Scaffold steel plate net building method based on BIM

Abstract

The invention discloses a scaffold steel plate net building method based on BIM, and relates to BIM modeling. The method comprises the steps that feature parameters of a scaffold steel plate net are obtained; according to the characteristic parameters, establishing a three-dimensional entity model of the scaffold steel screen by using a parametric modeling method; performing grid division on the three-dimensional solid model by adopting a self-adaptive grid division algorithm to obtain a finite element grid; identifying a stress concentration area in the finite element grid by adopting a self-adaptive grid encryption algorithm, and performing grid encryption on the stress concentration area to obtain an encrypted finite element grid; performing structure optimization on the encrypted finite element mesh by adopting a topological optimization algorithm to obtain an optimized three-dimensional entity model of the scaffold steel plate mesh; and performing component arrangement optimization on the three-dimensional entity model after structure optimization by adopting a discrete topological optimization algorithm to obtain a final scaffold steel plate net BIM model. In order to solve the problem that in the prior art, scaffold steel plate net erecting redundancy is large, the redundancy design is reduced.

Description

Technical Field

[0001] The present application relates to the field of BIM modeling, and in particular to a method for constructing scaffolding steel mesh based on BIM. Background Art

[0002] Scaffolding is an indispensable temporary engineering structure in construction, and is widely used in various types of buildings, bridges and other engineering fields. Traditional scaffolding is mostly constructed with steel pipes, which has problems such as low erection efficiency and low component reuse rate. In recent years, steel mesh has gradually become one of the main materials for scaffolding. It has the advantages of high strength, good rigidity and easy assembly. Therefore, scaffolding systems based on steel mesh have been increasingly used.

[0003] However, the existing steel mesh scaffolding still has some shortcomings in the design and erection process. One of the prominent problems is that the scaffolding has a large amount of redundancy, and there are a large number of repeated and unnecessary components, resulting in serious material waste. For example, traditional two-dimensional construction drawings are difficult to fully express the spatial structural relationship of the scaffolding, and are prone to problems such as inaccurate component positioning and unreasonable node connections, resulting in redundant components or scrap waste during construction. Summary of the invention

[0004] In response to the problem of large redundancy in the erection of scaffolding steel mesh in the prior art, the present application provides a scaffolding steel mesh construction method based on BIM, which reduces redundant design by modeling with BIM and performing topological optimization, and by setting volume constraints, structural stiffness constraints, and surface stability constraints.

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

[0006] The present application provides a method for constructing a scaffolding steel plate mesh based on BIM, comprising: obtaining characteristic parameters of the scaffolding steel plate mesh, wherein the characteristic parameters include the cross-sectional dimensions of the vertical bars, the cross-sectional dimensions of the horizontal bars, and the thickness of the steel plates; establishing a three-dimensional solid model of the scaffolding steel plate mesh according to the characteristic parameters by using a parametric modeling method; meshing the three-dimensional solid model using an adaptive meshing algorithm to obtain a finite element mesh; identifying stress concentration areas in the finite element mesh using an adaptive mesh encryption algorithm, and meshing the stress concentration areas to obtain an encrypted finite element mesh; structurally optimizing the encrypted finite element mesh using a topology optimization algorithm to obtain an optimized three-dimensional solid model of the scaffolding steel plate mesh; optimizing the component layout of the three-dimensional solid model after structural optimization using a discrete topology optimization algorithm to obtain a final BIM model of the scaffolding steel plate mesh.

[0007] Furthermore, a three-dimensional solid model of the scaffolding steel plate mesh is established, 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 plate, a constraint-based solid modeling method is used to establish a parametric geometric model of the scaffolding steel plate mesh; wherein the parametric geometric model includes the geometric dimension information and relative position relationship of the vertical poles, the cross bars and the steel plate; according to the parametric geometric model, in combination with the preset scaffolding design specifications, a parameter-driven rule reasoning method is used to determine the number and arrangement spacing of the vertical poles and the cross bars; wherein the scaffolding design specifications include scaffolding structure design specifications, component arrangement rules and component connection rules; according to the parametric geometric model, in combination with the preset construction process requirements, a case-based knowledge reasoning method is used to determine the connection method and node structure between the vertical poles and the steel plate, and the cross bars and the steel plate; wherein the construction process requirements include the scaffolding erection process and the construction sequence; according to the determined number and arrangement spacing of the vertical poles and the cross bars, as well as the determined connection method and node structure, entity merging and Boolean operations are used to generate a three-dimensional solid model of the scaffolding steel plate mesh.

[0008] Furthermore, an adaptive meshing 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 met, thereby generating an initial mesh unit; calculating the average value of the coordinate difference between each node and the corresponding adjacent node in the initial mesh unit, and making the Laplacian coordinates of the node; according to the Laplacian coordinates of the mesh nodes, the global stiffness matrix K and the mass matrix M of the component, a linear equation group of the mesh unit is established ; Where x is the node coordinate to be optimized, and f is the node Laplacian coordinate; Set the minimum size of the grid unit and maximum size Constraint, as an inequality constraint on the node coordinate to be optimized x ; Combine the global stiffness matrix K, the mass matrix M, and the linear equations after inequality constraints to obtain the overall linear equations; Use the conjugate gradient iteration algorithm to solve the overall linear equations and obtain the position correction value of the node coordinate to be optimized x , using the position correction The node coordinate quantity to be optimized x is corrected; the node coordinate updating step is iteratively executed until the maximum displacement of the mesh node is less than the preset threshold, and the final finite element mesh is obtained.

[0009] Furthermore, the mesh of the stress concentration area is encrypted, including: according to the initial finite element mesh, using the explicit finite element method to calculate the stress state of the scaffolding steel plate mesh under the preset load condition, and obtaining the stress tensor of each mesh unit; according to the stress tensor of each mesh unit, using the stress tensor of the adjacent unit at the node of the mesh unit, fitting the stress field function of the corresponding node by the least squares method, and calculating the gradient of the stress field function to obtain the node stress gradient value; interpolating the node stress gradient value into the inside of the mesh unit to obtain the stress gradient field of the mesh unit; comparing the stress gradient field with the preset stress gradient threshold, obtaining the mesh unit with a 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 area of ​​the vertical pole and the cross bar 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 encrypt the mesh; for the second area, a two-dimensional quadtree mesh subdivision algorithm in the plate plane is used to encrypt the mesh to obtain an encrypted finite element model.

