Full-automatic iterative pre-deformation form-finding method for complex free-form surface structure

Abstract

The present application relates to structural engineering shape finding analysis technical field, disclose a kind of complex free curved surface structure full-automatic iterative predeformation shape finding method, this method with the target node coordinates of complex free curved surface structure as convergence target, establish finite element analysis model, determine control node set, and receive node control proportion and difference control value;According to target load combination Automatic execution forward loading analysis, automatically read node displacement and deformation after shape, generate shape finding shape based on node displacement and write into finite element analysis model;Subsequently, repeatedly execute forward loading analysis, node difference value calculation, adjacent two times node displacement difference value calculation and current shape finding shape update, until meet node control proportion after automatically output design initial shape.The present application can reduce the error accumulation caused by artificial export coordinate, modify model and judge convergence, improve the efficiency, accuracy and reviewability of complex free curved surface structure predeformation shape finding.

Description

Technical Field

[0001] This invention relates to the field of form-finding analysis technology in structural engineering, specifically a fully automated iterative pre-deformation form-finding method for complex free-form surface structures. Background Technology

[0002] With the deep integration of architectural aesthetics and structural engineering, complex free-form surface structures have been widely applied in engineering scenarios such as large public buildings, irregularly shaped spatial steel structures, and curved curtain wall support structures. These structures are characterized by free form, complex boundary conditions, and significant variations in the spatial orientation of components. Under the combined action of target loads such as self-weight, additional dead loads, curtain wall loads, and equipment loads, they are prone to significant deformation. If manufacturing and installation are carried out directly according to the target configuration node coordinates provided by the architectural professionals, the structure will deviate from the target geometry after loading, affecting the building's appearance, the accuracy of the enclosure connections, and the structural performance. Therefore, it is necessary to solve for the initial design configuration of complex free-form surface structures during the design phase so that they can achieve the expected target configuration under the combined action of target loads.

[0003] In existing technologies, pre-deformation form finding for complex free-form surface structures typically employs a reverse loading method. This involves first establishing a structural model according to the target configuration, then applying the form-finding load in reverse to the model, and using the deformed configuration after reverse loading as the initial design configuration. However, this method alters the actual loading direction of the target load combination, causing inconsistencies between the structural stress mode, internal force distribution, and force transmission path and the actual construction loading state. On the other hand, there are also schemes using a forward loading iterative approach to form finding, which gradually approximates the target configuration through multiple forward loading analyses. However, this approach usually requires engineers to manually export node coordinates and displacement data, manually calculate differences, manually modify node coordinates, and resubmit the analysis, lacking automatic reading, automatic writing, automatic convergence judgment, and automatic iterative control mechanisms. Faced with a large number of nodes in complex free-form surface structures with irregular spatial distribution, manual iteration is not only inefficient but also prone to error accumulation due to incorrect node numbering, missing coordinate copies, or inconsistent human judgment standards, leading to insufficient accuracy and verifiability in the initial design configuration solution. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a fully automated iterative pre-deformation form-finding method for complex free-form surface structures. This method solves the problems of existing reverse loading form-finding methods, which are prone to causing distortion of the force pattern, and existing forward loading iterative form-finding methods, which rely on manual extraction of coordinates, manual modification of the model, and manual judgment of convergence, resulting in low iteration efficiency, easy accumulation of errors, and insufficient verifiability of form-finding results.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a fully automated iterative pre-deformation and shape-finding method for complex free-form surface structures, comprising:

[0006] Obtain the target configuration node coordinates and target load combinations for complex freeform surface structures;

[0007] A finite element analysis model is established based on the target configuration node coordinates, the set of control nodes is determined, and the node control ratio and differential control value are set.

[0008] Using the target configuration node coordinates as the zeroth analysis configuration, the finite element analysis model is subjected to forward loading analysis according to the target load combination to obtain the first node displacement and the first deformation configuration;

[0009] Based on the first node displacement, the target configuration node coordinates are corrected to generate the first form-finding configuration.

[0010] The first form-finding configuration is taken as the current form-finding configuration. The finite element analysis model is subjected to positive loading analysis according to the target load combination to obtain the current node displacement and the current deformed configuration.

[0011] Calculate the node difference value between the node coordinates of the current deformed configuration and the target configuration, and determine whether the proportion of the number of nodes whose node difference value is not greater than the difference control value to the total number of nodes in the control node set reaches the node control proportion.

[0012] If the node control ratio is reached, the current form-finding configuration is determined as the initial design configuration;

[0013] If the node control ratio is not reached, the difference between two adjacent node displacements is calculated based on the previous node displacement and the current node displacement. The current form-finding configuration is updated using the difference between two adjacent node displacements. The forward loading analysis, node difference value calculation, and current form-finding configuration update are repeated until the proportion of the number of nodes whose node difference value is not greater than the difference control value reaches the node control ratio of the total number of nodes in the control node set. The initial design configuration is then output.

