Construction method for shape-finding analysis of double-curved-surface crossed cable net and modular ring truss structure

Abstract

The invention discloses a hyperboloid cross cable net shape-finding analysis and modular ring truss structure construction method, which comprises the following steps of: analyzing a static balance state of a cable net by adopting a nonlinear finite element algorithm based on a geometric model and a pretension force of a current iteration round; obtaining an internal force value and a node deformation coordinate of each cable section, calculating a standard deviation and a variable coefficient of internal force distribution according to the standard deviation and the variable coefficient, if the standard deviation and the variable coefficient are not converged to a threshold value, analyzing the influence of node coordinate change on the cable force through a sensitivity matrix, solving an optimal coordinate adjustment amount, updating a geometric model, synchronously adjusting a pre-tension force, starting a new round of iteration, and cyclically performing the process, and the standard deviation and the variable coefficient both meet the convergence requirements. And finally, outputting an optimized cable net geometrical shape and an internal force distribution result, and providing an accurate basis for actual construction. According to the technical scheme, the overall process efficiency of the double-curved-surface crossed cable net structure from digital design to industrial construction can be systematically improved.

Description

Technical Field

[0001] This invention relates to the field of large-span spatial structure engineering technology, and in particular to a method for form-finding analysis of hyperboloid cross cable nets and construction of modular ring truss structures. Background Technology

[0002] With the increasing demands for spatial expressiveness and structural efficiency in large public buildings, the hyperboloid cable net and ring truss combination system has become the preferred solution for large-span buildings such as stadiums and transportation hubs. In an industry context of increasingly free architectural forms and continuously growing structural spans, traditional design methods based on simple geometric superposition and trial-and-error are proving inadequate in coordinating efficient force transfer under complex curved surfaces with the requirements of prefabricated construction. This has become a core bottleneck restricting the safety, economy, and construction efficiency of such structures.

[0003] While classic form-finding methods such as the force density method and dynamic relaxation method can determine the foundation shape, they focus on static equilibrium alone and lack quantitative control over the uniformity of prestress distribution, often requiring repeated adjustments during construction. The traditional "assemble first, then tension" approach for ring truss construction neglects the interaction between the cable net and the support system during the forming process, easily leading to high structural redundancy and low material utilization. This disconnect between precise shape control, optimized internal force distribution, and modular construction makes it difficult for existing technologies to simultaneously achieve the comprehensive performance goals of "optimal shape, uniform internal force, and sufficient stiffness" under complex boundary conditions. Summary of the Invention

[0004] This invention provides a method for hyperboloid cross cable net form-finding analysis and modular ring truss structure construction, which solves the problems of low form-finding efficiency, uneven internal forces and insufficient modular construction accuracy caused by the disconnection of various links in traditional design, thus making it difficult to improve performance.

[0005] According to one aspect of the present invention, a hyperboloid cross cable net shape-finding analysis method is provided, the method comprising:

[0006] Based on the current geometric model and preload of the target cable net in the current iteration, a nonlinear finite element analysis algorithm is used to analyze the current static equilibrium result of the target cable net in the current iteration; wherein, each node in the current geometric model has a preset standard node coordinate.

[0007] Based on the current static equilibrium results, obtain the current internal force values ​​of each cable segment and the nodal deformation coordinates of each node in the target cable net, and calculate the current standard deviation and current coefficient of variation that match the internal force distribution of the cable net based on the current internal force values ​​of each cable segment.

[0008] When the current standard deviation or the current coefficient of variation has not converged within the threshold, the sensitivity matrix of the change of node coordinates to the internal force value of the cable segment is calculated based on the current internal force value of each cable segment and the deformation coordinate of each node, and the optimal node coordinate adjustment amount of each node is solved based on the sensitivity matrix.

[0009] The current geometric model is updated based on the adjustment of the coordinates of each optimal node, and the current pretension is updated using the pretension actually applied in the current finite element analysis process. Then, a new iteration cycle is started.

[0010] Return to the operation of analyzing the current static equilibrium result of the target cable net in the current iteration round using a nonlinear finite element analysis algorithm based on the current geometric model and current pretension of the target cable net in the current iteration round, until the current standard deviation and current coefficient of variation converge within the threshold.

[0011] After the iteration ends, the target geometric model and target static equilibrium results corresponding to the target cable net are obtained for actual cable net construction.

[0012] According to another aspect of the present invention, a method for constructing a modular ring truss structure is provided, the method comprising:

[0013] High-precision positioning reference points are set on the embedded parts of the cable net foundation, and the reference modular units located in key positions are hoisted. The spatial coordinates of the modules are monitored and adjusted in real time by measuring instruments, and the node attitude adjustment mechanism is used to accurately fix them to the design position to form the reference frame for the assembly of the ring truss.

[0014] Based on the aforementioned reference frame, the remaining modular units are hoisted sequentially in a predetermined order. After each unit is in place, the initial locking and temporary fixing of the node connections are immediately completed, and the internal force status of the module is monitored in real time through an integrated sensing system.

[0015] After the initial assembly of all modules of the ring truss is completed, the cable net prestressing tensioning operation is started. Based on the real-time monitoring of the internal force of the cable net and the deformation data of the ring truss, the spatial position of the ring truss modules is dynamically fine-tuned.

[0016] After the cable net is tensioned and reaches the design equilibrium state, all nodes of the ring truss are finally grouted and solidified to form a permanent rigid connection. The overall shape data of the ring truss is obtained by 3D scanning technology, compared and verified with the design target shape, and the deviation is corrected to ensure that the final shape of the ring truss fits the boundary of the cable net closely.

[0017] According to another aspect of the present invention, a hyperboloid cross cable net shape-finding analysis device is provided, the device comprising:

[0018] The iterative initialization module is used to analyze the current static equilibrium result of the target cable net in the current iteration cycle based on the current geometric model and current preload of the target cable net in the current iteration cycle using a nonlinear finite element analysis algorithm; wherein, each node in the current geometric model has preset standard node coordinates;

[0019] The standard deviation and coefficient of variation calculation module is used to obtain the current internal force value of each cable segment and the nodal deformation coordinate of each node in the target cable net based on the current static equilibrium result, and to calculate the current standard deviation and coefficient of variation that match the internal force distribution of the cable net based on the current internal force value of each cable segment.

[0020] The adjustment calculation module is used to calculate the sensitivity matrix of the cable segment internal force value to the node coordinate change based on the current cable segment internal force value and the deformation coordinate of each node when the current standard deviation or the current coefficient of variation has not converged within the threshold. The module then solves for the optimal node coordinate adjustment amount for each node based on the sensitivity matrix.

[0021] The model update module is used to update the current geometric model based on the adjustment amount of each optimal node coordinate, and after updating the current pretension with the pretension actually applied in the current finite element analysis process, a new iteration cycle is started.

[0022] The convergence judgment module is used to return the operation of performing the current static equilibrium result of the target cable net in the current iteration round by using a nonlinear finite element analysis algorithm based on the current geometric model and current pretension of the target cable net in the current iteration round, until the current standard deviation and current coefficient of variation converge within the threshold.

[0023] The results output module is used to obtain the target geometric model and target static equilibrium results corresponding to the target cable net after the iteration ends, so as to carry out the actual cable net construction.

[0024] According to another aspect of the present invention, an electronic device is provided, the electronic device comprising:

[0025] At least one processor; and

[0026] A memory communicatively connected to the at least one processor; wherein,

[0027] The memory stores a computer program that can be executed by the at least one processor, which enables the at least one processor to perform the hyperboloid cross cable net form-finding analysis and modular ring truss structure construction method according to any embodiment of the present invention.

[0028] According to another aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium storing computer instructions, the computer instructions being configured to cause a processor to execute and implement the hyperboloid cross cable net form-finding analysis and modular ring truss structure construction method described in any embodiment of the present invention.

[0029] According to another aspect of the present invention, a computer program product is also provided, including a computer program / instructions that, when executed by a processor, implement the steps of the method as described in any embodiment of the present invention.

