as the parameters for mesh quality control. Convert and into the value range constraints of the node coordinates. For each node i, generate the inequality constraints for its coordinate components: , j = 1, 2, 3, where is the j-th coordinate component of node i.

[0041] Combine the global stiffness matrix K, the mass matrix M, and the linear equations after inequality constraints to obtain the overall linear equations. Convert the value range constraints of the node coordinates into the standard form, that is: Ax ≤ b, where A is the constraint matrix and b is the constraint vector, which is composed of and . Combine the linear equations and the inequality constraint Ax ≤ b into the overall linear equations: [ K − M A 0 ] [ x f ] = 0 , constraint condition: inequality constraint Ax ≤ b.

[0042] Use the conjugate gradient iteration algorithm to solve the overall linear equations to obtain the position correction amount Δx of the quantity to be optimized x of the node coordinates, and use the position correction amount Δx to correct the quantity to be optimized x of the node coordinates. Initialize the node coordinate vector x, and generally take the node coordinates of the initial mesh elements as the initial values. Set the iteration parameters of the conjugate gradient algorithm, such as the maximum number of iterations, error tolerance, etc. In each iteration step, calculate the residual vector of the current solution, and the search direction vector p. Use r and p to construct the conjugate gradient sub-problem and solve the position correction amount Δx. Update the node coordinate vector x using the position correction amount Δx: , where α is the step factor, which controls the magnitude of position correction for each iteration. Determine whether the iteration termination condition is satisfied, such as the residual norm being less than a given threshold, the number of iterations reaching the upper limit, etc. If satisfied, output the optimized node coordinates x; otherwise, continue the iteration. Iteratively execute the node coordinate update step until the maximum displacement of the mesh nodes is less than the preset threshold, and obtain the final finite element mesh. After each iteration is completed, calculate the displacement of the mesh nodes: , where and are the coordinate vectors of the i-th node after the k-th and (k + 1)-th iterations respectively. Determine whether the displacements of all nodes are less than the preset threshold ε. If so, it is considered that the mesh optimization has converged, and output the final finite element mesh; otherwise, continue the iterative optimization. According to the optimized node coordinates, update the geometric information of the mesh elements, such as element volume, shape function, etc. Conduct a quality assessment on the optimized finite element mesh, such as calculating quality indicators such as element size, shape ratio, Jacobian matrix, etc., to determine whether the mesh meets the requirements of numerical simulation. Through octree space partitioning and Laplacian smoothing algorithm, this application can improve the efficiency of mesh generation while ensuring mesh quality. By using the conjugate gradient iterative optimization method, it is possible to improve the mesh quality and numerical performance under the premise of meeting geometric constraint conditions, providing a high-quality discrete model for subsequent finite element analysis.

[0043] Such as Figure 4 shown, an adaptive mesh refinement algorithm is used to identify the stress concentration areas in the finite element mesh and refine the mesh in the stress concentration areas to obtain the refined finite element mesh; First, according to the initial finite element mesh, the explicit finite element method is used to calculate the stress state of the scaffolding steel mesh under the preset load conditions to obtain the stress tensors of each mesh element. Specifically, taking the initial finite element mesh as the input, a finite element model of the scaffolding steel mesh is established. Select appropriate element templates according to the type of mesh element (such as beam element, plate element, etc.), and define the geometric parameters and material properties of the element. According to the actual working conditions of the scaffolding, set the preset load conditions, such as self-weight, construction load, wind load, etc. Convert the load into the node load or element body load of the finite element model.

[0044] The explicit finite element method is used to perform stress analysis on the scaffolding steel mesh. The explicit algorithm calculates the displacements and velocities of the nodes through explicit time integration, and then obtains the strains and stresses of the elements. Compared with the implicit algorithm, the explicit algorithm does not need to solve large linear equations and has higher calculation efficiency. In explicit finite element calculations, the time domain is discretized into a series of small time increments Δt. In each time increment, the motion equation of the system can be expressed as: , where M, C, and K are the mass, damping, and stiffness matrices respectively, F is the external force vector, They are displacement, velocity, and acceleration vectors respectively. The explicit algorithm discretizes the time domain using the central difference scheme and represents the acceleration vector at time t as: , and through explicit time integration, the velocity vector at time t + Δt / 2 and the displacement vector at time t + Δt can be obtained: ; . The stability requirement for explicit integration is that the time increment Δt satisfies the Courant-Friedrichs-Lewy (CFL) condition: , where is the minimum characteristic length of the grid cell and c is the propagation speed of the stress wave in the material.

[0045] Within each time increment, the strain increment Δε of the element is calculated based on the nodal displacements: , where B is the strain-displacement matrix and ΔU is the vector of nodal displacement increments. According to the material constitutive relation, the stress increment Δσ of the element is calculated: , where D is the elastic matrix or tangent stiffness matrix of the material. The stress increment is accumulated to the stress value at the previous time step to obtain the stress tensor of the element at the current time : . The explicit algorithm avoids the solution of large-scale linear equations through step-by-step integration with small time increments, so the calculation efficiency is relatively high. However, to ensure numerical stability, the time increment needs to satisfy the CFL condition. Therefore, the explicit algorithm is often used in transient dynamic analysis or high-speed impact problems.

