A step-by-step form-finding method and system for a spatial cable-suspended system

Abstract

This invention relates to the fields of marine new energy engineering and civil engineering technology, specifically to a step-by-step form-finding method and system for a space wind cable system. The method includes: Step S1: Obtaining condition parameters based on the space wind cable system and projecting the space wind cable system onto a horizontal plane, constructing a segmented straight rod force model in the horizontal plane based on the condition parameters; Step S2: Performing static equilibrium analysis on the segmented straight rod force model according to the unknown parameters set for the space wind cable system, establishing a nonlinear equation system; Step S3: Determining the initial values ​​of the iterative equation system of the segmented straight rod using the initial value construction method of the iterative equation system of the segmented straight rod, obtaining the unknown parameters of the space wind cable system in the horizontal plane; Step S4: Defining the unknown parameters as known conditions, introducing the segmented catenary theory, and using the single-segment catenary iterative initial value construction method to obtain the remaining unknown parameters in the space wind cable system. By solving step by step, the risk of solution divergence caused by equation coupling in traditional methods can be effectively avoided.

Description

Technical Field

[0001] This invention relates to the fields of marine new energy engineering and civil engineering technology, specifically to a step-by-step form-finding method and system for a space wind cable system. Background Technology

[0002] Space-based wind cable systems are widely used in flexible structures sensitive to wind-induced vibrations, such as long-span pedestrian suspension bridges and long-span flexible photovoltaic supports, due to their ability to significantly improve the overall stiffness and wind resistance of structures. However, the spatial arrangement characteristics of wind cable systems result in complex stress behavior, posing challenges to the design, analysis, and construction control of the structures.

[0003] Form-finding analysis of space cable systems is a key issue in the design and construction of such structures. Currently, commonly used form-finding analysis methods mainly include the finite element method (FEM) and the piecewise catenary method. For example, patent application CN202010406229.0 proposes a finite element-based form-finding method for space cables in suspension bridges. This method has good convergence stability and strong applicability, making it easy for engineers to use; however, the FEM method typically suffers from low computational accuracy and inefficiency. In contrast, the piecewise catenary method offers advantages in high computational accuracy and efficiency. Existing space cable form-finding methods based on piecewise catenary theory usually simplify the complex space cable system into a three-variable nonlinear equation system for solution. Although this type of method can theoretically achieve high-precision form-finding, its difficulty lies in providing reasonable initial values ​​for the three unknowns. Furthermore, selecting these initial values ​​is challenging, requiring a high level of experience from designers. Inappropriate initial values ​​can easily lead to divergent iterative calculations and solution failures, thus limiting its widespread application in engineering practice. Summary of the Invention

[0004] To address the technical problems of initial value sensitivity and convergence difficulties in the form-finding of space wind cable systems in existing technologies, the present invention aims to provide a step-by-step form-finding method for space wind cable systems. The specific technical solution adopted is as follows: Step S1: Obtain the condition parameters based on the space wind cable system, project the space wind cable system onto the horizontal plane, and construct a segmented straight rod force model in the horizontal plane based on the condition parameters; Step S2: Based on the unknown parameters set for the space wind cable system, perform static equilibrium analysis on the segmented straight rod force model and establish a set of nonlinear equations; Step S3: Use the piecewise straight rod iterative equation system initial value construction method to determine the iterative initial value of the nonlinear equation system and obtain the unknown parameters of the space wind cable system in the horizontal plane; Step S4: Define the unknown parameters as known conditions, introduce the segmented catenary theory, and use the single-segment catenary iterative initial value construction method to obtain the remaining unknown parameters in the space wind cable system.

[0005] Preferably, in step S1, the condition parameters include, but are not limited to, the elastic modulus, cross-sectional area, and material density of the main cable and the suspender; the position of the anchor point, the horizontal position of the suspending point, and the vertical position of the control point in the main cable; the position of the suspending point in the suspender and the design value of the vertical force component of the suspender force at the suspending point.

