A method for optimizing the cross-section of waterproof curtain wall and cable net for low-temperature water treatment

Abstract

The present invention relates to the field of flexible waterproof curtain wall structures in the field of hydraulic structures, and discloses a method for optimizing the cross-section of curtain and cable net of waterproof curtain wall for low-temperature water treatment, including: obtaining the structural stress distribution in equilibrium; setting the stress exceeding limit conditions of cable unit and membrane unit; calculating the stress limit of cable unit and membrane unit; judging and identifying the exceeding limit unit; calculating the ideal cross-sectional area of ​​the exceeding limit cable unit and the ideal cross-sectional thickness of the exceeding limit membrane unit; matching the optimal size of components in the cross-sectional library; defining the optimization principle of longitudinal cable and curtain cross-sectional; assigning new cross-sectional sizes to all units of longitudinal cables and curtain components belonging to the exceeding limit cable and membrane unit; updating the cross-sectional sizes of the cable and membrane units in the numerical model until the stress of all units is less than the stress limit before the first optimization. The present invention uses a vector finite element method to obtain the stress distribution of the curtain and longitudinal cables of the waterproof curtain wall cable-membrane structure, matches the optimal cross-sectional model in the set cross-sectional library to optimize the internal force distribution and weaken the stress concentration.

Description

Technical Field

[0001] The invention relates to the field of flexible waterproof curtain wall structures in the field of hydraulic structures, and in particular to a method for optimizing the cross-section of a waterproof curtain wall and a cable net for low-temperature water treatment. Background Art

[0002] Large hydropower stations or high-dam reservoirs are affected by the water temperature stratification phenomenon, and low-temperature water near the water intake is discharged downstream for a long time, causing a variety of slow, long-term and even difficult-to-repair ecological problems. There are thousands of hydropower stations with the problem of low-temperature water discharge, and traditional low-temperature water treatment measures are not applicable or costly for the built high-dam power stations.

[0003] The water-blocking curtain wall is a waterproof flexible control curtain with a certain flow height built in front of the dam. According to the water temperature layered structure in front of the dam, the appropriate water retaining height is set to block the middle and bottom water bodies in front of the curtain wall so that the surface high-temperature water body passes through the curtain wall, accelerates the mixing of water bodies of different temperatures, changes the water temperature structure in front of the dam, and achieves the purpose of increasing the temperature of the downstream water. Compared with traditional water intake solutions such as stacked beam gates, the water-blocking curtain wall has the characteristics of simple structure, low cost, and no impact on power generation, especially suitable for existing hydropower stations.

[0004] As a flexible cable-membrane structure with large deformation, there is a complex interaction between the curtain wall and the flow field. The shape of the curtain wall and its stress condition are determined by the pressure of the flow field on the curtain wall, and the flow field will change with the change of the curtain wall shape. The water pressure on the curtain wall first acts on the curtain, and then is transmitted to the adjacent cable net through the curtain. The longitudinal cable is a force transmission component, and the transverse cable plays a structural role. Finally, all of it is transmitted to the ground anchor and upper steel through the upper and lower ends of the longitudinal cable. However, as the span of the curtain wall increases, the stress concentration near the curtain wall support becomes more obvious, even exceeding the design strength. Summary of the invention

[0005] The present invention aims to provide a method for optimizing the cross-section of a low-temperature water treatment waterproof curtain wall and a cable net, so as to solve the problem that the stress near the curtain wall support is obviously concentrated as the curtain wall span increases.

[0006] To achieve the above object, the present invention adopts the following technical solution: a method for optimizing and analyzing the cross-section of a low-temperature water treatment water-blocking curtain wall and a cable net, comprising:

[0007] Step 1: Analyze the internal force of the waterproof curtain wall structure and iteratively calculate the structural stress distribution of the initial equilibrium state;

[0008] Step 2: Set the cable element stress over-limit conditions and the membrane element stress over-limit conditions;

[0009] Step 3: Calculate the stress limit of cable element and the stress limit of membrane element;

[0010] Step 4: Compare the stress limit values ​​of the cable unit and the stress limit values ​​of the membrane unit with the corresponding stress exceeding limit conditions to identify the exceeding limit cable unit and the exceeding limit membrane unit;