[0046] For each grid cell, its stress tensor is extracted as the input for subsequent stress gradient calculations. In finite element analysis, the element stress is calculated from nodal displacements or strains and is stored at the element Gauss integration points or nodes. For each grid cell, all its integration points or nodes are traversed to extract the component values of the stress tensor : ; The extracted stress components are assembled into the stress tensor σ according to the arrangement of the tensor: σ = [ σ 11 σ 12 σ 13 σ 21 σ 22 σ 23 σ 31 σ 32 σ 33 ] ; For ease of subsequent calculations, the stress tensor can be vectorized, that is, arranged into a one-dimensional vector in a certain order : σ vec = [ σ 11 , σ 22 , σ 33 , σ 12 , σ 23 , σ 31 ] ; For each element, its stress tensor or vectorized stress tensor is stored in the corresponding data structure, such as an array or vector container. The process of extracting the element stress tensor can be implemented through the post-processing module of the finite element software or by writing a program to read the stress results in the output file.

[0047] Taking the extracted unit stress tensor as the input, subsequent analyses such as stress gradient calculation and stress concentration region identification can be carried out. The extraction and storage of the stress tensor are the basis for stress gradient calculation. Through reasonable data structure and algorithm design, efficient and scalable stress data processing can be achieved. At the same time, the extraction of the stress tensor also facilitates the calculation of other mechanical quantities, such as principal stress, von Mises equivalent stress, etc. These mechanical quantities can be used as important indicators for structural optimization and performance evaluation.

[0048] Based on the stress tensors of each grid element, using the stress tensors of adjacent elements at the nodes of the grid element, the stress field function corresponding to the node is fitted by the least squares method, and the gradient of the stress field function is calculated to obtain the node stress gradient value; the node stress gradient value is interpolated into the interior of the grid element to obtain the stress gradient field of the grid element. Specifically, for each grid node, the stress tensor data of its adjacent elements are extracted to construct a stress data set passing through the node. The moving least squares (MLS) method is used to fit the stress data set. MLS constructs the stress field function within the node neighborhood through local weighted regression, with good numerical stability and approximation accuracy. The gradient of the fitted node stress field function is calculated to obtain the stress gradient value at the node. The stress gradient reflects the rate of change of stress within the node neighborhood. Using the node stress gradient value, it is interpolated into the interior of the grid element by the finite element interpolation method. Common interpolation methods include linear interpolation, Gaussian integral interpolation, etc. The result of interpolation is the stress gradient field of the grid element. 。

[0049] Compare the stress gradient field with a preset stress gradient threshold to obtain the grid elements with a stress gradient greater than the stress gradient threshold as the stress concentration regions. Specifically, set the stress gradient threshold as the criterion for judging stress concentration. The selection of the threshold needs to comprehensively consider the material, geometric characteristics of the scaffolding structure and engineering experience. For each grid element, compare its stress gradient field with the threshold . If the stress gradient at any position within the element exceeds the threshold, that is , then mark the element as a stress concentration element. All stress concentration elements are grouped into a stress concentration region as the target region for subsequent grid refinement.

[0050] When dividing the stress concentration area into the first area and the second area, it is necessary to classify according to the corresponding relationship between the component types of the scaffolding steel mesh and the mesh units. Specifically, construct a corresponding relationship table between the component types and the mesh units. According to the component composition of the scaffolding steel mesh, define three main component types: vertical poles, horizontal bars, and steel plates. For each component type, determine the corresponding finite element mesh unit type. For example, vertical poles and horizontal bars can be simulated with beam elements, and steel plates can be simulated with plate elements or shell elements. Establish a corresponding relationship table between the component types and the mesh unit types in the form of {component type: unit type}. Traverse all the mesh units within the stress concentration area and judge the component type to which it belongs according to the unit type. For the stress concentration area For each mesh unit within it , judge its unit type . According to the corresponding relationship table, map the unit type to the component type) . For example, if it is a beam element, then its corresponding component type is a vertical pole or a horizontal bar. According to the component type of the mesh unit, divide it into the corresponding component stress concentration area. For each mesh unit , according to its component type , add it to the corresponding component stress concentration area: if it is a vertical pole, then add it to the vertical pole stress concentration area ; if it is a horizontal bar, then add it to the horizontal bar stress concentration area ; if it is a steel plate, then add it to the steel plate stress concentration area . Merge the stress concentration areas of the vertical poles and the horizontal bars to obtain the first area; the steel plate stress concentration area is used as the second area. Merge the vertical pole stress concentration area and the horizontal bar stress concentration area to obtain the first area: , and use the steel plate stress concentration area as the second area .

[0051] Through the above steps, according to the correspondence between grid cells and component types, the stress concentration area can be divided into a first area (including vertical poles and horizontal bars) and a second area (including steel plates). This division method fully considers the component characteristics of the scaffolding steel mesh and the finite element modeling method, and has clear physical meaning and algorithm implementation. This application comprehensively considers that the scaffolding steel mesh is composed of different components such as vertical poles, horizontal bars and steel plates, and the stress characteristics and stress distribution characteristics of different components vary greatly. The component classification method can adopt different grid encryption strategies for different components, improving the pertinence and effectiveness of encryption. Since the vertical poles and horizontal bars belong to rod members, their stress concentration usually distributes along the axial direction of the component, while the steel plate belongs to a planar component, and its stress concentration distributes within the plate surface. Classifying the vertical poles and horizontal bars into one category and the steel plates into another category facilitates the adoption of different subdivision strategies during grid encryption, such as one-dimensional subdivision along the axial direction and two-dimensional subdivision within the plate surface, so as to better capture the stress gradient changes of different components. Through component classification, it is possible to avoid adopting a unified grid encryption method for the entire stress concentration area, reducing unnecessary computational effort. For example, for the first area mainly composed of rod members, a more efficient one-dimensional subdivision algorithm can be adopted; while for the second area mainly composed of steel plates, a two-dimensional subdivision algorithm suitable for planar components can be adopted.

