Temperature-curvature model inverse finite element deformation reconstruction method of large plate under thermal load
By deploying sensors on a large plate to acquire data, establishing a temperature-curvature model, and combining it with the least squares optimization method, the problem of the inverse finite element algorithm being unable to reconstruct the deformation of large plates under thermal loads was solved, achieving high-precision structural deformation reconstruction and improving the applicability of the inverse finite element algorithm.
Patent Information
- Application Number
- CN202511407865.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-29
- Publication Date
- 2026-01-13
AI Technical Summary
Existing inverse finite element algorithms struggle to reconstruct the deformation of large plates under thermal loads, especially when performing single-surface strain measurements, as they cannot accurately reconstruct the displacement field of the antenna on track.
By arranging temperature and displacement sensors on a large plate to acquire thermal deformation data, a temperature-curvature model is established by fitting the temperature and curvature relationship using a power function. Combined with elasticity theory and least squares optimization method, the strain on both sides of the structure is obtained, and finally the global displacement field is reconstructed.
It achieves high-precision deformation reconstruction of large plates under thermal load, reduces the number of sensors required, improves the applicability of the inverse finite element algorithm, and enhances the feasibility of structural deformation reconstruction.
Smart Images
Figure CN121328197A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of deformation reconstruction and structural deformation monitoring, and in particular to a method for inverse finite element deformation reconstruction of a large plate under thermal load using a temperature-curvature model. Background Technology
[0002] With the increasing demands for improved performance in spaceborne radar, antenna apertures and power are growing larger, leading to greater on-orbit thermal deformation and a growing impact on electrical performance. Existing inverse finite element methods struggle to reconstruct the deformation of large plates under thermal loads when measuring single-surface strain. Therefore, it is necessary to achieve real-time, high-precision on-orbit displacement field reconstruction for ultra-large aperture spaceborne antennas, providing a foundation for adaptive compensation of radar antenna electrical performance. Summary of the Invention
[0003] To address the existing technical problems, this invention provides a method for reconstructing the temperature-curvature model of a large plate under thermal load using inverse finite element deformation.
[0004] The specific content of this invention is as follows: A method for reconstructing the temperature-curvature model of a large plate under thermal load using inverse finite element deformation, comprising the following steps:
[0005] S1. Apply thermal load to a large plate to conduct a thermal deformation experiment. By arranging temperature and displacement sensors on the structure, acquire temperature and displacement data at M moments during the entire heating period. Based on the acquired data, fit the temperature field and displacement field of the structure at M moments during the entire heating process.
[0006] S2, the displacement field input curvature and displacement at the M time points obtained in S1. The relationship is used to obtain the curvature field of the structure at M time points. ;
[0007] S3, based on the temperature field at M time points obtained in S1 and the curvature field of the structure at M time points obtained in S2, uses a power function to fit the temperature and curvature values at each position of the structure at M time points, obtains the temperature-curvature power function fitting coefficients at each position, and obtains the temperature-curvature model of the structure.
[0008] S4. When performing real-time online deformation monitoring of the structure, acquire the temperature data collected by the temperature sensor and the strain data collected by the strain sensor on the structure at a certain moment, fit the data to obtain the temperature field and single-plane strain field of the structure, and use the fitted temperature field as the input of the temperature curvature-model in S3 to further obtain the curvature field of the structure at that moment.
[0009] S5. Input the single-plane strain field and curvature field obtained in S4 into the structural strain-curvature relationship in the theory of elasticity to calculate the strain field of the other plane of the structure, so as to obtain the double-plane strain of the structure.
[0010] S6 uses the measured strain obtained in S5 as the error function of the inverse finite element algorithm to participate in the least squares optimization, and obtains the unit reconstruction equation set of each element under the inverse finite element algorithm. All unit reconstruction equation sets are assembled to obtain the overall reconstruction equation set. The boundary conditions are substituted and solved to realize the reconstruction of the global displacement field of the structure.
[0011] Furthermore, S1 includes:
[0012] Temperature and displacement sensors were deployed on the surface of a large plate structure to record the position coordinates of each sensor on the surface. An experimental system was built to conduct heating experiments. During the heating process, the structure will deform. The sensors collected temperature and displacement data at M moments within the heating period according to the system sampling rate. Based on the strain and temperature data collected by the system, combined with the sensor position coordinates, and using the internal fitting function of Matlab, the temperature and strain data collected by the experimental system were matched one-to-one with the position coordinates of the structure to obtain the temperature field and displacement field of the structure at M moments during the entire heating process.