[0014] Preferably, the step of establishing a finite element analysis model based on the target configuration node coordinates includes:

[0015] Import the target configuration node coordinates into the finite element modeling environment;

[0016] Establish a node number mapping relationship based on the target configuration node coordinates;

[0017] Based on the component connection relationships, material parameters, cross-sectional parameters, and boundary constraints of the complex freeform surface structure, a finite element analysis model corresponding to the node coordinates of the target configuration is generated.

[0018] Preferably, the steps for determining the set of control nodes include:

[0019] All nodes in the finite element analysis model are taken as the control node set;

[0020] Alternatively, the set of control nodes can be obtained by selecting from all nodes of the finite element analysis model based on the curvature variation region, support boundary region, cantilever boundary region, and external enclosure connection region of the complex freeform surface structure.

[0021] Preferably, the target load combination includes at least one of self-weight load, additional dead load, curtain wall load, equipment load, and construction stage dead load; each forward loading analysis maintains the same loading direction, load magnitude, and boundary constraint conditions for the target load combination.

[0022] Preferably, the step of correcting the configuration node coordinates of the target configuration based on the first node displacement includes:

[0023] Obtain the first node displacement of each node in the three-dimensional coordinate direction in the control node set;

[0024] The inverse vector of the first node displacement is superimposed onto the target configuration node coordinates of the corresponding node;

[0025] The first shape-finding configuration is generated based on the superimposed node coordinates.

[0026] Preferably, the step of calculating the node difference value between the node coordinates of the current deformed configuration and the target configuration includes:

[0027] Obtain the deformed node coordinates of the control nodes in the current deformed configuration;

[0028] Calculate the three-dimensional coordinate difference between the deformed node coordinates and the corresponding target configuration node coordinates;

[0029] The node difference value of the corresponding control node is determined based on the three-dimensional coordinate difference.

[0030] Preferably, the step of updating the current form-finding configuration using the difference between two adjacent node displacements includes:

[0031] Subtract the previous node displacement from the current node displacement to obtain the difference between the two adjacent node displacements;

[0032] The difference between two adjacent node displacements is superimposed on the node coordinates of the current form-finding configuration;

[0033] The superimposed node coordinates are used as the updated current shape and configuration.

[0034] Preferably, the steps of repeatedly performing forward loading analysis, node difference value calculation, and current shape-finding configuration update include:

[0035] The updated current form-finding configuration will be automatically written into the finite element analysis model.

[0036] The finite element analysis model is invoked to execute the next round of forward loading analysis;

[0037] Automatically read the current node displacement and current post-deformation configuration obtained from the next round of forward loading analysis;

[0038] Based on the results of the next round of forward loading analysis, continue to calculate the node difference value and update the current shape and configuration.

[0039] This invention also provides a fully automated iterative pre-deformation and form-finding system for complex free-form surface structures, used to execute the aforementioned fully automated iterative pre-deformation and form-finding method for complex free-form surface structures. The system includes:

[0040] The data acquisition module is used to acquire the target configuration node coordinates and target load combinations of complex freeform surface structures;

[0041] The model building module is used to establish a finite element analysis model based on the target configuration node coordinates, determine the set of control nodes, and set the node control ratio and differential control value.

[0042] The forward loading analysis module is used to perform forward loading analysis on the finite element analysis model according to the target load combination, and obtain the nodal displacements and deformed configurations.

[0043] The configuration correction module is used to generate the first form-finding configuration based on the first node displacement, and update the current form-finding configuration based on the difference between two adjacent node displacements;

[0044] The convergence determination module is used to calculate the node difference value between the node coordinates of the current deformed configuration and the target configuration, and to determine whether the proportion of the number of nodes whose node difference value is not greater than the difference control value to the total number of nodes in the control node set reaches the node control ratio.

[0045] The output module is used to output the initial configuration of the design when the node control ratio is reached.

[0046] The present invention also provides an electronic device, including a processor, a memory, and a computer program stored in the memory. When the computer program is executed by the processor, it causes the processor to perform the steps of the above-described fully automatic iterative pre-deformation and shape-finding method for complex freeform surface structures.

[0047] This invention provides a fully automated iterative pre-deformation form-finding method for complex free-form surface structures. It offers the following advantages:

[0048] 1. This invention automatically invokes the finite element analysis model, automatically reads nodal displacements and deformed configurations, automatically calculates nodal difference values, and automatically writes the updated current form-finding configuration. When convergence conditions are not met, it automatically enters the next round of forward loading analysis, forming a fully automated iterative closed loop of "model analysis—result reading—difference judgment—configuration update—re-analysis." Compared to existing methods that rely on manual nodal coordinate extraction, model modification, and convergence judgment in forward form-finding, this invention significantly reduces manual steps, minimizes errors caused by incorrect nodal numbering, missing coordinate copies, and inconsistent human judgments, and improves the computational efficiency and verifiability of fully automated iterative pre-deformation form-finding for complex freeform surfaces.