[0052] In this embodiment, according to the topological structure of the scaffolding steel mesh, the components are divided into three categories: vertical poles, horizontal bars and steel plates. Using the correspondence between grid cells and components, the stress concentration cells are respectively classified into the three types of components. For each type of component, its stress concentration cells are extracted to respectively form the stress concentration area of the vertical poles , the stress concentration area of the horizontal bars and the stress concentration area of the steel plates . The stress concentration area of the vertical poles and the stress concentration area of the horizontal bars are merged into the first area , and the stress concentration area of the steel plates is used as the second area .

[0053] For the first area, a one-dimensional quadtree grid subdivision algorithm along the axial direction of the component is used for grid encryption; for the second area, a two-dimensional quadtree grid subdivision within the plate plane is used for grid encryption to obtain the encrypted finite element model. For the first area , the one-dimensional quadtree subdivision algorithm is used to encrypt the vertical pole and horizontal bar components. For the first area , the one-dimensional quadtree subdivision algorithm is used to encrypt the vertical pole and horizontal bar components. The specific implementation steps are as follows: for each stress concentration cell , its axial direction vector is extracted. It can be obtained by calculating the difference in the node coordinates at both ends of the cell. Along the axial direction , denote the geometric dimension (length) of the unit as . According to the preset number of encryption layers n and the target unit size , calculate the encryption threshold of the unit : , if and , then add the unit to the queue of units to be subdivided . For each unit in the queue , divide it into four sub-units along the axial direction , and the lengths of the sub-units are all . For each sub-unit , repeat until the encryption layer requirement is met or the unit size is less than . Update the node coordinates and unit connection relationships of the subdivided units to obtain the encrypted grid of the vertical / horizontal bar members.

[0054] For the second region , use a two-dimensional quadtree subdivision algorithm to encrypt the grid of the steel plate members. The specific implementation steps are as follows: For each stress concentration unit , extract two tangential basis vectors in the plane of the steel plate where it is located. This can be obtained by calculating the principal component direction of the unit node coordinates. In the plane of the steel plate, denote the geometric dimension (area) of the unit as . According to the preset number of encryption layers n and the target unit size , calculate the encryption threshold of the unit : , if and , then add the unit to the queue of units to be subdivided . For each unit in the queue , divide it into four sub-units in the tangential basis direction, and the areas of the sub-units are all . For each sub-unit , repeat until the encryption layer requirement is met or the unit size is less than . Update the node coordinates and unit connection relationships of the subdivided units to obtain the encrypted grid of the steel plate members.

[0055] Reassemble the grid units of the encrypted vertical poles, horizontal bars, and steel plate components to obtain the encrypted overall finite element model. During the assembly process, it is necessary to update the global numbers of the nodes and the connection relationships of the elements to ensure the integrity and continuity of the grid. The partitioned grid encryption method can make full use of the component characteristics of the scaffolding steel mesh, improving the pertinence and efficiency of grid refinement. The one-dimensional and two-dimensional quadtree subdivision algorithms can effectively capture the stress gradient changes in the axial direction of the members and within the steel plate surface, generating encrypted grids adapted to the stress distribution. Compared with global unified encryption, the partitioned grid encryption method can reduce unnecessary computational effort and improve computational efficiency.

[0056] Use the topology optimization algorithm to optimize the structure of the encrypted finite element grid to obtain the three-dimensional solid model of the optimized scaffolding steel mesh; take the encrypted finite element grid as the design area for topology optimization, and use the SIMP (Solid Isotropic Material with Penalization) interpolation method to divide the design area into several hexahedral sub-areas, and assign a relative density design variable to each sub-area ; among them, the relative density is used to characterize the material properties of this sub-area, and the value range is [ ρ min , 1 ] , is the lower limit value, usually taken as 0.001 to avoid the singularity of the total stiffness matrix. Specifically, import the encrypted finite element grid into the topology optimization software as the design area Ω for topology optimization. Discretize the design area Ω using hexahedral elements to obtain the topology optimization model. Each hexahedral element corresponds to a design sub-area. Assign a relative density design variable to each design sub-area e (e = 1, 2,....... N) to characterize the material properties of this sub-area. The value range of [ ρ min , 1 ] is , where is the lower limit value, usually taken as 0.001 to avoid the singularity of the total stiffness matrix. Using the SIMP interpolation model, the material elastic modulus of sub-area e is associated with the relative density : , where is the elastic modulus of the solid material, and p is the penalty factor, usually taken as 3, used to suppress the appearance of intermediate density values . Through SIMP interpolation, the discrete topology optimization problem can be represented by the continuous variable

