Self-adaptive load iteration method for ETFE air pillow structure

Abstract

The invention discloses a self-adaptive load iteration method for an ETFE air pillow structure, and belongs to the technical field of mechanical analysis and calculation of building structures. According to the method, a cable net-membrane surface dynamic friction contact model is established, the theoretical internal pressure value of the air pillow is calculated in real time in combination with the Boyle law and a volume formula, and internal pressure parameters are iteratively optimized by adopting a self-adaptive step length adjustment strategy. In specific implementation, MATLAB and ANSYS cooperate to complete parametric modeling, finite element analysis and data feedback, and a'driving-updating-verification 'closed-loop process is formed. According to the invention, the problem of prediction distortion caused by neglecting a slip effect in a traditional method is solved; the number of iterations is reduced by 50%-60%, and the single analysis time is compressed to be within 2 hours; and quick response to complex working conditions such as typhoon and extreme snow load is supported. According to the method, an efficient and accurate technical means is provided for design optimization and safety evaluation of the large-span ETFE air pillow structure.

Description

Technical Field

[0001] The present invention belongs to the technical field of architectural structural mechanics analysis and calculation, and specifically relates to an adaptive load iteration method for ETFE (ethylene-tetrafluoroethylene copolymer) air-cushion structures. Background Art

[0002] ETFE air-cushion structures are widely used in large-span buildings such as stadiums and airport terminals due to their light weight, high light transmittance, and excellent mechanical properties. However, the existing analysis methods have the following technical defects:

[0003] 1. Distorted friction-slip modeling: The traditional finite element model simplifies the contact between the cable net and the membrane surface as a fixed constraint, without considering the dynamic friction-slip effect, resulting in a structural deformation prediction error exceeding 20%.

[0004] 2. Decoupling problem of internal pressure and volume: The existing methods assume a constant internal pressure in the air-cushion and ignore the volume change under external loads, resulting in a serious deviation between the calculated value of the internal pressure and the actual physical state.

[0005] 3. Low efficiency of manual iteration: Engineers need to repeatedly trial and error to adjust the internal pressure parameters, which takes a long time for a single analysis and it is difficult to ensure convergence (especially for complex working conditions such as wind load and snow load). Summary of the Invention

[0006] The purpose of the present invention is to comprehensively consider the cable-membrane friction-slip effect and the pressure-volume coupling effect, and solve the key analysis problems of ETFE air-cushion structures under external loads. Aiming at the above defects, the core of the present invention is to realize the real-time coupling of the internal pressure and volume change of the air-cushion based on the cable-membrane contact finite element model, and to automatically iterate and optimize the internal pressure parameters and the structural form of the air-cushion, which is especially suitable for solving the dynamic response problem of the internal pressure of the air-cushion caused by the cable net friction-slip and volume change under external loads, and can significantly improve the design accuracy and safety evaluation efficiency of large-span ETFE air-cushion structures.

[0007] The purpose of the present invention is achieved by the following technical solutions: An adaptive load iteration method (ALIA) for ETFE air-cushion structures is proposed, and the specific steps are as follows:

[0008] S1. Establish a friction contact model between the cable net and the membrane surface, and preset the initial internal pressure range of the air-cushion;

[0009] S2. Calculate the equilibrium state of the air-cushion under the joint action of the preset initial internal pressure and the external load through finite element analysis, and output the deformed geometric data and the internal pressure calculated by the finite element;

[0010] S3. Calculate the theoretical internal pressure value based on the gas state equation and the volume formula according to the deformed geometric data;

[0011] S4. Compare the internal pressure calculated by finite element with the theoretical internal pressure value, iteratively optimize the preset internal pressure value through the step-by-step adjustment method, and update the geometric shape and structural stiffness of the pneumatic pillow until the error tolerance is met.

[0012] Further, in the step S1, establish a cable-net - membrane friction contact model through ANSYS APDL script, define the contact pair as the "point - surface" type, and adopt the Coulomb model for the friction behavior. Preset the initial internal pressure range of the pneumatic pillow (such as 100 Pa to 1000 Pa), and input parameters such as material properties (ETFE membrane elastic modulus, Poisson's ratio), cable-net friction coefficient (μ = 0.2 to 0.4), external loads (wind pressure, snow load), etc.

