Free-form surface cable support single-layer reticulated shell form optimization method and system

Abstract

The invention provides a form optimization method and system for a free-form surface cable-supported single-layer latticed shell, and relates to the technical field of large-span space structure design, and the method comprises the steps: setting initial conditions for form optimization of the free-form surface cable-supported single-layer latticed shell; based on initial conditions, taking strain energy and curved surface smoothness as optimization targets, taking node height as an optimization variable, and taking a node height feasible region as an optimization constraint, constructing an objective function, taking the optimization constraint as a penalty function and adding the penalty function into the objective function through an interior point method, and converting a constrained optimization problem into an unconstrained optimization problem, so as to achieve the optimization of the curved surface. Establishing an optimization equation under the corresponding weight coefficient in combination with the weight coefficient; and traversing the set weight coefficients, optimizing the form of the free-form surface cable support single-layer reticulated shell for each weight coefficient, solving an optimization equation under the corresponding weight coefficient, exiting the optimization loop until a constraint boundary is reached, and outputting an optimization solution under the current weight coefficient to obtain the optimal form of the free-form surface.

Description

Technical Field

[0001] The present disclosure relates to the technical field of long - span space structure design, and particularly relates to a method and system for optimizing the form of a free - form surface cable - supported single - layer reticulated shell. Background Art

[0002] The statements in this part merely provide background technical information related to the present disclosure and do not necessarily constitute prior art.

[0003] As a new type of space structure system with a two - way lattice - type single - layer reticulated shell as the basic structure and formed by configuring supports (high - strength cables or tie rods) within the grid, the cable - supported single - layer reticulated shell has the advantages of light self - weight, rich curved surface shapes, and large structural stiffness, and has high application value and engineering prospects. The theory of free - form surface structure form optimization can effectively improve the overall mechanical performance of the structure and provide a novel and beautiful structural appearance with the help of computer technology, and is currently a research hotspot.

[0004] Combining free - form surface form optimization with cable - supported single - layer reticulated shell structures can not only improve the overall mechanical performance of the structure and optimize the internal force distribution of the structure, but also provide more diverse and novel curved surface types to meet the dual requirements of people for structural performance and appearance. However, there are currently few methods for optimizing the form of cable - supported reticulated shell structures, and the situation where the optimized curved surface is not smooth due to the existence of local extrema cannot be considered, which makes the practicality of the form optimization method relatively low. Summary of the Invention

[0005] To solve the above problems, the present disclosure proposes a method and system for optimizing the form of a free - form surface cable - supported single - layer reticulated shell. Taking the strain energy and surface smoothness of the cable - supported single - layer reticulated shell under load as the optimization objectives, the node height as the optimization variable, regarding multi - dimensional optimization as multi - objective optimization and obtaining its Pareto solution, a multi - dimensional form - optimized curved surface is obtained, effectively improving the mechanical performance of the cable - supported single - layer reticulated shell and ensuring the smoothness of the optimized curved surface, with good practical value.

[0006] According to some embodiments, the present disclosure adopts the following technical solutions:

[0007] A method for optimizing the form of a free - form surface cable - supported single - layer reticulated shell includes:

[0008] Setting the initial conditions for the form optimization of the free - form surface cable - supported single - layer reticulated shell;

[0009] Based on the initial conditions, taking the strain energy and surface smoothness as the optimization objectives, the node height as the optimization variable, and the node height feasible region as the optimization constraint, constructing an objective function, and adding the optimization constraint as a penalty function to the objective function through the interior - point method, transforming the constrained optimization problem into an unconstrained optimization problem, and establishing an optimization equation corresponding to the weight coefficient by combining the weight coefficient;

[0010] Traverse the set weight coefficients, optimize the form of the free-form surface cable-supported single-layer reticulated shell for each weight coefficient, solve the optimization equation corresponding to the weight coefficient, and exit the optimization loop until the constraint boundary is reached. Output the optimization solution under the current weight coefficient to obtain the optimal free-form surface.