[0057] Taking the minimum total strain energy of the scaffolding steel mesh structure as the optimization goal and the relative density variables of each sub-region as the optimization variables, a topology optimization model is established. Specifically, the optimization objective function is defined as: , where is the total strain energy of the scaffolding steel mesh structure, is the displacement vector of the structure under construction loads, is the total stiffness matrix obtained by SIMP interpolation, and ρ is the vector composed of the relative densities of all sub-regions. The physical meaning of this objective function is to minimize the total strain energy of the structure under given loads, that is, to minimize the strain energy of the structure. The total strain energy can be expressed as the quadratic form of the structure displacement vector and the total stiffness matrix K(ρ). The total stiffness matrix adopts the SIMP (Solid Isotropic Material with Penalization) interpolation method to establish the relationship between the relative density of each sub-region and its material stiffness matrix : , where is the reference stiffness matrix of the solid material, and p is the penalty factor, usually taken as 3. Through SIMP interpolation, the total stiffness matrix becomes a function of the relative density vector ρ, making the design variables in the optimization problem continuous variables, which is convenient for mathematical solution.

[0058] Define the volume constraint condition: , where is the actual material volume of the optimized design, is the initial volume of the design area, is the upper limit of the volume fraction, and its value range is 0.3 - 0.5. The volume constraint condition limits the material volume that can be used in the optimized design, avoiding the increase in cost caused by excessive use of materials. By adjusting the upper limit of the volume fraction, the material usage of the optimization result can be controlled within a certain range. Define the structural stiffness constraint condition: , where is the total strain energy of the initial design. This constraint ensures that the overall stiffness of the optimized design is not lower than that of the initial design. The structural stiffness constraint condition is to ensure that the optimized structure has sufficient overall stiffness, avoiding insufficient structural stiffness caused by excessive pursuit of lightweight, which affects the service performance. By comparing the total strain energy of the optimized design with the total strain energy of the initial design, it is ensured that the stiffness of the optimized structure meets the requirements.

[0059] Introduce the penalty factor λ to construct the optimization objective function considering constraints: min O ( ρ ) = C ( ρ ) + λ × [ V ( ρ ) − f v × V 0 ] where λ is the penalty factor, which is used to balance the relative importance of minimizing the total strain energy and satisfying the volume constraint. The larger the value of λ, the more conducive it is to satisfying the volume constraint, but it may reduce the optimization effect of the total strain energy. By introducing the penalty factor λ, the volume constraint condition is combined with the objective function to construct an optimization objective function considering the constraint. By adjusting the value of λ, the relative importance of minimizing the total strain energy and satisfying the volume constraint can be weighed, and an optimization result meeting the design requirements can be obtained.

[0060] Establish the static equilibrium equation of the scaffolding expanded metal structure under the construction condition as the constraint condition: where F is the nodal load vector of the structure under the construction condition. The static equilibrium equation describes the force balance state of the structure under the external load and is the basic control equation for structural analysis. Taking the static equilibrium equation as the constraint condition for topology optimization ensures that the optimized structure can maintain force balance under the given load and meet the basic requirements of structural design. Considering the buckling stability of the structure, establish the buckling constraint condition: where is the geometric stiffness matrix, and is the i-th buckling mode corresponding to the critical buckling load factor. This constraint ensures the buckling stability and safety of the optimized design.

[0061] Buckling stability is an important index for evaluating the structural performance, especially for the scaffolding structure with more compression bar members. By establishing the buckling constraint condition, it is ensured that the optimized structure remains stable under the critical buckling load and avoids buckling instability leading to structural failure. Combining the above objective function and constraint conditions, establish the topology optimization mathematical model: min O ( ρ ) = C ( ρ ) + λ × [ V ( ρ ) − f v × V 0 ] Constraint conditions: , , , , , where n is the number of buckling mode orders considered, and N is the total number of design sub-regions.

[0062] The topology optimization mathematical model combines the optimization objective function, volume constraint condition, structural stiffness constraint condition, static equilibrium equation and buckling constraint condition to form a complete mathematical description. By solving this optimization model, an optimal material distribution scheme that meets various constraint conditions and minimizes the total strain energy can be obtained, guiding the topology optimization design of the scaffolding expanded metal structure. In this application, the SIMP interpolation method is used to transform the discrete material distribution problem into a continuous density distribution problem, which is convenient for solving by mathematical programming methods and improves the optimization efficiency. By introducing the penalty factor, the multi-objective optimization problem is transformed into a single-objective optimization problem, simplifying the solution difficulty of the optimization model.

[0063] Solve the topology optimization model to obtain the optimal relative density of each sub-region , specifically, set the initial relative density field , and the initial number of iteration steps t = 0. Before the optimization iteration starts, it is necessary to set the initial relative density value for each design sub-region e , which constitutes the initial relative density field . Common methods for setting the initial relative density are: Uniform initial density method: The initial relative density of all sub-regions takes the same value, such as ; Random initial density method: Randomly generate the initial relative density of each sub-region within the range of [ ρ min , 1 ] ; Initial density method based on experience: According to the preliminary design experience of the structure, set different initial relative densities for different regions. The selection of the initial relative density will affect the starting point and convergence speed of the optimization, but usually does not affect the final optimization result. Set the initial value of the Lagrange multiplier Λ , and let the iteration number k = 0. The Lagrange multiplier Λ is used to handle the volume constraint condition in the topology optimization model. Before the optimization iteration starts, it is necessary to set the initial value for the Lagrange multiplier , which is usually taken as 0. At the same time, set the iteration number k of the Lagrange multiplier to 0. Calculate the objective function value under the current relative density field , volume and structural stiffness . For the relative density field at the t-th iteration step, calculate its corresponding objective function value, volume and structural stiffness: Objective function value: O ( ρ t ) = C ( ρ t ) + λ × [ V ( ρ t ) − f v × V 0 ] ; Volume: , where is the volume of the e-th sub-region; Structural stiffness: , where is under the displacement field. Through finite element analysis, calculate the displacement field Ut and the total stiffness matrix , and then obtain the objective function value, volume and structural stiffness