[0013] Further, apply the initial internal pressure as a boundary condition to the membrane surface, calculate the equilibrium state of the pneumatic pillow under the action of the load through a finite element solver, and output the node displacement, stress distribution, and contact slip amount.

[0014] Further, in the step S3, the gas state equation is Boyle's law or the adiabatic state equation, and its expression is:

[0015] (P theory +P atm )v κ =(P+P atm )V κ =eonst

[0016] where κ is the isentropic constant, P theory is the theoretical internal pressure after the deformation of the pneumatic pillow, P and V are the initial internal pressure and volume of the pneumatic pillow, and P atm is the external atmospheric pressure; when κ = 1, the adiabatic change simplifies to Boyle's law.

[0017] Further, in the step S3, the volume formula of the ETFE pneumatic pillow in the local coordinate system is:

[0018]

[0019] where ζ and η are the local coordinates on the ETFE membrane surface, x(ζ, η) is the surface vector, n * =x ，ξ ×x ，η is the non - normalized form of the normal vector, x ，ξ is the partial derivative of the surface vector x(ζ, η) with respect to the coordinate ξ, and x ，η is the partial derivative of the surface vector x(ζ, η) with respect to the coordinate η.

[0020] Further, in the step S4, compare the internal pressure P FEM calculated by finite element with the theoretical value P theory, if the absolute error exceeds the tolerance threshold ε (e.g., ±2%): If the internal pressure P calculated by the finite element method FEM is higher than the theoretical internal pressure value P theory , it indicates that the internal pressure setting is too high, resulting in an increase in the structural stiffness of the pneumatic pillow and a decrease in deformation. The internal pressure is reduced by the step size AP; conversely, if the internal pressure P calculated by the finite element method FEM is lower than the theoretical internal pressure value P theory , it means that the internal pressure setting is too low, the structural stiffness decreases, and the deformation increases. The internal pressure is increased by the step size AP; the step-by-step adjustment method is adopted to increase or decrease the preset internal pressure by the step size AP, and then the finite element calculation is performed again until the difference between the calculation and the theoretical value meets the established error requirements. The final internal pressure value and parameters such as node displacement and stress distribution are output.

[0021] Furthermore, the step size AP decreases with the number of iterations, ΔP = F0 / 2 i , where F0 is the externally applied load and i is the number of the next iteration. During the iteration process, the system continuously updates the geometric shape and structural stiffness of the pneumatic pillow to accurately reflect the physical state changes caused by the internal pressure adjustment.

[0022] Furthermore, in the step S2, the finite element analysis is realized by the cooperation of MATLAB and ANSYS. The MATLAB main program defines the material properties, load parameters and initial internal pressure. ANSYS calls the APDL script to execute parametric modeling and restart analysis. MATLAB reads the result data and triggers the iteration loop until the tolerance standard is met. The specific process is as follows:

[0023] 1. Write the main program of the adaptive load iteration algorithm based on MATLAB. The geometric shape of the structure is imported into the ANSYS software in the.sat file format.

[0024] 2. All key parameters, such as material properties, working internal pressure, friction coefficient and external load, etc., are defined in MATLAB and stored in a.txt file.

[0025] 3. Develop a complete parametric analysis model based on APDL, and integrate and apply various variables defined in MATLAB to the model.

[0026] 4. In the integrated model, each iteration is completed by modifying the node coordinates and executing the restart analysis, so as to update the structural shape and stiffness.

[0027] 5. The structural analysis results are exported in.txt format, including the deformed node coordinates and element information. These data are then used in MATLAB to calculate the volume and pressure changes of the structure and evaluate whether these changes meet the predetermined tolerance standards.

[0028] The beneficial effects of the present invention compared with the prior art are as follows:

[0029] 1) By means of the friction contact model and the internal pressure - volume coupling calculation, the present invention solves the problem of prediction distortion caused by ignoring the slip effect in the traditional method.