[0006] Preferably, step S2 includes: Step S21: Set unknown parameters, including the vertical position of the suspension point in the main cable, the horizontal force component at the anchor point in the main cable, and the horizontal force component of the suspender at the suspension point; Step S22: Perform static equilibrium analysis on the segmented straight bar force model based on unknown parameters, establish force equilibrium equations with the same number of unknown parameters, and integrate them to construct a nonlinear equation set.

[0007] Preferably, step S22 specifically includes: Force balance analysis was performed on the suspenders on both sides of the suspension point, and force balance analysis was performed on the cable segment in the horizontal and vertical directions. The corresponding force balance equations were established and the nonlinear equations were obtained by combining them.

[0008] Preferably, step S3 includes: Step S31: Determine that the initial values ​​of the force balance equations in the nonlinear equation system are equal, and determine the horizontal force components of the cable segment; Step S32: Obtain the vertical position of the suspension point in the main cable based on the parabola, and combine it with the force component along the horizontal direction at the anchor point in the main cable to obtain the unknown parameters of the space wind cable system in the horizontal plane.

[0009] Preferably, step S4 includes: Step S41: Define the unknown parameters as known conditions, introduce the piecewise catenary theory, and simplify the spatial cable form-finding analysis problem into a univariate nonlinear equation system solution problem with the vertical force of the cable segment at the anchor point of the wind cable as the unknown parameter; Step S42: Use the single-segment catenary iterative initial value construction method to determine the iterative initial value of the univariate nonlinear equation system, and iteratively solve the vertical force of the cable segment at the anchorage point of the wind cable; Step S43: Determine the remaining unknown parameters in the space wind cable system based on the vertical force of the cable segment at the anchor point of the wind cable.

[0010] Preferably, step S41 includes: Step S411: Set the vertical force of the cable segment at the anchor point of the wind cable as an unknown parameter; Step S412: Based on the segmented catenary theory, starting from the initial anchor point, the vertical position of the suspension point in the main cable is obtained segment by segment by combining the known conditions, and the vertical position of the terminal anchor point is obtained. Step S413: Establish a set of univariate nonlinear equations about the vertical force of the cable segment at the anchor point of the wind cable based on the vertical position of the terminal anchor point.

[0011] Preferably, step S42 includes: Step S421: Simplify the space cable system into a single catenary in the vertical plane, with both ends anchored to the anchor point in the main cable and the suspension point in the suspender, respectively; Step S422: Apply tension along the vertical direction of the wind cable suspender rod to the suspension point in the simplified catenary suspender rod in the form of a concentrated force; Step S423: Combine the known conditions to obtain the total weight of the space wind cable system and distribute it evenly across the horizontal span to determine the equivalent linear density of the simplified catenary; Step S424: Using the equivalent linear density and the piecewise catenary theory, the vertical force of the cable segment at the anchor point of the wind cable is obtained and defined as the initial value of the iterative system of the univariate nonlinear equations.

[0012] To address the problems of the prior art, the present invention also provides: a step-by-step form-finding system for a space wind cable system, the system comprising: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus, and the processor calls logical instructions in the memory to execute the step-by-step form-finding method for a space wind cable system described in any of the preceding claims.

[0013] The present invention has the following beneficial effects: 1. A step-by-step form-finding method for space wind cable systems based on offshore photovoltaic structures is proposed. This method transforms the traditional solution of a strongly coupled ternary nonlinear equation system into a solution where a segmented straight-bar model is first used for force equilibrium analysis in the horizontal plane to solve for relevant parameters. These parameters are then used as known conditions to solve for the remaining unknown parameters. The nonlinear equation system is established based solely on the force equilibrium of two-force members, avoiding the convergence difficulties caused by highly nonlinear catenary theory and exhibiting strong convergence. The solution for the remaining unknown parameters is based on the obtained unknown parameters as known conditions, reducing the problem's order and improving computational stability. This step-by-step solution effectively avoids the risk of solution divergence caused by equation coupling in traditional methods, improving overall solvability and engineering robustness at the algorithmic level. In addition, an initial value construction method for the iterative equation system of piecewise straight rods and an iterative initial value construction method for single-segment catenary are proposed. In the corresponding two stages, an initial value construction strategy with clear physical meaning and direct calculation can be given, which effectively reduces the dependence on empirical initial values, reduces the amount of manual trial and error, and significantly improves the success rate and repeatability of the solution.