[0010] Furthermore, a topology optimization algorithm is used to perform structural optimization on the encrypted finite element mesh, including: using the encrypted finite element mesh as the design area for topology optimization, using a 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 steel mesh structure as the optimization goal, the relative density variables of each sub-area To optimize the variables, a topology optimization model is established; the topology optimization model is solved 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.

[0011] Furthermore, an initial topology optimization model is established, including: setting the volume constraint conditions and structural stiffness constraint conditions of the scaffolding steel plate mesh; the expression of the volume constraint condition 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; through this constraint condition, the overall stiffness of the optimized structure is guaranteed to be no less than the initial design; the penalty factor λ is set, and the optimization target is constructed according to the constraint condition. : O ( r ) = C ( r ) + l [ V ( r ) − f v × V 0 ] , where λ is a 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 is, the more conducive it is to satisfying the volume constraint, but it may reduce the optimization effect of the total strain energy. The static equilibrium equation of the scaffolding steel plate 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 construction conditions; the buckling constraint conditions of the scaffolding steel mesh are established: ,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; through this constraint condition, the buckling stability and safety of the optimized structure are guaranteed; a topology optimization model is established: Minimize: O ( r ) = C ( r ) + l [ V ( r ) − f v × V 0 ] ; Constraints: ; ; ; ;in, is the lower limit of the relative density variable, usually taken as 0.001 to avoid the singularity of the total stiffness matrix; n is the buckling mode order considered.

[0012] Furthermore, is the upper limit of volume fraction, ranging from 0.3 to 0.5.

[0013] Furthermore, the topology optimization model is solved to obtain the optimal relative density of each sub-region. , including: (1) setting the initial relative density field , the initial iteration number t=0; (2) Set 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 : ; r e , t + 1 = max { r minutes ,min[ r e , t × B e , t or , 1 ] } , e = 1 , 2 ,....., N ;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;

[0014] (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 length of Λ change; (7) Determine Is it less than or equal to the set threshold? If so, then let , go to step (9); 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, return to step (3); (9) use , return to step (5).

[0015] Furthermore, 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.

[0016] Furthermore, η is the numerical damping coefficient, which is taken as 0.3~0.5.

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

[0018] By using an adaptive mesh encryption algorithm, the stress concentration area can be identified and the mesh refined through stress gradient criteria and component classification, which can greatly improve the pertinence and efficiency of mesh encryption.

[0019] In the topology optimization model, the total strain energy of the scaffolding steel mesh structure is minimized as the optimization target, and the relative density of the material is used as the optimization variable. The optimal material distribution is obtained by solving the density field. On the premise of meeting the volume constraints and structural performance requirements, the theoretically optimal topological configuration can be obtained, giving full play to the efficiency of the material and reducing redundancy and waste.

[0020] In topology optimization, the actual volume constraint, overall stiffness constraint and buckling stability constraint are comprehensively considered to obtain an optimization result that meets engineering practice and is safe and reliable. The constraint conditions are combined with the objective function through the penalty function method, which can efficiently solve complex constraint problems. The overall stability of the scaffolding structure can be further guaranteed through critical buckling load analysis.

[0021] In the iterative solution process of topology optimization, the optimization criteria are continuously updated through the Lagrange multiplier method, which can find a balance between volume constraints and optimal goals, satisfying both the volume fraction requirements and the optimization effect of total strain energy. Combined with numerical damping and sensitivity filtering technology, the optimization convergence speed can be accelerated and the checkerboard phenomenon in the density field can be avoided. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The present application will be further described in the form of exemplary embodiments, which will be described in detail by the accompanying drawings. These embodiments are not restrictive, and in these embodiments, the same number represents the same structure, wherein:

[0023] Figure 1 is an exemplary flow chart of a method for constructing a scaffolding steel plate mesh based on BIM according to some embodiments of the present application;

[0024] Figure 2 is an exemplary flow chart of constructing a three-dimensional solid model of a scaffolding steel plate mesh according to some embodiments of the present application;

[0025] Figure 3 is an exemplary flow chart of generating a finite element mesh according to some embodiments of the present application;

[0026] Figure 4 This is an exemplary flow chart for generating an encrypted finite element model according to some embodiments of the present application. DETAILED DESCRIPTION

[0027] The method and system provided in the embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0028] like Figure 1 As shown in the figure, the characteristic parameters of the scaffolding steel mesh are obtained, and the characteristic parameters include the cross-sectional dimensions of the uprights, the cross-sectional dimensions of the crossbars and the thickness of the steel plate; according to the characteristic parameters, a three-dimensional solid model of the scaffolding steel mesh is established by using a parametric modeling method; an adaptive meshing algorithm is used to mesh the three-dimensional solid model to obtain a finite element mesh; an adaptive mesh encryption algorithm is used to identify stress concentration areas in the finite element mesh, and the mesh of the stress concentration area is encrypted to obtain an encrypted finite element mesh; a topology optimization algorithm is used to structurally optimize the encrypted finite element mesh to obtain an optimized three-dimensional solid model of the scaffolding steel mesh; a 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 mesh BIM model.

[0029] Specifically, the characteristic parameters of the scaffolding steel mesh are obtained. The characteristic parameters include the cross-sectional dimensions of the vertical poles, the cross-sectional dimensions of the horizontal bars, and the thickness of the steel plate. 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 thickness of the steel plate. The system receives and stores these parameter values ​​to form structured parameter data. The pre-entered characteristic parameter values ​​are read from an external data file (such as an Excel table). The system parses the file format, extracts the cross-sectional dimensions of the vertical poles, the cross-sectional dimensions of the horizontal bars, and the thickness of the steel plate, and converts them into the data structure inside the program. Extract characteristic parameters from BIM models or CAD graphic files. Using geometric recognition algorithms, identify the vertical poles, cross bars, and steel plate components in the model, extract their cross-sectional dimensions and thickness information, and convert them into structured parameter data.