[0011] Step 5: Calculate the ideal cross-sectional area of ​​the over-limit cable element a based on the cable element stress limit and the membrane element stress limit and the ideal cross-sectional thickness of the over-limit membrane element b ;

[0012] Step 6: Set up the curtain and longitudinal cable section library, and match the best size for the component in the section library;

[0013] Step 7: Set the cross-section optimization principle for the stress exceeding limit of the longitudinal cable unit and the cross-section optimization principle for the stress exceeding limit of the curtain membrane unit;

[0014] Step 8: According to the cross-sectional optimization principle defined in step 7, obtain the corresponding over-limit cable unit, the longitudinal cable belonging to the membrane unit, and all units of the curtain component and assign new cross-sectional dimensions;

[0015] Step 9: Update the cross-sectional dimensions of the cable and membrane units in the numerical model and repeat steps 1 to 8 until the stress levels of all units are below the stress limit before the first optimization.

[0016] Preferably, the step 1 specifically includes:

[0017] Step 11: Calculate the mass of particle i and hydrodynamic pressure ;

[0018] Step 12: Calculate the particle displacement;

[0019]

[0020] in, , , They represent the coordinates of particle i at the n+1th, nth, and n-1th iteration steps respectively; c is the virtual damping of the iterative calculation; h is the iteration step length; , They represent the external force and internal force of particle i in the nth iteration step respectively.

[0021] Step 13: Calculate the iterative step stress of cable unit stress and membrane unit stress, and perform stress sorting, where:

[0022]

[0023] in, , They represent the stress of cable element a at the n+1th and nth iteration steps respectively; represents the elastic modulus of cable unit a; , They represent the length increment and length of cable unit a in the nth iteration step respectively;

[0024]

[0025] in, , They represent the stress matrices of membrane element b at the n+1th and nth iteration steps respectively; , , They represent the x-stress, y-stress and shear stress of membrane element b in the n+1th iteration step respectively; , denote the constitutive matrix and elastic matrix of membrane element b respectively; represents the deformation increment of membrane element b in the nth iteration step;

[0026] Step 14: After all the mass points are balanced, the stress of the cable element is obtained and the Mises stress of the membrane element , the specific calculation formula is:

[0027]

[0028]

[0029] in, represents the stress of cable element a at the last iteration step; , , They respectively represent the x-stress, y-stress and shear stress of membrane element b in the last iteration step.

[0030] Preferably, the step 11 specifically includes: discretizing the structure into mass points, cable units and triangular membrane units, wherein the structural mass and the hydrodynamic pressure are all allocated to the mass points,

[0031]

[0032] in, , They respectively represent the mass assigned to particle i by cable and membrane elements.

[0033]

[0034] in, represents the pressure on membrane unit k; represents the area of ​​the membrane unit; represents the normal vector of membrane element k; Represents the number of membrane units connected to particle i.

[0035] Preferably, the cable unit stress limit , membrane element stress limit for:

[0036]

[0037]

[0038] in Indicates that the serial number is 0.96 sum1 stress of cable element; Indicates that the serial number is 0.99 sum2 Mises stress of membrane element; , They represent the design strength of cable unit a and membrane unit b respectively; sum1 and sum2 represent the total number of cable and membrane units respectively.

[0039] Preferably, the ideal cross-sectional area of ​​the super-limit cable unit a is and the ideal cross-sectional thickness of the over-limit membrane element b The specific calculation formula is:

[0040]

[0041]

[0042] in, To optimize the cross-sectional area of ​​the front cable unit a, To optimize the thickness of the front membrane unit b.

[0043] Preferably, the mass point equilibrium condition in step 14 is: the coordinate difference of all mass points in the two previous and next iteration steps is less than a preset threshold.

[0044] Preferably, the cable unit stress exceeding limit condition and the membrane unit stress exceeding limit condition in step 2 include: for cable units, the units that account for the top 4% after being sorted by stress and whose stress exceeds 50% of the design strength are defined as exceeding limit units; for membrane units, the units that account for the top 1% after being sorted by stress and whose stress exceeds 50% of the design strength are defined as exceeding limit units and need to perform cross-sectional optimization.