[0014] 2. The step-by-step shape-finding system for a space wind cable system provided by this invention has the same beneficial effects as the step-by-step shape-finding method for a space wind cable system provided by this invention, and will not be described in detail here. Attached Figure Description

[0015] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the 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.

[0016] Figure 1 A flowchart illustrating the steps of a step-by-step form-finding method for a space wind cable system according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the structure of a space wind cable system according to a step-by-step form-finding method for a space wind cable system provided in an embodiment of the present invention; Figure 3 This is a structural schematic diagram of a segmented straight rod force model for a step-by-step form-finding method for a space wind cable system according to an embodiment of the present invention. Figure 4 This is a schematic diagram of the force balance analysis of a segmented straight rod force model in a step-by-step form-finding method for a space wind cable system according to an embodiment of the present invention, wherein... Figure 4 The sub-diagram 'a' represents the force balance analysis of the suspension point in the boom; Figure 4 The b-sub-diagram represents the force balance analysis in the x-direction of a portion of the main cable segment; Figure 4 The c-subgraph represents the force balance analysis of the control point in the main cable along the y-direction; Figure 5 This is a schematic diagram of the initial value construction method of the segmented straight rod iterative equation system for a step-by-step form-finding method for a space wind cable system provided in an embodiment of the present invention; Figure 6 A force analysis diagram of a space wind cable system based on the segmented catenary theory, provided in an embodiment of the present invention, for a step-by-step form-finding method of a space wind cable system; Figure 7 This is a force analysis diagram of a single-segment catenary in a step-by-step form-finding method for a space wind cable system provided in an embodiment of the present invention; Figure 8 This is a schematic diagram of a step-by-step shape-finding method for a space wind cable system according to an embodiment of the present invention, specifically an iterative initial value construction method for a single cable segment catenary. Detailed Implementation

[0017] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a step-by-step form-finding method and system for a space wind cable system proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0019] The following description, in conjunction with the accompanying drawings, details a step-by-step shape-finding method and specific system scheme for a space wind cable system provided by the present invention.

[0020] To better illustrate, offshore photovoltaic structures refer to solar photovoltaic power generation systems built in marine environments such as nearshore or offshore areas. The core structure typically includes semi-submersible or tension leg floating platforms, photovoltaic module arrays, anchoring systems, mooring cables, and related power transmission and control systems. They usually need to cope with complex marine environments such as waves, currents, wind loads, salt spray corrosion, and possible extreme weather such as typhoons, and have extremely high requirements for the stability, durability, and economy of the structure.

[0021] Among them, the wind cable system is used to resist wind loads and maintain the structural attitude; however, the floating platform and wind cable system of offshore photovoltaic structures usually have complex three-dimensional spatial morphology, and there may be a large deviation between the initial design morphology and the actual equilibrium morphology after being subjected to force. The traditional form-finding method has certain technical defects. Therefore, a step-by-step form-finding method for spatial wind cable systems is proposed. Specifically, for the complex stress characteristics of offshore photovoltaic structures under the coupling of wind, waves and currents, a form-finding method for spatial wind cable systems with both accuracy and convergence is proposed. This method can effectively solve the key mechanical problems in the wind resistance stability analysis of offshore photovoltaic support structures and provide technical support for the simulation analysis and optimization design of flexible support structures.