[0049] 2. This invention automatically converges and determines the node difference values ​​between the node coordinates of the current deformed configuration and the target configuration by setting node control ratios and difference control values. This eliminates the reliance on engineers' experience in judging a few nodes with the largest displacements during the form-finding process. Instead, it uses a unified judgment based on the proportion of nodes in the control node set that meet the difference control values. This method can adapt to the characteristics of complex freeform surface structures with a large number of nodes and irregular spatial distribution, improving the consistency and objectivity of convergence judgment while ensuring overall form-finding accuracy.

[0050] 3. This invention allows for the customization of the control node set and node control ratio based on the engineering characteristics of complex freeform surface structures. It can use all nodes as a control node set for overall precision control, or select key nodes for focused control in areas of curvature variation, support boundaries, cantilever boundaries, and external enclosure connections. This avoids ineffective iterations caused by all nodes simultaneously meeting the same precision requirement, improving the iteration efficiency of large-scale freeform surface models while ensuring the geometrical accuracy of key areas.

[0051] 4. In each round of form-finding analysis, this invention performs forward loading analysis according to the actual direction of the target load combination, and uses the difference in nodal displacements as the basis for geometric correction of the current form-finding configuration, without changing the force direction of the structure through reverse loading. This allows the force mode, internal force distribution, and boundary response during the analysis process to more closely approximate the actual construction loading state, avoiding fundamental errors introduced by reverse loading due to inconsistencies between the force transmission path and the actual loading path, and improving the matching accuracy between the initial design configuration and the target configuration.

[0052] 5. This invention manages the target configuration node coordinates, current form-finding configuration, node displacement, current deformed configuration, and node difference values ​​by mapping node numbers. This ensures that coordinate corrections in each iteration are accurately applied to the same nodes, avoiding node mismatches or coordinate update misalignments when there are a large number of nodes in a complex freeform surface structure. This improves the data consistency and engineering reliability of the form-finding process. Attached Figure Description

[0053] Figure 1 This is a flowchart of the fully automated iterative pre-deformation and shape-finding method for complex free-form surface structures according to the present invention;

[0054] Figure 2 This is a schematic diagram of the pre-deformation form-finding process of the target displacement method of the present invention. Figure 1 ;

[0055] Figure 3 This is a schematic diagram of the pre-deformation form-finding process of the target displacement method of the present invention. Figure 2 ;

[0056] Figure 4 This is a schematic diagram comparing the reverse loading force states of the present invention;

[0057] Figure 5 This is a schematic diagram of the framework of the fully automatic iterative pre-deformation and shape-finding system for complex free-form surface structures according to the present invention. Detailed Implementation

[0058] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0059] Example 1

[0060] This embodiment provides a fully automated iterative pre-deformation form-finding method for complex free-form surface structures. This method is used to solve the initial design configuration of complex free-form surface structures before construction, so that the complex free-form surface structures can achieve the target configuration required by the building after the target load combination.

[0061] To facilitate understanding of the difference between forward loading iterative shape finding and reverse loading shape finding in this embodiment, as follows: Figure 4As shown, reverse loading form finding involves applying an equivalent load in the opposite direction to the target load combination based on the target configuration, using the deformed configuration after reverse loading as the initial design configuration. In contrast, this embodiment maintains the actual direction of the target load combination unchanged in each round of form finding. By automatically reading nodal displacements, automatically calculating nodal differences, and automatically updating the current form finding configuration, the current deformed configuration gradually approaches the nodal coordinates of the target configuration. Therefore, this embodiment does not obtain the pre-deformed configuration by changing the load direction, but rather obtains the initial design configuration through fully automatic iterative correction under forward loading conditions.

[0062] Complex free-form surface structures can be complex free-form surface steel structures, spatial grid shell structures, irregular truss structures, curved curtain wall support structures, spatial beam-rod composite structures, or spatial structures formed by one or more combinations of beam units, rod units, shell units, and cable units. In this embodiment, the complex free-form surface structure is preferably a large-span complex free-form surface steel structure.

[0063] like Figure 1 As shown, the fully automated iterative pre-deformation and shape-finding method for complex free-form surface structures in this embodiment includes the following steps:

[0064] Obtain the target configuration node coordinates and target load combination of complex freeform surface structures.

[0065] Specifically, the target configuration node coordinates refer to the node coordinates corresponding to the target geometric shape that the complex free-form surface structure should achieve after the application of the target load combination. The target configuration node coordinates can be derived from the node coordinate tables in 3D surface models, structural design models, BIM models, construction detailing models, or finite element analysis models provided by the architectural profession. The target configuration node coordinates represent a pre-determined target geometric shape, serving as the convergence target for pre-deformation form finding. The output of this method is the initial design configuration, ensuring that the complex free-form surface structure reaches the target configuration node coordinates corresponding to the target configuration after the application of the target load combination.

[0066] Specifically, the target configuration node coordinates include the three-dimensional coordinates of each node in a unified global coordinate system. To ensure that the subsequent coordinate correction process can accurately correspond to the nodes, the system reads the node number simultaneously when reading the target configuration node coordinates and establishes a one-to-one correspondence between the node number and the node coordinates.