[0030] The technical solution of this invention involves analyzing the current static equilibrium result using a nonlinear finite element analysis algorithm based on the current geometric model and current preload of the target cable net in the current iteration. Based on this result, the current internal force value of each cable segment and the node deformation coordinates of each node are obtained, and the current standard deviation and current coefficient of variation matching the internal force distribution of the cable net are calculated. If the current standard deviation or current coefficient of variation does not converge to a threshold, the sensitivity matrix of node coordinate changes to the cable segment internal force value is calculated based on the current internal force value of the cable segment and the node deformation coordinates, thereby solving for the optimal node coordinate adjustment amount for each node. The current geometric model is updated based on this adjustment amount, and the current preload is updated simultaneously before starting a new iteration. The above analysis, evaluation, and adjustment process is repeated until the current standard deviation and current coefficient of variation both converge to the threshold. Finally, the target geometric model and target static equilibrium result are obtained to guide actual construction. This solution deeply integrates shape creation, internal force distribution uniformity control, and iterative optimization, solving the technical problems of low efficiency, uneven prestress distribution, and disconnection from construction caused by the reliance on experience and trial and error in traditional shape-finding methods. It achieves the beneficial effects of improving design accuracy, ensuring uniform distribution of internal forces in the structure, and realizing efficient collaboration between design and construction.

[0031] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of the present invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 This is a flowchart of a hyperboloid cross cable net shape finding analysis method provided in Embodiment 1 of the present invention;

[0034] Figure 2 This is a flowchart of another hyperboloid cross cable net shape finding analysis method provided in Embodiment 2 of the present invention;

[0035] Figure 3 This is a flowchart of a hyperboloid cross cable net shape finding analysis scheme in a specific scenario applicable to the embodiments of the present invention;

[0036] Figure 4 This is a schematic diagram of a cable arrangement along the principal curvature direction in a specific scenario applicable to an embodiment of the present invention;

[0037] Figure 5 This is a flowchart of a modular ring truss structure construction method according to Embodiment 3 of the present invention;

[0038] Figure 6 This is a schematic diagram of the structure of a hyperboloid cross cable net shape finding analysis device according to Embodiment 4 of the present invention;

[0039] Figure 7 This is a schematic diagram of an electronic device that implements a hyperboloid cross cable net form-finding analysis and modular ring truss structure construction method according to an embodiment of the present invention. Detailed Implementation

[0040] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0041] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0042] Example 1

[0043] Figure 1This is a flowchart of a hyperboloid cross cable net form-finding analysis method provided in Embodiment 1 of the present invention. This embodiment can be applied to the morphological optimization and internal force homogenization analysis of hyperboloid cross cable nets in large-span spatial structures. The method can be executed by a hyperboloid cross cable net form-finding analysis device, which can be implemented in hardware and / or software and is generally configured in electronic devices.

[0044] Correspondingly, such as Figure 1 As shown, the method includes:

[0045] S110. Based on the current geometric model and current preload of the target cable net in the current iteration, the current static equilibrium result of the target cable net in the current iteration is analyzed using a nonlinear finite element analysis algorithm; wherein, each node in the current geometric model has a preset standard node coordinate.

[0046] Pre-tension refers to the initial tension actively applied to the cables of the cable net structure during the construction tensioning stage. Nonlinear finite element analysis (FEM) is an advanced computer numerical simulation technique that accurately simulates the mechanical behavior of a structure under stress by discretizing a complex continuum structure into a large number of small, simple elements and considering nonlinear factors in materials, geometry, or boundary conditions. Static equilibrium refers to a state obtained through nonlinear finite element analysis. In this state, the resultant force on each node of the cable net structure is zero, and the node acceleration is zero, meaning the entire structure is in a static and stable equilibrium state. Standard node coordinates are the spatial data used to define the geometry of the cable net at the beginning of a specific iteration. They represent the specific positions of all nodes in the cable net in three-dimensional space under the current state. These coordinates are the input conditions for finite element analysis and determine the overall shape of the cable net.

[0047] In this embodiment, an initial cable net shape, i.e., the current geometric model, needs to be established first, and all cable segments are assigned the same design preload. Subsequently, nonlinear finite element theory is used to calculate and analyze this initial state, aiming to determine a preliminary static equilibrium state that the cable net structure can achieve under these geometric and prestressing conditions. The equilibrium result obtained in this step forms the basis for all subsequent evaluations and optimizations.

[0048] Optionally, based on the above embodiments, according to the current geometric model and current preload of the target cable net in the current iteration, a nonlinear finite element analysis algorithm is used to analyze the current static equilibrium result of the target cable net in the current iteration, including:

[0049] Based on the current geometric model of the target cable net, after inputting the basic parameters of the cable net material, the current preload is applied as an initial condition to all cable segments of the target cable net, and boundary constraints are set to complete the establishment of the finite element calculation model.

[0050] The Newton-Raphson iterative method was used to perform iterative calculations on the established finite element calculation model;

[0051] After each iteration, the unbalanced force norm of each node in the target cable net is calculated;

[0052] The unbalanced force norm of each node is compared with the preset convergence tolerance. The iterative calculation process ends when the unbalanced force norm of all nodes is less than the convergence tolerance, and the current static equilibrium result is output.

[0053] Generally, the core of this process is to establish and solve the nonlinear equilibrium equations of the cable net structure. Its physical basis is the static equilibrium of the cable segment intersection nodes in three spatial directions (i.e., i=1,2,3). For any node k, its equilibrium condition can be expressed by the formula:

[0054] , , .

[0055] in, The current computing node number, In terms of spatial coordinate direction, For nodes Connected cable segment numbers, To and Node No. 1 passes through cable segment The number of the other adjacent node connected to it. To converge at the first The total number of cable segments at node number 1 Represented as the first Node No. Spatial coordinates in the direction, In order to be with the first The adjacent nodes of node number are Spatial coordinates in the direction, For the first The current length of the cable segment. For the first The initial preload value applied in the cable segment, For the first The direction cosine of the cable section is in Components in direction, To actively apply in the first Node No. External force in the direction, For the first Node No. The constraint reaction force received in the direction and They are equal. The sum of the internal force vectors of all connected cable segments at a node should be zero. In the numerical solution, let the arbitrary assumed initial state node geometric vectors be... The initial equilibrium state node geometric vector is Then the equilibrium equation can be written in the following form:

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] in, For nodes Under the initial assumed geometry, the coordinate position is... For nodes Under the initial assumed geometry, the coordinate position is... For nodes exist Displacement components in the direction, For nodes exist Displacement components in the direction, For nodes exist Internal forces at the nodes in the direction of The nodal unbalanced forces are calculated under the initial assumed geometry. The equivalent external force. The displacement between the initial equilibrium state nodal geometry and any assumed nodal geometry. As variables, deriving the Newton iteration sequence from the above equation yields:

[0062]

[0063] in, This represents the sequence number of the iteration step. For the set of all degrees of freedom, Here is the tangent stiffness matrix. This is the node displacement increment vector. This is the equivalent nodal external force vector. For the first In the next iteration, the nodal internal force vector caused by the internal forces of the cable segment. For the first After the [number] iterations, the [number]th iteration... The node displacement vector before the start of the next iteration. For the first The node displacement vectors at the start of the next iteration. The geometry of the initial equilibrium state is: Through iterative loops, continuously applying the formula: Update the nodal displacements and correct the structural geometry until the nodal unbalanced forces converge. For the first Tangent stiffness matrix of the next iteration For displacement increment, This is the equivalent nodal external force vector. This represents the internal force vector of the node.

[0064] S120. Based on the current static equilibrium results, obtain the current internal force values ​​of each cable segment and the nodal deformation coordinates of each node in the target cable net, and calculate the current standard deviation and current coefficient of variation that match the internal force distribution of the cable net based on the current internal force values ​​of each cable segment.

