Method and system for predicting film wrinkles in thermal environment
By constructing a multi-layer iterative cycle model and higher-order derivative Leibniz multiplication, the accuracy and convergence of film fold prediction in thermal environments are solved, and the accurate calculation of out-of-surface displacement and stress of films is achieved, providing a more comprehensive prediction of fold characteristics.
Patent Information
- Application Number
- CN202510396139.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-31
- Publication Date
- 2025-07-08
AI Technical Summary
The existing film fold theoretical model under thermal environment cannot accurately predict fold details, and the calculation convergence is poor, so it cannot effectively obtain parameters such as out-of-surface displacement and stress of the film.
A thin film fold prediction method is adopted in a thermal environment, and a multi-layer iterative cycle model is constructed, including the input layer, the previous order calculation layer of the thin film fold under the thermal environment, the spatial discrete layer, the polynomial calculation layer, the least squares method layer, etc., combined with the higher-order derivative Leibniz multiplication and the least squares method, the out-of-plane displacement and stress of the thin film are calculated to achieve accurate prediction of the thin film fold deformation image.
The out-of-surface displacement deformation caused by temperature changes can be calculated stably, which solves the accuracy and convergence of film fold prediction in the prior art, and achieves a more accurate and comprehensive prediction of the fold characteristics of film in the thermal environment.
Smart Images
Figure CN120277733A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of film wrinkle detection, and in particular relates to a film wrinkle prediction method in a thermal environment. Background Art
[0002] As an important component of the deployable structure in space of aerospace systems, membrane structures have attracted widespread attention in recent years due to their light weight, easy folding, low cost, and rapid deployment. However, the bending stiffness of the membrane is low, and even a small compressive stress will cause membrane wrinkles. For space flexible membrane structures, wrinkles will not only affect the surface accuracy, but also change the stress distribution in the membrane, and the stiffness matrix will also change accordingly, thereby changing the dynamic characteristics of the structure.
[0003] Temperature changes in the space environment have been identified as one of the factors that affect the shape accuracy of thin film structures. Many scholars have theoretically studied the wrinkling characteristics of thin films under thermal environments. For example, Taylor and Steigman derived the two-dimensional equation of a laminated film + reflective coating double-layer film based on the three-dimensional thermoelastic theory of isotropic materials, and solved the equation by embedding it in a dynamic system with artificial inertia and damping to obtain the wrinkle and relaxation area of the film under force-heat load. Deng and Pellegrino proposed a simplified numerical simulation technology for orthogonal anisotropic viscoelastic membranes considering temperature effects. The model has been successfully implemented in Abaqus / Explicit. Attipou et al. used the dual-scale Fourier series method to derive the macroscopic membrane wrinkle equation, and based on this model, studied the wrinkle characteristics of the film caused by thermal loads, including critical loads, wavelengths, and positions, but this method requires the wave number of the wrinkling mode to be determined in advance. Ren et al. proposed a mechanical-thermal dual-modulus constitutive model under finite deformation by introducing different elastic constants under tension and compression. Based on this model, they regularized the classical tension field theory and achieved the prediction of the film wrinkle area and its evolution under mechanical-thermal loads.
[0004] In summary, most of the existing theoretical models of film wrinkles under thermal environments are based on membrane theory, which cannot obtain parameters such as the out-of-plane displacement and stress of the wrinkled film. A few models established by shell theory also require assumptions and constraints on the wrinkle waveform before they can be solved. Therefore, in order to better guide the design of deployable film structures based on mechanical properties, it is necessary to establish a theoretical method that can predict the details of film wrinkles under thermal environments without the need for assumptions. Summary of the invention
[0005] The purpose of the present invention is to provide a method and system for predicting film wrinkles in a thermal environment, which solves the problem of difficulty in accurately predicting the evolution image of film wrinkles and difficulty in computational convergence in a complex thermal environment.
[0006] The present invention is achieved through the following technical solutions: A method for predicting film wrinkles under a thermal environment, comprising the following steps: S1. Obtain input parameters, which include the geometric dimensions of the film model, the elastic constants of the film material, the displacement load at the film boundary, the temperature load, the truncation order of the path discretization layer 、 the initial value for expressing the approximate solution of the film wrinkle image, and other initial parameters; S2. Input the input parameters into a pre-constructed film wrinkle prediction model under a thermal environment, calculate the out-of-plane displacement and stress of the film, and obtain the film wrinkle deformation image under the thermal environment; The film wrinkle prediction model under the thermal environment includes the first layer to the eleventh layer, specifically: The first layer is the input layer, the second layer is the calculation layer for the previous order of film wrinkles under the thermal environment, the third layer is the spatial discretization layer of film wrinkles under the thermal environment, and the fourth layer is the K polynomial calculation layer of the nth-order spatial discretization layer, the fifth layer is the least squares method layer, and the sixth layer is the K polynomial calculation layer of the nth-order path discretization layer, the seventh layer is the order K judgment layer, the eighth layer is the calculation layer for the effective range of path parameters, the ninth layer is the calculation layer for scalar load parameters, the tenth layer is the judgment layer for displacement or temperature conditions, and the eleventh layer is the output layer; Among them, the second layer to the seventh layer form the first-level iterative loop layer. When K is not less than the truncation order of the path discretization layer, it enters the eighth layer; otherwise, it iteratively loops through the second layer to the seventh layer; K is a positive integer; The first layer to the tenth layer form the second-level iterative loop layer. When the displacement boundary condition calculated by the tenth layer is greater than or equal to the displacement load at the film boundary given in the input parameters and the temperature boundary condition is greater than or equal to the temperature load given in the input parameters, it enters the output layer; otherwise, it iteratively loops through the first layer to the tenth layer.