[0013] Furthermore, S2 includes:
[0014] The displacement field at the M time points obtained in S1 is input curvature. With displacement The relationship is used to calculate the curvature field of the structure. The specific form of the relationship is as follows.
[0015]
[0016] in, For the structural curvature field, This represents the curvature of the mid-surface of a large plate in the x-direction after bending. This represents the curvature of the mid-surface of a large plate in the x-direction after bending. This indicates the curvature of the mid-surface of a large plate in the x and y directions after bending. This represents the structural displacement field.
[0017] Furthermore, S3 includes:
[0018] Based on the temperature fields obtained from the fitted temperature data in S1 at M time points, and the curvature fields obtained from the curvature-displacement relationship in S2 at M time points, the temperature and curvature values at each location of the structure at M time points are obtained. A power function is then used to fit the temperature and curvature values, where the specific form of the power function is:
[0019]
[0020] in, For the temperature field Temperature values corresponding to discrete points ; , , To characterize the first The fitting coefficients of the power function relating temperature values and curvature at discrete points. The temperature field provides The function represents the temperature value at each location, reflecting the overall structure. The mapping relationship between temperature and curvature at each location, i.e., the structural temperature-curvature model, enables the acquisition of temperature-curvature.
[0021] Taking the first discrete point as an example, temperature values at M time points during the structural heating process are obtained in S1, and curvature values at M time points are obtained in S2. Using the temperature values as the independent variable and the curvature values as the dependent variable, a fitting operation is performed in Matlab to obtain the fitting coefficients for the temperature-curvature power function relationship at the first discrete point. , , In Matlab The same process is performed at each discrete location to obtain all the fitting coefficients, and then... , , By writing the power function coefficient matrix A, the exponent matrix B, and the constant matrix C, the temperature-curvature model can be obtained.
[0022] Furthermore, S4 includes:
[0023] Temperature and strain sensors were deployed on the surface of a large plate structure to record the position coordinates of each sensor. An experimental system was built to conduct heating experiments, during which the structure deformed. The sensors collected temperature and strain data at specific moments within the heating period. Based on the collected strain and strain data, combined with the sensor position coordinates, and using a Matlab-based fitting function, the temperature and strain data collected by the experimental system were mapped one-to-one with the structure's position coordinates to obtain the temperature and strain fields at a specific heating moment. Based on the obtained temperature fields, the surface temperature and strain data of the structure were obtained. Temperature values at discrete points , ,Will A temperature value is used as the independent variable of the power function in S3, and input into the temperature-curvature model to obtain... Curvature values at discrete points That is, the structural curvature field is obtained.
[0024] Furthermore, S5 includes:
[0025] The strain field obtained in S4 and the curvature field obtained through the temperature-curvature model are substituted into the structural strain-curvature relationship in elasticity theory. The relationship is determined by linear elasticity theory. For a large plate structure with thickness H, the surface strain is determined by the membrane strain. and structural curvature field Linear representation:
[0026]
[0027] Where h represents the strain of the surface with unknown strain, i.e. the structural surface without strain sensors; c represents the strain of the surface with known strain, i.e. the structural surface with sensors. Depend on and curvature Linear representation:
[0028]
[0029] The single-surface strain field in S4 is fitted based on measured data. Substituting the curvature field obtained through the temperature-curvature model into the above equation, the strain field on the other side of the structure can be calculated. This enables the acquisition of strain on both sides of the structure.
[0030] Furthermore, the least squares optimization in S6 is as follows:
[0031] Converting biplane strain into structural neutral plane strain and curvature:
[0032]
[0033]
[0034] in, These represent the surface strain field and curvature field of the structure, respectively. and It is a two-sided strain;
[0035] Construct the error function between all measured strains and theoretical strains within the inverse element of the structure:
[0036] in, The displacement field to be determined for the structure is... For weighting coefficients, For the strain field of the inverse element theory, The structure is respectively The measured strain and curvature field of each element, where H is the structural thickness. For the first The area of each unit, where n represents the area of the structure divided into n discrete reverse units;
[0037] Take the partial derivative of the error function and set it to zero:
[0038]
[0039] The system of equations satisfied by the nodal displacements of the reverse element of the structure is as follows:
[0040]
[0041] in, The displacement field to be determined for the structure is... These are the coefficient matrix and coefficient vector of the above system of equations, respectively;
[0042] By assembling this system of equations and substituting the boundary conditions, the global displacement field of the structure can be reconstructed.