[0011] According to some embodiments, the present disclosure adopts the following technical solutions:

[0012] A free-form surface cable-supported single-layer reticulated shell form optimization system, comprising:

[0013] An initialization module for setting the initial conditions for the optimization of the free-form surface cable-supported single-layer reticulated shell form;

[0014] A target function construction module for constructing a target function based on the initial conditions, using strain energy and surface smoothness as optimization objectives, node height as the optimization variable, and the feasible region of node height as the optimization constraint. By using the interior point method, the optimization constraint is added to the target function as a penalty function to transform the constrained optimization problem into an unconstrained optimization problem, and an optimization equation corresponding to the weight coefficient is established in combination with the weight coefficient;

[0015] An optimization solution module for traversing the set weight coefficients, optimizing the form of the free-form surface cable-supported single-layer reticulated shell for each weight coefficient, solving the optimization equation corresponding to the weight coefficient, and exiting the optimization loop until the constraint boundary is reached. Output the optimization solution under the current weight coefficient to obtain the optimal free-form surface.

[0016] According to some embodiments, the present disclosure adopts the following technical solutions:

[0017] A computer program product, including a computer program, where when the computer program is executed by a processor, it implements the described free-form surface cable-supported single-layer reticulated shell form optimization method.

[0018] According to some embodiments, the present disclosure adopts the following technical solutions:

[0019] A non-transitory computer-readable storage medium for storing computer instructions, where when the computer instructions are executed by a processor, they implement the described free-form surface cable-supported single-layer reticulated shell form optimization method.

[0020] According to some embodiments, the present disclosure adopts the following technical solutions:

[0021] An electronic device, comprising: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device runs, the processor executes the computer program stored in the memory so that the electronic device executes a method for optimizing the form of a free-form cable-supported single-layer reticulated shell as described above.

[0022] Compared with the prior art, the beneficial effects of the present disclosure are as follows:

[0023] In the method for optimizing the form of a free-form cable-supported single-layer reticulated shell of the present disclosure, an optimization objective function is established, the interior point method is adopted, a penalty factor is used to convert the constrained optimization into an unconstrained optimization equation, and the surface smoothness is introduced by combining a weight coefficient to establish an optimization equation under the corresponding weight coefficient. In this way, the surface smoothness can be considered during the structural form optimization process, and the influence of the surface smoothness on the structural form optimization can be determined by setting the weight coefficient.

[0024] In the method for optimizing the form of a free-form cable-supported single-layer reticulated shell of the present disclosure, the set weight coefficients are traversed, the form of the free-form cable-supported single-layer reticulated shell is optimized for each weight coefficient, the optimization equation under the corresponding weight coefficient is solved, and the optimization loop is exited until the constraint boundary is reached, and the optimization solution under the current weight coefficient is output to obtain the optimal free-form surface. By optimizing the optimization equations for a set of weight coefficients, a Pareto optimization frontier can be obtained, that is, a set of non-dominated optimization solutions, where each frontier solution corresponds to a smooth and better-performing free-form surface.

[0025] In the method for optimizing the form of a free-form cable-supported single-layer reticulated shell of the present disclosure, the gradient method is used as the main optimization algorithm, the strain energy of the cable-supported single-layer reticulated shell under load and the surface smoothness are used as the optimization objectives, the node height is used as the optimization variable, the multi-dimensional optimization is regarded as a multi-objective optimization and its Pareto solution is obtained. The optimized surface obtained has the advantages of high stiffness, smooth surface, uniform stress distribution of members, and high load-bearing capacity. It can effectively improve the mechanical properties of the cable-supported single-layer reticulated shell while ensuring the smoothness of the optimized surface, and has good practical value. Description of the Drawings

[0026] The specification drawings forming a part of the present disclosure are used to provide a further understanding of the present disclosure. The schematic embodiments and descriptions thereof of the present disclosure are used to explain the present disclosure and do not constitute an improper limitation of the present disclosure.