[0022] Please see Figure 1 The diagram illustrates a step-by-step form-finding method for a space wind cable system according to an embodiment of the present invention, used for offshore photovoltaic structures. The method includes: Step S1: Obtain the condition parameters based on the space wind cable system, project the space wind cable system onto the horizontal plane, and construct a segmented straight rod force model in the horizontal plane based on the condition parameters; Step S2: Based on the unknown parameters set for the space wind cable system, perform static equilibrium analysis on the segmented straight rod force model and establish a set of nonlinear equations; Step S3: Use the piecewise straight rod iterative equation system initial value construction method to determine the iterative initial value of the nonlinear equation system and obtain the unknown parameters of the space wind cable system in the horizontal plane; Step S4: Define the unknown parameters as known conditions, introduce the segmented catenary theory, and use the single-segment catenary iterative initial value construction method to obtain the remaining unknown parameters in the space wind cable system.

[0023] As an optional implementation method, the space cable system refers to a flexible cable system used to stabilize and fix offshore photovoltaic arrays such as floating photovoltaic power stations. It is typically used to resist wind loads, wave forces and other external forces in the marine environment to ensure the stability, safety and long-term operational reliability of the photovoltaic structure. The system forms a spatial constraint network by connecting the photovoltaic array to seabed anchor points or floating platforms, which effectively disperses and transmits external loads.

[0024] Please see Figure 2 Furthermore, in step S1, the condition parameters include, but are not limited to, the elastic modulus, cross-sectional area, and material density of the main cable and the suspender; the position of the anchor point in the main cable, the horizontal position of the suspending point, and the vertical position of the control point; the position of the suspending point in the suspender and the design value of the vertical force component of the suspender force at the suspending point.

[0025] It can be explained that the modulus of elasticity is a physical quantity used to measure the elastic deformation capacity of a material, referring to the ratio of stress to strain in the elastic stage of the material; the cross-sectional area is the geometric area of ​​the cross-section of the main cable and the suspender, used to determine the stress state; the material density is the mass of material per unit volume of the main cable and the suspender, affecting the self-weight of the components and thus the overall load of the wind cable; the anchorage point in the main cable, i.e. and The three-dimensional coordinates (x, y, z coordinates) of the two anchoring points, and the lifting point The horizontal position, i.e., the x-coordinate, of the control point. The vertical position, i.e., the y-coordinate of the lifting point analyzed in the current task; the lifting point in the boom. The x, y, and z coordinates; the design value of the vertical force component of the boom at the lifting point, i.e., the lifting point... The design value of the y-direction component of the suspender force is denoted as . .

[0026] Please see Figure 3 Furthermore, step S2 includes: Step S21: Set unknown parameters, including the vertical position of the suspension point in the main cable, the horizontal force component at the anchor point in the main cable, and the horizontal force component of the suspender at the suspension point; that is, the suspension point in the main cable. The vertical position, i.e., the y-coordinate, is denoted as . Anchorage points in the main cable The component of the force along the horizontal direction, i.e., the x-axis, is denoted as . The boom is at the lifting point. The component of the force in the horizontal direction, i.e., the x-axis direction, is denoted as . Count all unknown parameters, total indivual.

[0027] Step S22: Perform static equilibrium analysis on the segmented straight bar force model based on unknown parameters, establish force equilibrium equations with the same number of unknown parameters, and integrate them to construct a nonlinear equation set.

[0028] To clarify, static equilibrium analysis refers to the systematic analysis and calculation of various external forces acting on an object or structure when it is at rest or in uniform linear motion, in order to determine the equilibrium relationship between these forces and the stress distribution inside the object.

[0029] Please see Figure 4 Furthermore, in step S22, specifically: Force balance analysis was performed on the suspenders on both sides of the suspension point, and force balance analysis was performed on the cable segment in the horizontal and vertical directions. The corresponding force balance equations were established and the nonlinear equations were obtained by combining them.

[0030] Specifically, based on any lifting point in the boom Further analysis reveals that the y-direction components of the forces on the left and right wind cable suspenders at this suspension point are determined and denoted as follows: and A force balance analysis was performed on it, and the corresponding logical expression was established as follows:

[0031]

[0032]

[0033] The derivation yields:

[0034] in, Indicates the lifting point The component of the force along the y-axis; , , Representing the lifting points Control points and the next adjacent control point Position on the xy plane.