[0030] like Figure 2 As shown in the figure, according to the characteristic parameters, the parametric modeling method is used to establish the three-dimensional solid model of the scaffolding steel plate mesh; the cross-section size of the vertical pole, the cross-section size of the cross-section and the thickness of the steel plate are used as parameter variables to establish a parametric cross-section profile sketch. The sketch constraint tools provided by the parametric modeling software, such as vertical, horizontal, and collinear, are used to define the geometric constraint relationship of the cross-section profile. Based on the parametric cross-section profile, the three-dimensional solid models of the vertical pole, cross-bar and steel plate are generated by using solid modeling commands such as stretching and rotation. In the modeling process, the dimensional parameters such as the length, width, and height of the component are associated with the corresponding characteristic parameters to form a parameter-driven solid model. The relative position relationship of the vertical pole, cross-bar and steel plate in space is defined by geometric constraints such as corresponding points and corresponding edges. Assembly constraints between components are established using assembly constraint tools such as parallel, vertical, and coincident to form a parametric assembly model.

[0031] According to the parametric geometric model and the scaffolding design specifications, the parameter-driven rule reasoning method is used to determine the number and spacing of the vertical poles and horizontal bars. Specifically, the scaffolding design specifications are formalized as a series of parametric rules, such as "the spacing between vertical poles should not be greater than 1.2m" and "the spacing between horizontal bars should not be greater than 1.5m". Each rule contains attributes such as rule number, rule description, associated parameters, and constraints. According to the vertical pole and horizontal bar size parameters in the parametric geometric model, the corresponding design specification rules are matched. The forward reasoning or reverse reasoning method is used to automatically identify the rules that meet the constraints and extract the spacing parameters. Driven by the spacing parameters obtained by reasoning, the vertical pole and horizontal bar components are automatically inserted in the parametric geometric model. Through the programming interface, the component instance is copied in the specified position and direction, and the constraint relationship between the components is updated to generate a complete scaffolding facade.

[0032] According to the parametric geometric model and the construction process requirements, the case-based knowledge reasoning method is used to determine the connection mode and node structure between the vertical pole and the steel plate, and between the horizontal pole and the steel plate; specifically, a scaffolding construction process case library is established in the database, and each case contains the following attributes: scaffolding type: such as door scaffolding, cup-hook scaffolding, etc.; component type: such as vertical pole, horizontal pole, steel plate, etc.; connection method: such as welding, bolt connection, pin connection, etc.; node structure: such as node plate, flange, connector, etc.; three-dimensional model data: the geometric information of the case is stored in the form of BIM model or CAD model; these attributes can be structured in the form of fields for subsequent retrieval and analysis. The three-dimensional model data can be associated with the attribute field to realize the integrated management of geometric information and process information. Through the collection and organization of historical engineering cases, the case library is continuously enriched and improved to form a process knowledge base covering different types of scaffolding.

[0033] Similarity-based case retrieval uses a similarity calculation method to retrieve several historical cases that are most similar to the current model in the case library based on the characteristic parameters of the parametric geometric model. The similarity calculation considers the following factors: Scaffolding type: prioritize cases that are consistent with the current model type; Span: prioritize cases that are close to the span of the current model; Height: prioritize cases that are close to the height of the current model; Load: prioritize cases that are similar to the load conditions of the current model. Methods such as weighted Euclidean distance can be used to calculate the similarity between the current model and each case in the case library on the above factors to obtain a similarity score. According to the similarity score, select several cases with the highest scores 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 similar cases retrieved, and extract the connection methods and node construction knowledge. The specific steps include: statistical analysis of the connection methods of similar cases to obtain the applicable frequency and evaluation indicators (such as construction difficulty, cost, reliability, etc.) of different connection methods; optimize the connection methods according to the characteristics and requirements of the current model to obtain the recommended connection methods; summarize the node structures of similar cases to extract key node construction knowledge (such as node force characteristics, construction points, etc.); optimize and combine the node construction knowledge to obtain the node construction scheme suitable for the current model; in the process of analysis and optimization, data mining and statistical analysis techniques can be used to discover the rules and associations in the case data to improve the efficiency and accuracy of knowledge extraction.

[0035] By using knowledge fusion and transfer learning technology, the extracted and optimized connection mode and node construction knowledge are applied to the current parametric model to generate a matching connection and node construction scheme. The extracted connection mode knowledge is matched with the characteristic parameters of the current model to generate a suitable connection mode scheme, and the extracted node construction knowledge is fused with the geometric information of the current model to generate a three-dimensional model of the node structure; using transfer learning technology, the node model of similar cases is adapted to the current model to achieve rapid generation of node construction schemes; the generated connection and node construction schemes are checked and optimized to ensure that they meet the process requirements and constraints of the current model; through knowledge fusion and transfer learning, the experience knowledge of historical cases can be fully utilized to improve the generation efficiency and quality of the current model process scheme and avoid repeated design and trial and error.