[0007] Furthermore, in S1, among the input parameters, the geometric dimensions of the film model include length L width W and thickness h ; The elastic constants of the film material include E 1, E 2, G 12 , v 21 and v 12 ; E 1 is the elastic modulus along the x direction; E 2 is the elastic modulus along the y direction; G12 is x - y the in-plane shear modulus; v 21 is y the Poisson's ratio when the stress in the x direction produces a transverse strain in the v 12 is x the Poisson's ratio when the stress in the y direction produces a transverse strain in the The thin-film boundary displacement load includes the displacement x quantity in the , the displacement y quantity in the , and the transverse pressure load on the thin-film surface p ; The temperature load includes the temperature change Δ T on the thin-film surface, the coefficient of thermal expansion x of the thin film in the direction, and the coefficient of thermal expansion y of the thin film in the direction; The initial values used to represent the approximate solution of the thin-film wrinkle image include the initial value f 0 of the stress function, the initial value w 0 of the deflection function, the initial value λ 0 of the scalar load parameter, the initial value x 0 of the displacement variable in the u direction, and the initial value y 0 of the displacement variable in the v direction; Other initial parameters include the number P of thin-film subdomains, the truncation order N T of the spatial discrete layer, and the first K -1 approximate solutions used to represent the path discrete layer of the thin-film wrinkle image.
[0008] Furthermore, in S2, the specific calculation process of the previous order calculation layer of the thin-film wrinkle under the thermal environment is as follows: Input the first K -1 order approximate solutions used to represent the path discrete layer of the thin-film wrinkle image into the previous order calculation layer of the thin-film wrinkle under the thermal environment, and based on the Leibniz multiplication of high-order derivatives, obtain the Leibniz product corresponding to the K th order; In S2, the processing process of the order K judgment layer is specifically as follows: If K is less than , let , and return the second layer to calculate the new K order corresponding Leibniz product; if K is greater than or equal to , then the calculation ends and proceeds to the next layer; where is the truncation order of the path discrete layer.
[0009] Furthermore, in S2, the calculation process of the thin film fold space discrete layer under the thermal environment is specifically as follows: Input the input parameters and the Leibniz product corresponding to the K order obtained from the previous order calculation layer of the thin film fold under the thermal environment into the thin film fold space discrete layer under the thermal environment, and obtain the dimensionality reduction mapping relationship of the K order approximate solution for expressing the thin film fold image space discrete layer.
[0010] Furthermore, in S2, in the K order space discrete layer polynomial calculation layer, there is a preset K order space discrete layer polynomial, and the specific calculation process is as follows: Input the dimensionality reduction mapping relationship of the K order approximate solution for expressing the thin film fold image space discrete layer obtained from the thin film fold space discrete layer under the thermal environment into the K order space discrete layer polynomial calculation layer, and obtain an expression of the K order approximate solution for expressing the thin film fold image space discrete layer containing unknown coefficients.
[0011] Furthermore, in S2, the calculation process of the least squares layer is as follows: Input the expression of the K order approximate solution for expressing the thin film fold image space discrete layer obtained from the K order space discrete layer polynomial calculation layer into the least squares layer, and output an expression of the K order approximate solution for expressing the thin film fold image space discrete layer without unknown coefficients.
[0012] Furthermore, in S2, in the K order path discrete layer polynomial calculation layer, there is a preset K order path discrete layer polynomial, and the calculation process of the K order path discrete layer polynomial is as follows: Input the expression of the K order approximate solution for expressing the thin film fold image space discrete layer obtained from the least squares layer into the K order path discrete layer polynomial calculation layer, and output all approximate solutions of the 1st to K order path discrete layers.
[0013] Further, in S2, the specific process of the path parameter effective range calculation layer is as follows: The K 1st to K all approximate solutions of the ； The specific process of the scalar load parameter calculation layer is as follows: The initial value of the scalar load in the input parameters and the maximum value of the effective range of the path parameter obtained by the path parameter effective range calculation layer are input into the scalar load parameter calculation layer to obtain the maximum value of the scalar load parameter.