[0035] According to the lifting point Similarly, we can obtain The force balance equations along the y-direction at each suspension point are statistically analyzed to yield a total of One force balance equation.

[0036] Next, a force balance analysis is performed on the cable segments. For ease of explanation, this embodiment uses the first four cable segments as an example to illustrate the process. The force balance equations are established, and the corresponding calculation formulas are as follows:

[0037] By transforming it, we get:

[0038] Therefore, it was extended to the front Each cable segment, meaning that based on the first four cable segments, can be used to deduce the component of the horizontal force in any cable segment and the anchorage point. Component of force along the x-axis The relationship is used to complete the horizontal force analysis of the cable segment, and the corresponding calculation formula is:

[0039] Then, a vertical force analysis is performed on the cable segment. In this embodiment, the stress on the main cable segment is analyzed. Force analysis was performed on the corresponding cable segment to obtain the relationship between its internal forces and nodal coordinates. The corresponding calculation formula is as follows:

[0040] For control points Force equilibrium analysis along the y-direction yields:

[0041] The derivation yields:

[0042] Further derivation yields:

[0043] By combining the two derivation formulas and proceeding to the next step, we obtain:

[0044] According to the cable section By applying the same analysis, the suspension points in the main cable can be determined. The force balance equations, statistically, total... One force balance equation; integrating the force balance equations of each suspension point in the boom and the suspension point in the main cable, totaling... A set of force equilibrium equations is constructed, with the number of unknown parameters being the same. All force equilibrium equations are then combined to form a nonlinear equation system.

[0045] Furthermore, step S3 includes: Step S31: Determine that the initial values ​​of the force balance equations in the nonlinear equation system are equal, and determine the horizontal force components of the cable segment.

[0046] Specifically, based on the aforementioned steps, it is assumed that to The initial values ​​are equal, based on the control points. With lifting point The cable segments formed between The design value of the y-direction component of the lifting rod force that bears half of the corresponding lifting point. Based on the principle, the component of the force in the horizontal direction (x-direction) of the cable segment is calculated, and the corresponding calculation formula is:

[0047] in, Indicates the current analysis segment The component of the force in the x-direction.

[0048] Please see Figure 5 Step S32: Obtain the vertical position of the suspension point in the main cable based on the parabola, and combine the force component along the horizontal direction at the anchor point in the main cable to obtain the unknown parameters of the space wind cable system in the horizontal plane.

[0049] Specifically, each intermediate suspension point in the main wind cable The vertical position, i.e., the y-coordinate, passes through the starting point and the ending point, i.e., the anchor point. and and control points The parabolic interpolation is obtained; then, based on the set unknown parameters, the horizontal force component at the anchor point in the main cable, that is, the force component of the main cable at the anchor point... The component along the x-direction Based on this, the unknown parameters of the space wind cable system in the horizontal plane can be obtained by numerical solution using software such as MATLAB and Python. These parameters include the y-coordinates of each suspension point of the main cable, the horizontal components of the internal forces in each cable segment, and the horizontal geometric length of each stressed member.

[0050] Please combine Figure 6 and Figure 7 Furthermore, step S4 includes: Step S41: Define the unknown parameters as known conditions, introduce the piecewise catenary theory, and simplify the spatial cable form-finding analysis problem into a univariate nonlinear equation system solution problem with the vertical force of the cable segment at the anchor point of the wind cable as the unknown parameter.

[0051] To clarify, the segmented catenary theory refers to a theoretical method in cable structure analysis where, when a cable is composed of multiple catenary segments with different loads or boundary conditions, the overall complex spatial cable system is decomposed into several independent planar catenary segments for analysis.

[0052] Further, step S41 includes: Step S411: Set the vertical force of the cable segment at the anchor point of the wind cable as an unknown parameter; denote this unknown parameter as... There is a total of 1 position parameter.

[0053] Step S412: Based on the segmented catenary theory, starting from the initial anchor point, the vertical position of the suspension point in the main cable is obtained segment by segment by combining the known conditions, and the vertical position of the terminal anchor point is obtained.