[0067] Specifically, the target load combination is used to characterize the actual load state that a complex free-form surface structure needs to withstand after its formation. The target load combination includes at least one of the following: self-weight load, additional dead load, curtain wall load, equipment load, and construction stage dead load. In each analysis, the load is applied according to the actual direction of action of the target load combination, and the initial design configuration is not solved by reverse loading.

[0068] A finite element analysis model is established based on the target configuration node coordinates, the set of control nodes is determined, and the node control ratio and differential control value are set.

[0069] Specifically, the target configuration node coordinates are imported into the finite element modeling environment, and a node number mapping relationship is established based on the target configuration node coordinates. The node number mapping relationship is used to correspond one-to-one with the node numbers in the target configuration node coordinates, avoiding coordinate correction errors caused by changes in node order during subsequent iterations.

[0070] Specifically, based on the component connection relationships, material parameters, cross-sectional parameters, and boundary constraints of the complex freeform surface structure, a finite element analysis model corresponding to the node coordinates of the target configuration is generated. Component connection relationships include beam element connection relationships, rod element connection relationships, shell element connection relationships, or cable element connection relationships between nodes; material parameters include at least one of elastic modulus, Poisson's ratio, density, and coefficient of thermal expansion; cross-sectional parameters include at least one of cross-sectional area, moment of inertia, cross-sectional height, cross-sectional width, or shell thickness; boundary constraints include support constraints, hinge constraints, sliding constraints, elastic support constraints, or temporary constraints during the construction phase.

[0071] Preferably, the set of control nodes can be all nodes in the finite element analysis model. For complex freeform surface structures with a large number of nodes, the set of control nodes can also be obtained by selecting from all nodes in the finite element analysis model based on the curvature variation region, support boundary region, cantilever boundary region, and external enclosure connection region of the complex freeform surface structure.

[0072] Specifically, curvature variation regions can be identified by the included angle between adjacent components, the degree of change in surface normal, or the degree of change in mesh curvature; support boundary regions can be identified by the node constraint status; cantilever boundary regions can be identified by the topological distance between the node and the nearest support point; and external enclosure connection regions can be identified by curtain wall connection nodes, purlin connection nodes, or peripheral control line nodes. By selecting the control node set in the above manner, the amount of iterative computation can be reduced while ensuring the control accuracy of key geometric regions.

[0073] Specifically, the node control ratio represents the proportion of nodes in the control node set that need to meet the difference control value requirement. The difference control value represents the allowable node coordinate deviation between the node coordinates of the current deformed configuration and the target configuration. The node control ratio can be set from 80% to 100% according to engineering accuracy requirements, and the difference control value can be set according to the structural span, processing and installation accuracy, and model units, such as 1mm, 2mm, 5mm, or other values ​​that meet engineering requirements.

[0074] Using the target configuration node coordinates as the zeroth analysis configuration, the finite element analysis model is subjected to forward loading analysis according to the target load combination to obtain the first node displacement and the configuration after the first deformation.

[0075] Specifically, such as Figure 2 and Figure 3 The target structural configuration and the configuration after the first deformation are shown in the diagram. The target configuration node coordinates are used as the zeroth analysis configuration. After performing a forward loading analysis according to the target load combination, the configuration after the first deformation is obtained. The zeroth analysis configuration is the structural configuration corresponding to the target configuration node coordinates. After writing the zeroth analysis configuration into the finite element analysis model, a forward loading analysis is performed on the finite element analysis model according to the target load combination. Forward loading analysis refers to applying the target load combination according to the actual force direction of the structure. For example, the self-weight load is still applied in the gravity direction, and the additional dead load, curtain wall load, and equipment load are still applied in the actual action direction of the project.

[0076] Specifically, after the finite element analysis model completes the first positive loading analysis, it outputs the first nodal displacements and the first post-deformation configuration. The first nodal displacements are the set of displacements of each node under the target load combination, from the zeroth analysis configuration to the first post-deformation configuration. The first post-deformation configuration is the new equilibrium configuration reached by the zeroth analysis configuration after the target load combination.

[0077] In a preferred embodiment, the target configuration is denoted as... The first nodal displacement is denoted as The configuration after the first deformation is denoted as The configuration after the first deformation is obtained according to the following relationship: ;

[0078] in, Indicates the coordinates of the target configuration node. This indicates the first nodal displacement. This indicates the configuration after the first deformation.

[0079] Based on the first node displacement, the target configuration node coordinates are corrected to generate the first form-finding configuration.

[0080] Specifically, such as Figure 2 and Figure 3The first form-finding configuration of the structure is shown in the diagram. The first nodal displacements are superimposed in the opposite direction to the target configuration nodal coordinates to generate the first form-finding configuration. The system obtains the first nodal displacements from the first forward loading analysis and superimposes them onto the target configuration nodal coordinates in the opposite direction to generate the first form-finding configuration. In other words, the first form-finding configuration pre-applies geometric corrections in the opposite direction to the first nodal displacements based on the target configuration, enabling the complex freeform surface structure to revert to the target configuration after subsequent forward loading according to the target load combination.