[0030] 2) The present invention adopts an adaptive step - size adjustment strategy, reducing the number of convergence times for typical working conditions from more than 15 times in the traditional trial - and - error method to 5 - 8 times, and improving the iteration efficiency by 50% - 60%.

[0031] 3) Through the deep integration of MATLAB and ANSYS, the present invention constructs an integrated analysis framework of "parameter - driven - automatic update - closed - loop feedback", providing a general technical paradigm for the analysis of similar inflatable structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the technical solutions of the present invention, the following will briefly introduce the drawings. Obviously, for those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0033] Figure 1 Flow chart of the adaptive load iteration algorithm.

[0034] Figure 2 Flow chart of the numerical implementation. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0035] The following will clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments only represent some implementation manners of the present invention, rather than all implementation manners. Based on these embodiments of the present invention, those of ordinary skill in the art can derive various other embodiments without creative efforts. All these embodiments, as long as they do not exceed the creative core of the present invention, shall be regarded as within the protection scope of the present invention.

[0036] The purpose of the present invention is to realize the real - time coupling of the internal pressure and volume change of the air pillow based on the cable - membrane contact finite - element model, and optimize the internal pressure parameters through automatic iteration. As Figure 1 shown, the following are the specific implementation steps of this method:

[0037] Step 1: Parameter initialization and model construction

[0038] Preset the initial internal pressure P range of the air pillow (such as 100 Pa to 1000 Pa), and input parameters such as material properties (elastic modulus and Poisson's ratio of the ETFE film), cable net friction coefficient (μ = 0.2 to 0.4), and external load F0 (wind pressure, snow load); establish a cable net-membrane surface friction contact model through ANSYS APDL script, define the contact pair as the "point-surface" type, and adopt the Coulomb model for the friction behavior.

[0039] Step 2: Equilibrium state calculation

[0040] Apply the initial internal pressure as the boundary condition to the membrane surface, calculate the equilibrium state of the air pillow under the load through the finite element solver, and output the node displacement, stress distribution, and contact slip amount. The internal pressure calculated by the finite element is:

[0041] (P FEM ) i =(P FEM ) i-1 + F0 / 2 i

[0042] where P FEM is the internal pressure calculated by the finite element, and i is the number of the next iteration.

[0043] Step 3: Solution of the gas state equation

[0044] Write a MATLAB numerical solution program based on Poisson's law formula and the air pillow volume formula, and automatically calculate the theoretical internal pressure value P theory .

[0045] Poisson's law formula is:

[0046] (P theory + P atm )v κ =(P + P atm )V κ = const

[0047] where κ is the isentropic constant, P theory is the theoretical internal pressure after the deformation of the air pillow, P and V are the initial pressure and volume of the air pillow, and P atm is the external atmospheric pressure. When κ = 1, the adiabatic change simplifies to Boyle's law.

[0048] The volume formula of the ETFE air pillow in the local coordinate system is:

[0049]

[0050] where ζ and η are the local coordinates on the ETFE film surface, x(ζ, η) is the surface vector, and n * = x ，ξ × x，η is the non - standardized form of the normal vector, x ，ξ is the partial derivative of the surface vector x(ζ, η) with respect to the coordinate ξ, x ，η is the partial derivative of the surface vector x(ζ, η) with respect to the coordinate η, V i is the volume after the i - th iteration of deformation.

[0051] Step 4: Internal pressure adaptive iteration

[0052] Compare the internal pressure P calculated by finite element method FEM with the theoretical value P theory , if the absolute error exceeds the tolerance threshold ε (such as ±2%): when P FEM > P theory , reduce the internal pressure by the step size ΔP; when P FEM < P theory , increase the internal pressure by the step size ΔP, and then re - perform the finite element calculation until the difference between the calculated value and the theoretical value meets the established error requirements. The step size ΔP = F0 / 2 i , where F0 is the externally applied load and i is the number of the next iteration.