[0065] The internal force value of a cable segment refers to the actual tensile force borne by each individual steel cable when the cable net structure is in static equilibrium. Standard deviation is a classic statistical indicator used to measure the dispersion of a set of data. In this scheme, it is used to quantify the average deviation of all cable segment internal force values ​​from their mean. The coefficient of variation is the ratio of the standard deviation to the mean, expressed as a percentage. Its core advantage lies in eliminating the influence of the mean value itself, providing a dimensionless measure of relative dispersion.

[0066] In this embodiment, once the cable net reaches preliminary static equilibrium, key data can be extracted from the calculation results. This data includes the current internal force value borne by each cable segment and the precise position coordinates of each node after equilibrium. Next, based on the internal force values ​​of all cable segments, a performance quantification evaluation is performed, specifically calculating the standard deviation and coefficient of variation of these internal force values. These two statistics are used to measure the absolute and relative dispersion of the prestress within the cable net, respectively, thereby scientifically determining whether the internal force distribution under the current condition is uniform.

[0067] S130. When the current standard deviation or the current coefficient of variation has not converged within the threshold, calculate the sensitivity matrix of the change in node coordinates to the internal force value of the cable segment based on the current internal force value of each cable segment and the deformation coordinate of each node, and solve for the optimal node coordinate adjustment amount of each node based on the sensitivity matrix.

[0068] Among these, the sensitivity matrix is ​​a key mathematical tool that precisely quantifies the interaction between changes in the spatial position of nodes and changes in the internal forces of cable segments in a cable net structure. This matrix establishes a linear mapping model between node displacement and cable force adjustment by systematically analyzing the impact of minute disturbances in the coordinates of each node on the internal forces of all cable segments.

[0069] In this embodiment, if the calculated standard deviation or coefficient of variation indicates that the internal force distribution is not uniform enough, i.e., the preset optimization target has not been achieved, the core optimization algorithm is activated. The key to this algorithm lies in calculating the so-called sensitivity matrix, which uses mathematical methods to precisely analyze how small changes in the coordinates of each node will affect the internal force of each cable segment. Based on this sensitivity matrix and the difference between the current cable force and the target cable force, it is possible to inversely solve for what adjustments need to be made to the spatial position of each node to make the cable force distribution more uniform, thereby obtaining a set of optimal node coordinate adjustment amounts.

[0070] S140. Update the current geometric model based on the adjustment amount of each optimal node coordinate, and update the current pretension using the pretension actually applied in the current finite element analysis process, then start a new iteration cycle.

[0071] In this embodiment, the optimal node coordinate adjustment is applied to the current geometric model, i.e., the spatial coordinates of all nodes are updated, thereby generating a new, optimized cable net shape. Simultaneously, the effective preload value used in the current analysis is updated to the initial value for the next iteration. At this point, the optimization operation for this iteration is complete, and the process is ready to enter the next calculation cycle.

[0072] S150. Return to execution. Based on the current geometric model and current preload of the target cable net in the current iteration, use a nonlinear finite element analysis algorithm to analyze the current static equilibrium result of the target cable net in the current iteration until the current standard deviation and current coefficient of variation converge within the threshold.

[0073] In this embodiment, after updating the geometric model and preload, the process jumps back to the first step, and restarts the series of operations—nonlinear finite element analysis, internal force extraction, and uniformity assessment—based on the new model and parameters. This "analysis-assessment-optimization-update" cycle will be performed automatically and repeatedly until the calculated standard deviation and coefficient of variation, two key indicators, simultaneously meet the preset convergence criteria, meaning that the cable net morphology and internal force distribution have reached an ideal state.

[0074] S160. After the iteration ends, obtain the target geometric model and target static equilibrium results corresponding to the target cable net, so as to carry out the actual cable net construction.

[0075] In this embodiment, the entire form-finding analysis process ends when the iterative loop terminates after satisfying the convergence condition. At this point, the final cable net geometric model (i.e., the final coordinates of all nodes) and the corresponding cable segment internal force distribution results are the final outputs of the entire optimization process. These results constitute the most direct basis for the subsequent construction of the cable net structure, ensuring that the actually constructed structure can accurately achieve the expected shape and mechanical performance of the design.

[0076] Furthermore, based on the above embodiments, after obtaining the target geometric model and target static equilibrium results corresponding to the target cable net, the following may also be included:

[0077] Based on the boundary geometric conditions of the target geometric model of the target cable net, an analysis model of a ring truss with different outer ring beam inclination angles is established.

[0078] In each ring truss analysis model, the target geometric model, the current preload updated at the end of the iteration, and the boundary constraints are kept unchanged to perform a complete structural mechanical performance analysis.

[0079] The influence of the ring truss on the uniformity of the internal force distribution of the cable net under different tilt angles was compared, and the distribution of internal forces in the ring truss members and the overall deformation characteristics of the structure were evaluated.

[0080] The most suitable geometric parameters for the outer ring beam are selected based on the comprehensive optimization objectives of achieving the most uniform internal force distribution of the cable net, the optimal stress state of the ring truss, and the minimum overall deformation.

[0081] Generally, in a defined target cable net geometry model, the spatial coordinates of its boundary points are fixed. Based on the positions of these boundary points, various ring truss analysis models with different outer ring beam inclination angles can be constructed. These different angle schemes cover the reasonable range of values ​​commonly used in engineering.

[0082] Generally, when comparing the mechanical properties of different ring truss schemes, all other conditions must be kept completely consistent to ensure the fairness of the comparison and the reliability of the conclusions. This means that in each ring truss analysis model, the final geometry of the cable net, the preload values ​​of each cable segment determined through form-finding iterations, and the constraint conditions at the boundary points remain unchanged. Based on this uniformity, a complete structural mechanics analysis is performed on each scheme to examine the independent effects of variations in the ring truss parameters.

[0083] Generally, the comparison of analysis results mainly revolves around several key performance indicators. First, it's crucial to observe whether the optimized, uniform distribution of internal forces in the cable net is affected under different outer ring beam angles, and to determine the extent and pattern of such impact. Second, a detailed assessment of the stress state of the ring truss itself is necessary, including whether the distribution of internal forces in each member is uniform and whether stress concentration exists. Simultaneously, the overall deformation characteristics of the structure, especially the magnitude of deformation of the ring truss under the tension of the cable net, is also an important evaluation criterion.

[0084] Generally, the final decision-making process is a multi-objective comprehensive optimization process. The ideal geometric parameters of the outer ring beam need to simultaneously satisfy multiple conditions: it should best maintain the uniformity of the optimized internal force distribution of the cable net; it should ensure the most reasonable stress distribution on the ring truss members, avoiding excessive local stress; and it should effectively control the overall deformation of the structure. By comprehensively comparing and weighing the calculation results of different angle schemes, the geometric parameters of the outer ring beam that can simultaneously and optimally or nearly optimally satisfy these comprehensive requirements can be selected, thus completing the collaborative design of the cable net and the ring truss.

[0085] The technical solution of this invention involves analyzing the current static equilibrium result using a nonlinear finite element analysis algorithm based on the current geometric model and current preload of the target cable net in the current iteration. Based on this result, the current internal force value of each cable segment and the node deformation coordinates of each node are obtained, and the current standard deviation and current coefficient of variation matching the internal force distribution of the cable net are calculated. If the current standard deviation or current coefficient of variation does not converge to a threshold, the sensitivity matrix of node coordinate changes to the cable segment internal force value is calculated based on the current internal force value of the cable segment and the node deformation coordinates, thereby solving for the optimal node coordinate adjustment amount for each node. The current geometric model is updated based on this adjustment amount, and the current preload is updated simultaneously before starting a new iteration. The above analysis, evaluation, and adjustment process is repeated until the current standard deviation and current coefficient of variation both converge to the threshold. Finally, the target geometric model and target static equilibrium result are obtained to guide actual construction. This solution deeply integrates shape creation, internal force distribution uniformity control, and iterative optimization, solving the technical problems of low efficiency, uneven prestress distribution, and disconnection from construction caused by the reliance on experience and trial and error in traditional shape-finding methods. It achieves the beneficial effects of improving design accuracy, ensuring uniform distribution of internal forces in the structure, and realizing efficient collaboration between design and construction.