[0045] Preferably, the cross-sectional optimization principle for longitudinal cable unit stress exceeding limit and the cross-sectional optimization principle for curtain membrane unit stress exceeding limit in step 7 include: for the longitudinal cable, if the stress of longitudinal cable unit a exceeds limit, all longitudinal cable units on the longitudinal cable where unit a is located must be cross-sectionally optimized; for the curtain, if the stress of membrane unit b exceeds limit, all membrane units in the same longitudinal and transverse cable grid as unit b must be cross-sectionally optimized.

[0046] Advantages of the present invention: The present invention uses the vector finite element method to obtain the stress distribution of the curtain and longitudinal cables of the cable-membrane structure of the waterproof curtain wall, and optimizes the internal force distribution and weakens the stress concentration by automatically matching the best section model in a given section library; the present invention innovatively uses the vector finite element method to perform cross-section optimization analysis of the waterproof curtain wall, avoiding the problems of stiffness matrix singularity and iterative non-convergence that exist in traditional finite elements when performing flexible large deformation structure analysis; for the first time, a cross-section optimization analysis method for a large-span waterproof curtain wall is proposed; the present invention gives a detailed introduction to the cross-section optimization analysis process of the cable-membrane structure of the waterproof curtain wall, clarifies the section optimization principles and internal force distribution optimization standards, expands from stress-exceeding units to all units of the same component, and achieves a more uniform internal force distribution by adjusting the cross-section size of the component. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Schematic diagram of a flow chart of an embodiment of the present invention.

[0048] Figure 2 This is the Mises stress distribution diagram of the curtain before optimization of the embodiment of the present invention.

[0049] Figure 3 This is the Mises stress distribution diagram of the optimized curtain according to the embodiment of the present invention.

[0050] Figure 4 This is a histogram of the Mises stress distribution of the curtain before optimization according to an embodiment of the present invention.

[0051] Figure 5 This is the optimized Mises stress distribution histogram of the curtain according to the embodiment of the present invention.

[0052] Figure 6 This is a stress distribution diagram of the longitudinal cable before optimization of an embodiment of the present invention.

[0053] Figure 7 This is a diagram of the optimized longitudinal cable stress distribution according to an embodiment of the present invention.

[0054] Figure 8 FIG. 4 is a histogram of longitudinal cable stress distribution before optimization according to an embodiment of the present invention.

[0055] Fig. 9 Optimized longitudinal cable stress distribution histogram according to an embodiment of the present invention. DETAILED DESCRIPTION

[0056] The following is further described in detail through specific implementation methods:

[0057] A method for optimizing the cross-section of low-temperature water treatment water-blocking curtain wall and cable net, such as Figure 1 As shown, the specific steps include:

[0058] Step 11: Calculate the mass of particle i and hydrodynamic pressure .

[0059] This step specifically includes: discretizing the structure into mass points, cable elements and triangular membrane elements, where the structural mass and hydrodynamic pressure are all assigned to the mass points.

[0060] (1)

[0061] in, , They respectively represent the mass assigned to particle i by cable and membrane elements.

[0062] (2)

[0063] in, represents the pressure on membrane unit k; represents the area of ​​the membrane unit; represents the normal vector of membrane element k; Represents the number of membrane units connected to particle i.

[0064] The cable net is discretized into mass points and cable units, and the curtain is discretized into mass points and membrane units. If the coordinate positions of the mass points obtained by discretizing the cable net coincide with those of the mass points obtained by discretizing the curtain, the two mass points are merged.

[0065] Step 12: Calculate the displacement of the particle, specifically according to the central difference formula.

[0066] (3)

[0067] in, , , They represent the coordinates of particle i at the n+1th, nth, and n-1th iteration steps respectively; c is the virtual damping of the iterative calculation; h is the iteration step length; , They represent the external force and internal force of particle i in the nth iteration step respectively.

[0068] Among them, the central difference formula is a numerical method used to approximate the solution of the derivative.

[0069] It should be noted that the particle in this application is the name used in the numerical model of the dynamic relaxation method (such as calculating displacement), while the node is the name used in the physical model of the cable net structure (calculating radial distance, actuator length). Particles and nodes are actually different ways of representing the same object (cable net node).