[0081] In a preferred embodiment, the first location and form marker is... The first geometries are obtained according to the following relationship:

[0082] ;

[0083] in, This indicates the first time the shape and position are being searched. Indicates the coordinates of the target configuration node. This indicates the first node displacement.

[0084] Specifically, after generating the first form-finding configuration, the system writes the node coordinates from the first form-finding configuration into the finite element analysis model. For nodes that are not included in the control node set but belong to the finite element analysis model, they can be updated synchronously according to the displacement correction amount of their corresponding node number, or interpolated and updated according to the coordinate correction relationship of adjacent control nodes, so as to maintain the overall geometric continuity of the complex freeform surface structure.

[0085] The first form-finding configuration is taken as the current form-finding configuration. The finite element analysis model is subjected to forward loading analysis according to the target load combination to obtain the current node displacement and the current deformed configuration.

[0086] Specifically, the initial form-finding configuration is written into the finite element analysis model, updating the node coordinates while keeping the component connection relationships, material parameters, section parameters, boundary constraints, and target load combinations unchanged. Then, a forward loading analysis is performed again according to the target load combination to obtain the current node displacements and the current deformed configuration.

[0087] When performing the second forward loading analysis using the first form-position finding as the current form-position finding, the current node displacement obtained from the second forward loading analysis can be denoted as... The current deformed configuration can be denoted as At this point, the current deformed configuration is obtained according to the following relationship:

[0088] ;

[0089] in, This indicates the current deformed configuration after the second forward loading analysis. This indicates the first time the shape and position are being searched. This represents the current node displacement obtained from the second forward loading analysis.

[0090] Calculate the node difference value between the node coordinates of the current deformed configuration and the target configuration, and determine whether the proportion of the number of nodes whose node difference value is not greater than the difference control value reaches the node control ratio.

[0091] Specifically, the system acquires the deformed node coordinates of each control node in the current deformed configuration and compares them with the node coordinates of the same node number in the target configuration node coordinates to obtain the node difference value of each control node. The node difference value can be the comprehensive coordinate deviation in the three-dimensional coordinate direction, or it can be the maximum value among the deviations in each coordinate direction. The specific value selection method can be determined according to the engineering accuracy control rules.

[0092] Specifically, the system counts the number of control nodes whose node difference value is not greater than the difference control value, and determines whether the proportion of this number to the total number of nodes in the control node set reaches the node control ratio. If the node control ratio is reached, the current form-finding configuration is considered to meet the convergence requirement; if the node control ratio is not reached, the current form-finding configuration is considered not to be able to enable the complex free-form surface structure to reach the target configuration requirement after the target load combination, and configuration updates are required.

[0093] For example, when the node control ratio is set to 95%, if the node difference values ​​of at least 95% of the control nodes in the control node set are not greater than the difference control value, then the current form-finding configuration is determined to meet the convergence requirement; if less than 95% of the control nodes meet the difference control value requirement, then the current form-finding configuration is determined to not meet the convergence requirement.

[0094] If the node control ratio is reached, the current form-finding configuration will be determined as the initial design configuration.

[0095] Specifically, when the proportion of control nodes whose node difference value is no greater than the difference control value to the total number of nodes in the control node set reaches the node control ratio, it indicates that the current form-finding configuration can achieve the geometric shape within the allowable error range of the target configuration after the target load combination. At this point, the iterative calculation is stopped, and the current form-finding configuration is determined as the initial design configuration.

[0096] Specifically, the initial design configuration is the pre-deformed configuration used for manufacturing, layout, installation, or construction control of complex free-form surface structures. When outputting the initial design configuration, one or more of the following can be output: node coordinate table, member endpoint coordinate table, component fabrication control point coordinate table, BIM model, finite element model file, or construction layout file.

[0097] If the node control ratio is not reached, the difference between two adjacent node displacements is calculated based on the previous node displacement and the current node displacement. The current form-finding configuration is updated using the difference between two adjacent node displacements, and the forward loading analysis, node difference calculation, and current form-finding configuration update are repeated until the convergence requirement is met.

[0098] Specifically, such as Figure 2 and Figure 3 As shown in the second deformation configuration and the second form-finding configuration of the structure, the system continues to update the current form-finding configuration based on the difference between two adjacent node displacements until the convergence requirement is met. When the proportion of the number of control nodes whose node difference value is not greater than the difference control value to the total number of nodes in the control node set does not reach the node control ratio, the system obtains the previous node displacement obtained from the previous forward loading analysis and the current node displacement obtained from the current forward loading analysis, and calculates the difference between two adjacent node displacements. Subsequently, the system superimposes the difference between two adjacent node displacements onto the current form-finding configuration to obtain the updated current form-finding configuration.

[0099] In a preferred embodiment, the first nodal displacement is denoted as... The current node displacement obtained from the second forward loading analysis is denoted as... The difference between two adjacent node displacements is denoted as The difference between two adjacent node displacements is obtained according to the following relationship:

[0100] ;

[0101] in, This represents the difference between two adjacent nodal displacements, one obtained from the first nodal displacement analysis and the other from the current nodal displacement obtained from the second forward loading analysis. This indicates the first nodal displacement. This represents the current node displacement obtained from the second forward loading analysis.