[0086] Example 2

[0087] Figure 2This is a flowchart of another hyperboloid cross-cable net shape-finding analysis method provided in Embodiment 2 of the present invention. This embodiment is based on the above embodiments and optimized. Specifically, the operation of "calculating the sensitivity matrix of the cable segment internal force value based on the current cable segment internal force value and the deformation coordinate of each node, and solving the optimal node coordinate adjustment amount of each node based on the sensitivity matrix" has been refined.

[0088] Correspondingly, such as Figure 2 As shown, the method includes:

[0089] S210. Based on the current geometric model and current preload of the target cable net in the current iteration, the current static equilibrium result of the target cable net in the current iteration is analyzed using a nonlinear finite element analysis algorithm; wherein, each node in the current geometric model has a preset standard node coordinate.

[0090] S220. Based on the current static equilibrium results, obtain the current internal force values ​​of each cable segment and the nodal deformation coordinates of each node in the target cable net, and calculate the current standard deviation and current coefficient of variation that match the internal force distribution of the cable net based on the current internal force values ​​of each cable segment.

[0091] Optionally, based on the above embodiments, the current standard deviation and current coefficient of variation matching the cable net internal force distribution are calculated according to the current internal force value of each cable segment, including:

[0092] The current internal force values ​​of all cable segments are summed, and the sum is divided by the total number of cable segments in the target cable net to obtain the arithmetic mean of the internal forces of all cable segments.

[0093] Calculate the difference between the internal force value of each current cable segment and the arithmetic mean of the internal forces to obtain the internal force deviation value of each cable segment;

[0094] Squaring all internal force deviations separately and summing the results of each squaring calculation, we obtain the sum of squares of the internal force deviations.

[0095] Subtract one from the total number of cable segments to obtain the standard divisor. Then, calculate the sum of squares of the internal force deviations and divide it by the standard divisor. This result is used as the target variance. Finally, calculate the arithmetic square root of the target variance and use it as the current standard deviation, which characterizes the absolute dispersion of the internal forces of the cable net.

[0096] Calculate the quotient obtained by dividing the current standard deviation by the arithmetic mean of the internal forces, and convert the quotient into the current coefficient of variation in percentage form.

[0097] Generally, in order to perform statistical analysis on the internal force values ​​of all cable segments under the current equilibrium state, it is first necessary to calculate the arithmetic mean of these internal force values. This mean represents the overall level of cable-net prestress and is the basis for all subsequent calculations. The formula for calculating it is the sum of the internal forces of all cable segments divided by the total number of cable segments.

[0098] Generally, after obtaining the average value, the next step is to measure the degree of deviation of the internal force of each cable segment from this average center. This is achieved by calculating the difference between the current internal force value of each cable segment and the arithmetic mean; this difference is called the internal force deviation value. A positive deviation value indicates that the tension in that cable segment is greater than the average level, while a negative value indicates that it is less than the average level. The algebraic sum of all deviation values ​​is zero.

[0099] Generally, to eliminate the canceling effect of positive and negative deviations and highlight the degree of dispersion, it is necessary to square all internal force deviation values. Then, these squared values ​​are summed to obtain the sum of squares of the internal force deviations. This sum of squares reflects the total variation of the internal forces in all cable segments relative to the average value; the larger the value, the more uneven the distribution of internal forces.

[0100] Generally, to obtain a standardized dispersion index, variance needs to be calculated. Variance is the average of the sum of squared deviations, but to obtain an unbiased estimate, when calculating the sample variance, the divisor is the total number of segments minus one, rather than the total number itself. Dividing the sum of squared internal force deviations by this standard divisor yields the target variance. Although variance eliminates the influence of data magnitude, its unit is the square of the original unit, which is not convenient for direct understanding.

[0101] Generally, to obtain a dispersion index consistent with the original internal force values ​​and to facilitate cross-project comparisons, it is necessary to calculate the standard deviation and coefficient of variation. The standard deviation is the arithmetic square root of the variance, and its formula is: ,in Let be the tension of the i-th cable segment. Let N be the average tension across all cable segments, and N be the total number of cable segments. This formula reflects the absolute dispersion of internal forces. The coefficient of variation is the ratio of the standard deviation to the mean, calculated using the following formula: This formula is a dimensionless relative index, eliminating the influence of the absolute value of prestress and allowing for a fair comparison of the uniformity of internal forces in the cable net under different prestress levels. These two indices together constitute a dual standard for judging whether the internal force distribution converges.

[0102] S230. When the current standard deviation or the current coefficient of variation has not converged within the threshold, define the current cable force vector of each cable segment based on the current geometric model and the current internal force value of each cable segment.

[0103] In this embodiment, the optimization process is initiated when the evaluation reveals that the uniformity of internal force distribution does not meet the standard. First, the internal force values ​​of all cable segments in the current iteration need to be systematically organized and combined into a complete mathematical vector. This vector accurately represents the overall stress state of the cable net under the current geometry, providing a clear data foundation for subsequent quantitative comparisons and optimization calculations.

[0104] S240. Subtract the current cable force vector of each cable segment from the preset target cable force vector of each cable segment to obtain the cable force deviation vector of each cable segment.

[0105] In this embodiment, after defining the current internal force state, it needs to be quantitatively compared with the ideal target. This step is achieved by subtracting the corresponding elements of the current cable force vector constructed in the previous step from the pre-set target cable force vector. The result of the subtraction is a new vector, where each component represents the specific deviation between the current internal force of the corresponding cable segment and the target value. This deviation vector clearly indicates the specific location and magnitude that needs to be optimized.

[0106] S250. Decompose the nodal deformation coordinates of each node into the coordinate values ​​of each node in each coordinate degree of freedom, and generate the sensitivity of each node in each coordinate degree of freedom based on the coordinate values ​​of each node in each coordinate degree of freedom and the tension values ​​of each cable segment.

[0107] In this embodiment, in order to find a geometric adjustment method to correct the internal force deviation, it is necessary to analyze the influence of cable net shape changes on internal forces. This analysis is achieved by calculating sensitivity, specifically by decomposing the spatial coordinates of each node into components in different directions, and then using specific mathematical methods (such as the perturbation method) to calculate the change in internal forces of each cable segment when the coordinate components of each node change slightly.

[0108] S260. Based on the sensitivity of each node in each coordinate degree of freedom, form a sensitivity matrix of the internal force value of the cable segment to the change of node coordinates.

[0109] In this embodiment, after calculating the influence coefficients of all nodal coordinate components on the internal forces of all cable segments, these dispersed coefficients are arranged and organized according to specific rules to form a complete sensitivity matrix. This matrix mathematically establishes a linear model that comprehensively describes the global quantitative relationship between minute changes in nodal coordinates and changes in cable segment internal forces. The formula for calculating the sensitivity matrix is: ,in, Let be the tension of the i-th cable segment. Let M be the coordinate component of the j-th node, M be the number of cable segments, and N be the number of degrees of freedom of the node.

[0110] S270. Based on the sensitivity matrix and the cable force deviation vector of each cable segment, construct a system of linear equations with the goal of minimizing the cable force deviation, and calculate the optimal node coordinate adjustment vector of each node that minimizes the L2 norm of the cable force deviation vector.

[0111] In this embodiment, the sensitivity matrix and the cable force deviation vector are combined to construct a system of linear equations aimed at eliminating the deviation. Solving this system of equations yields an optimal set of nodal coordinate adjustments. These adjustments minimize geometric changes and most effectively bring the internal force distribution of the cable segment closer to the preset target state. The formula for calculating the nodal coordinate adjustments is as follows: ,in, The generalized inverse of the sensitivity matrix is... Let the target cable force vector be... This is the current cable force vector.

[0112] S280. Update the current geometric model based on the adjustment amount of each optimal node coordinate, and update the current pretension using the pretension actually applied in the current finite element analysis process, then start a new iteration cycle.