[0014] Further, in S2, the specific process of the displacement or temperature condition judgment layer is as follows: The maximum value of the scalar load parameter obtained by the scalar load parameter calculation layer is input into the displacement or temperature condition judgment layer to obtain the theoretical maximum values of the displacement and the thermal external load under the current path; If the theoretical maximum values of the displacement and the thermal external load under the current path are less than the external load parameters given by the input layer, the initial value for expressing the approximate solution of the thin film wrinkling image is updated, and the process returns to the first layer to continue the calculation; otherwise, it enters the output layer; the external load parameters are the thin film boundary displacement load and the temperature load; The specific process of the output layer is as follows: The initial value for expressing the approximate solution of the thin film wrinkling image and the K 1st to K all approximate solutions of the
[0015] The present invention also discloses a thin film wrinkling prediction system under a thermal environment, including: A data acquisition module, configured to acquire input parameters, where the input parameters include the geometric dimensions of the thin film model, the elastic constants of the thin film material, the thin film boundary displacement load, the temperature load, the truncation order of the path discretization layer 、 the initial value for expressing the approximate solution of the thin film wrinkling image, and other initial parameters; A prediction module, configured to input the input parameters into a pre-constructed thin film wrinkling prediction model under a thermal environment, calculate the out-of-plane displacement and stress of the thin film, and obtain a thin film wrinkling deformation image under the thermal environment; The thin film wrinkling prediction model under the thermal environment includes the first layer to the eleventh layer, specifically: The first layer is the input layer, the second layer is the layer for calculating the previous order of the film fold under the thermal environment, the third layer is the spatial discretization layer of the film fold under the thermal environment, and the fourth layer is the K polynomial calculation layer of the nth-order spatial discretization layer, the fifth layer is the least squares method layer, and the sixth layer is the K polynomial calculation layer of the mth-order path discretization layer. The seventh layer is the order K judgment layer, the eighth layer is the layer for calculating the effective range of path parameters, the ninth layer is the layer for calculating scalar load parameters, the tenth layer is the layer for judging displacement or temperature conditions, and the eleventh layer is the output layer; Among them, the second layer to the seventh layer form the first-level iterative loop layer. When K is not less than the truncation order of the path discretization layer, it enters the eighth layer; otherwise, it iteratively loops through the second layer to the seventh layer; K is a positive integer; The first layer to the tenth layer form the second-level iterative loop layer. When the displacement boundary condition calculated by the tenth layer is greater than or equal to the given film boundary displacement load in the input parameters and the temperature boundary condition is greater than or equal to the input Compared with the prior art, the present invention has the following beneficial technical effects: This patent provides a method for predicting film folds under a thermal environment. This method takes into account the film bending stiffness effect, can solve the out-of-plane displacement deformation of the film caused by temperature changes, and has a stable algorithm and good convergence. Especially for the problem of multiple instability modes existing in the equilibrium path of film folds. It can effectively solve the problem that the prior art does not consider the influence of bending stiffness on the instability of film folds under a thermal environment. It can not only solve the film fold region, but also solve information such as the out-of-plane displacement and stress and strain of the folded film, realizing a more accurate and comprehensive prediction of the characteristics of film folds under a thermal environment. BRIEF DESCRIPTION OF THE DRAWINGS
[0016] Figure 1 is a flowchart of the method for predicting film folds under a thermal environment of the present invention.
[0017] Figure 2 is a schematic diagram of film folds after applying a load to the film under a thermal environment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0018] In order to make the purpose, technical solutions and advantages of the present invention clearer, the following will be further described in detail with reference to the drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, and are not used to limit the present invention, that is, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments.
[0019] The components described and illustrated in the accompanying drawings and embodiments of the present invention can be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of the present invention provided in the following drawings is not intended to limit the scope of the claimed invention, but merely represents a selected embodiment of the present invention. All other embodiments obtained by those skilled in the art based on the accompanying drawings and embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.
[0020] It should be noted that the term "comprising", "including" or any other variant is intended to cover non-exclusive inclusion, such that a process, element, method, article or device comprising a series of elements not only includes those elements but also other elements not expressly listed, or elements inherent to the process, element, method, article or device.
[0021] The features and performance of the present invention are further described in detail below in conjunction with embodiments.