[0036] According to the determined number and spacing of the vertical poles and horizontal poles, as well as the determined connection method and node structure, entity merging and Boolean operations are used to generate a three-dimensional solid model of the scaffolding steel plate mesh. Specifically, according to the number and spacing of the vertical poles, the three-dimensional coordinate position of the vertical pole instance is calculated to form a spatial array of the vertical pole instance. According to the number and spacing of the horizontal poles, the three-dimensional coordinate position of the horizontal pole instance is calculated to form a spatial array of the horizontal pole instance. Through array replication and coordinate transformation, the required vertical pole and horizontal pole component instances are generated in batches. In the process of array generation, parametric modeling technology can be used to parameterize the geometric size, number, spacing, etc. of the vertical poles and horizontal poles to achieve rapid generation and modification of component instances. At the same time, spatial indexing technology, such as octree, KD tree, 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, the corresponding connector entities, such as bolts, nuts, and connecting plates, are generated at the intersection of the vertical poles and horizontal bars; according to the node construction plan, node component entities, such as stiffening plates and connecting angles, are generated around the connectors; the entity merging operation is used to combine the connectors with the vertical poles and horizontal bars to form an integrated connection node; in the node construction process, parametric modeling technology can be used to parameterize the geometric dimensions, quantity, and position of the connectors and node components to achieve rapid generation and modification of the node structure. At the same time, collision detection technology can be used to check whether there is interference and collision between the connectors and node components and the vertical poles and horizontal bars, and automatic adjustment and optimization can be performed to ensure the rationality and feasibility of the node construction. The three-dimensional solid model of the steel plate is spatially superimposed with the instance array of the vertical poles and crossbars to form the initial model of the steel plate mesh. The Boolean difference operation is used, with the vertical pole and crossbar entities as the subtrahend and the steel plate entity as the minuend, to remove the intersection of the steel plate and the vertical pole or crossbar to generate the assembled three-dimensional solid model of the scaffolding steel plate mesh. During the assembly process, space segmentation techniques such as octrees and BSP trees can be used to divide and index the spatial position relationship between the steel plate and the component instances to improve the computational efficiency of Boolean operations. At the same time, multi-threaded parallel computing technology can be used to distribute Boolean operation tasks to multiple processors or cores for parallel execution to further improve computing performance. The generated three-dimensional solid model is topologically checked to determine the integrity and validity of the model. The topological rule verification algorithm is used to check whether there are errors such as dangling edges and non-manifold surfaces in the model, and automatic repair or manual correction is performed. This application adopts parametric modeling and instance array technology to realize the rapid batch generation and layout of scaffolding components, adopts entity merging and Boolean operation technology to realize the automatic construction of connection nodes and the assembly of steel mesh, adopts topological rule verification and automatic repair technology to realize the inspection and maintenance of model integrity, and adopts spatial indexing, parallel computing and other technologies to improve the computational efficiency of model generation and operation.

[0038] like Figure 3As shown, the adaptive meshing algorithm is used to mesh the three-dimensional solid model to obtain a finite element mesh; the octree space partitioning algorithm is used to recursively divide the bounding box of the three-dimensional solid model into eight sub-cubes until the preset mesh size is met to generate the initial mesh unit; 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, a minimum rectangular area that can completely contain the model. The bounding box is used as the root node and the octree is recursively partitioned. The bounding box is divided into two parts in the three directions of x, y, and z to obtain 8 sub-bounding boxes as the child nodes of the current node. For each sub-bounding box, it is judged whether it intersects with the three-dimensional solid model. If it intersects, the sub-bounding box is added to the next layer of the octree and the recursive partitioning continues; if it does not intersect, the sub-bounding box is discarded. During the recursive partitioning process, it is constantly judged whether the size of the current bounding box meets the preset mesh size threshold. If it meets, the bounding box is marked as a leaf node and the recursion is stopped; if it does not meet, the partitioning continues. Traverse all leaf nodes of the octree and use them as initial grid cells. Each initial grid cell contains the geometric information and topological relationship of its bounding box.

[0039] Calculate the average value of the coordinate difference between each node in the initial grid unit and the corresponding adjacent node, and use it as the Laplacian coordinate of the node; specifically, for each initial grid unit, extract its 8 vertices as grid nodes and establish a node index table. Traverse each grid node and find its adjacent nodes in the node index table according to its index. For each node, calculate the average value of the coordinate difference between it and its adjacent nodes to obtain the Laplacian coordinate of the node. : , ,in, is the set of adjacent nodes of node i, is the number of adjacent nodes, and are the coordinate vectors of the adjacent node j and the current node i respectively. The calculated Laplacian coordinates are stored as node attributes, and together with the node coordinates, they constitute the complete data structure of the node. According to the Laplacian coordinates of the grid nodes, the global stiffness matrix K and mass matrix M are constructed, and the linear equations of the grid unit are established. ; Where x is the node coordinate to be optimized, and f is the node Laplacian coordinate. Initialize the global stiffness matrix and the mass matrix , the dimension of the matrix is ​​determined according to the number of grid cells. K is a sparse symmetric positive definite matrix, and M is a diagonal matrix. Traverse each grid cell and calculate its local stiffness matrix and the mass matrix . According to the geometric information and material properties of the unit, numerical integration methods (such as Gaussian integration) are used to calculate and . The local stiffness matrix and the mass matrix Assemble into the global stiffness matrix K and mass matrix M, and determine the position of the matrix elements according to the global number of the node. Construct the linear equation system of the mesh element Among them, x is the node coordinate to be optimized, 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] Sets the minimum size of the grid cells and maximum size Constraint, as an inequality constraint on the node coordinate to be optimized x According to the requirements of meshing and the characteristics of the geometric model, set the minimum size of the mesh unit and maximum size , as a parameter for mesh quality control. and Transformed into the range constraints of node coordinates. For each node i, generate the inequality constraints of its coordinate components: , j=1,2,3, where is the j-th coordinate component of node i.

[0041] The global stiffness matrix K, mass matrix M, and the linear equations constrained by inequality are combined to obtain the overall linear equations. The node coordinate range constraints are converted into the standard form, that is, Ax≤b, where A is the constraint matrix and b is the constraint vector. and The linear equations are composed of And the inequality constraint Ax≤b is combined into the overall linear equation system: [ K − M A 0 ] [ x f ] = 0 , Constraints: Inequality constraint Ax≤b.

[0042] The conjugate gradient iteration algorithm is used to solve the overall linear equations to obtain the position correction value Δx of the node coordinate quantity to be optimized x, and the position correction value Δx is used to correct the node coordinate quantity to be optimized x. Initialize the node coordinate vector x, generally taking the node coordinates of the initial grid unit as the initial value. Set the iterative 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 search direction vector p. Use r and p to construct a conjugate gradient subproblem and solve the position correction Δx. Use the position correction Δx to update the node coordinate vector x: , where α is the step size factor, which controls the position correction amplitude of each iteration. Determine whether the iteration termination conditions are met, such as the residual norm is less than a given threshold, the number of iterations reaches the upper limit, etc. If satisfied, output the optimized node coordinates x; otherwise, continue to iterate. Iterate the node coordinate update step until the maximum displacement of the mesh node is less than the preset threshold, and obtain the final finite element mesh. After each iteration, calculate the displacement of the mesh node: ,in, and are the coordinate vectors of the ith node after the kth and k+1th iterations, respectively. Determine whether the displacements of all nodes are less than the preset threshold ε. If so, the mesh optimization is considered to have converged, and the final finite element mesh is output; otherwise, continue the iterative optimization. According to the optimized node coordinates, the geometric information of the mesh unit, such as the unit volume, shape function, etc., is updated. Perform a quality assessment on the optimized finite element mesh, such as calculating the unit size, shape ratio, Jacobian matrix and other quality indicators to determine whether the mesh meets the requirements of numerical simulation. This application uses octree space partitioning and Laplacian smoothing algorithm to improve the efficiency of mesh generation while ensuring mesh quality. The conjugate gradient iterative optimization method can be used to improve the quality and numerical performance of the mesh while satisfying geometric constraints, providing a high-quality discrete model for subsequent finite element analysis.