[0070] Step 13: Calculate the iterative step stress of cable unit stress and membrane unit stress, and perform stress sorting, where:

[0071] (4)

[0072] in, , They represent the stress of cable element a at the n+1th and nth iteration steps respectively; represents the elastic modulus of cable unit a; , They represent the length increment and length of cable unit a in the nth iteration step respectively;

[0073] (5)

[0074] in, , They represent the stress matrices of membrane element b at the n+1th and nth iteration steps respectively; , , They represent the x-stress, y-stress and shear stress of membrane element b in the n+1th iteration step respectively; , denote the constitutive matrix and elastic matrix of membrane element b respectively; represents the deformation increment of membrane element b in the nth iteration step;

[0075] Step 14: After all the mass points are balanced, the stress of the cable element is obtained and the Mises stress of the membrane element , the specific calculation formula is:

[0076] (6)

[0077] (7)

[0078] in, represents the stress of cable element a at the last iteration step; , , They respectively represent the x-stress, y-stress and shear stress of membrane element b in the last iteration step.

[0079] In this step, the coordinate difference of all particles in the previous and next iterations is less than 10 -4 m, all particles are considered to be balanced.

[0080] Step 2: Define stress exceeding principle and identify exceeding elements.

[0081] In this step, for cable elements, the elements that account for the top 4% after stress sorting and whose stress exceeds 50% of the design strength are defined as over-limit elements; for membrane elements, the elements that account for the top 1% after stress sorting and whose stress exceeds 50% of the design strength are defined as over-limit elements and require cross-sectional optimization.

[0082] Step 3: Calculate the stress limit of cable element and membrane element.

[0083] The cable element stress limit in this step , membrane element stress limit for:

[0084] (8)

[0085] (9)

[0086] in Indicates that the serial number is 0.96 sum1 stress of cable element; Indicates that the serial number is 0.99 sum2 Mises stress of membrane element; , They represent the design strength of cable unit a and membrane unit b respectively; sum1 and sum2 represent the total number of cable and membrane units respectively.

[0087] Step 4: Determine whether there are over-limit cables and membrane units. If so, identify the over-limit units and proceed to the next step. If no over-limit units exist, output the waterproof curtain wall cable membrane structure model.

[0088] Step 5: Calculate the ideal cross-sectional area of ​​the over-limit cable element a based on the cable element stress limit and the membrane element stress limit and the ideal cross-sectional thickness of the over-limit membrane element b .

[0089] Among them, the ideal cross-sectional area of ​​the super-limit cable unit a is and the ideal cross-sectional thickness of the over-limit membrane element b The specific calculation formula is:

[0090] (10)

[0091] (11)

[0092] in, To optimize the cross-sectional area of ​​the front cable unit a, To optimize the thickness of the front membrane unit b.

[0093] Step 6: Set up the longitudinal cable and curtain section library, and match the best size for the components in the section library.

[0094] The longitudinal cable section library contains section diameters of 12mm, 18mm, 24mm, 30mm, 36mm, etc., and the curtain section library contains thicknesses of 0.5mm, 0.7mm, 1mm, 1.5mm, 2mm, 2.5mm, 3mm, etc. According to the calculation results of step 5, the relevant section size data is matched in the section library. For example, if the ideal section thickness of membrane unit b is 2.3mm, the thickness with the smallest absolute difference from 2.3mm is matched in the section library, that is, 2.5mm. If the ideal section thickness of membrane unit b is 2.2mm, 2mm is matched (that is, the section size with the smallest absolute difference from the ideal section size calculated in step 5 is matched in the section library). Similarly, the relevant dimensions of the curtain are also matched using the above method.

[0095] Step 7: Set the cross-sectional optimization principle for longitudinal cable unit stress exceeding limit and the cross-sectional optimization principle for curtain membrane unit stress exceeding limit.

[0096] In this step, for the longitudinal cable, if the stress of longitudinal cable unit a exceeds the limit, all longitudinal cable units on the longitudinal cable where unit a is located must be cross-sectionally optimized; for the curtain, if the stress of membrane unit b exceeds the limit, all membrane units in the same longitudinal and transverse cable grid as unit b must be cross-sectionally optimized.

[0097] Step 8: According to the section optimization principle defined in step 7, obtain the corresponding over-limit cable unit, the longitudinal cables belonging to the membrane unit, and all units of the curtain component and assign new section sizes.

[0098] Longitudinal cable diameter (cross section is the diameter, through Converted to area) and curtain thickness.