[0022] Embodiment 1 The present invention provides a method for predicting film wrinkles in a thermal environment, providing theoretical and technical support for accurately predicting the surface accuracy of a deployable film structure in space. As Figure 1 shown, the method specifically includes the following steps: S1. Obtain input parameters, which include the geometric dimensions of the film model, the elastic constants of the film material, the boundary displacement load of the film, the temperature load, the truncation order of the path discrete layer 、 for expressing the initial value of the approximate solution of the film wrinkle image, and other initial parameters; S2. Input the input parameters into a pre-constructed film wrinkle prediction model in a thermal environment, calculate the out-of-plane displacement and stress of the film, and obtain the film wrinkle deformation image in the thermal environment; The film wrinkle prediction model in the thermal environment includes the first layer to the eleventh layer, specifically: The second layer is the calculation layer for the previous order of film wrinkles in the thermal environment, the third layer is the spatial discrete layer for film wrinkles in the thermal environment, the fourth layer is the K polynomial calculation layer for the nth order spatial discrete layer, the fifth layer is the least squares method layer, the sixth layer is the K polynomial calculation layer for the mth order path discrete layer, the seventh layer is the order K judgment layer, the eighth layer is the calculation layer for the effective range of path parameters, the ninth layer is the calculation layer for scalar load parameters, the tenth layer is the judgment layer for displacement or temperature conditions, and the eleventh layer is the output layer.
[0023] Among them, the second layer to the seventh layer constitute the first-level iterative loop layer. When K is not less than the truncation order of the path discrete layer N AWhen it is, enter the eighth layer; otherwise, iteratively loop through the second to seventh layers. The first to tenth layers form the second-level iterative loop layer. When the displacement boundary conditions calculated in the tenth layer are greater than or equal to the film boundary displacement load given in the input parameters and the temperature boundary conditions are greater than or equal to the temperature load given in the input parameters, enter the output layer; otherwise, iteratively loop through the first to tenth layers.
[0024] Example 2 Based on Example 1, in the input parameters, the geometric dimensions include length L , width W and thickness h ; The elastic constants of the film material include E 1, E 2, G 12 , v 21 and v 12 ; E 1 is the elastic modulus along the x direction; E 2 is the elastic modulus along the y direction; G 12 is the x - y in-plane shear elastic modulus; v 21 is the Poisson's ratio when the stress in the y direction produces a transverse strain in the x direction; v 12 is the Poisson's ratio when the stress in the x direction produces a transverse strain in the y direction; The film boundary displacement load includes the displacement amount x along the direction, the displacement amount y along the direction, and the transverse pressure load on the film surface; The temperature load is the temperature change Δ T on the film surface, the coefficient of thermal expansion x along the direction of the film, and the coefficient of thermal expansion y along the direction of the film; The initial values used to represent the approximate solution of the film wrinkle image include the initial value f 0 of the stress function, the initial value w 0 of the deflection function, the initial value λ 0 of the scalar load parameter, along thex Initial value of the directional displacement variable u 0 and along y Initial value of the directional displacement variable v 0; Other initial parameters include the number of thin-film subdomains P、 Truncation order of the spatial discretization layer N T , used to represent the first K -1 approximate solution of the discrete layer of the thin-film fold image path
[0025] The calculation process of the previous order calculation layer of the thin-film fold in the thermal environment is as follows: Input the first K -1 order approximate solution of the thin-film fold image into the previous order calculation layer of the thin-film fold in the thermal environment. Based on the Leibniz multiplication of high-order derivatives, the Leibniz product corresponding to the K order is obtained. The specific formula is as follows: When time,
[0026] When time,
[0027] In the formula, and are the first and second Leibniz products corresponding to the f order of the stress function w and the deflection function K of the approximate solution of the thin-film fold image; , and are the third, fourth, and fifth Leibniz products corresponding to the x order of the displacement function u along the y direction and the displacement function v along the K direction of the approximate solution of the thin-film fold image; is the reference lateral pressure; is the reference temperature change; and are the f order approximate solutions of the stress w and out-of-plane displacement R functions in any subdomain of the folded thin film; the subscript R represents an integer that changes from 1 to K- 1; the superscript P represents the subdomain number; K is the current order of the discrete layer of the path.
[0028] Example 3 Based on Example 2, this mainly introduces the calculation process of the third layer - the spatial discrete layer of film wrinkles under a thermal environment. Specifically: all the parameters of the film input layer and the Leibniz products corresponding to the previous order of film wrinkles under the thermal environment are input into the spatial discrete layer of film wrinkles under the thermal environment, and all the unknown coefficient relationships of the approximate solution of the K order for expressing the spatial discrete layer of the film wrinkle image are obtained, that is, a dimensionality reduction mapping relationship for characterizing high-order unknown coefficients with low-order unknown coefficients in the K region is established. The specific formula is: In the formula,
[0029] where , and are correlation coefficients;
[0030] Among them, , , and represent the elastic constants of the orthotropic film; h represents the thickness of the film.
[0031] In the formula, and are coefficients regarding variables m , n , m 1, and n 1, and are defined as: .
[0032] In the formula, is the f th spatial discrete unknown coefficient of the film stress function K ; is the w th spatial discrete unknown coefficient of the out-of-plane displacement K of the film; is the x th spatial discrete unknown coefficient of the displacement u of the film along the K direction; is the y th spatial discrete unknown coefficient of the displacement v of the film along the K direction.