[0027] Figure 1 It is the method flow chart of the embodiment of the present disclosure;

[0028] Figure 2 It is the weight coefficient update method flow chart of the embodiment of the present disclosure;

[0029] Figure 3 Schematic diagram for calculating the slope change at node i according to an embodiment of the present disclosure;

[0030] Figure 4 Schematic diagram of node numbers according to an embodiment of the present disclosure;

[0031] Figure 5 Schematic diagram of a cable-supported system with in-plane prestressed cables according to an embodiment of the present disclosure;

[0032] Figure 6 Schematic diagram of a derivative unit of a cable-supported system according to an embodiment of the present disclosure;

[0033] Figure 7 Structural member divided into multiple segments according to an embodiment of the present disclosure;

[0034] Figure 8 Schematic diagram of a Pareto curve according to an embodiment of the present disclosure;

[0035] Figure 9 Initial surface form according to an embodiment of the present disclosure;

[0036] Figure 10 Optimized surface form with a weight of 0.02 according to an embodiment of the present disclosure;

[0037] Figure 11 Optimized surface form with a weight of 0.01 according to an embodiment of the present disclosure. Detailed implementation manners

[0038] The present disclosure will be further described below in conjunction with the accompanying drawings and embodiments.

[0039] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further explanations of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present disclosure belongs.

[0040] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0041] Embodiment 1

[0042] In an embodiment of the present disclosure, a method for optimizing the form of a free-form surface cable-supported single-layer reticulated shell is provided. The gradient method is used as the main optimization algorithm, and the strain energy and surface smoothness of the cable-supported single-layer reticulated shell under load are used as the optimization objectives, and the node height is used as the optimization variable. The multi-dimensional optimization is regarded as a multi-objective optimization to find its Pareto solution. The steps include:

[0043] Step 1: Set the initial conditions for the form optimization of the free-form surface cable-supported single-layer reticulated shell;

[0044] Step 2: Based on the initial conditions, with the strain energy and surface smoothness as the optimization objectives, the node height as the optimization variable, and the node height feasible region as the optimization constraint, construct the objective function, and use the interior point method to add the optimization constraint as a penalty function to the objective function, transforming the constrained optimization problem into an unconstrained optimization problem, and establishing an optimization equation corresponding to the weight coefficient in combination with the weight coefficient;

[0045] Step 3: Traverse the set weight coefficients, optimize the form of the free-form surface cable-supported single-layer reticulated shell for each weight coefficient, solve the optimization equation corresponding to the weight coefficient, and exit the optimization loop until the constraint boundary is reached, output the optimization solution under the current weight coefficient, and obtain the optimal free-form surface.

[0046] As an embodiment, the specific implementation process of a method for optimizing the form of a free-form surface cable-supported single-layer reticulated shell of the present disclosure is as follows:

[0047] Step 1: Set the initial conditions for the form optimization of the free-form surface cable-supported single-layer reticulated shell;

[0048] Specifically, setting the initial conditions for the form optimization of the free-form surface cable-supported single-layer reticulated shell includes: the initial surface form, the constraints and load conditions applied to the structure, the structural parameters, the optimization parameters, the value range of the weight coefficient, the feasible region range of the optimization variable, the optimization constraint conditions, and the iteration convergence criterion; the initial surface form is as Figure 9 shown.

[0049] Step 2: Based on the initial conditions, with the strain energy and surface smoothness as the optimization objectives, the node height as the optimization variable, and the node height feasible region as the optimization constraint, construct the objective function, and use the interior point method to add the optimization constraint as a penalty function to the objective function, transforming the constrained optimization problem into an unconstrained optimization problem, and establishing an optimization equation corresponding to the weight coefficient in combination with the weight coefficient;

[0050] Specifically, establish the expression of the optimization objective function, calculate the structural strain energy in the initial state, and the specific implementation method is as follows:

[0051] Taking the strain energy and the surface smoothness as the optimization objectives, the node height as the optimization variable, and the feasible region of the node height as the optimization constraint, the optimization constraint is added to the objective function as a penalty function by the interior point method, and the constrained optimization problem is transformed into an unconstrained optimization problem. The objective function is established, and after dimensionlessization, the expression of the objective function is obtained as follows:

[0052]

[0053] In the formula, Z represents the node height of the cable-supported single-layer reticulated shell, i is the node number, τ is the domain of the independent variable. β is the weight coefficient of the surface smoothness, E 0 is the strain energy of the structure in the initial state. E(Z) represents the strain energy of the structure under the action of the load, S(Z) represents the surface smoothness, and α k is the penalty factor. and are the upper and lower limits of the feasible region of the height of the i-th node respectively. Z i represents the height of the i-th node of the cable-supported single-layer reticulated shell.

[0054] Furthermore, the strain energy E(Z) of the structure under the action of the load is calculated by the following formula:

[0055]

[0056] In the formula, F is the given load vector; U is the node displacement vector, which can be obtained by the finite element method from KU = F, where K is the overall elastic stiffness matrix of the structure.

[0057] Furthermore, as Figure 3 shown, taking the change degree of the slopes of the members in two directions at each node as the standard to measure whether the local area where the point is located is smooth, which is called the surface smoothness at this node, and its calculation formula is as follows:

[0058]

[0059] In the formula, dt i x and dt i y represent the differences in the slopes of the straight members on both sides of node i in the x and y directions respectively, where l(i, i + 1) represents the length of the member between node i and node i + 1, and d i is the smoothness value at node i. In addition, the smoothness of the boundary points is not calculated. In this embodiment, the reticulated shell grid is divided into ten segments along the x and y directions, then the relationship between the adjacent members and adjacent nodes of each node is as Figure 4 shown, then and are calculated by the following formula:

[0060]

[0061] Furthermore, the penalty factor α k is calculated by the following formula:

[0062] α k = λ·α k-1 (6)

[0063] where k is the iteration number of the outer loop, λ is a positive real number and λ < 1, and in this embodiment, λ takes 0.1.

[0064] Step 3: Traverse the set weight coefficients, optimize the form of the free-form surface cable-supported single-layer reticulated shell for each weight coefficient, solve the optimization equation corresponding to the weight coefficient, and exit the optimization loop until the constraint boundary is reached. Output the optimization solution under the current weight coefficient to obtain the optimal free-form surface.

[0065] Specifically, let the weight coefficient β in this embodiment take values uniformly in the range [0.01, 0.04], traverse the set weight coefficients, calculate the weights of the strain energy and the surface adjustment term for each weight coefficient and enter the optimization and solution steps, which specifically include:

[0066] Solve the optimization equation corresponding to the weight coefficient, calculate the gradients of the strain energy and the surface smoothness, and calculate the gradient of the objective function expression f(Z, α k ). The specific calculation process is as follows:

[0067] First, the gradient expression of the objective function is:

[0068]

[0069] where is the gradient of the structural strain energy with respect to the optimization variable Z, and the i-th element is which is called the sensitivity of the strain energy to z i ; is the gradient of the surface smoothness with respect to the optimization variable Z, and the j-th element is which is called the sensitivity of the surface smoothness to the optimization variable Z.

[0070] Furthermore, the sensitivity of the strain energy to the node height is calculated by the following formula:

[0071]

[0072] where U is the node displacement vector and K is the overall structural elastic stiffness matrix.

[0073] For Figure 5As shown in the cable-supported unit, it can be seen that there are four reticulated shell members and four cables connected to the surface node i. Let all the members connected to node i be collectively called a derivative unit associated with node i in this cable-supported unit, as shown in Figure 6 shown. In finite element analysis, if each member is divided into n beam elements and each cable is a bar element, then the derivative of the overall structural elastic stiffness matrix K of the system with respect to the height of node i can be calculated by the following formula:

[0074]

[0075] where is the stiffness matrix assembled from all elements in member n, is the stiffness matrix of cable p, and K represents the matrix obtained by assembling the stiffness matrices of all elements in the derivative unit according to the finite element relationship.