[0054] Specifically, based on the segmented catenary theory, the space wind cable system is decomposed into several single-segment catenary units for solution. The control parameters for each single-segment catenary unit include the horizontal span. Vertical height Stress-free length Horizontal tension at nodes in the wind cable system and vertical tension The unknown parameters are determined based on the known conditions, and the corresponding calculation formula is as follows:

[0055]

[0056] in, This indicates the number of catenary segments in a single cable.

[0057] It can be explained that, based on cable segments To explain, the vertical force of the cable segment at the aforementioned unknown parameter anchorage point is combined with the above-mentioned unknown parameters. The lifting point is obtained by solving the problem using this formula. The vertical coordinate is denoted as Then, combine the cable segments. Analysis was conducted to determine the cable segment. The vertical force on the left, i.e. Finally, the anchorage points are obtained segment by segment from left to right, based on the main cable. The vertical coordinate of the point is denoted as . .

[0058] Step S413: Establish a set of univariate nonlinear equations concerning the vertical force of the cable segment at the anchor point based on the vertical position of the terminal anchor point; using the terminal anchor point... Vertical coordinates of a point To design given values, establish information about the unknown parameters. The system of univariate nonlinear equations is obtained based on the aforementioned governing equations and is related to the unknown parameter.

[0059] Please see Figure 8 Step S42: Use the single-segment catenary iterative initial value construction method to determine the iterative initial value of the univariate nonlinear equation system, and iteratively solve the vertical force of the cable segment at the anchor point of the wind cable.

[0060] Further, step S42 includes: Step S421: Simplify the space cable system into a single catenary in the vertical plane, with both ends anchored to the anchor points in the main cable and the suspension points in the suspenders, respectively; in this step, simplify the entire space cable system into a single catenary segment in the yz plane, with both ends anchored to the anchor points. and The horizontal span and vertical height of the simplified single-segment catenary can be directly determined by the coordinates of the two anchor points. The cross-sectional area of ​​the simplified single-segment catenary is twice that of the main cable in the actual wind cable, but the elastic modulus before simplification is consistent with that of the actual cable.

[0061] Step S422: Apply the tension of the wind cable suspenders along the vertical direction as a concentrated force to the suspension points of the simplified catenary suspenders; that is, apply the tension of all wind cable suspenders along the y-direction as a concentrated force to the suspension points. This setting can effectively simplify complex spatial force systems.

[0062] Step S423: Combine the known conditions to obtain the total weight of the space wind cable system and determine the equivalent linear density of the simplified catenary by uniformly distributing it horizontally; that is, estimate the total weight of the cable system by the total length of each cable determined in the previous steps, and then determine the equivalent linear density of the simplified catenary based on the uniform horizontal span distribution. The equivalent linear density refers to a virtual linear density parameter introduced in the simplified catenary model to make the stress and deformation characteristics of the model consistent with the distribution characteristics of the actual space wind cable system in the horizontal span direction.

[0063] Step S424: Using the equivalent linear density and the piecewise catenary theory, obtain the vertical force of the cable segment at the anchorage point of the wind cable, and define it as the initial value for the iteration of a univariate nonlinear equation system; that is, calculate and determine the starting anchorage point in the main cable based on the governing equations corresponding to the single-segment catenary. Vertical force at the point This parameter is used as the initial iterative value for the aforementioned univariate nonlinear equation. Based on this, the vertical force is determined numerically using software such as MATLAB and Python. The true solution.

[0064] Step S43: Determine the remaining unknown parameters in the space wind cable system based on the vertical force of the cable segment at the anchor point; in this embodiment, the actual vertical force determined in step S42 is used to determine the result value of the remaining unknown parameters in the space wind cable system.