[0064] Calculate the structural displacement field and stress field under the current relative density field . By solving the eigenvalue problem , obtain the critical buckling load factor . Use the finite element method to solve the static equilibrium equation , and obtain the displacement field . According to the stress-strain relationship, calculate the stress field By solving the generalized eigenvalue problem , the critical buckling load factor is obtained and buckling mode .in, is the geometric stiffness matrix, and the stress field Through buckling analysis, determine whether the structure meets the buckling stability requirements. , by updating the formula ρ e t + 1 = max ( ρ min ,min [ ρ e t × β e η , 1 ] ) }Update the relative density field and get .in, is the relative rate of change of strain energy of the e-th unit, η is the numerical damping coefficient, ranging from 0.3 to 0.5. Fix the current Lagrange multiplier value According to the relative density update formula, the relative density of the designed sub-areas is updated one by one to obtain a new relative density field .

[0065] In the relative density update formula, It represents the relative change rate of strain energy of the e-th unit, reflecting the contribution of the unit to the optimization objective function. The calculation formula is: ,in, is the sensitivity of the structural stiffness to the relative density of the e-th element, is the sensitivity of the volume to the relative density of the e-th unit. η is the numerical damping coefficient, which is used to control the step size of the relative density update to avoid oscillation or divergence in the optimization process. The value of η is usually between 0.3 and 0.5. Whether the volume constraint is satisfied If satisfied, let , go to the next step; otherwise, , return to continue iteration. Among them, is the changing step size of Λ.

[0066] After updating the relative density field, calculate its corresponding volume , to determine whether the volume constraint is met. If the constraint is met, then appropriately reduce the value of the Lagrange multiplier and let , go to the next step; if the constraint is not satisfied, increase the value of the Lagrange multiplier appropriately, and let , return to continue iteration and re-update the relative density field. is the step size of the Lagrange multiplier, which controls the adjustment rate of the Λ value. The selection of needs to balance the optimization efficiency and stability. Is it less than the set threshold? If so, let , proceed to the next step; otherwise, let k = k + 1 and return for continued iteration. Judge the updated relative density field corresponding volume and the target volume to see if the difference between them is less than the set threshold . If , it is considered that the volume constraint condition has been satisfied, and the current Lagrange multiplier value is taken as the optimal value Λ*, and proceed to the next step; if , it is considered that the volume constraint condition has not been satisfied, let k = k + 1, return for continued iteration, continue to adjust the Lagrange multiplier value, and update the relative density field. The selection of the threshold needs to balance the optimization accuracy and calculation efficiency. The smaller it is, the higher the requirement for meeting the volume constraint, the higher the optimization accuracy, but the calculation time may be longer. Judge whether the difference between and is less than the set threshold . If so, output the optimal relative density and terminate the optimization; otherwise, return for continued iteration. Judge whether the difference between the updated relative density field and the relative density field of the previous step is less than the set threshold . If , it is considered that the relative density field has converged, output the optimal relative density and terminate the optimization; if , it is considered that the relative density field has not converged, return for continued iteration and enter the next round of iteration. The selection of the threshold needs to balance the optimization accuracy and calculation efficiency. The smaller it is, the higher the requirement for relative density convergence, the higher the optimization accuracy, but the calculation time may be longer. Use to update the relative density field. If the optimal Lagrange multiplier value has been obtained, then use to re-update the relative density field until the convergence condition is met.

[0067] In this application, the solution process of the topology optimization model is an iterative optimization process. By continuously updating the relative density field and Lagrange multiplier value, under the premise of meeting the constraint conditions, the optimization objective function is minimized to obtain the optimal material distribution scheme. In particular, this application introduces Lagrange multipliers to handle complex constraint conditions, transforms the constrained optimization problem into a series of unconstrained optimization sub-problems, and approximates the optimal solution of the original problem by iteratively solving the sub-problems. The optimization algorithm introduces a damping coefficient in the relative density update formula, which improves the numerical stability of the optimization process.

[0068] According to the optimal relative density of each sub-region , update the material properties of each sub-region to obtain an optimized three-dimensional solid model. Specifically, for each design sub-region e, according to its optimal relative density , update its material elastic modulus: , where is the initial elastic modulus of the solid material, and p is the penalty factor of the SIMP interpolation model. In topology optimization, the SIMP (Solid Isotropic Material with Penalization) interpolation model is used to establish the relationship between the design variables (relative density) and the material properties (elastic modulus). For the e-th design sub-region, its optimal relative density is , and according to the SIMP interpolation formula, update its material elastic modulus: , where is the updated material elastic modulus, E0 is the initial elastic modulus of the solid material, and p is the penalty factor, usually taken as 3. The role of the penalty factor p is to penalize the intermediate state where the density value is between 0 and 1, making the optimization result tend to the discrete distribution of "solid - void", and avoiding the appearance of a large number of "gray" regions. The larger the p value, the more severe the penalty for the intermediate density, and the more discrete the optimization result tends to be.