[0033] In the formula, is the initial value of the film stress fSpatial known discrete coefficient of 0; is the initial value of the out-of-plane displacement of the thin film w Spatial known discrete coefficient of 0.
[0034] In the formula, m , n , m 1 and n1 represent variables, that is, positive integers varying from 1 to N T changing; N T is the truncation order of the spatial discrete layer.
[0035] In the formula, and are the spatial known discrete coefficients of the previous order function and solved in the previous step; , and are the spatial known discrete coefficients of the previous order function , and solved in the previous step.
[0036] The above equation defines an affine subspace of a polynomial, which means that for unknown coefficients and all unknown coefficients can be expressed in terms of the coefficients and this set of coefficients is defined as the unknown coefficients of the spatial discrete layer.
[0037] Example 4 Based on Example 3, the fourth - order spatial discrete layer polynomial calculation layer is introduced. The specific calculation process is as follows: The dimensionality - reduction mapping relationship of the K -th order approximate solution obtained from the spatial discrete layer of the thin - film wrinkles in the thermal environment and used to represent the spatial discrete layer of the thin - film wrinkle image is input into the K -th order spatial discrete layer polynomial calculation layer, and an expression of the K -th order approximate solution used to represent the spatial discrete layer of the thin - film wrinkle image is obtained. K expression of the approximate solution of the
[0038] In the K -th order spatial discrete layer polynomial calculation layer, there is a preset K -th order spatial discrete layer polynomial. The specific formula of the K -th order spatial discrete layer polynomial is:
[0039] In the formula, and are the coordinates of the known points on the thin film.
[0040] Combined with the relationship between the unknown coefficients in the previous spatial discretization layer, the expression of the K -order spatial discretization layer polynomial can be transformed into:
[0041] In the formula, and are particular solutions; and are vectors composed of polynomials respectively; is a vector composed of unknown coefficients .
[0042] Example 5 Based on Example 4, the calculation process of the least squares layer is introduced. Specifically: Input the expression of the K -order approximation solution of the spatial discretization layer representing the thin film wrinkling image obtained from the K -order spatial discretization layer polynomial calculation layer into the least squares layer, and output the K -order approximation solution expression of the path discretization layer representing the thin film wrinkling image without unknown coefficients.
[0043] The function for determining the unknown coefficients based on the least squares collocation method is:
[0044] In the formula, is a function about the boundary conditions; is a function about the transmission conditions.
[0045] Example 6 Based on Example 5, the calculation process of the K -order path discretization layer polynomial is introduced: Input the K -order approximation solution of the spatial discretization layer representing the thin film wrinkling image obtained from the least squares layer into the K -order path discretization layer polynomial calculation layer, and output all approximation solutions of the 1st to K -order path discretization layer.
[0046] According to , calculate ; When ,
[0047] When ,
[0048] Then, calculate the K -th order path discrete layer polynomial according to the following path discrete polynomial calculation formula , , and ; When ,
[0049] When , .
[0050] Example 7 On the basis of Example 2, the specific judgment process of the order K judgment layer is as follows: If K is less than , let , and return to the second layer to calculate the new Leibniz product corresponding to the K -th order; if K is greater than or equal to , the calculation ends and proceeds to the next layer.
[0051] Example 8 On the basis of Example 6, in S2, the specific calculation process of the path parameter effective range calculation layer is to input all the approximate solutions of the 1st to K -th order path discrete layer polynomials obtained by the K -th order path discrete layer polynomial calculation layer into the path parameter effective range calculation layer to obtain the maximum value a max of the path parameter effective range. The specific formula is:
[0052] where is the precision parameter; and are the path discrete layer polynomials when K = 1; and are the path discrete layer polynomials when K = N A .
[0053] Example 9 On the basis of Example 1, in S2, the calculation process of the maximum value of the scalar load parameter is to use the initial value of the scalar load in the input parametersThe maximum value of the effective range of the path parameter obtained by the path parameter effective range calculation layer is input into the scalar load parameter calculation layer to obtain the maximum value of the scalar load parameter. . The specific formula is:
[0054] Among them, a is the path parameter, and its superscript K represents a positive integer that changes from 1 to N A ; λ 0 is the initial value of the scalar load parameter; is the K -th order approximate solution of the thin film scalar load parameter, and the subscript K represents an integer that changes from 1 to N A ; the superscript P represents the number of the subdomain.