[0076] For a structural member divided into multiple segments of elements as shown in Figure 7 shown, the derivatives of the stiffness matrices of the entire member and the sum of element e k and with respect to node i can be calculated by the following formulas respectively:

[0077]

[0078] The sensitivity of the surface smoothness to the node height is calculated by the following formula:

[0079]

[0080] where and can be calculated by the following formulas respectively:

[0081]

[0082] (3) Calculate the conjugate gradient direction. The specific calculation steps are as follows:

[0083] First, let The initial conjugate gradient direction can be calculated by the formula At this time, j = 0. For subsequent iteration steps, the conjugate gradient direction can be calculated by the following formula:

[0084]

[0085] where p j represents the initial conjugate gradient direction, and p j+1 represents the new conjugate gradient direction.

[0086] (4) Based on the calculated conjugate gradient direction, use the golden section method to perform a line search in this direction. The specific calculation steps are as follows:

[0087] First, use the golden section method for line search and calculate the step size δ j , and calculate the updated node coordinates from the formula Z j+1 =Z j +δ j p j ; After that, update the coefficient j, and the new coefficient j can be calculated by the formula j = j + 1.

[0088] (5) Judge the convergence of the inner loop. If the inner loop convergence condition is not satisfied, return to step (2). If the inner loop convergence condition is satisfied, exit the inner loop. The specific implementation process is as follows:

[0089] The judgment condition for the convergence of the inner loop is |f j+1 -f j |<σ, where σ is the error tolerance value, and the initial error tolerance value σ≥0. When the convergence condition is judged to be false, return to step (2) to continue the optimization loop. When the convergence condition is judged to be true, exit the inner loop.

[0090] (6) Judge the constraint conditions. If the constraint boundary is not reached, reduce the penalty factor and return to step (1). If the constraint boundary is reached, perform step (5). The specific implementation process is as follows:

[0091] First, judge the constraint conditions. If the constraint boundary is not reached, update the node coordinates After that, update the penalty factor α and the error tolerance value σ. The new penalty factor α k+1 and the new error tolerance value σ k+1 can be calculated by the formulas α k+1 =λ·α k and σ k+1 =λ·σ k respectively; then return to step (1) to continue the optimization loop. If the constraint boundary is reached, exit the optimization loop and perform step (4).

[0092] As an embodiment, before judging the constraint conditions in step (6), after judging the convergence of the inner loop in step (5), an improved form optimization method for updating the weight coefficient during the optimization process is proposed. Update the weight coefficient and the penalty factor, and return to step (2) for iterative calculation. The improved form optimization method for updating the weight coefficient can gradually eliminate the influence of the surface smoothness, avoid multiple calculations, and only need one optimization to obtain the global optimal surface. The weight coefficient of the optimization equation is gradually updated with the outer loop iteration. The specific calculation formula is:

[0093]

[0094] In the formula, both w and v are given parameters, and w>0, v>1; k represents the weight update step, which is consistent with the change step of the penalty factor.

[0095] It can be seen that as the iteration progresses, the weight coefficient changes. As the update step k increases, the weight coefficient β gradually approaches 0. Eventually, a free-form surface with a smooth surface and good mechanical properties can be obtained, as Figure 11 shown.

[0096] Step 4: Output the optimal solution under the current weight and determine whether the traversal is completed. If the traversal is not completed, return to Step 2. If the traversal is completed, output the optimal solutions under all weight coefficients, and draw a Pareto curve based on the strain energy and surface smoothness of the optimal solutions. Figure 8 For the schematic diagram of the Pareto curve, the optimal solutions are all non-dominated solutions, which are a point on the curve in Figure 8 . Furthermore, the surface forms under different weights can be obtained, as Figure 10 shown.