[0069] Through SIMP interpolation, the continuously changing relative density is mapped to the material properties, realizing the "discrete - continuous" conversion in topology optimization, which is convenient for solving by mathematical programming methods. In the finite element software, update the material properties of each sub-region to , to obtain an optimized finite element model. According to the updated material elastic modulus , modify the material properties of each design sub-region in the finite element software. For the e-th sub-region, modify the elastic modulus property value of its material to . After completing the update of the material properties of all sub-regions, an optimized finite element model is obtained. The optimized finite element model reflects the optimal material distribution, and the material properties of the sub-regions correspond to their optimal relative densities. This step realizes the mapping of the optimization result to the finite element model, providing a basis for subsequent performance analysis and structural reconstruction.

[0070] Perform a structural reanalysis on the optimized finite element model to evaluate its mechanical properties and buckling stability, and verify the optimization effect. Using finite element analysis software, perform static analysis and buckling analysis on the optimized finite element model to evaluate the mechanical properties and stability of the optimized structure. Static analysis: Apply the same boundary conditions and load cases as the optimized model, calculate the stress distribution, displacement field, etc. of the structure under the action of the load, and evaluate whether the strength and stiffness of the structure meet the requirements. Buckling analysis: On the basis of the static analysis, solve the eigenvalue problem to obtain the critical buckling load and buckling mode of the structure, and evaluate whether the buckling stability of the structure meets the requirements. Through the structural reanalysis, verify whether the optimized structure meets the design requirements and judge the quality of the optimization effect. If the structural performance fails to meet the requirements, it may be necessary to adjust the parameter settings of the optimization model (such as volume fraction, penalty factor, etc.) and re-optimize until a satisfactory design scheme is obtained. Structural reanalysis is an important link to verify the feasibility and effectiveness of the optimization results. By quantitatively analyzing the mechanical properties and stability of the structure, it provides reliable data support and decision-making basis for engineering applications.

[0071] According to the optimized finite element model, reconstruct the three-dimensional solid model of the scaffolding expanded metal mesh. Adopt fairing technology to smooth the optimized structural form to obtain a three-dimensional solid model with manufacturing feasibility. The results of topology optimization usually show the "solid - void" distribution of materials. The optimized structural form may have a large number of irregular features such as acute angles, spikes, holes, etc., which are difficult to directly apply to actual manufacturing. In order to obtain a smooth and continuous structural form, it is necessary to post-process and reconstruct the optimization results. According to the material properties of each sub-region in the optimized finite element model, extract the material distribution information and generate an initial three-dimensional solid model. Adopt fairing technology, such as surface reconstruction, surface fitting, etc., to smooth the initial solid model, eliminate irregular features such as acute angles and spikes, and obtain a three-dimensional solid model with smooth and continuous geometric form. According to the actual manufacturing process requirements, make necessary adjustments and modifications to the reconstructed three-dimensional solid model, such as adjusting the structural details according to the minimum machining size, adding connecting parts according to the assembly requirements, etc., to obtain a three-dimensional solid model that meets the manufacturing feasibility. This application uses the SIMP interpolation model to establish a continuous mapping relationship between material properties and design variables, enabling the topology optimization problem to be solved by mathematical programming methods, and improving the optimization efficiency. Through structural reanalysis, quantitatively evaluate the feasibility and effectiveness of the optimization results, providing a reliable basis for engineering decisions. Introduce fairing technology to achieve a smooth transition from the optimization results to a manufacturable solid model, solving the problem that the topology optimization results are difficult to directly apply to engineering practice.

[0072] The component layout of the three-dimensional solid model after structural optimization is optimized using a discrete topology optimization algorithm to obtain the final BIM model of the scaffolding expanded metal mesh, including the following steps: taking the continuous density field obtained from topology optimization as the input, using the BESO (Bi-Evolutionary Structural Optimization) method for discretization, and continuously iteratively removing low-sensitivity elements and adding high-sensitivity elements by defining sensitivity values to convert the continuous density field into a discrete topological structure represented by 0-1 variables; among them, the element sensitivity is calculated by the formula: , where in the formula, is the sensitivity of the structural flexibility to the element density, is the element volume.

[0073] Data processing is performed on the BESO discretization result to extract the skeleton information of the topological structure. Using a skeleton extraction algorithm, such as the Medial Axis Transform or the Distance Field Method, the discrete point cloud is converted into a one-dimensional skeleton curve; the skeleton curve can be represented as a coordinate sequence of a series of points ; local smoothing processing is performed on the skeleton curve to eliminate the jagged noise caused by discretization. Using the Laplacian smoothing algorithm, by minimizing the Laplace operator of the curve, the curve becomes smooth while maintaining the skeleton shape; the coordinate sequence of the smoothed curve is ; the Laplacian operator is defined as: , where L is the Laplace operator, is the coordinate vector of the i-th point, is the neighborhood point set of is the number of neighborhood points.