[0099] Step 9: Update the cross-sectional dimensions of the cable and membrane units in the numerical model and repeat steps 1 to 7 until the stress levels of all units are below the stress limit before the first optimization.

[0100] In this step, the numerical model refers to the set of all the previous formulas and the meanings of the symbols in the formulas.

[0101] The following is an example of optimization analysis of the curtain and cable net section of a waterproof curtain wall: In the initial model, the curtain elastic modulus is 0.65MPa, the thickness is 0.7mm, the elastic modulus of the longitudinal and transverse cables is 30GPa, the longitudinal cable is 36mm, and the transverse cable diameter is 10mm. Before optimization, the maximum stress of the curtain is 14.3GPa, and only 1% of the curtain unit stress exceeds 12GPa; the maximum cable force of the longitudinal cable is 439.2KPa, and only 4% of the longitudinal cable unit stress exceeds 393.0KPa. The curtain Mises stress distribution, curtain Mises stress distribution histogram, cable net stress distribution, and longitudinal cable stress distribution histogram before and after optimization are shown in the figure below. Figure 2~Figure 9 As shown, Figure 2 and Figure 3The unit of the middle coordinate is MPa. In the figure, MN represents the minimum value, MX represents the maximum value, and the positions of MN and MX are where the maximum and minimum values ​​are located. Figure 6 and Figure 7 The coordinate unit is KPa. Figure 2~Figure 9 It can be seen that after the optimization analysis, the stress concentration phenomenon at the upper end of the curtain and the lower end of the longitudinal cable has been weakened to a certain extent.

[0102] The present invention proposes for the first time a method for optimizing the cross-section analysis of a large-span waterproof curtain wall; the present invention gives a detailed introduction to the cross-section optimization analysis process of the cable-membrane structure of the waterproof curtain wall, clarifies the cross-section optimization principles and internal force distribution optimization standards, expands from stress-exceeding units to all units of the same component, and achieves a more uniform internal force distribution by adjusting the cross-section size of the component; uses a vector finite element method to obtain the stress distribution of the curtain and longitudinal cables of the cable-membrane structure of the waterproof curtain wall, and optimizes the internal force distribution and weakens stress concentration by automatically matching the best cross-section model in a given cross-section library; the present invention innovatively uses a vector finite element method to perform cross-section optimization analysis of waterproof curtain walls, avoiding the problems of stiffness matrix singularity and iterative non-convergence that exist in traditional finite elements when performing flexible large deformation structure analysis.

[0103] The above is only an embodiment of the present invention, and the common knowledge such as the known specific technical schemes and / or characteristics in the scheme is not described in detail here. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the technical scheme of the present invention. In the present invention, unless otherwise clearly specified and limited, the terms should be understood in a broad sense. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A method for optimizing and analyzing the cross-section of a waterproof curtain wall and a cable net for low-temperature water treatment, characterized in that: include: Step 1: Analyze the internal force of the waterproof curtain wall structure and iteratively calculate the structural stress distribution of the initial equilibrium state; Step 2: Set the cable element stress over-limit conditions and the membrane element stress over-limit conditions; Step 3: Calculate the stress limit of cable element and the stress limit of membrane element; Step 4: Compare the stress limit values ​​of the cable unit and the stress limit values ​​of the membrane unit with the corresponding stress exceeding limit conditions to identify the exceeding limit cable unit and the exceeding limit membrane unit; Step 5: Calculate the ideal cross-sectional area of ​​the over-limit cable element a based on the cable element stress limit and the membrane element stress limit and the ideal cross-sectional thickness of the over-limit membrane element b ; Step 6: Set up the curtain and longitudinal cable section library, and match the best size for the component in the section library; Step 7: Set the cross-section optimization principle for the stress exceeding limit of the longitudinal cable unit and the cross-section optimization principle for the stress exceeding limit of the curtain membrane unit; Step 8: According to the cross-sectional optimization principle defined in step 7, obtain the corresponding over-limit cable unit, the longitudinal cable belonging to the membrane unit, and all units of the curtain component and assign new cross-sectional dimensions; Step 9: Update the cross-sectional dimensions of the cable and membrane units in the numerical model and repeat steps 1 to 8 until the stress levels of all units are below the stress limit before the first optimization.