[0043] like Figure 4 As shown in the figure, an adaptive mesh encryption algorithm is used to identify stress concentration areas in the finite element mesh, and the mesh of the stress concentration area is encrypted to obtain the encrypted finite element mesh; first, based on 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. Specifically, the initial finite element mesh is used as input to establish a finite element model of the scaffolding steel mesh. According to the type of mesh unit (such as beam unit, plate unit, etc.), a suitable unit template is selected to define the geometric parameters and material properties of the unit. According to the actual working conditions of the scaffolding, preset load conditions are set, such as self-weight, construction load, wind load, etc. The load is converted into a node load or unit 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 displacement and velocity of the node through explicit time integration, and then obtains the strain and stress of the unit. Compared with the implicit algorithm, the explicit algorithm does not need to solve a large set of linear equations, and has higher computational efficiency. In the explicit finite element calculation, the time domain is discretized into a series of small time increments Δt. In each time increment, the system's equation of motion can be expressed as: , where M, C, K are the mass, damping and stiffness matrices respectively, and F is the external force vector. are displacement, velocity and acceleration vectors respectively. The explicit algorithm uses the central difference format to discretize the time domain and express the acceleration vector at time t as: , through explicit time integration, we can get the velocity vector at time t+Δt / 2 and the displacement vector at time t+Δt: ; The stability of explicit integration requires that the time increment Δt satisfies the Courant-Friedrichs-Lewy (CFL) condition: ,in, is the minimum characteristic length of the mesh element, and c is the propagation speed of the stress wave in the material.

[0045] In each time increment, the element strain increment Δε is calculated based on the nodal displacement: , where B is the strain-displacement matrix and ΔU is the node displacement increment vector. According to the material constitutive relationship, the stress increment Δσ of the unit is calculated: , where D is the elastic matrix or tangent stiffness matrix of the material. Add the stress increment to the stress value of the previous moment to obtain the stress tensor of the unit at the current moment : , the explicit algorithm avoids solving large-scale linear equations by stepwise integration of small time increments, so the computational efficiency is higher. However, in order to ensure numerical stability, the time increment needs to meet the CFL condition, so the explicit algorithm is often used for transient dynamic analysis or high-speed impact problems.

[0046] For each mesh element, extract its stress tensor , as the input for subsequent stress gradient calculation. In finite element analysis, unit stress is calculated by node displacement or strain and stored at the unit Gaussian integration point or node. For each mesh element, traverse all its integration points or nodes to extract the stress tensor Component value: ; Assemble the extracted stress components into a stress tensor σ according to the arrangement of tensors: s = [ s 11 s 12 s 13 s 21 s 22 s 23 s 31 s 32 s 33 ] ; To facilitate subsequent calculations, the stress tensor can be vectorized, that is, it can be arranged into a one-dimensional vector in a certain order : s vec = [ s 11 , s 22 , s 33 , s 12 , s 23 , s 31 ] ; For each element, store its stress tensor or vectorized stress tensor into a 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] The extracted unit stress tensor is used as input for subsequent stress gradient calculation, stress concentration area identification and other analyses. The extraction and storage of stress tensors is 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 stress tensors 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] According to the stress tensor of each grid unit, the stress tensor of the adjacent units at the node of the grid unit is used to fit the stress field function of the corresponding node through 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 unit to obtain the stress gradient field of the grid unit. Specifically, for each grid node, the stress tensor data of its adjacent units 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 in the node neighborhood through local weighted regression, which has 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 in the neighborhood of a node. The node stress gradient value is interpolated into the mesh unit using the finite element interpolation method. Common interpolation methods include linear interpolation and Gaussian integral interpolation. The result of the interpolation is the stress gradient field of the mesh unit. .

[0049] Compare the stress gradient field with the preset stress gradient threshold, and obtain the grid cells with stress gradient greater than the stress gradient threshold as the stress concentration area. Specifically, set the stress gradient threshold , as the criterion for judging stress concentration. The selection of the threshold value needs to comprehensively consider the material, geometric characteristics and engineering experience of the scaffolding structure. For each grid unit, compare its stress gradient field With threshold If the stress gradient at any position in the unit exceeds the threshold, that is, , then the unit is marked as a stress concentration unit. All stress concentration units are grouped into stress concentration areas. , as the target area for subsequent mesh refinement.

[0050] When dividing the stress concentration area into the first area and the second area, it is necessary to classify it according to the correspondence between the component type and the grid unit of the scaffolding steel plate mesh. Specifically, construct a correspondence table between component type and grid unit. According to the component composition of the scaffolding steel plate mesh, three main component types are defined: vertical poles, horizontal poles and steel plates. For each component type, determine its corresponding finite element grid unit type. For example, vertical poles and horizontal poles can be simulated with beam units, and steel plates can be simulated with plate units or shell units. Establish a correspondence table between component type and grid unit type, such as: {component type: unit type}. Traverse all grid units in the stress concentration area and determine the component type to which they belong based on the unit type. For the stress concentration area Each grid cell in , determine its unit type . According to the correspondence table, the unit type is mapped to the component type) For example, if For beam elements, the corresponding component type is a vertical bar or a horizontal bar. According to the component type of the grid element, it is divided into the corresponding component stress concentration area. , according to its component type , which is added to the corresponding component stress concentration area: If For the vertical pole, Add to the stress concentration area of ​​the pole ;if For the crossbar, Added to the crossbar stress concentration area ;if For steel plate, Add to the stress concentration area of ​​the steel plate The stress concentration areas of the vertical pole and the horizontal pole are combined to obtain the first area; the stress concentration area of ​​the steel plate is taken as the second area. and crossbar stress concentration area Merge to get the first region: , the stress concentration area of ​​the steel plate As the second area : .