[0113] Optionally, based on the above embodiments, updating the current geometric model according to the adjustment amount of each optimal node coordinate may include:

[0114] The optimal node coordinate adjustment obtained from the solution is added to the standard node coordinates of each node in the current geometric model to obtain the updated standard node coordinates of each node in the target cable net.

[0115] Based on the updated standard node coordinates of each node in the target cable net, a new current geometric model is formed for use in the next iteration.

[0116] Generally, the geometric correction scheme obtained from sensitivity analysis needs to be applied to the cable net model. This process begins with the optimal coordinate adjustment of each node, which has been solved. These adjustment values ​​exist in the form of vectors, indicating the optimal distance and direction that each node needs to move in each direction of space.

[0117] Generally, the specific mathematical operation for updating is vector addition. This involves adding the vector containing the coordinate adjustments for each node to the standard node coordinate vector, which records the spatial positions of each node in the current geometric model, element by element.

[0118] Generally, after updating the coordinates of all nodes, these new coordinate data collectively define a completely new and optimized cable net spatial shape. This new shape is formally established as the current geometric model used in the next iteration. It will replace the old model as the geometric input for the new round of nonlinear finite element static equilibrium analysis. In this way, each iteration moves the geometry of the cable net closer to the ideal state of more uniform internal force distribution, repeating this process until the convergence criterion is met.

[0119] S290. Return to execution. Based on the current geometric model and current preload of the target cable net in the current iteration, use a nonlinear finite element analysis algorithm to analyze the current static equilibrium result of the target cable net in the current iteration until the current standard deviation and current coefficient of variation converge within the threshold.

[0120] S2100. After the iteration ends, obtain the target geometric model and target static equilibrium results corresponding to the target cable net, so as to carry out the actual cable net construction.

[0121] The technical solution of this invention solves the static equilibrium state of the cable net using a nonlinear finite element analysis algorithm based on the geometric model and preload under the current iteration. It then extracts the internal force values ​​and node coordinates of each cable segment, calculates the standard deviation and coefficient of variation of the internal force distribution to assess uniformity. If convergence is not achieved, a sensitivity matrix is ​​formed by constructing the deviation between the current cable force vector and the target vector, combined with node coordinate sensitivity analysis. Based on this matrix and the deviation vector, a system of linear equations is established to solve for the optimal node coordinate adjustment. The geometric model and preload are updated accordingly, and the next iteration begins, repeating until the uniformity index converges. Finally, the optimized cable net geometry and internal force distribution are output. This solution solves the problems of low efficiency, uneven internal force distribution, and disconnect between design and construction caused by the reliance on manual trial and error in traditional shape-finding methods. It achieves precise control of internal force distribution and fully automated optimization, improving design accuracy and efficiency.

[0122] For ease of understanding, the specific application scenarios applicable to each embodiment of the invention are described. In this specific embodiment, in order to solve the problem of hyperboloid cross-cable net shape-finding analysis method, the present invention provides a complete hyperboloid cross-cable net shape-finding analysis scheme.

[0123] Figure 3 A flowchart of a hyperboloid cross cable net form-finding analysis scheme, such as... Figure 3 As shown, the process is an automated iterative loop driven by clear quantitative indicators and consisting of four core steps, which aims to obtain a stable structure with a highly uniform internal force distribution by systematically adjusting the geometry of the cable net.

[0124] Step 1: Nonlinear finite element analysis is the starting point for each iteration. In this step, a cable net geometry model needs to be established or inherited, and a uniform initial preload force needs to be defined for it. For example, for a cable net planned for use in a large-span roof, it can be based on... Figure 4 The diagram shows the cable arrangement along the principal curvature direction. Its projection plane is set as a square of 45.365 meters × 45.365 meters with a grid spacing of 2.97 meters. By raising and lowering two sets of diagonal points by 17.416 meters respectively, a saddle-shaped initial surface with negative Gaussian curvature is formed. Under this setting, the program will calculate the static equilibrium state of the cable net under the existing geometry and prestress (e.g., 10 kN) conditions by solving a set of nonlinear equilibrium equations, and output the corresponding nodal coordinates and cable segment internal forces.

[0125] Step Two: Calculating the dual control indices aims to quantitatively evaluate the equilibrium results of Step One. The program automatically extracts the current internal force values ​​of all cable segments and calculates their standard deviation and coefficient of variation. The standard deviation characterizes the absolute dispersion of internal forces, while the coefficient of variation (in percentage form) eliminates the influence of dimensions and better reflects the relative uniformity of internal forces. These two statistics together constitute the core criteria for evaluating whether the internal force distribution is optimized.

[0126] If the evaluation results show that the standard deviation or coefficient of variation does not reach the preset threshold (e.g., coefficient of variation > 3%), the process proceeds to step three: dynamic adjustment of prestress, which is the key to the optimization of this scheme. This step first performs sensitivity matrix calculation to establish the quantitative impact of small changes in node coordinates on the internal forces of each cable segment. Then, based on this matrix and the deviation between the current cable force and the target cable force (usually the design preload), the optimal geometric adjustment amount that makes the cable force distribution most effectively approach the target is solved through prestress redistribution logic and node coordinate correction calculation.

[0127] The next step is step four: updating the state. This step applies the optimal node coordinate adjustment obtained in step three to the current model, updating the node coordinates and generating a new, optimized cable net geometry. Simultaneously, the program updates calculation parameters such as the stiffness matrix based on the new geometric state, preparing for the next iteration.

[0128] After completing the above four steps, the process does not end but enters the convergence judgment stage. This is a strict decision point: the system will use the updated model as the starting point to re-perform the nonlinear finite element analysis of step one and calculate the new control indicators. The iteration is considered complete only when the standard deviation and coefficient of variation calculated using the new input results are both lower than the preset convergence threshold. As shown in the figure, if the judgment is "no", it returns to step two to continue the iterative optimization; if the judgment is "yes", the process terminates and outputs the final shape and internal forces. For example, in a certain engineering case, after about 200 such iterations, the internal forces of the cable net are finally concentrated uniformly in the range of 9.95-10.05 kN, the standard deviation is reduced to 0.28 kN, and the coefficient of variation is only 2.8%. At this point, the accurate geometry and internal force distribution output constitute the final basis for guiding construction. The structural diagrams under the "yes" and "no" branches in the flowchart visually compare the intermediate shape in the iteration process with the final optimized stable shape.

[0129] Example 3

[0130] Figure 5 This is a flowchart of a modular ring truss structure construction method provided in Embodiment 3 of the present invention. This embodiment can be applied to the modular collaborative construction of complex curved cable nets and ring trusses in large-span spatial structures.

[0131] Correspondingly, such as Figure 5 As shown, the method includes:

[0132] S310. Set high-precision positioning reference points on the embedded parts of the cable net foundation, hoist the reference modular units located in key positions, monitor and adjust the spatial coordinates of the modules in real time through measuring instruments, and use the node attitude adjustment mechanism to accurately fix them to the design position to form the reference frame for the assembly of the ring truss.

[0133] In this embodiment, the benchmark establishment phase of modular construction first involves setting high-precision positioning points on the embedded parts of the cable net foundation to provide spatial coordinate references for the entire ring truss. Benchmark modular units located at key positions such as corners are hoisted, and the three-dimensional coordinates of the module nodes are tracked in real time using precision measuring instruments such as total stations. Fine adjustments are made using the node's built-in attitude adjustment mechanism, ultimately fixing it precisely in the designed position. These benchmark units collectively constitute the benchmark framework for subsequent ring truss assembly operations, and their accuracy directly determines the overall installation quality.

[0134] S320. Based on the reference frame, the remaining modular units are hoisted in sequence according to a predetermined order. After each unit is in place, the initial locking and temporary fixing of the node connection are completed immediately, and the internal force status of the module is monitored in real time through the integrated sensing system.