[0065] Understandably, this paper proposes a step-by-step form-finding method for space wind cable systems based on offshore photovoltaic structures. The method transforms the traditional solution of a strongly coupled ternary nonlinear equation system into a process where a segmented straight-bar model is used in the horizontal plane for force equilibrium analysis to solve for relevant parameters. These parameters are then used as known conditions to solve for the remaining unknown parameters. The establishment of the nonlinear equation system is based solely on the force equilibrium of two-force members, avoiding the convergence difficulties caused by highly nonlinear catenary theory and exhibiting strong convergence. The solution for the remaining unknown parameters is based on the already obtained unknown parameters as known conditions, reducing the problem's order and improving computational stability. This step-by-step solution effectively avoids the risk of solution divergence caused by equation coupling in traditional methods, improving overall solvability and engineering robustness at the algorithmic level. In addition, an initial value construction method for the iterative equation system of piecewise straight rods and an iterative initial value construction method for single-segment catenary are proposed. In the corresponding two stages, an initial value construction strategy with clear physical meaning and direct calculation can be given, which effectively reduces the dependence on empirical initial values, reduces the amount of manual trial and error, and significantly improves the success rate and repeatability of the solution.

[0066] To better illustrate and verify the feasibility of the method proposed in this invention, let's assume that the anchor points of the space wind cable system currently being analyzed are as follows: and Lifting point in the boom and In the coordinate data, the unit is meters (m), and the current control point is... Its y-coordinate is 7.8m, and the spacing of the booms along the x-direction is 6.66m. The booms are at... The design tension force along the y-direction is 45 kN; while the cross-sectional area, elastic modulus, and linear density of the wind cable and suspender are 62.80 cm³. 2 158 GPa, 528.78 N / m and 5.22 cm 2 165 GPa and 45.21 N / m were used to determine the shape and internal forces of the space cable.

[0067] Based on the current design parameters, the accuracy of the finite element method proposed in the prior art and the step-by-step form-finding method for a space wind cable system proposed in this invention are compared and verified to ensure that the method proposed in this invention can meet the actual engineering requirements. The coordinates of each node in the space wind cable system are determined in sequence, as shown in Table 1. The tension of each cable segment in the main cable of the space wind cable system is determined, as shown in Table 2. The tension of each cable segment in the suspender of the space wind cable system is determined, as shown in Table 3.

[0068] Table 1. Coordinate data of each node in the space wind cable system

[0069] Table 2 Tension data of each cable segment in the main cable of the space wind cable system

[0070] Table 3 Tension data of each cable segment in the suspender of the space wind cable system

[0071] It can be noted that, according to the relevant data in the data table, the step-by-step form-finding method for a space wind cable system proposed in this invention is very different from the finite element method, and fully meets the engineering requirements.

[0072] The second embodiment of the present invention provides a step-by-step form-finding system for a space wind cable system. The system includes a processor, a communication interface, a memory, and a communication bus. The processor, the communication interface, and the memory communicate with each other through the communication bus. The processor calls logical instructions in the memory to execute a step-by-step form-finding method for a space wind cable system as described in any embodiment of the present invention.

[0073] During its operation, it requires the use of a step-by-step shape-finding method for a space wind cable system. Therefore, whether the system and program data are integrated or different hardware is configured to produce functions similar to those achieved by this invention, they all fall within the protection scope of this invention. This system has the same beneficial effects as the aforementioned step-by-step shape-finding method for a space wind cable system, and will not be elaborated here.

[0074] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0075] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. A spatial cable system step-by-step form finding method for offshore photovoltaic structures, characterized by, The method includes: Step S1: Obtain the condition parameters based on the space wind cable system, project the space wind cable system onto the horizontal plane, and construct a segmented straight rod force model in the horizontal plane based on the condition parameters; Step S2: Based on the unknown parameters set for the space wind cable system, perform static equilibrium analysis on the segmented straight rod force model and establish a set of nonlinear equations; Step S3: Use the piecewise straight rod iterative equation system initial value construction method to determine the iterative initial value of the nonlinear equation system and obtain the unknown parameters of the space wind cable system in the horizontal plane; Step S4: Define the unknown parameters as known conditions, introduce the segmented catenary theory, and use the single-segment catenary iterative initial value construction method to obtain the remaining unknown parameters in the space wind cable system.