[0102] The system superimposes the difference between two adjacent nodal displacements onto the first form-finding configuration to obtain the second form-finding configuration. The second form-finding configuration is denoted as... The second geodesic analysis is obtained according to the following relationship:

[0103] ;

[0104] in, This indicates the second time to find the shape and position. This indicates the first time the shape and position are being searched. This represents the difference in displacement between two adjacent nodes.

[0105] In subsequent iterations, the system repeats the above forward loading analysis and configuration update process. The current node displacement is denoted as... The current node displacement is denoted as The difference between two adjacent node displacements is denoted as The difference between two adjacent node displacements is obtained according to the following relationship:

[0106] ;

[0107] in, This represents the difference between two adjacent nodal displacements between the (k-1)th nodal displacement and the kth nodal displacement. Indicates the previous node displacement. This indicates the displacement of the current node.

[0108] The updated current geodesic is as follows: The current location and shape before the update are denoted as The current shape and position are then updated according to the following relationship:

[0109] ;

[0110] in, This indicates the updated current shape and configuration. This indicates the current shape and configuration before the update. This represents the difference in displacement between two adjacent nodes.

[0111] Find the current shape and configuration after the update. Next, the system performs a forward loading analysis again according to the target load combination to obtain the configuration after the next deformation. The relationship is as follows:

[0112] ;

[0113] in, This represents the current form-finding configuration after deformation under the target load combination, as updated. This indicates the updated current shape and configuration. This represents the nodal displacement obtained from the corresponding forward loading analysis.

[0114] Specifically, the system repeatedly performs forward loading analysis, nodal difference value calculation, and current form-finding configuration update until, under the target load combination, the nodal difference value between the nodal coordinates of the current deformed configuration and the target configuration meets the control requirements. At this point, the current form-finding configuration before deformation is the initial design configuration.

[0115] Preferably, in each iteration, the following process is executed automatically:

[0116] The updated current form-finding configuration will be automatically written into the finite element analysis model.

[0117] Call the finite element analysis model to execute the next round of forward loading analysis;

[0118] Automatically read the current node displacement and current post-deformation configuration obtained from the next round of forward loading analysis;

[0119] Based on the results of the next round of forward loading analysis, continue to calculate the node difference value and update the current shape and configuration.

[0120] Specifically, in one optional implementation, automatic iteration can be achieved through the open interface of the finite element analysis program. For example, the program interface can read node numbers, node coordinates, node displacements, and analysis results; write the updated node coordinates back to the finite element analysis model; and automatically invoke analysis commands and read the analysis results. The finite element analysis program can be SAP2000, MIDAS, ANSYS, ABAQUS, or other software platforms capable of performing finite element analysis of spatial structures. This embodiment does not limit the application to a specific type of finite element software.

[0121] Preferably, the system can also set a maximum number of iterations. When the maximum number of iterations is reached but the node control ratio is still not met, the system outputs a non-convergence prompt and marks the control nodes whose node difference values ​​exceed the difference control values. Engineers can use this information to check whether the boundary constraints, target load combinations, component connection relationships, or node control ratio settings of the finite element analysis model are reasonable.

[0122] Preferably, the system can also generate an iteration record after each iteration. The iteration record includes the iteration number, the current form-finding configuration file, the target load combination number, the maximum node difference value, the average node difference value, the number of nodes that meet the difference control value, the proportion that meets the control value, the list of nodes that do not meet the control value, and the node coordinate correction amount. Through the iteration record, the form-finding process can be traced and the construction control can be verified.

[0123] Using the method in this embodiment, the complex freeform surface structure is always subjected to the positive target load combination throughout the entire form-finding process, and the force path is consistent with the actual construction loading state. At the same time, by automatically updating the current form-finding configuration through the difference between two adjacent node displacements, the current deformed configuration of the complex freeform surface structure after the target load combination is applied can gradually converge to the target configuration node coordinates, thereby obtaining the initial design configuration that meets the construction requirements.

[0124] Example 2

[0125] like Figure 5As shown, this embodiment provides a fully automated iterative pre-deformation form-finding system for complex free-form surface structures. This system is used to execute the fully automated iterative pre-deformation form-finding method for complex free-form surface structures described in Embodiment 1. The system includes a data acquisition module, a model construction module, a forward loading analysis module, a configuration correction module, a convergence determination module, and an output module.

[0126] The data acquisition module is used to obtain the target configuration node coordinates and target load combinations of complex freeform surface structures.

[0127] Specifically, the data acquisition module can read the target configuration node coordinates from 3D model files, BIM model files, finite element model files, node coordinate tables, or engineering databases, and obtain the target load combination corresponding to the target configuration node coordinates. The target load combination includes at least one of the following: self-weight load, additional dead load, curtain wall load, equipment load, and construction stage dead load.

[0128] The model building module is used to establish a finite element analysis model based on the target configuration node coordinates, determine the set of control nodes, and set the node control ratio and differential control value.