[0051] Through the above steps, the stress concentration area can be divided into the first area (including the vertical pole and the crossbar) and the second area (including the steel plate) according to the correspondence between the grid unit and the component type. This division method fully considers the component characteristics and finite element modeling method of the scaffolding steel plate mesh, and has clear physical meaning and algorithm implementation. This application comprehensively considers that the scaffolding steel plate mesh is composed of different components such as vertical poles, crossbars and steel plates, and the force characteristics and stress distribution characteristics of different components are quite different. The component classification method can adopt different grid encryption strategies for different components to improve the pertinence and effectiveness of encryption. Since the vertical poles and crossbars belong to rods, their stress concentration is usually distributed along the axial direction of the component, while the steel plate belongs to a planar component, and its stress concentration is distributed within the plate surface. The vertical poles and crossbars are classified into one category and the steel plates are classified into another category, which is convenient for adopting different subdivision strategies when meshing, 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 and reduce unnecessary calculations. For example, for the first area mainly composed of rods, a more efficient one-dimensional subdivision algorithm can be used; and for the second area mainly composed of steel plates, a two-dimensional subdivision algorithm suitable for planar components can be used.

[0052] In this embodiment, according to the topological structure of the scaffolding steel mesh, the components are divided into three categories: vertical poles, horizontal poles and steel plates. The corresponding relationship between the grid unit and the component is used to classify the stress concentration units into three types of components. For each type of component, its stress concentration unit is extracted to form the stress concentration area of ​​the vertical pole. , Crossbar stress concentration area and stress concentration area of ​​steel plate . The stress concentration area of ​​the pole and crossbar stress concentration area Merge into the first area , the stress concentration area of ​​the steel plate As the second area .

[0053] For the first area, the one-dimensional quadtree mesh subdivision algorithm along the axial direction of the component is used for mesh encryption; for the second area, the two-dimensional quadtree mesh subdivision algorithm in the plate plane is used for mesh encryption to obtain the encrypted finite element model. , the one-dimensional quadtree subdivision algorithm is used to refine the mesh of the vertical and horizontal members. , the one-dimensional quadtree subdivision algorithm is used to encrypt the grid of the vertical and horizontal members. The specific implementation steps are as follows: For each stress concentration unit , extract its axial direction vector It can be obtained by calculating the difference between the node coordinates at both ends of the unit. , the unit The geometric size (length) is recorded as . According to the preset number of encryption layers n and target cell size , computing unit Encryption threshold: ,if and , then the unit Join the queue of units to be subdivided For the queue Each unit in , along the axial direction Divide it into four subunits The length of each subunit is For each subunit Repeat until the number of encryption layers is met or the cell size is smaller than The node coordinates and unit connection relationship of the subdivided unit are updated to obtain the encrypted vertical bar / cross bar component mesh.

[0054] For the second area , the two-dimensional quadtree subdivision algorithm is used to encrypt the mesh of the steel plate component. The specific implementation steps are as follows: For each stress concentration unit , extract the two tangent basis vectors of the steel plate plane It can be obtained by calculating the principal component direction of the unit node coordinates. The geometric size (area) of . According to the preset number of encryption layers n and target cell size , computing unit Encryption threshold: ,if and , then the unit Join the queue of units to be subdivided For the queue Each unit in , on the tangential basis It is divided into four subunits The area of ​​each subunit is For each subunit Repeat until the number of encryption layers is met or the cell size is smaller than . Update the node coordinates and unit connection relationship of the subdivided unit to obtain the encrypted steel plate component mesh.

[0055] Reassemble the mesh units of the encrypted vertical poles, horizontal poles and steel plate components to obtain the encrypted overall finite element model. During the assembly process, it is necessary to update the global number of nodes and the connection relationship of units to ensure the integrity and continuity of the mesh. The partitioned mesh encryption method can make full use of the component characteristics of the scaffolding steel plate mesh and improve the pertinence and efficiency of mesh refinement. The one-dimensional and two-dimensional quadtree subdivision algorithms can effectively capture the stress gradient changes in the axial direction of the rod and the surface of the steel plate, and generate an encrypted mesh that adapts to the stress distribution. Compared with global unified encryption, the partitioned mesh encryption method can reduce unnecessary calculations and improve calculation efficiency.

[0056] 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 mesh; the encrypted finite element mesh is used as the design area for topology optimization, and the SIMP (Solid Isotropic Material with Penalization) interpolation method is used to divide the design area into several hexahedral sub-areas, and each sub-area is assigned a relative density design variable. ; Among them, the relative density Used to characterize the material properties of this sub-region, The value range is [ r minutes , 1 ] , is the lower limit, usually 0.001, to avoid the singularity of the total stiffness matrix. Specifically, the encrypted finite element mesh is imported into the topology optimization software as the design area Ω for topology optimization. The design area Ω is discretized using hexahedral units to obtain a topology optimization model. Each hexahedral unit corresponds to a design sub-area. A relative density design variable is assigned to each design sub-area e (e=1, 2, ......., N) , characterizing the material properties of this sub-region. The value range is [ r minutes , 1 ] ,in is the lower limit, usually 0.001, to avoid singularity of the total stiffness matrix. Using the SIMP interpolation model, the elastic modulus of the material in sub-region e is With relative density Related: ,in, is the elastic modulus of the solid material, and p is the penalty factor, usually 3, which is used to suppress the intermediate density value Through SIMP interpolation, continuous variables can be used Represent the discrete topology optimization problem and transform the topology optimization into a size optimization problem.