[0074] According to the smoothed skeleton curve, a pipeline spline curve is generated. Using the cubic B-spline curve fitting method, with the skeleton points as control vertices, a smooth pipeline spline curve is generated; the cubic B-spline basis function is: ; ; ; . Then the parametric equation of the pipeline spline curve is: C ( u ) = ∑ i = 0 3 N i , 3 ( u ) P i , u ∈ [ 0 , 1 ] , where is the coordinate of the i-th control vertex;

[0075] Based on the pipeline spline curve, a pipeline solid extending along the curve is generated through a sweeping operation. Using the pipeline spline curve It is a sweeping path, with a circular cross-section as the sweeping object. The radius of the circular cross-section is determined according to the actual specifications of the scaffolding. Through sweeping, a three-dimensional solid model of the scaffolding vertical poles and horizontal bars can be obtained. Integrate the three-dimensional solid models of the vertical poles and horizontal bars with the optimized steel plate mesh model, and realize the assembly of pipes and plates through Boolean operations. Use the parametric assembly function of BIM software to automatically judge the spatial position relationship between pipes and plates and generate node connection components. During this process, make full use of the parametric association characteristics of BIM to realize the association and automatic adjustment of parameters such as pipe diameter and plate thickness. Conduct a clash check on the assembled overall model to detect interference and collision between components. Use the clash detection function of BIM software to automatically identify the clash points in the model and generate a clash report. Fine-tune the local nodes according to the clash report to eliminate the interference between components. Generate the final BIM model of the scaffolding steel mesh, and add information such as the material and attributes of the components through parametric settings to form a complete BIM model. The BIM model can be directly used for applications such as construction drawing generation, engineering quantity statistics, and virtual construction, providing comprehensive information support for the scaffolding project.

Claims

1. A method for constructing scaffolding steel plate mesh based on BIM, characterized in that: include: Obtain characteristic parameters of the scaffolding steel plate mesh, which include the cross-sectional dimensions of the vertical bars, the cross-sectional dimensions of the horizontal bars, and the thickness of the steel plate; According to the characteristic parameters, the three-dimensional solid model of the scaffolding steel plate mesh is established by using the parametric modeling method; Adopting adaptive meshing algorithm to mesh the three-dimensional solid model and obtain finite element mesh; Adopting adaptive mesh encryption algorithm to identify stress concentration areas in finite element mesh, and encrypting the stress concentration areas to obtain encrypted finite element mesh; The topology optimization algorithm is used to optimize the structure of the encrypted finite element mesh to obtain the optimized three-dimensional solid model of the scaffolding steel plate mesh; The discrete topology optimization algorithm is used to optimize the component layout of the three-dimensional solid model after structural optimization to obtain the final scaffolding steel plate mesh BIM model; And mesh encryption is performed in stress concentration areas, including: According to the initial finite element mesh, the explicit finite element method is used to calculate the stress state of the scaffolding steel mesh under the preset load condition, and the stress tensor of each mesh unit is obtained; According to the stress tensor of each grid unit, the stress tensor of the adjacent unit at the node of the grid unit is used to fit the stress field function of the corresponding node through the least square method, and the gradient of the stress field function is calculated to obtain the stress gradient value of the node; the stress gradient value of the node is interpolated into the interior of the grid unit to obtain the stress gradient field of the grid unit; Compare the stress gradient field with a preset stress gradient threshold, and obtain the grid cells whose stress gradient is greater than the stress gradient threshold as stress concentration areas; The stress concentration area is divided into a first area and a second area by using a component classification method; the first area includes the stress concentration area of ​​the vertical pole and the horizontal pole components, and the second area includes the stress concentration area of ​​the steel plate components; For the first area, a one-dimensional quadtree mesh subdivision algorithm along the axial direction of the component is used to perform mesh encryption; For the second region, a two-dimensional quadtree mesh subdivision algorithm is used within the plate plane to perform mesh encryption to obtain an encrypted finite element model.

2. The method for constructing scaffolding steel plate mesh based on BIM according to claim 1, characterized in that: Establish a three-dimensional solid model of the scaffolding steel mesh, including: According to the obtained cross-sectional dimensions of the vertical poles, the cross-sectional dimensions of the horizontal bars and the thickness of the steel plates, a parametric geometric model of the scaffolding steel plate mesh is established by using a constraint-based solid modeling method; wherein the parametric geometric model includes the geometric dimension information and relative position relationship of the vertical poles, the cross bars and the steel plates; According to the parametric geometric model and the preset scaffolding design specifications, the number and arrangement spacing of the vertical poles and horizontal poles are determined by using the parameter-driven rule reasoning method; wherein the scaffolding design specifications include the scaffolding structure design specifications, component arrangement rules and component connection rules; According to the parametric geometric model and the preset construction process requirements, the case-based knowledge reasoning method is used to determine the connection method and node structure between the vertical pole and the steel plate, and between the horizontal pole and the steel plate; the construction process requirements include the scaffolding erection process and construction sequence; According to the determined number and arrangement spacing of the vertical poles and horizontal poles, as well as the determined connection method and node structure, the three-dimensional solid model of the scaffolding steel plate mesh is generated by using entity merging and Boolean operations.