[0129] Specifically, the model building module establishes a node number mapping relationship based on the target configuration node coordinates, and builds a finite element analysis model based on the component connection relationships, material parameters, section parameters, and boundary constraints of the complex freeform surface structure. The model building module is also used to determine the set of control nodes based on all nodes, curvature variation regions, support boundary regions, cantilever boundary regions, or external enclosure connection regions.

[0130] The forward loading analysis module is used to perform forward loading analysis on the finite element analysis model according to the target load combination, and obtain the nodal displacements and deformed configurations.

[0131] Specifically, the forward loading analysis module maintains consistency in the loading direction, load magnitude, and boundary constraints of the target load combination in each round of analysis. The forward loading analysis module can call finite element analysis programs to complete static analysis, geometric nonlinear analysis, or construction stage analysis, and read nodal displacements and post-deformation configurations.

[0132] The configuration correction module is used to generate the first configuration based on the first node displacement, and update the current configuration based on the difference between two adjacent node displacements.

[0133] Specifically, after the first forward loading analysis, the configuration correction module superimposes the inverse vector of the first node displacement onto the target configuration node coordinates to generate the first configuration. In subsequent iterations, the configuration correction module subtracts the previous node displacement from the current node displacement to obtain the difference between two adjacent node displacements, and superimposes the difference between two adjacent node displacements onto the current configuration to generate the updated current configuration.

[0134] The convergence determination module is used to calculate the node difference value between the node coordinates of the current deformed configuration and the target configuration, and to determine whether the proportion of the number of nodes whose node difference value is not greater than the difference control value to the total number of nodes in the control node set reaches the node control ratio.

[0135] Specifically, the convergence determination module calculates the node difference value for each control node in the control node set and counts the number of control nodes that meet the difference control value. When the proportion of the number of control nodes that meet the difference control value to the total number of nodes in the control node set reaches the node control ratio, the convergence determination module sends a shape finding completion instruction to the output module; when the node control ratio is not reached, the convergence determination module sends a continue iteration instruction to the configuration correction module.

[0136] The output module is used to output the initial configuration of the design when the node control ratio is reached.

[0137] Specifically, the output module can output a table of node coordinates corresponding to the initial design configuration, a table of component endpoint coordinates, a finite element model file, a BIM model file, a construction layout control file, or a form-finding calculation report. The form-finding calculation report may include target load combinations, node control ratios, differential control values, number of iterations, maximum node differential value, average node differential value, and a list of unmet control nodes.

[0138] Preferably, the system also includes an automatic interaction module. This module interacts with the finite element analysis program, automatically writing the current form-finding configuration, automatically initiating forward loading analysis, automatically reading nodal displacements and post-deformation configurations, and transmitting the results to the configuration correction module and convergence determination module. The automatic interaction module reduces the workload of manually modifying nodal coordinates and manually comparing nodal differences.

[0139] Example 3

[0140] This embodiment provides an electronic device, which includes a processor, a memory, and a computer program stored in the memory. When the computer program is executed by the processor, it causes the processor to perform the steps of the fully automated iterative pre-deformation and shape-finding method for complex free-form surface structures according to Embodiment 1.

[0141] Specifically, the electronic device can be a server, workstation, personal computer, engineering computing terminal, or computing device that deploys finite element analysis programs. The memory stores the target configuration node coordinates, target load combinations, node number mapping relationships, finite element analysis model, node control scales, difference control values, and form-finding iteration programs.

[0142] When the processor executes the computer program, it acquires the target configuration node coordinates and target load combination of the complex freeform surface structure. Based on the target configuration node coordinates, it establishes a finite element analysis model, determines the set of control nodes, and sets the node control ratio and differential control value. Then, it performs a forward loading analysis on the finite element analysis model according to the target load combination to obtain the node displacements and the deformed configuration. Next, it corrects the current form-finding configuration based on the node displacements and determines whether convergence has been achieved through the node differential value, differential control value, and node control ratio. When the node control ratio is reached, the initial design configuration is output.

[0143] The aforementioned electronic devices can be used to program and automate the fully automatic iterative pre-deformation and form-finding process of complex freeform surface structures, making the solution results of the initial configuration verifiable and repeatable.

[0144] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A fully automated iterative pre-deformation and shape-finding method for complex free-form surface structures, characterized in that, include: Obtain the target configuration node coordinates and target load combinations for complex freeform surface structures; A finite element analysis model is established based on the target configuration node coordinates, the set of control nodes is determined, and the node control ratio and differential control value are set. Using the target configuration node coordinates as the zeroth analysis configuration, the finite element analysis model is subjected to forward loading analysis according to the target load combination to obtain the first node displacement and the first deformation configuration; Based on the first node displacement, the target configuration node coordinates are corrected to generate the first form-finding configuration. The first form-finding configuration is taken as the current form-finding configuration. The finite element analysis model is subjected to positive loading analysis according to the target load combination to obtain the current node displacement and the current deformed configuration. Calculate the node difference value between the node coordinates of the current deformed configuration and the target configuration, and determine whether the proportion of the number of nodes whose node difference value is not greater than the difference control value to the total number of nodes in the control node set reaches the node control proportion. If the node control ratio is reached, the current form-finding configuration is determined as the initial design configuration; If the node control ratio is not reached, the difference between two adjacent node displacements is calculated based on the previous node displacement and the current node displacement. The current form-finding configuration is updated using the difference between two adjacent node displacements. The forward loading analysis, node difference value calculation, and current form-finding configuration update are repeated until the proportion of the number of nodes whose node difference value is not greater than the difference control value reaches the node control ratio of the total number of nodes in the control node set. The initial design configuration is then output.