[0055] Example 10 On the basis of Example 1, in S2, the specific process of the displacement or temperature condition layer is as follows: The maximum value of the scalar load parameter obtained by the scalar load parameter calculation layer is input into the displacement or temperature condition layer to obtain the theoretical maximum values of the displacement and thermal external load under the current path; If the theoretical maximum values of the displacement and thermal external load under the current path are less than the external load parameters given by the input layer, update the initial value used to represent the approximate solution of the thin film wrinkling image, and return to the first layer to continue the calculation; otherwise, enter the output layer; the external load parameters are the thin film boundary displacement load and the temperature load.
[0056] Specifically, if the displacement load or the temperature load satisfies all the following inequalities, the inequalities are:
[0057] then enter the output layer; if one of the above inequalities does not hold, update , and return to the second layer to continue the calculation.
[0058] Among them, represents the theoretical maximum value of the displacement load along the y direction under the current path; represents the theoretical maximum value of the transverse pressure load on the thin film surface under the current path; represents the theoretical maximum value of the displacement load along the x direction under the current path; represents the theoretical maximum value of the thermal load under the current path.
[0059] Example 11 Based on Embodiment 2, in S2, the specific process of the output layer is as follows: The initial value of the approximate solution of the thin film wrinkle image and the first to K approximate solutions of all orders of the path discrete layer polynomial calculation layer up to the K th order are input into the output layer, and the final expression for expressing the approximate solution of the thin film wrinkle image is output. The specific formula is: Update according to the following formula :
[0060] Calculate the path parameter according to the updated scalar load parameter a :
[0061] Calculate the final result thin film wrinkle parameter according to the following formula , , and expressions: .
[0062] In summary, as Figure 1 shown, the thin film wrinkle prediction method of the present invention is implemented as follows: 1) Define the geometric dimensions of the thin film model, including the length L , width W and thickness h ; The elastic constants of the thin film material include E 1, E 2, G 12 , v 21 and v 12 ; The thin film boundary displacement load, including the displacement amount x along the direction and the displacement amount y along the direction; The thin film surface lateral pressure load p ; The thin film thermal expansion coefficients and ; The temperature change condition is the temperature change on the thin film surface; The number of thin film subdomains P ; The truncation order of the path discrete layer N A and the truncation order of the space discrete layer N T ; The initial values for expressing the approximate solution of the thin film wrinkle image are the initial value f 0 of the stress function and the initial value w0. Initial values of scalar load parameters λ 0. Along x Initial value of displacement variable u 0 and along y Initial value of displacement variable v 0; The previous K -1 approximate solutions for expressing the discrete layers of the film wrinkle image path under the action of given thermal loads and displacement variables.
[0063] 2) Input the previous K -1 order approximate solutions for expressing the film wrinkle image into the calculation layer of the previous order of film wrinkles in the thermal environment. Based on the Leibniz multiplication of high-order derivatives, obtain the Leibniz product corresponding to the K th order ; 3) Input all the parameters of the film input layer and the Leibniz product corresponding to the K th order obtained from the calculation layer of the previous order of film wrinkles in the thermal environment into the spatial discrete layer of film wrinkles in the thermal environment, and obtain all the relationships of the unknown coefficients of the K th order approximate solution for expressing the spatial discrete layer of the film wrinkle image, that is, establish a dimensionality reduction mapping relationship that characterizes the higher-order unknown coefficients with lower-order unknown coefficients in the region; 4) Input the dimensionality reduction mapping relationship of the K th order approximate solution for expressing the spatial discrete layer of the film wrinkle image obtained from the spatial discrete layer of film wrinkles in the thermal environment into the polynomial calculation layer of the K th order spatial discrete layer, and obtain the expression of the K th order approximate solution for expressing the spatial discrete layer of the film wrinkle image; 5) Input the expression of the K th order approximate solution for expressing the spatial discrete layer of the film wrinkle image obtained from the polynomial calculation layer of the K th order spatial discrete layer into the least squares method layer, and output the expression of the K th order approximate solution for expressing the spatial discrete layer of the film wrinkle image without unknown coefficients; 6) Input the K th order approximate solution for expressing the spatial discrete layer of the film wrinkle image obtained from the least squares method layer into the polynomial calculation layer of the K th order path discrete layer, and output the expression of the K th order approximate solution for expressing the path discrete layer of the film wrinkle image; 7) If K is less than , let , and return to the second layer to calculate the new Leibniz product corresponding to the K th order; If K is greater than or equal to , the calculation ends and proceeds to the next layer; 8) Input all approximate solutions of the 1st to K order path discretization layer into the path parameter effective range calculation layer to obtain the maximum path parameter ; 9) Input the initial scalar load value of the said thin film input layer and the maximum path parameter into the scalar load parameter calculation layer to obtain the maximum scalar load parameter ; 10) Only when the displacement or temperature boundary condition calculated by the said judgment displacement or temperature condition layer is not less than the displacement or temperature boundary condition given in the input parameters can it enter the output layer; otherwise, iterate and execute the first layer to the tenth layer in a loop.
[0064] 11) Output the final calculation result of the thin film wrinkles in the thermal environment.