[0057] 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 the variables, a topology optimization model is established. Specifically, the optimization objective function is defined as: ,in, is the total strain energy of the scaffolding steel mesh structure, is the displacement vector of the structure under the construction load, is the total stiffness matrix obtained by SIMP interpolation, and ρ is the vector composed of the relative density of all sub-regions. The physical meaning of this objective function is to minimize the total strain energy of the structure under a given load, that is, to minimize the deformation potential energy of the structure. Total strain energy It can be expressed as the structural displacement vector The total stiffness matrix K(ρ) is a quadratic form. The SIMP (Solid Isotropic Material with Penalization) interpolation method is used to calculate the relative density of each sub-region. With its material stiffness matrix Create a connection: ,in, is the base stiffness matrix of the solid material, and p is the penalty factor, which is usually 3. Through SIMP interpolation, the total stiffness matrix It 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 volume constraints: ,in, To optimize the actual material volume of the design, is the initial volume of the design area, is the upper limit of the volume fraction, ranging from 0.3 to 0.5. The volume constraint limits the volume of material that can be used in the optimization design, avoiding excessive use of materials and increasing costs. , the material usage of the optimization result can be controlled within a certain range. Define the structural stiffness constraint: ,in, 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 is to ensure that the optimized structure has sufficient overall stiffness to avoid excessive pursuit of lightweight and insufficient structural stiffness, which affects the performance. Total strain energy from the initial design , ensuring that the optimized structural stiffness meets the requirements.

[0059] Introduce the penalty factor λ and construct the optimization objective function considering the constraints: minutes O ( r ) = C ( r ) + l × [ V ( r ) − f v × V 0 ] , where λ is a 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, and the optimization objective function considering the constraint is constructed. By adjusting the value of λ, the relative importance of minimizing the total strain energy and satisfying the volume constraint can be weighed to obtain an optimization result that meets the design requirements.

[0060] The static equilibrium equation of the scaffolding steel plate mesh structure under construction conditions is established as a constraint condition: , where F is the node load vector of the structure under construction conditions. The static equilibrium equation describes the force equilibrium state of the structure under the action of external loads and is the basic control equation for structural analysis. The static equilibrium equation is used as a constraint condition for topological optimization to ensure that the optimized structure can maintain force equilibrium under a given load and meet the basic requirements of structural design. Considering the buckling stability of the structure, the buckling constraint condition is established: ,in, is the geometric stiffness matrix, is the i-th order buckling mode The corresponding critical buckling load factor. This constraint ensures the buckling stability and safety of the optimized design.

[0061] Buckling stability is an important indicator for evaluating structural performance, especially for scaffolding structures with more compression rods. By establishing buckling constraints, we can ensure that the optimized structure remains stable under the critical buckling load to avoid buckling instability and structural damage. Based on the above objective functions and constraints, a topology optimization mathematical model is established: minutes O ( r ) = C ( r ) + l × [ V ( r ) − f v × V 0 ] , constraints: , , , , , where n is the number of buckling modes considered and N is the total number of design sub-regions.

[0062] The mathematical model of topological optimization integrates the optimization objective function, volume constraints, structural stiffness constraints, static equilibrium equations and buckling constraints to form a complete mathematical description. By solving the optimization model, the optimal material distribution scheme that satisfies various constraints and minimizes the total strain energy can be obtained, guiding the topological optimization design of the scaffolding steel mesh structure. In this application, the SIMP interpolation method is used to convert the discrete material distribution problem into a continuous density distribution problem, which is convenient for solving using mathematical programming methods and improves the optimization efficiency. The penalty factor is introduced to convert the multi-objective optimization problem into a single-objective optimization problem, simplifying the difficulty of solving 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 , the initial iteration step is t=0. Before the optimization iteration begins, the initial relative density value needs to be set for each design sub-area e , forming the initial relative density field Common initial relative density setting methods include: Uniform initial density method: The initial relative density of all sub-areas takes the same value, such as ; Random initial density method: [ r minutes , 1 ] The initial relative density of each sub-region is randomly generated within the range; the initial density method based on experience: according to the preliminary design experience of the structure, different initial relative densities are set for different regions. The selection of 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 , set the number of iterations k = 0. The Lagrange multiplier Λ is used to handle the volume constraints in the topology optimization model. Before the optimization iteration begins, you need to set the initial value for the Lagrange multiplier , usually set to 0. At the same time, set the number of iterations of the Lagrange multiplier k = 0. Calculate the current relative density field The objective function value under ,volume and structural stiffness For the relative density field of the t-th iteration , calculate the corresponding objective function value, volume and structural stiffness: Objective function value: O ( r t ) = C ( r t ) + l × [ V ( r t ) − f v × V 0 ] ;volume: ,in, is the volume of the e-th sub-region; structural stiffness: ,in for Through finite element analysis, the displacement field Ut and the total stiffness matrix are calculated. , and then obtain the objective function value, volume and structural stiffness.

[0064] Calculate the current relative density field The structural displacement field under and stress field By solving the eigenvalue problem , the critical buckling load factor is obtained . Using the finite element method, solve the static equilibrium equation , and the displacement field is obtained . According to the stress-strain relationship, the stress field is calculated 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 r e t + 1 = max ( r minutes ,min [ r e t × β e or , 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, 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 , go to the next step; otherwise, set k=k+1 and return to continue iteration. Determine the updated relative density field The corresponding volume With target volume Is the difference between the two values ​​less than the set threshold? .like , then the volume constraint is considered to have been satisfied, and the current Lagrange multiplier value is As the optimal value Λ*, proceed to the next step; if , it is considered that the volume constraint condition has not been met, so let k=k+1, return to continue the iteration, continue to adjust the Lagrange multiplier value, and update the relative density field. The selection of needs to balance optimization accuracy and computational efficiency. The smaller it is, the higher the requirement for satisfying the volume constraint, the higher the optimization accuracy, but the longer the calculation time may be. and Is the difference less than the set threshold? If yes, output the optimal relative density , terminate the optimization; otherwise, return to continue iteration. Determine the updated relative density field Relative density field with the previous step Is the difference less than the set threshold? .like , then the relative density field is considered to have converged, and the optimal relative density is output. , terminate the optimization; if , it is considered that the relative density field has not converged yet, and the iteration is continued and the next round of iteration is entered. The selection of needs to balance the optimization accuracy and computational efficiency. The smaller it is, the higher the requirement for relative density convergence, the higher the optimization accuracy, but the longer the calculation time may be. , update the relative density field. If the optimal Lagrange multiplier value has been obtained , then use , 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 the Lagrange multiplier value, the optimization objective function is minimized under the premise of satisfying the constraints to obtain the optimal material distribution solution. In particular, this application introduces the Lagrange multiplier to handle complex constraints, 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 to improve the numerical stability of the optimization process.