2. The fully automated iterative pre-deformation and shape-finding method for complex free-form surface structures according to claim 1, characterized in that, The steps for establishing a finite element analysis model based on the target configuration node coordinates include: Import the target configuration node coordinates into the finite element modeling environment; Establish a node number mapping relationship based on the target configuration node coordinates; Based on the component connection relationships, material parameters, cross-sectional parameters, and boundary constraints of the complex freeform surface structure, a finite element analysis model corresponding to the node coordinates of the target configuration is generated.

3. The fully automated iterative pre-deformation and shape-finding method for complex free-form surface structures according to claim 1, characterized in that, The steps to determine the set of control nodes include: All nodes in the finite element analysis model are taken as the control node set; Alternatively, the set of control nodes can be obtained by selecting from all nodes of the finite element analysis model based on the curvature variation region, support boundary region, cantilever boundary region, and external enclosure connection region of the complex freeform surface structure.

4. The fully automated iterative pre-deformation and shape-finding method for complex free-form surface structures according to claim 1, characterized in that, The target load combination includes at least one of the following: self-weight load, additional dead load, curtain wall load, equipment load, and construction stage dead load; each forward loading analysis maintains the same loading direction, load magnitude, and boundary constraint conditions for the target load combination.

5. The fully automated iterative pre-deformation and shape-finding method for complex free-form surface structures according to claim 1, characterized in that, The step of correcting the configuration node coordinates of the target configuration based on the first node displacement includes: Obtain the first node displacement of each node in the three-dimensional coordinate direction in the control node set; The inverse vector of the first node displacement is superimposed onto the target configuration node coordinates of the corresponding node; The first shape-finding configuration is generated based on the superimposed node coordinates.

6. The fully automated iterative pre-deformation and shape-finding method for complex free-form surface structures according to claim 1, characterized in that, The steps for calculating the node difference values ​​between the node coordinates of the current deformed configuration and the target configuration include: Obtain the deformed node coordinates of the control nodes in the current deformed configuration; Calculate the three-dimensional coordinate difference between the deformed node coordinates and the corresponding target configuration node coordinates; The node difference value of the corresponding control node is determined based on the three-dimensional coordinate difference.

7. The fully automated iterative pre-deformation and shape-finding method for complex free-form surface structures according to claim 1, characterized in that, The step of updating the current form-finding configuration using the difference between two adjacent node displacements includes: Subtract the previous node displacement from the current node displacement to obtain the difference between the two adjacent node displacements; The difference between two adjacent node displacements is superimposed on the node coordinates of the current form-finding configuration; The superimposed node coordinates are used as the updated current shape and configuration.

8. The fully automated iterative pre-deformation and shape-finding method for complex free-form surface structures according to claim 1, characterized in that, The steps of repeatedly performing forward loading analysis, node difference calculation, and current shape-finding configuration update include: The updated current form-finding configuration will be automatically written into the finite element analysis model. The finite element analysis model is invoked to execute the next round of forward loading analysis; Automatically read the current node displacement and current post-deformation configuration obtained from the next round of forward loading analysis; Based on the results of the next round of forward loading analysis, continue to calculate the node difference value and update the current shape and configuration.

9. A fully automated iterative pre-deformation and form-finding system for complex free-form surface structures, characterized in that, The system is used to execute the fully automated iterative pre-deformation and form-finding method for complex free-form surface structures according to any one of claims 1 to 8, the system comprising: The data acquisition module is used to acquire the target configuration node coordinates and target load combinations of complex freeform surface structures; The model building module is used to establish a finite element analysis model based on the target configuration node coordinates, determine the set of control nodes, and set the node control ratio and differential control value. The forward loading analysis module is used to perform forward loading analysis on the finite element analysis model according to the target load combination, and obtain the nodal displacements and deformed configurations. The configuration correction module is used to generate the first form-finding configuration based on the first node displacement, and update the current form-finding configuration based on the difference between two adjacent node displacements; The convergence determination module is used to calculate the node difference value between the node coordinates of the current deformed configuration and the target configuration, and to determine whether the proportion of the number of nodes whose node difference value is not greater than the difference control value to the total number of nodes in the control node set reaches the node control ratio. The output module is used to output the initial configuration of the design when the node control ratio is reached.

10. An electronic device, characterized in that, The system includes a processor, a memory, and a computer program stored in the memory. When the computer program is executed by the processor, it causes the processor to perform the steps of a fully automated iterative pre-deformation and shape-finding method for complex free-form surface structures as described in any one of claims 1 to 8.

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