[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications or equivalent replacements can still be made to the specific implementation manners of the present invention, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered by the protection scope of the claims of the present invention.
Claims
1. A method for predicting film wrinkles in a thermal environment, characterized in that, It includes the following steps: S1. Obtain input parameters, which include the geometric dimensions of the thin film model, the elastic constants of the thin film material, the boundary displacement load of the thin film, the temperature load, and the truncation order of the path discrete layer 、 The initial value for expressing the approximate solution of the thin film wrinkling image, and other initial parameters; S2. Input the input parameters into the pre-constructed thin film wrinkling prediction model under a thermal environment, calculate the out-of-plane displacement and stress of the thin film, and obtain the thin film wrinkling deformation image under the thermal environment; The thin film wrinkling prediction model under the thermal environment includes the first layer to the eleventh layer, specifically: The first layer is the input layer, the second layer is the previous order calculation layer of film wrinkles under thermal environment, the third layer is the spatial discretization layer of film wrinkles under thermal environment, and the fourth layer is the K The fifth layer is the least squares layer, and the sixth layer is the polynomial calculation layer. K Order path discrete layer polynomial calculation layer, the seventh layer is the order K The eighth layer is the path parameter effective range calculation layer, the ninth layer is the scalar load parameter calculation layer, the tenth layer is the displacement or temperature condition judgment layer, and the eleventh layer is the output layer; Among them, the second layer to the seventh layer constitute the first-level iterative loop layer. When K it is not less than the truncation order of the path discretization layer, it enters the eighth layer; otherwise, it iteratively loops through the second layer to the seventh layer. K is a positive integer; The first layer to the tenth layer form the second-level iterative loop layer. When the displacement boundary condition calculated by the tenth layer is greater than or equal to the thin film boundary displacement load given in the input parameters and the temperature boundary condition is greater than or equal to the temperature load given in the input parameters, enter the output layer; otherwise, iteratively loop and execute the first layer to the tenth layer.
2. The method for predicting film wrinkles in a thermal environment according to claim 1, wherein In S1, among the input parameters, the geometric dimensions of the thin film model include the length L , width W and thickness h ; The elastic constants of the thin film material include E 1, E 2, G 12 , v 21 and v 12 ; E 1 is the elastic modulus along the x direction; E 2 is the elastic modulus along the y direction; G 12 is the shear elastic modulus in the x - y plane; v 21 is the Poisson's ratio when the stress in the y direction produces a transverse strain in the x direction; v 12 is the Poisson's ratio when the stress in the x direction produces a transverse strain in the y direction; The thin-film boundary displacement load includes the displacement amount along x direction , the displacement amount along y direction , and the lateral pressure load on the thin-film surface p ; The temperature load includes the change in the surface temperature of the thin film Δ T , the coefficient of thermal expansion x of the thin film in the direction and the coefficient of thermal expansion y of the thin film in the direction; Initial values for expressing approximate solutions of thin-film wrinkling images, including initial values of stress functions f 0, initial values of deflection functions w 0, initial values of scalar load parameters λ 0, along x direction displacement variable initial values u 0 and along y direction displacement variable initial values v 0; Other initial parameters include the number of thin film sub-domains P , the truncation order of the spatial discretization layer N T , and the front K -1 approximate solution used to represent the discrete layer of the thin film wrinkle image path.
3. A method for predicting film wrinkles in a thermal environment according to claim 2, characterized in that, In S2, the specific calculation process of the previous order calculation layer of the thin film wrinkling under the thermal environment is: Input the previous - 1st order approximate solution used to represent the discrete layer of the thin - film fold image path into the thin - film fold previous - order calculation layer under the thermal environment. Based on the Leibniz multiplication of high - order derivatives, obtain the Leibniz product corresponding to the K order; K In S2, the order K The processing procedure of the judgment layer is specifically as follows: If K is less than , let , and return the Leibniz product corresponding to the new K -th order in the second layer; if K is greater than or equal to , the calculation ends and proceeds to the next layer; Among them, is the truncation order of the path discretization layer.
4. A method for predicting film wrinkles in a thermal environment according to claim 3, characterized in that, In S2, the calculation process of the spatial discretization layer of the thin film wrinkling under the thermal environment is specifically: Input the Leibniz product corresponding to the K th order obtained from the previous order calculation layer of the film fold in the thermal environment into the spatial discretization layer of the film fold in the thermal environment, and obtain the dimensionality reduction mapping relationship for expressing the K th order approximate solution of the spatial discretization layer of the film fold image.