[0097] Embodiment 2

[0098] In an embodiment of the present disclosure, a free-form surface cable-supported single-layer reticulated shell form optimization system is provided, including:

[0099] An initialization module for setting the initial conditions for the free-form surface cable-supported single-layer reticulated shell form optimization;

[0100] A target function construction module for constructing a target function based on the initial conditions, using strain energy and surface smoothness as optimization objectives, node height as an optimization variable, and the node height feasible region as an optimization constraint. The optimization constraint is added to the target function as a penalty function through the interior point method to transform the constrained optimization problem into an unconstrained optimization problem, and an optimization equation corresponding to the weight coefficient is established in combination with the weight coefficient;

[0101] An optimization solution module for traversing the set weight coefficients, optimizing the free-form surface cable-supported single-layer reticulated shell form for each weight coefficient, solving the optimization equation corresponding to the weight coefficient, and exiting the optimization loop until the constraint boundary is reached, outputting the optimization solution under the current weight coefficient, and obtaining the optimal free-form surface form.

[0102] Embodiment 3

[0103] In an embodiment of the present disclosure, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, it implements the free-form surface cable-supported single-layer reticulated shell form optimization method described above.

[0104] Embodiment 4

[0105] In one embodiment of the present disclosure, a non-transitory computer-readable storage medium is provided. The non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the above-mentioned free-form surface cable-supported single-layer reticulated shell form optimization method is implemented.

[0106] Embodiment 5

[0107] In one embodiment of the present disclosure, an electronic device is provided, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device runs, the processor executes the computer program stored in the memory, so that the electronic device executes the above-mentioned free-form surface cable-supported single-layer reticulated shell form optimization method.

[0108] The present disclosure is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present disclosure. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for realizing the functions specified in one or more flows and / or one or more blocks. Figure 1 one or more flows and / or Figure 1 one or more blocks

[0109] These computer program instructions can also be loaded onto a computer or other programmable data processing devices, so that a series of operation steps are executed on the computer or other programmable devices to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable devices provide steps for realizing the functions specified in one or more flows and / or one or more blocks. Figure 1 one or more flows and / or Figure 1 one or more blocks

[0110] Although the specific implementation manners of the present disclosure have been described above in conjunction with the accompanying drawings, it is not a limitation to the protection scope of the present disclosure. Those skilled in the art should understand that, based on the technical solutions of the present disclosure, various modifications or deformations that can be made by those skilled in the art without creative efforts are still within the protection scope of the present disclosure.

Claims

1. A method for optimizing the morphology of a free-form cable-supported single-layer lattice shell, characterized in that: include: Set the initial conditions for the morphology optimization of the free-form cable-supported single-layer lattice shell; Based on the initial conditions, the strain energy and surface smoothness are used as optimization targets, the node height is used as the optimization variable, and the node height feasible region is used as the optimization constraint to construct the objective function. The optimization constraint is added to the objective function as a penalty function through the interior point method, and the constrained optimization problem is transformed into an unconstrained optimization problem. The optimization equation under the corresponding weight coefficient is established in combination with the weight coefficient. Traverse the set weight coefficients, optimize the free-form surface cable-supported single-layer lattice shell shape for each weight coefficient, solve the optimization equation under the corresponding weight coefficient, and exit the optimization loop until the constraint boundary is reached. Output the optimization solution under the current weight coefficient to obtain the optimal free-form surface shape.

2. A free-form cable-supported single-layer lattice shell morphology optimization method as claimed in claim 1, characterized in that: The initial conditions for the optimization of the free-form surface cable-supported single-layer lattice shell shape are set, including: initial surface shape, constraints and load conditions imposed on the structure, structural parameters, optimization parameters, value range of weight coefficients, feasible domain range of optimization variables and optimization constraints, and iterative convergence criteria.