[0053] Adopt the step - by - step adjustment method (ΔP decreases with the number of iterations) until the error requirement is met, and output the final internal pressure value and parameters such as node displacement and stress distribution. During the iteration process, the system continuously updates the geometric shape and structural stiffness of the air pillow to accurately reflect the physical state changes caused by the internal pressure adjustment.

[0054] According to the above steps, as Figure 2 shown, combine ANSYS and MATLAB to complete the numerical implementation of the above adaptive load iteration algorithm:

[0055] 1. Write the main program of the adaptive load iteration algorithm based on MATLAB. The geometric shape of the structure is imported into the ANSYS software in the.sat file format.

[0056] 2. Define all key parameters, such as material properties, working internal pressure, friction coefficient, and external load, etc., in MATLAB and store them in a.txt file.

[0057] 3. Develop a complete parametric analysis model based on APDL, and integrate and apply various variables defined in MATLAB to the model.

[0058] 4. In the integrated model, complete each iteration by modifying the node coordinates and performing a restart analysis, so as to update the structural shape and stiffness.

[0059] 5. The results of the structural analysis are exported in.txt format, including the deformed node coordinates and element information. These data are then used in MATLAB to calculate the volume and pressure changes of the structure and to evaluate whether these changes meet the predetermined tolerance criteria.

[0060] Example: Taking the double-layer ETFE pneumatic structure with crossed ropes as an example, the implementation process of the adaptive load iteration method is described; the specific steps are as follows:

[0061] Step 1: First, establish a finite element model of the double-layer ETFE pneumatic structure with crossed ropes. The model is a square ETFE pneumatic structure with a length of 3m and a height of 0.3m, and two steel cables are vertically and crosswise arranged on the upper and lower membrane surfaces respectively. The SHELL41 element in the ANSYS program is selected to simulate the ETFE membrane, the L1NK10 element is used to simulate the cable, and the membrane element and the cable element are set as tension-only elements through element settings.

[0062] Step 2: Set the material parameters: the elastic modulus of the membrane material is 6.5×10 8 N / m 2 , the thickness is 0.25mm, the Poisson's ratio is 0.42, and the density is 1750kg / m 3 . The diameter of the steel cable is 5mm, the elastic modulus is 1.2×10 11 N / m 2 , the Poisson's ratio is 0.3, and the density is 7850kg / m 3 . Import the geometric model into the ANSYS software for initial form analysis. The initial internal pressure of the structure P0 = 500Pa, and the node coordinates and element information in the prestress equilibrium state are extracted to calculate the initial volume V0.

[0063] Step 3: In the first round of calculation of the adaptive load method, apply a uniformly distributed load F0 of half the span, with a value of 400Pa. Set the initial internal pressure P1, P i = P0 + F0 / 2 = 700Pa. After the preliminary calculation, it is necessary to update the geometric shape of the structure to accurately reflect the deformed state after loading. Extract the deformed structure data, including node displacement, stress distribution and contact slip amount, and calculate the deformed volume V1.

[0064] Step 4: Using the relationship of gas volume change, further calculate the theoretical value P1 * of the internal pressure. Compare the simulated pressure value with the theoretical pressure value to evaluate whether the difference between them is within an acceptable range, so as to judge the accuracy of the current simulation and whether further iteration is required.

[0065] Step 5: During the iteration process, the calculation was completed after only 6 iterations. Due to the action of the external load, the volume of the air pillow decreased significantly, and the internal air pressure increased to 600 Pa.

[0066] In Step 1, the cables on the ETFE air cushion structure were divided into multiple small cable segments, and the nodes of all cable segments formed point - surface contact pairs with the ETFE membrane surface. TARGE170 target elements were covered on the membrane elements, and CONTA175 contact elements were covered on the cable element nodes. It should be noted that the outer normal direction of the contact element must point to the target element, and the outer normal direction of the target element must also point to the contact element. The standard contact mode was adopted, allowing contact sliding between the cable and the membrane. The contact algorithm used the extended Lagrangian algorithm, and the friction between the cable and the membrane was processed according to Coulomb's friction law, where the static friction coefficient was set to 0.4 and the dynamic friction coefficient was not considered.