[0135] In this embodiment, the main body expansion assembly process of the ring truss uses the already installed reference frame as a spatial support. Following a predetermined sequence from the corners to the center and from bottom to top, the remaining straight segments and corner modular units are hoisted sequentially. After each unit is hoisted into place, its connection nodes are immediately hydraulically locked or temporarily fixed with bolts to ensure stability. Simultaneously, strain sensors embedded in the modules monitor changes in the internal forces of the members in real time during assembly, ensuring that the internal forces are under control and avoiding excessive installation stress.

[0136] After the initial assembly of all modules of S330 and the ring truss is completed, the cable net prestressing tensioning operation is started. Based on the real-time monitoring of the internal forces of the cable net and the deformation data of the ring truss, the spatial position of the ring truss modules is dynamically fine-tuned.

[0137] In this embodiment, the prestressing tensioning of the cable net is initiated simultaneously when all modules of the ring truss are assembled (but the nodes have not yet been finally grouted and cured). During the tensioning process, the distribution of internal forces in the cable net and the deformation data of key nodes of the ring truss are monitored in real time. Based on this feedback data, the spatial position of the ring truss modules is dynamically adjusted through the micro-adjustment mechanism of the nodes, so that the uniformity of internal forces in the cable net and the deformation control target of the ring truss are achieved in synergy.

[0138] S340. After the cable net tensioning is completed and the design equilibrium state is reached, all nodes of the ring truss are finally grouted and solidified to form a permanent rigid connection. The overall shape data of the ring truss is obtained through three-dimensional scanning technology, compared and verified with the design target shape, and the deviation parts are corrected to ensure that the final shape of the ring truss is highly consistent with the boundary of the cable net.

[0139] In this embodiment, the final verification work of the construction is carried out after the cable net tensioning is completed and reaches the design equilibrium state. Pressure grouting is performed on the grouting cavities of all ring truss nodes to form a permanent rigid connection between the modules. Subsequently, the as-built point cloud data of the ring truss is acquired by a 3D laser scanning device mounted on a UAV and compared with the target shape obtained from the form-finding analysis. Any parts that exceed the allowable deviation are finally corrected by the node fine-tuning mechanism to ensure that the final shape of the ring truss is highly consistent with the boundary of the cable net.

[0140] The technical solution of this invention involves setting high-precision positioning reference points on the pre-embedded parts of the cable net foundation, hoisting reference modular units at key positions, and using measuring instruments to monitor and adjust the module coordinates in real time. A node attitude adjustment mechanism is then used to precisely fix the modules to form an assembly reference frame. Based on this frame, the remaining modular units are hoisted sequentially, and initial node locking and temporary fixing are completed immediately after placement. Simultaneously, an integrated sensing system monitors the internal force state of the modules in real time. After the initial assembly of all ring truss modules is completed, the cable net prestressing tensioning operation is initiated. Based on the real-time monitored cable net internal force and ring truss deformation data, the spatial position of the ring truss modules is dynamically fine-tuned. After the cable net tensioning reaches the design equilibrium state, the ring truss nodes are finally grouted and solidified to form a permanent connection. Three-dimensional scanning technology is used to obtain overall morphological data, which is compared with the design target to verify and correct deviations, ensuring that the ring truss shape and cable net boundary are highly aligned. This solves the problems of disconnection between the cable net and ring truss assembly, low efficiency, and insufficient morphological control precision in traditional construction, achieving beneficial effects such as improved construction coordination, guaranteed structural morphological accuracy, and uniform internal force distribution.

[0141] Example 4

[0142] Figure 6 This is a schematic diagram of a hyperboloid cross-cable net shape-finding analysis device provided in Embodiment 4 of the present invention. Figure 6 As shown, the device includes:

[0143] The iterative initialization module 610 is used to analyze the current static equilibrium result of the target cable net in the current iteration cycle based on the current geometric model and current preload of the target cable net in the current iteration cycle using a nonlinear finite element analysis algorithm; wherein, each node in the current geometric model has preset standard node coordinates;

[0144] The standard deviation and coefficient of variation calculation module 620 is used to obtain the current internal force value of each cable segment and the nodal deformation coordinate of each node in the target cable net based on the current static equilibrium result, and to calculate the current standard deviation and current coefficient of variation that match the internal force distribution of the cable net based on the current internal force value of each cable segment.

[0145] The adjustment calculation module 630 is used to calculate the sensitivity matrix of the change of node coordinates to the internal force value of the cable segment based on the current internal force value of each cable segment and the deformation coordinate of each node when the current standard deviation or the current coefficient of variation has not converged within the threshold. The module then solves for the optimal node coordinate adjustment of each node based on the sensitivity matrix.

[0146] The model update module 640 is used to update the current geometric model based on the adjustment amount of each optimal node coordinate, and after updating the current pretension with the pretension actually applied in the current finite element analysis process, a new iteration cycle is started.

[0147] The convergence judgment module 650 is used to return the operation of performing the current static equilibrium result of the target cable net in the current iteration round by using a nonlinear finite element analysis algorithm based on the current geometric model and current pretension of the target cable net in the current iteration round, until the current standard deviation and current coefficient of variation converge within the threshold.

[0148] The result output module 660 is used to obtain the target geometric model and target static equilibrium results corresponding to the target cable net after the iteration ends, so as to carry out the actual cable net construction.

[0149] The technical solution of this invention involves analyzing the current static equilibrium result using a nonlinear finite element analysis algorithm based on the current geometric model and current preload of the target cable net in the current iteration. Based on this result, the current internal force value of each cable segment and the node deformation coordinates of each node are obtained, and the current standard deviation and current coefficient of variation matching the internal force distribution of the cable net are calculated. If the current standard deviation or current coefficient of variation does not converge to a threshold, the sensitivity matrix of node coordinate changes to the cable segment internal force value is calculated based on the current internal force value of the cable segment and the node deformation coordinates, thereby solving for the optimal node coordinate adjustment amount for each node. The current geometric model is updated based on this adjustment amount, and the current preload is updated simultaneously before starting a new iteration. The above analysis, evaluation, and adjustment process is repeated until the current standard deviation and current coefficient of variation both converge to the threshold. Finally, the target geometric model and target static equilibrium result are obtained to guide actual construction. This solution deeply integrates shape creation, internal force distribution uniformity control, and iterative optimization, solving the technical problems of low efficiency, uneven prestress distribution, and disconnection from construction caused by the reliance on experience and trial and error in traditional shape-finding methods. It achieves the beneficial effects of improving design accuracy, ensuring uniform distribution of internal forces in the structure, and realizing efficient collaboration between design and construction.

[0150] Based on the above embodiments, the iterative initialization module 610 is specifically used for:

[0151] Based on the current geometric model of the target cable net, after inputting the basic parameters of the cable net material, the current preload is applied as an initial condition to all cable segments of the target cable net, and boundary constraints are set to complete the establishment of the finite element calculation model.

[0152] The Newton-Raphson iterative method was used to perform iterative calculations on the established finite element calculation model;

[0153] After each iteration, the unbalanced force norm of each node in the target cable net is calculated;

[0154] The unbalanced force norm of each node is compared with the preset convergence tolerance. The iterative calculation process ends when the unbalanced force norm of all nodes is less than the convergence tolerance, and the current static equilibrium result is output.

[0155] Based on the above embodiments, the standard deviation and coefficient of variation calculation module 620 is specifically used for:

[0156] The current internal force values ​​of all cable segments are summed, and the sum is divided by the total number of cable segments in the target cable net to obtain the arithmetic mean of the internal forces of all cable segments.

[0157] Calculate the difference between the internal force value of each current cable segment and the arithmetic mean of the internal forces to obtain the internal force deviation value of each cable segment;

[0158] Squaring all internal force deviations separately and summing the results of each squaring calculation, we obtain the sum of squares of the internal force deviations.

[0159] Subtract one from the total number of cable segments to obtain the standard divisor. Then, calculate the sum of squares of the internal force deviations and divide it by the standard divisor. This result is used as the target variance. Finally, calculate the arithmetic square root of the target variance and use it as the current standard deviation, which characterizes the absolute dispersion of the internal forces of the cable net.