[0068] 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. Specifically, for each design sub-region e, according to its optimal relative density , update its material elastic modulus: ,in, 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 variable (relative density) and the material property (elastic modulus). For the e-th design sub-region, its optimal relative density is , according to the SIMP interpolation formula, update its material elastic modulus: ,in, is the updated material elastic modulus, E0 is the initial elastic modulus of the solid material, and p is the penalty factor, which is usually 3. The role of the penalty factor p is to penalize the intermediate state of density values ​​between 0 and 1, so that the optimization results tend to the discrete distribution of "solid-void" and avoid the appearance of a large number of "grayscale" areas. The larger the p value, the more severe the penalty for the intermediate density, and the more discrete the optimization results tend to be.

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

[0070] The optimized finite element model is re-analyzed to evaluate its mechanical performance and buckling stability and verify the optimization effect. The optimized finite element model is subjected to static analysis and buckling analysis using finite element analysis software to evaluate the mechanical performance and stability of the optimized structure. Static analysis: Apply the same boundary conditions and load conditions as the optimized model to calculate the stress distribution, displacement field, etc. of the structure under load, and evaluate whether the strength and stiffness of the structure meet the requirements. Buckling analysis: On the basis of 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 structural re-analysis, verify whether the optimized structure meets the design requirements and judge the quality of the optimization effect. If the structural performance cannot 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 solution is obtained. Structural re-analysis is an important link in verifying the feasibility and effectiveness of the optimization results. By quantitatively analyzing the mechanical performance and stability of the structure, reliable data support and decision-making basis are provided for engineering applications.

[0071] According to the optimized finite element model, the three-dimensional solid model of the scaffolding steel mesh is reconstructed. The optimized structural morphology is smoothed by using the smoothing technology to obtain a three-dimensional solid model with manufacturing feasibility. The result of topological optimization is usually manifested as the "solid-void" distribution of the material. The optimized structural morphology may have a large number of irregular features such as sharp angles, spikes, holes, etc., which are difficult to be directly applied to actual manufacturing. In order to obtain a smooth and continuous structural morphology, the optimization results need to be post-processed and reconstructed. According to the material properties of each sub-region in the optimized finite element model, the material distribution information is extracted to generate the initial three-dimensional solid model. The initial solid model is smoothed by using smoothing technology, such as surface reconstruction and surface fitting, to eliminate irregular features such as sharp angles and spikes, and obtain a three-dimensional solid model with smooth and continuous geometric shape. According to the actual manufacturing process requirements, the reconstructed three-dimensional solid model is adjusted and modified as necessary, such as adjusting the structural details according to the minimum processing size, adding connectors 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, so that the topology optimization problem can be solved using mathematical programming methods, improving the optimization efficiency. Through structural reanalysis, the feasibility and effectiveness of the optimization results are quantitatively evaluated, providing a reliable basis for engineering decision-making. The introduction of smoothing processing technology achieves a smooth transition from optimization results to manufacturable solid models, solving the problem that topology optimization results are difficult to directly apply to engineering practice.

[0072] 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, which includes the following steps: the continuous density field obtained by topology optimization is used as input, and the BESO (Bi-Evolutionary Structural Optimization) method is used for discretization processing. By defining the sensitivity value, the low-sensitivity units are continuously removed and the high-sensitivity units are added iteratively, and the continuous density field is converted into a discrete topological structure represented by a 0-1 variable; among them, the unit sensitivity The calculation formula is: , where is the sensitivity of structural flexibility to element density, is the unit volume.

[0073] Data processing is performed on the BESO discretization results to extract the skeleton information of the topological structure. The skeleton extraction algorithm, such as the Medial Axis Transform or the Distance Field Method, is used to convert the discrete point cloud into a one-dimensional skeleton curve; the skeleton curve can be represented as a series of coordinate sequences of points. ; Perform local smoothing on the skeleton curve to eliminate the jagged noise caused by discretization. Use the Laplacian smoothing algorithm to minimize the Laplace operator of the curve while maintaining the skeleton shape to make the curve smooth; the smoothed curve coordinate sequence is ; The Laplacian operator is defined as: , where L is the Laplace operator, is the coordinate vector of the ith point, for The neighborhood point set of is the number of neighborhood points.

[0074] Generate a pipeline spline curve based on the smoothed skeleton curve, use the cubic B-spline curve fitting method, take the skeleton points as control vertices, and generate a smooth pipeline spline curve ; The cubic B-spline basis function is: ; ; ; . Then the pipeline spline curve The parametric equation is: C ( u ) = ∑ i = 0 3 N i , 3 ( u ) P i , u ∈ [ 0 , 1 ] ,in, is the coordinate of the i-th control vertex;

[0075] Based on the pipe spline curve, a pipe entity extending along the curve is generated by sweeping operation. The three-dimensional solid model of the scaffolding poles and crossbars is obtained by sweeping. The three-dimensional solid model of the poles and crossbars is integrated with the optimized steel plate mesh model, and the assembly of pipes and plates is realized through Boolean operation. The parametric assembly function of BIM software is used to automatically determine the spatial position relationship between pipes and plates and generate node connection components. In this process, the parameter association characteristics of BIM are fully utilized to realize the association and automatic adjustment of parameters such as pipe diameter and plate thickness. The assembled overall model is checked for conflicts, interference and collision between components are checked, and the conflict detection function of BIM software is used to automatically identify conflict points in the model and generate conflict reports. According to the conflict report, local nodes are fine-tuned to eliminate interference between components. The final scaffolding steel plate mesh BIM model is generated, and the material, attribute and other information of the components are added through parametric settings to form a complete BIM model. The BIM model can be directly used for construction drawing generation, engineering quantity statistics, virtual construction and other applications to provide comprehensive information support for scaffolding projects.

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.

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 claim 3, characterized in that: 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.

5. The method for constructing scaffolding steel plate mesh based on BIM according to any one of claims 2 to 4, 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.

6. The method for constructing scaffolding steel plate mesh based on BIM according to claim 5, 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.

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

5.

8. The method for constructing scaffolding steel plate mesh based on BIM according to claim 5, 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 (9); 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, return to step (3); (9) Utilization , return to step (5).

9. The method for constructing scaffolding steel plate mesh based on BIM according to claim 8, 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.

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

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