2. The method of claim 1, wherein, In step S1, the condition parameters include, but are not limited to, the elastic modulus, cross-sectional area, and material density of the main cable and the suspender; the position of the anchor point, the horizontal position of the suspending point, and the vertical position of the control point in the main cable; the position of the suspending point in the suspender and the design value of the vertical force component of the suspender force at the suspending point.

3. The method of claim 2, wherein, Step S2 includes: Step S21: Set unknown parameters, including the vertical position of the suspension point in the main cable, the horizontal force component at the anchor point in the main cable, and the horizontal force component of the suspender at the suspension point; Step S22: Perform static equilibrium analysis on the segmented straight bar force model based on unknown parameters, establish force equilibrium equations with the same number of unknown parameters, and integrate them to construct a nonlinear equation set.

4. The method of claim 3, wherein, In step S22, specifically: Force balance analysis was performed on the suspenders on both sides of the suspension point, and force balance analysis was performed on the cable segment in the horizontal and vertical directions. The corresponding force balance equations were established and the nonlinear equations were obtained by combining them.

5. The method of claim 3, wherein, Step S3 includes: Step S31: Determine that the initial values ​​of the force balance equations in the nonlinear equation system are equal, and determine the horizontal force components of the cable segment; Step S32: Obtain the vertical position of the suspension point in the main cable based on the parabola, and combine it with the force component along the horizontal direction at the anchor point in the main cable to obtain the unknown parameters of the space wind cable system in the horizontal plane.

6. The step-by-step form-finding method for a space wind cable system according to claim 5, characterized in that, Step S4 includes: Step S41: Define the unknown parameters as known conditions, introduce the piecewise catenary theory, and simplify the spatial cable form-finding analysis problem into a univariate nonlinear equation system solution problem with the vertical force of the cable segment at the anchor point of the wind cable as the unknown parameter; Step S42: Use the single-segment catenary iterative initial value construction method to determine the iterative initial value of the univariate nonlinear equation system, and iteratively solve the vertical force of the cable segment at the anchorage point of the wind cable; Step S43: Determine the remaining unknown parameters in the space wind cable system based on the vertical force of the cable segment at the anchor point of the wind cable.

7. The step-by-step form-finding method for a space wind cable system according to claim 6, characterized in that, Step S41 includes: Step S411: Set the vertical force of the cable segment at the anchor point of the wind cable as an unknown parameter; Step S412: Based on the segmented catenary theory, starting from the initial anchor point, the vertical position of the suspension point in the main cable is obtained segment by segment by combining the known conditions, and the vertical position of the terminal anchor point is obtained. Step S413: Establish a set of univariate nonlinear equations about the vertical force of the cable segment at the anchor point of the wind cable based on the vertical position of the terminal anchor point.

8. The step-by-step form-finding method for a space wind cable system according to claim 6, characterized in that, Step S42 includes: Step S421: Simplify the space cable system into a single catenary in the vertical plane, with both ends anchored to the anchor point in the main cable and the suspension point in the suspender, respectively; Step S422: Apply tension along the vertical direction of the wind cable suspender rod to the suspension point in the simplified catenary suspender rod in the form of a concentrated force; Step S423: Combine the known conditions to obtain the total weight of the space wind cable system and distribute it evenly across the horizontal span to determine the equivalent linear density of the simplified catenary; Step S424: Using the equivalent linear density and the piecewise catenary theory, the vertical force of the cable segment at the anchor point of the wind cable is obtained and defined as the initial value of the iterative system of the univariate nonlinear equations.

9. A step-by-step form-finding system for a space wind cable system, characterized in that, The system includes a processor, a communication interface, a memory, and a communication bus. The processor, the communication interface, and the memory communicate with each other through the communication bus. The processor calls logical instructions in the memory to execute the step-by-step shape finding method for a space wind cable system as described in any one of claims 1 to 8.

Images