[0160] Calculate the quotient obtained by dividing the current standard deviation by the arithmetic mean of the internal forces, and convert the quotient into the current coefficient of variation in percentage form.

[0161] Based on the above embodiments, the quantity calculation module 630 is adjusted to specifically be used for:

[0162] Based on the current geometric model and the current internal force values ​​of each cable segment, define the current cable force vector of each cable segment;

[0163] Subtract the current cable force vector of each cable segment from the preset target cable force vector of each cable segment to obtain the cable force deviation vector of each cable segment.

[0164] The nodal deformation coordinates of each node are decomposed into the coordinate values ​​of each node in each degree of freedom, and the sensitivity of each node in each degree of freedom is generated based on the coordinate values ​​of each node in each degree of freedom and the tension values ​​of each cable segment.

[0165] Based on the sensitivity of each node in each coordinate degree of freedom, a sensitivity matrix is ​​formed to the internal force value of the cable segment caused by the change of node coordinates.

[0166] Based on the sensitivity matrix and the cable force deviation vector of each cable segment, a system of linear equations is constructed with the goal of minimizing the cable force deviation, and the optimal node coordinate adjustment vector of each node that minimizes the L2 norm of the cable force deviation vector is calculated.

[0167] Based on the above embodiments, the model update module 640 is specifically used for:

[0168] The optimal node coordinate adjustment obtained from the solution is added to the standard node coordinates of each node in the current geometric model to obtain the updated standard node coordinates of each node in the target cable net.

[0169] Based on the updated standard node coordinates of each node in the target cable net, a new current geometric model is formed for use in the next iteration.

[0170] Furthermore, based on the above embodiments, a hyperboloid cross cable net shape-finding analysis device may further include:

[0171] A ring truss analysis module is established to establish ring truss analysis models with different outer ring beam inclination angles based on the boundary geometric conditions of the target geometric model of the target cable net after obtaining the target geometric model and target static equilibrium results corresponding to the target cable net.

[0172] The mechanical analysis module is used to perform a complete structural mechanical performance analysis in each ring truss analysis model while keeping the target geometric model, the current preload updated at the end of the iteration, and the boundary constraints unchanged.

[0173] The comparison module is used to compare the influence of the ring truss on the uniformity of the internal force distribution of the cable net under different tilt angles, and at the same time evaluate the distribution of the internal forces of the ring truss members and the overall deformation characteristics of the structure.

[0174] The optimal module is selected to determine the most suitable geometric parameters of the outer ring beam, with the comprehensive optimization objectives of achieving the most uniform internal force distribution of the cable net, the optimal stress state of the ring truss, and the minimum overall deformation.

[0175] The hyperboloid cross cable net form-finding analysis device provided in the embodiments of the present invention can execute the hyperboloid cross cable net form-finding analysis method provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the execution method.

[0176] The collection, storage, use, processing, transmission, provision, and disclosure of user personal information involved in the technical solution disclosed herein comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0177] Example 5

[0178] Figure 7A schematic diagram of an electronic device 10, which can be used to implement embodiments of the present invention, is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices (e.g., helmets, glasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein.

[0179] like Figure 7 As shown, the electronic device 10 includes at least one processor 11 and a memory, such as a read-only memory (ROM) 12 or a random access memory (RAM) 13, communicatively connected to the at least one processor 11. The memory stores computer programs executable by the at least one processor. The processor 11 can perform various appropriate actions and processes based on the computer program stored in the ROM 12 or loaded from storage unit 18 into the RAM 13. The RAM 13 can also store various programs and data required for the operation of the electronic device 10. The processor 11, ROM 12, and RAM 13 are interconnected via a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.

[0180] Multiple components in electronic device 10 are connected to I / O interface 15, including: input unit 16, such as keyboard, mouse, etc.; output unit 17, such as various types of displays, speakers, etc.; storage unit 18, such as disk, optical disk, etc.; and communication unit 19, such as network card, modem, wireless transceiver, etc. Communication unit 19 allows electronic device 10 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0181] Processor 11 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of processor 11 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. Processor 11 performs the various methods and processes described above, such as a hyperboloid cross-cable net shape-finding analysis method, namely:

[0182] Based on the current geometric model and preload of the target cable net in the current iteration, a nonlinear finite element analysis algorithm is used to analyze the current static equilibrium result of the target cable net in the current iteration; wherein, each node in the current geometric model has a preset standard node coordinate.

[0183] Based on the current static equilibrium results, obtain the current internal force values ​​of each cable segment and the nodal deformation coordinates of each node in the target cable net, and calculate the current standard deviation and current coefficient of variation that match the internal force distribution of the cable net based on the current internal force values ​​of each cable segment.

[0184] When the current standard deviation or the current coefficient of variation has not converged within the threshold, the sensitivity matrix of the change of node coordinates to the internal force value of the cable segment is calculated based on the current internal force value of each cable segment and the deformation coordinate of each node, and the optimal node coordinate adjustment amount of each node is solved based on the sensitivity matrix.

[0185] The current geometric model is updated based on the adjustment of the coordinates of each optimal node, and the current pretension is updated using the pretension actually applied in the current finite element analysis process. Then, a new iteration cycle is started.

[0186] Return to the operation of analyzing the current static equilibrium result of the target cable net in the current iteration round using a nonlinear finite element analysis algorithm based on the current geometric model and current pretension of the target cable net in the current iteration round, until the current standard deviation and current coefficient of variation converge within the threshold.

[0187] After the iteration ends, the target geometric model and target static equilibrium results corresponding to the target cable net are obtained for actual cable net construction.

[0188] Alternatively, for example, a modular ring truss structure construction method, namely:

[0189] High-precision positioning reference points are set on the embedded parts of the cable net foundation, and the reference modular units located in key positions are hoisted. The spatial coordinates of the modules are monitored and adjusted in real time by measuring instruments, and the node attitude adjustment mechanism is used to accurately fix them to the design position to form the reference frame for the assembly of the ring truss.

[0190] Based on the aforementioned reference frame, the remaining modular units are hoisted sequentially in a predetermined order. After each unit is in place, the initial locking and temporary fixing of the node connections are immediately completed, and the internal force status of the module is monitored in real time through an integrated sensing system.

[0191] After the initial assembly of all modules of the ring truss is completed, the cable net prestressing tensioning operation is started. Based on the real-time monitoring of the internal force of the cable net and the deformation data of the ring truss, the spatial position of the ring truss modules is dynamically fine-tuned.

[0192] After the cable net is tensioned and reaches the design equilibrium state, all nodes of the ring truss are finally grouted and solidified to form a permanent rigid connection. The overall shape data of the ring truss is obtained by 3D scanning technology, compared and verified with the design target shape, and the deviation is corrected to ensure that the final shape of the ring truss fits the boundary of the cable net closely.

[0193] In some embodiments, a method for form-finding analysis of hyperboloid cross-cable nets and construction of a modular ring truss structure can be implemented as a computer program tangibly contained in a computer-readable storage medium, such as storage unit 18. In some embodiments, part or all of the computer program can be loaded and / or installed on electronic device 10 via ROM 12 and / or communication unit 19. When the computer program is loaded into RAM 13 and executed by processor 11, one or more steps of the method for form-finding analysis of hyperboloid cross-cable nets and construction of a modular ring truss structure described above can be performed. Alternatively, in other embodiments, processor 11 can be configured by any other suitable means (e.g., by means of firmware) to perform a method for form-finding analysis of hyperboloid cross-cable nets and construction of a modular ring truss structure.

[0194] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0195] Computer programs used to implement the methods of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor, the computer programs cause the functions / operations specified in the flowcharts and / or block diagrams to be performed. The computer programs may be executed entirely on a machine, partially on a machine, or as a standalone software package, partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0196] In the context of this invention, a computer-readable storage medium can be a tangible medium that may contain or store a computer program for use by or in conjunction with an instruction execution system, apparatus, or device. A computer-readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination thereof. Alternatively, a computer-readable storage medium may be a machine-readable signal medium. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0197] To provide interaction with a user, the systems and techniques described herein can be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the electronic device. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0198] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or middleware components (e.g., application servers), or frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include local area networks (LANs), wide area networks (WANs), blockchain networks, and the Internet.