3. The method for constructing scaffolding steel plate mesh based on BIM according to claim 1, characterized in that: Adopt adaptive meshing algorithm to mesh the 3D solid model, including: The octree space partitioning algorithm is used to recursively divide the bounding box of the 3D solid model into eight sub-cubes until the preset grid size is met to generate the initial grid unit; Calculate the average value of the coordinate difference between each node and the corresponding adjacent node in the initial grid unit, and make the Laplacian coordinate of the node; According to the Laplacian coordinates of the grid nodes, the global stiffness matrix K and the mass matrix M of the component, the linear equations of the grid elements are established: ; Where x is the node coordinate to be optimized, and f is the node Laplacian coordinate; Sets the minimum size of the grid cells and maximum size Constraint, as an inequality constraint on the node coordinate to be optimized x ; The global stiffness matrix K, the mass matrix M, and the linear equations constrained by the inequality are combined to obtain the overall linear equations; The conjugate gradient iteration algorithm is used to solve the overall linear equations to obtain the position correction value of the node coordinate to be optimized x , using the position correction Correct the node coordinate quantity x to be optimized; The node coordinate update step is iterated until the maximum displacement of the mesh node is less than the preset threshold, and the final finite element mesh is obtained.

4. The method for constructing scaffolding steel plate mesh based on BIM according to any one of claims 2 or 3, characterized in that: The topology optimization algorithm is used to optimize the structure of the encrypted finite element mesh, including: The encrypted finite element mesh is used as the design area for topology optimization. The design area is divided into multiple sub-areas using a variable density algorithm. A relative density variable is set for each sub-area. ; The total strain energy of the scaffolding steel mesh structure is minimized as the optimization goal, and the relative density variables of each sub-area are used to To optimize variables, a topology optimization model is established; Solve the topology optimization model to obtain the optimal relative density of each sub-region ; According to the optimal relative density of each sub-area , update the material properties of each sub-region and obtain the optimized three-dimensional solid model.

5. The method for constructing scaffolding steel plate mesh based on BIM according to claim 4, characterized in that: Create an initial topology optimization model, including: Set volume constraints and structural stiffness constraints for the scaffolding steel mesh; The volume constraint condition expression is as follows: in, is the actual material volume of the optimized structure represented by the SIMP interpolation method, is the initial volume of the design area, is the upper limit of volume fraction; The structural stiffness constraint condition expression is as follows: in, To optimize the total strain energy of the structure under construction conditions, is the total strain energy of the initial design area under the same working conditions; Set the penalty factor λ and construct the optimization goal according to the constraints. : Among them, λ is the penalty factor; The static equilibrium equation of the scaffolding steel mesh structure under construction conditions is established as the constraint condition for topology optimization: in, is the total stiffness matrix obtained by SIMP interpolation method, and its relative density of each sub-region U is the displacement vector of the structure under the construction load; F is the node load vector of the structure under the construction condition; Establish the bending surface constraint conditions of the scaffolding steel mesh: in, is the geometric stiffness matrix, which is related to the stress state of the structure; is the i-th order buckling mode The corresponding critical buckling load factor; this constraint condition ensures the buckling stability and safety of the optimized structure; Create a topology optimization model: Minimize: Constraints: ； ； ； in, is the lower limit of the relative density variable; n is the buckling mode order considered.

6. The method for constructing scaffolding steel plate mesh based on BIM according to claim 5, characterized in that: is the upper limit of volume fraction, ranging from 0.3 to 0.

5.

7. The method for constructing scaffolding steel plate mesh based on BIM according to claim 4, characterized in that: Solve the topology optimization model to obtain the optimal relative density of each sub-region ,include: (1) Setting the initial relative density field , the initial iteration number t=0; (2) Setting the Lagrange multiplier The initial value of is 0, let The number of iterations k=0; (3) Calculate the current relative density field The objective function value under ,volume and structural stiffness ; (4) Calculate the current relative density field The structural displacement field under and stress field ; By solving the following eigenvalue problem, the critical buckling load factor is obtained : in, is the total stiffness matrix obtained by SIMP interpolation method, is the geometric stiffness matrix, is the buckling mode; (5) Fixed , update the relative density field through the following formula to obtain the updated relative density field : in, is the relative density of the e-th unit at the t-th step, is the relative density of the e-th unit at step t+1; is the relative change rate of strain energy of the e-th unit, is the numerical damping coefficient; N is the total number of units divided into the design area; (6) Determine the updated relative density field Whether the volume constraint is met If so, then , go to step (7); if not, then let , return to step (5); where, is the step size of Λ (7) Judgment Is it less than or equal to the set threshold? If so, then let , go to step (8); if not, then let , return to step (5); (8) Determine the updated relative density field With the previous step Is the difference less than the set threshold? If yes, then output the optimal relative density ,in, That is, the optimal relative density of the e-th unit, and the optimization is terminated; if not, go to step (9); (9) Utilization , return to step (5).

8. The method for constructing scaffolding steel plate mesh based on BIM according to claim 7, characterized in that: The expression is as follows: in, is the partial derivative of the objective function with respect to the relative density of the e-th unit, is the partial derivative of the volume with respect to the relative density of the e-th unit.

9. The method for constructing scaffolding steel plate mesh based on BIM according to claim 8, characterized in that: η is the numerical damping coefficient, which is between 0.3 and 0.5.

Images