[0067] In Step 2, a parametric initial geometric model was established and imported into ANSYS software for finite element analysis to solve the prestress equilibrium state of the air cushion structure under internal pressure. The midpoint height in the prestress state was compared with the target height, and the height error was set to be less than 1%. When the error did not meet the requirements, the height parameter of the geometric model was adjusted and recalculated until the midpoint height met the design requirements.

[0068] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0069] The above embodiments are used to explain the present invention rather than limit the present invention. Any modifications and changes made to the present invention within the spirit and protection scope of the claims of the present invention fall within the protection scope of the present invention.

Claims

1. An adaptive load iterative algorithm for ETFE air pillow structure, characterized in that, It includes the following steps: S1. Establish a friction contact model between the cable net and the membrane surface, and preset the initial internal pressure range of the air pillow; S2. Calculate the equilibrium state of the air pillow under the combined action of the preset initial internal pressure and the external load through finite element analysis, and output the deformed geometric data and the internal pressure calculated by the finite element; S3. Based on the gas state equation and the volume formula, calculate the theoretical internal pressure value according to the deformed geometric data; S4. Compare the internal pressure calculated by the finite element with the theoretical internal pressure value, and iteratively optimize the preset internal pressure value by the step-by-step adjustment method, and update the geometric shape and structural stiffness of the air pillow until the error tolerance is satisfied.

2. The adaptive load iterative algorithm for the ETFE air-cushion structure according to claim 1, wherein: In the step S1, a cable net-membrane surface friction contact model is established through ANSYS APDL script, the contact pair is defined as the "point-surface" type, and the Coulomb model is used for the friction behavior.

3. The adaptive load iterative algorithm for the ETFE air-cushion structure according to claim 1, wherein: In the step S3, the gas state equation is Boyle's law or the adiabatic state equation, and its expression is: (P theory + P atm )v κ =(P + P atm )V κ = const where κ is the isentropic constant, P theory is the theoretical internal pressure after the deformation of the air pillow, P and V are the initial internal pressure and volume of the air pillow, and P atm is the external atmospheric pressure; when κ = 1, the adiabatic change simplifies to Boyle's law.

4. The adaptive load iterative algorithm for the ETFE air-cushion structure according to claim 1, characterized in that: In the step S3, the volume formula of the ETFE air pillow in the local coordinate system is: where ζ and η are local coordinates on the ETFE film surface, x(ζ, η) is the surface vector, and n * = x ，ξ × x ，η is the non-normalized form of the normal vector, and x ，ξ is the partial derivative of the surface vector x(ζ, η) with respect to the coordinate ξ, and x ，η is the partial derivative of the surface vector x(ζ, η) with respect to the coordinate η.

5. The adaptive load iterative algorithm for ETFE air pillow structure according to claim 1, wherein: In the step S4, if the internal pressure calculated by the finite element is higher than the theoretical internal pressure value, it indicates that the internal pressure setting is too high, resulting in an increase in the structural stiffness of the air pillow and a decrease in deformation; on the contrary, if the internal pressure calculated by the finite element is lower than the theoretical internal pressure value, it means that the internal pressure setting is too low, the structural stiffness decreases, and the deformation increases; the step-by-step adjustment method is used to increase or decrease the preset internal pressure by the step size ΔP until the difference between the calculation and the theoretical value meets the established error requirements.

6. The adaptive load iterative algorithm for the ETFE air pillow structure according to claim 5, characterized in that: The step size ΔP decreases with the number of iterations, and ΔP = F0 / 2 i , where F0 is the externally applied load and i is the number of the next iteration.

7. The adaptive load iteration algorithm for the ETFE air pillow structure according to claim 1, characterized in that: In the step S2, the finite element analysis is realized through the cooperation of MATLAB and ANSYS. The MATLAB main program defines the material properties, load parameters and initial internal pressure. ANSYS calls the APDL script to execute parametric modeling and restart analysis. MATLAB reads the result data and triggers the iterative loop until the tolerance standard is met.

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