3. The method for optimizing the morphology of a free-form cable-supported single-layer lattice shell according to claim 1, characterized in that: Taking strain energy and surface smoothness as optimization targets, node height as optimization variable, and node height feasible region as optimization constraint, the optimization constraint is added to the objective function as penalty function through interior point method, and the constrained optimization problem is transformed into an unconstrained optimization problem. The objective function is established and the expression of the objective function is obtained after dimensionless transformation: Where Z represents the node height of the cable-supported single-layer lattice shell, i is the node number, τ is the domain of the independent variable, β is the weight coefficient of the surface smoothness, E0 is the strain energy of the structure in the initial state, E(Z) represents the strain energy of the structure under load, S(Z) represents the surface smoothness, α k is the penalty factor, and are the upper and lower limits of the feasible region of the i-th node height, Z i Represents the height of the ith node of the cable-supported single-layer lattice shell.

4. A free-form cable-supported single-layer lattice shell morphology optimization method as claimed in claim 3, characterized in that: The calculation process of the strain energy of the structure under load is: Where F is the given load vector; U is the node displacement vector, which is calculated by KU=F using the finite element method, where K is the overall elastic stiffness matrix of the structure.

5. The method for optimizing the morphology of a free-form cable-supported single-layer lattice shell according to claim 3, characterized in that: The degree of change in the slope of the rod in two directions at each node is used as a measure of whether the local area at the point is smooth, which is called the surface smoothness at the node. The calculation formula is as follows: In the formula, and represents the difference in slope of the straight rod on both sides of node i in the x and y directions, respectively, where l(i, i+1) represents the length of the rod between node i and node i+1, and d i is the smoothness value at node i. In addition, the surface smoothness of the boundary points is not calculated.

6. The method for optimizing the morphology of a free-form cable-supported single-layer lattice shell according to claim 1, characterized in that: The weight coefficient is uniformly selected within the value range, and the set weight coefficient is traversed. The weight of the strain energy and the surface adjustment item is calculated for each weight coefficient and the optimization solution step is entered. The specific steps are as follows: (1) Based on the given initial conditions, the structural strain energy and surface smoothness in the initial state are calculated, and the optimization equation under the corresponding weight coefficient is established; (2) Solve the optimization equation under the corresponding weight coefficient, calculate the gradient of strain energy and surface smoothness, and calculate the objective function expression f(Z,α k )’s gradient; (3) Calculate the conjugate gradient direction; (4) Based on the calculated conjugate gradient direction, a line search is performed in this direction using the golden section method; (5) Determine the convergence of the inner loop. If the inner loop convergence condition is not met, return to step (2). If the inner loop convergence condition is met, exit the inner loop. (6) Perform constraint condition judgment. If the constraint boundary is not reached, reduce the penalty factor and return to step (1). If the constraint boundary is reached, proceed to step (5).

7. A free-form cable-supported single-layer lattice shell morphology optimization system, characterized in that: include: Initialization module, used to set the initial conditions for the morphology optimization of free-form cable-supported single-layer lattice shells; The objective function construction module is used to construct the objective function based on the initial conditions, with strain energy and surface smoothness as optimization targets, node height as optimization variables, and node height feasible domain as optimization constraints. The optimization constraints are added to the objective function as penalty functions through the interior point method, and the constrained optimization problem is converted into an unconstrained optimization problem. The optimization equation under the corresponding weight coefficient is established in combination with the weight coefficient. The optimization solution module is used to traverse the set weight coefficients, optimize the free-form surface cable-supported single-layer lattice shell shape for each weight coefficient, solve the optimization equation under the corresponding weight coefficient, and exit the optimization loop until the constraint boundary is reached. The optimization solution under the current weight coefficient is output to obtain the optimal free-form surface shape.

8. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, a method for optimizing the morphology of a free-form cable-supported single-layer lattice shell as described in any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by the processor, a free-form cable-supported single-layer lattice shell morphology optimization method as described in any one of claims 1 to 6 is implemented.

10. An electronic device, characterized in that: include: A processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device executes a free-form cable-supported single-layer lattice shell morphology optimization method as described in any one of claims 1-6.

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