5. A method for predicting film wrinkles in a thermal environment according to claim 4, characterized in that In S2, in the K -order spatial discrete layer polynomial calculation layer, there is a K -order spatial discrete layer polynomial preset. The specific calculation process is as follows: Input the reduced-dimensional mapping relationship of the K -order approximate solution for expressing the spatial discrete layer of the thin-film fold image obtained from the spatial discrete layer of the thin-film fold in the thermal environment into the K -order spatial discrete layer polynomial calculation layer to obtain the K -order approximate solution expression for expressing the spatial discrete layer of the thin-film fold image with unknown coefficients.
6. A method for predicting film wrinkles in a thermal environment according to claim 5, characterized in that In S2, the calculation process of the least squares layer is: Input the K -th order approximate solution expression for representing the spatial discrete layer of the thin film wrinkling image obtained from the spatial discrete layer polynomial calculation layer into the least squares method layer, and output the K -th order approximate solution expression for representing the spatial discrete layer of the thin film wrinkling image without unknown coefficients. K 7. A method for predicting film wrinkles in a thermal environment according to claim 6, characterized in that In S2, in the K -order path discrete layer polynomial calculation layer, there is a K -order path discrete layer polynomial. The calculation process of the K -order path discrete layer polynomial is as follows: Input the expression of the K -order approximate solution for representing the spatially discrete layer of the thin film wrinkle image obtained by the least squares method layer into the K -order path discrete layer polynomial calculation layer, and output all approximate solutions of the 1st to K -order path discrete layer.
8. A method for predicting film wrinkles in a thermal environment according to claim 7, characterized in that In S2, the specific process of the effective range calculation layer of the path parameter is: Input the 1st to K order path discrete layer polynomial calculation layer obtained approximate solutions of all order path discrete layers to the path parameter effective range calculation layer, and obtain the maximum value of the effective range of the path parameter K ； The specific process of the scalar load parameter calculation layer is: The initial value of the scalar load in the input parameters The maximum value of the effective range of the path parameter obtained from the path parameter effective range calculation layer and the maximum value of the effective range of the path parameter are input to the scalar load parameter calculation layer to obtain the maximum value of the scalar load parameter.
9. A method and system for predicting film wrinkles in a thermal environment according to claim 8, characterized in that, In S2, the specific process of the displacement or temperature condition judgment layer is: Input the maximum value of the scalar load parameter obtained by the scalar load parameter calculation layer into the displacement or temperature condition judgment layer to obtain the theoretical maximum values of the displacement and the thermal external load under the current path; If the theoretical maximum values of the displacement and the thermal external load under the current path are less than the external load parameters given by the input layer, update the initial value used to represent the approximate solution of the thin film wrinkling image, and return to the first layer to continue the calculation; otherwise, enter the output layer; the external load parameters are the thin film boundary displacement load and the temperature load; The specific process of the output layer is: The initial value used to represent the approximate solution of the thin film wrinkling image is combined with the 1st to K approximate solutions obtained from all the K order path discrete layer polynomial calculation layers and input into the output layer, and the output is the final expression used to represent the approximate solution of the thin film wrinkling image. Based on the approximate solution expression, the thin film wrinkling deformation image under the thermal environment can be drawn.
10. A thin film wrinkle prediction system under a thermal environment, characterized in that, It includes: A data acquisition module, which is used to acquire input parameters, where the input parameters include the geometric dimensions of the thin film model, the elastic constants of the thin film material, the boundary displacement load of the thin film, the temperature load, and the truncation order of the path discrete layer 、 which is used to represent the initial value of the approximate solution of the thin film wrinkle image and other initial parameters; A prediction module for inputting the input parameters into the pre-constructed thin film wrinkling prediction model under a thermal environment, calculating the out-of-plane displacement and stress of the thin film, and obtaining the thin film wrinkling deformation image under the thermal environment; The thin film wrinkling prediction model under the thermal environment includes the first layer to the eleventh layer, specifically: The first layer is the input layer, the second layer is the previous order calculation layer of the film fold under the thermal environment, the third layer is the spatial discretization layer of the film fold under the thermal environment, and the fourth layer is the K polynomial calculation layer of the nth order spatial discretization layer, the fifth layer is the least squares method layer, and the sixth layer is the K polynomial calculation layer of the mth order path discretization layer, the seventh layer is the order K judgment layer, the eighth layer is the effective range calculation layer of the path parameters, the ninth layer is the scalar load parameter calculation layer, the tenth layer is the displacement or temperature condition judgment layer, and the eleventh layer is the output layer; Among them, the second layer to the seventh layer form the first-level iterative loop layer. When K is not less than the truncation order of the path discretization layer, it enters the eighth layer; otherwise, it iteratively loops through the second layer to the seventh layer; K is a positive integer; The first layer to the tenth layer form the second-level iterative loop layer. When the displacement boundary condition calculated by the tenth layer is greater than or equal to the thin film boundary displacement load given in the input parameters and the temperature boundary condition is greater than or equal to the temperature load given in the input parameters, enter the output layer; otherwise, iteratively loop and execute the first layer to the tenth layer.