[0199] A computing system can include clients and servers. Clients and servers are generally located far apart and typically interact through communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. The server can be a cloud server, also known as a cloud computing server or cloud host, which is a hosting product within the cloud computing service system to address the shortcomings of traditional physical hosts and VPS services, such as high management difficulty and weak business scalability.

[0200] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and no limitation is imposed herein.

[0201] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for shape-finding analysis of hyperboloid intersecting cable nets, characterized in that, The method includes: Based on the current geometric model and preload of the target cable net in the current iteration, a nonlinear finite element analysis algorithm is used to analyze the current static equilibrium result of the target cable net in the current iteration; wherein, each node in the current geometric model has a preset standard node coordinate. Based on the current static equilibrium results, obtain the current internal force values ​​of each cable segment and the nodal deformation coordinates of each node in the target cable net, and calculate the current standard deviation and current coefficient of variation that match the internal force distribution of the cable net based on the current internal force values ​​of each cable segment. When the current standard deviation or the current coefficient of variation has not converged within the threshold, the sensitivity matrix of the change of node coordinates to the internal force value of the cable segment is calculated based on the current internal force value of each cable segment and the deformation coordinate of each node, and the optimal node coordinate adjustment amount of each node is solved based on the sensitivity matrix. The current geometric model is updated based on the adjustment of the coordinates of each optimal node, and the current pretension is updated using the pretension actually applied in the current finite element analysis process. Then, a new iteration cycle is started. Return to the operation of analyzing the current static equilibrium result of the target cable net in the current iteration round using a nonlinear finite element analysis algorithm based on the current geometric model and current pretension of the target cable net in the current iteration round, until the current standard deviation and current coefficient of variation converge within the threshold. After the iteration ends, the target geometric model and target static equilibrium results corresponding to the target cable net are obtained for actual cable net construction.

2. The method according to claim 1, characterized in that, Based on the current geometric model and preload of the target cable net in the current iteration, a nonlinear finite element analysis algorithm is used to analyze the current static equilibrium results of the target cable net in the current iteration, including: Based on the current geometric model of the target cable net, after inputting the basic parameters of the cable net material, the current preload is applied as an initial condition to all cable segments of the target cable net, and boundary constraints are set to complete the establishment of the finite element calculation model. The Newton-Raphson iterative method was used to perform iterative calculations on the established finite element calculation model; After each iteration, the unbalanced force norm of each node in the target cable net is calculated; The unbalanced force norm of each node is compared with the preset convergence tolerance. The iterative calculation process ends when the unbalanced force norm of all nodes is less than the convergence tolerance, and the current static equilibrium result is output.

3. The method according to claim 1, characterized in that, Based on the current internal force values ​​of each cable segment, calculate the current standard deviation and current coefficient of variation that match the internal force distribution of the cable net, including: The current internal force values ​​of all cable segments are summed, and the sum is divided by the total number of cable segments in the target cable net to obtain the arithmetic mean of the internal forces of all cable segments. Calculate the difference between the internal force value of each current cable segment and the arithmetic mean of the internal forces to obtain the internal force deviation value of each cable segment; Squaring all internal force deviations separately and summing the results of each squaring calculation, we obtain the sum of squares of the internal force deviations. Subtract one from the total number of cable segments to obtain the standard divisor. Then, calculate the sum of squares of the internal force deviations and divide it by the standard divisor. This result is used as the target variance. Finally, calculate the arithmetic square root of the target variance and use it as the current standard deviation, which characterizes the absolute dispersion of the internal forces of the cable net. Calculate the quotient obtained by dividing the current standard deviation by the arithmetic mean of the internal forces, and convert the quotient into the current coefficient of variation in percentage form.

4. The method according to claim 1, characterized in that, Based on the current internal force values ​​of each cable segment and the deformation coordinates of each node, calculate the sensitivity matrix of the cable segment internal force values ​​to changes in node coordinates, and solve for the optimal node coordinate adjustment for each node based on the sensitivity matrix, including: Based on the current geometric model and the current internal force values ​​of each cable segment, define the current cable force vector of each cable segment; Subtract the current cable force vector of each cable segment from the preset target cable force vector of each cable segment to obtain the cable force deviation vector of each cable segment. The nodal deformation coordinates of each node are decomposed into the coordinate values ​​of each node in each degree of freedom, and the sensitivity of each node in each degree of freedom is generated based on the coordinate values ​​of each node in each degree of freedom and the tension values ​​of each cable segment. Based on the sensitivity of each node in each coordinate degree of freedom, a sensitivity matrix is ​​formed to the internal force value of the cable segment caused by the change of node coordinates. Based on the sensitivity matrix and the cable force deviation vector of each cable segment, a system of linear equations is constructed with the goal of minimizing the cable force deviation, and the optimal node coordinate adjustment vector of each node that minimizes the L2 norm of the cable force deviation vector is calculated.

5. The method according to claim 1, characterized in that, Update the current geometric model based on the adjustment of the optimal node coordinates, including: The optimal node coordinate adjustment obtained from the solution is added to the standard node coordinates of each node in the current geometric model to obtain the updated standard node coordinates of each node in the target cable net. Based on the updated standard node coordinates of each node in the target cable net, a new current geometric model is formed for use in the next iteration.

6. The method according to claim 1, characterized in that, After obtaining the target geometric model and target static equilibrium results corresponding to the target cable net, the following is also included: Based on the boundary geometric conditions of the target geometric model of the target cable net, an analysis model of a ring truss with different outer ring beam inclination angles is established. In each ring truss analysis model, the target geometric model, the current preload updated at the end of the iteration, and the boundary constraints are kept unchanged to perform a complete structural mechanical performance analysis. The influence of the ring truss on the uniformity of the internal force distribution of the cable net under different tilt angles was compared, and the distribution of internal forces in the ring truss members and the overall deformation characteristics of the structure were evaluated. The most suitable geometric parameters for the outer ring beam are selected based on the comprehensive optimization objectives of achieving the most uniform internal force distribution of the cable net, the optimal stress state of the ring truss, and the minimum overall deformation.

7. An electronic device, characterized in that, The electronic device includes: At least one processor; and a memory communicatively connected to said at least one processor; wherein, The memory stores a computer program that can be executed by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform the hyperboloid cross cable net shape-finding analysis method according to any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause a processor to execute the hyperboloid cross-cable net shape-finding analysis method according to any one of claims 1-6.

9. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the hyperboloid cross cable net shape-finding analysis method according to any one of claims 1-6.

10. A method for constructing a modular ring truss structure, characterized in that, The method includes: High-precision positioning reference points are set on the embedded parts of the cable net foundation, and the reference modular units located in key positions are hoisted. The spatial coordinates of the modules are monitored and adjusted in real time by measuring instruments, and the node attitude adjustment mechanism is used to accurately fix them to the design position to form the reference frame for the assembly of the ring truss. Based on the aforementioned reference frame, the remaining modular units are hoisted sequentially in a predetermined order. After each unit is in place, the initial locking and temporary fixing of the node connections are immediately completed, and the internal force status of the module is monitored in real time through an integrated sensing system. After the initial assembly of all modules of the ring truss is completed, the cable net prestressing tensioning operation is started. Based on the real-time monitoring of the internal force of the cable net and the deformation data of the ring truss, the spatial position of the ring truss modules is dynamically fine-tuned. After the cable net is tensioned and reaches the design equilibrium state, all nodes of the ring truss are finally grouted and solidified to form a permanent rigid connection. The overall shape data of the ring truss is obtained by 3D scanning technology, compared and verified with the design target shape, and the deviation is corrected to ensure that the final shape of the ring truss fits the boundary of the cable net closely.

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