2. The method for optimizing and analyzing the cross-section of a low-temperature water treatment waterproof curtain wall and a cable net according to claim 1, characterized in that: The step 1 specifically includes: Step 11: Calculate the mass of particle i and hydrodynamic pressure ; Step 12: Calculate the particle displacement; in, , , They represent the coordinates of particle i at the n+1th, nth, and n-1th iteration steps respectively; c is the virtual damping of the iterative calculation; h is the iteration step length; , They represent the external force and internal force of particle i at the nth iteration step respectively; Step 13: Calculate the iterative step stress of cable unit stress and membrane unit stress, and perform stress sorting, where: in, , They represent the stress of cable element a at the n+1th and nth iteration steps respectively; represents the elastic modulus of cable unit a; , They represent the length increment and length of cable unit a in the nth iteration step respectively; in, , They represent the stress matrices of membrane element b at the n+1th and nth iteration steps respectively; , , They represent the x-stress, y-stress and shear stress of membrane element b in the n+1th iteration step respectively; , denote the constitutive matrix and elastic matrix of membrane element b respectively; represents the deformation increment of membrane element b in the nth iteration step; Step 14: After all the mass points are balanced, the stress of the cable element is obtained and the Mises stress of the membrane element , the specific calculation formula is: in, represents the stress of cable element a at the last iteration step; , , They respectively represent the x-stress, y-stress and shear stress of membrane element b in the last iteration step.

3. The method for optimizing and analyzing the cross-section of a low-temperature water treatment waterproof curtain wall and a cable net according to claim 2, characterized in that: The step 11 specifically includes: discretizing the structure into mass points, cable units and triangular membrane units, wherein the structural mass and hydrodynamic pressure are all allocated to the mass points, in, , They represent the mass assigned to particle i by cable and membrane elements respectively; in, represents the pressure on membrane unit k; represents the area of ​​the membrane unit; represents the normal vector of membrane element k; Represents the number of membrane units connected to particle i.

4. The method for optimizing and analyzing the cross-section of a low-temperature water treatment waterproof curtain wall and a cable net according to claim 2, characterized in that: The cable element stress limit , membrane element stress limit for: in Indicates that the serial number is 0.96 sum1 stress of cable element; Indicates that the serial number is 0.99 sum2 Mises stress of membrane element; , They represent the design strength of cable unit a and membrane unit b respectively; sum1 and sum2 represent the total number of cable and membrane units respectively.

5. The method for optimizing and analyzing the cross-section of a low-temperature water treatment waterproof curtain wall and a cable net according to claim 4, characterized in that: The ideal cross-sectional area of ​​the super-limit cable unit a and the ideal cross-sectional thickness of the over-limit membrane element b The specific calculation formula is: in, To optimize the cross-sectional area of ​​the front cable unit a, To optimize the thickness of the front membrane unit b.

6. The method for optimizing and analyzing the cross-section of a low-temperature water treatment waterproof curtain wall and a cable net according to claim 2, characterized in that: The mass point equilibrium condition in step 14 is that the coordinate difference of all mass points in the two iteration steps before and after is less than a preset threshold.

7. The method for optimizing and analyzing the cross-section of a low-temperature water treatment waterproof curtain wall and a cable net according to claim 1, characterized in that: The cable unit stress exceeding limit condition and the membrane unit stress exceeding limit condition in step 2 include: for the cable unit, the units that account for the top 4% after being sorted by stress and whose stress exceeds 50% of the design strength are defined as exceeding limit units; for the membrane unit, the units that account for the top 1% after being sorted by stress and whose stress exceeds 50% of the design strength are defined as exceeding limit units and need to perform cross-sectional optimization.

8. The method for optimizing and analyzing the cross-section of a low-temperature water treatment waterproof curtain wall and a cable net according to claim 1, characterized in that: The cross-sectional optimization principle for longitudinal cable unit stress exceeding limit in step 7 and the cross-sectional optimization principle for curtain membrane unit stress exceeding limit include: for the longitudinal cable, if the stress of longitudinal cable unit a exceeds limit, all longitudinal cable units on the longitudinal cable where unit a is located must be cross-sectionally optimized; for the curtain, if the stress of membrane unit b exceeds limit, all membrane units in the same longitudinal and transverse cable grid as unit b must be cross-sectionally optimized.

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