[0043] This invention calculates the curvature field of a structure based on its displacement field at different times and fits the mapping relationship between the curvature and temperature at each point on the structure to obtain a temperature curvature model. During real-time deformation reconstruction, the measured single-sided temperature is input into the temperature curvature model to obtain the structural curvature, and the strain-curvature relationship is combined to obtain the two-sided strain of the structure. Finally, the two-sided strain is used as the input to the error function of the inverse finite element method to achieve deformation reconstruction of the structure. This invention solves the problem that the inverse finite element method is difficult to realize deformation reconstruction of large plate structures under thermal load when measuring single-sided strain, and has broad application prospects in the field of online deformation monitoring of complex structures. Attached Figure Description
[0044] The invention will be further explained below with reference to the accompanying drawings.
[0045] Figure 1 This is a flowchart of the method of the present invention.
[0046] Figure 2 This is a layout diagram of the fiber Bragg grating for the temperature reference of the antenna sub-board.
[0047] Figure 3 This is a layout diagram of the fiber optic grating for strain measurement on the antenna sub-board.
[0048] Figure 4 The figure shows the fitting results of the displacement field under typical heating conditions.
[0049] Figure 5a shows the curvature distribution in the x-direction under typical heating conditions.
[0050] Figure 5b shows the curvature distribution in the y-direction under typical heating conditions.
[0051] Figure 5c shows the curvature distribution in the xy direction under typical heating conditions.
[0052] Figure 6 Let k be the temperature and the curvature in the x-direction. x Relationship diagram.
[0053] Figure 7 This is a schematic diagram of the temperature field fitted under typical heating conditions in the experiment.
[0054] Figure 8a is a schematic diagram of the measured strain field in the 0-degree direction.
[0055] Figure 8b is a schematic diagram of the measured strain field in the 90-degree direction.
[0056] Figure 8c is a schematic diagram of the measured strain field in the 45-degree direction.
[0057] Figure 9 This is a schematic diagram of the strain field in the 90-degree direction.
[0058] Figure 10a A schematic diagram for reconstructing the displacement field.
[0059] Figure 10b This is a schematic diagram of the measured displacement field.
[0060] Figure 10c This is a schematic diagram showing the difference between the measured displacement field and the reconstructed displacement field. Detailed Implementation
[0061] Combination Figure 1-Figure 1 0. The present invention provides a temperature curvature model of a large plate under thermal load - an inverse finite element deformation reconstruction method, the steps of which are as follows:
[0062] (1) Apply thermal load to the large plate to carry out thermal deformation test. By arranging temperature sensors and displacement sensors on the structure, acquire temperature data and displacement data at M moments during the entire heating period. Based on the acquired data, fit the temperature field and displacement field of the structure at M moments during the entire heating process.
[0063] (2) Input the displacement field at the M time points obtained in step (1) into the curvature. With displacement The relationship is used to obtain the curvature field of the structure at M time points;
[0064] (3) Based on the temperature field at M time points obtained in step (1) and the curvature field of the structure at M time points obtained in step (2), the temperature and curvature values at each position of the structure at M time points are fitted by a power function to obtain the temperature-curvature power function fitting coefficients at each position and obtain the temperature-curvature model of the structure.
[0065] (4) When performing real-time online deformation monitoring of the structure, acquire the temperature data collected by the temperature sensor and the strain data collected by the strain sensor on the structure at a certain moment, fit the data to obtain the temperature field and single-surface strain field of the structure, and use the fitted temperature field as the input of the temperature curvature-model in step (3) to further obtain the curvature field of the structure at that moment.
[0066] (5) Input the single-surface strain field and curvature field obtained in step (4) into the structural strain-curvature relationship in the elasticity theory to calculate the strain field of the other surface of the structure, so as to obtain the double-surface strain of the structure.
[0067] (6) The structural double-sided strain obtained in step (5) is used as the measured strain input in the error function of the inverse finite element algorithm to participate in the least squares optimization, and the unit reconstruction equation set of each element under the inverse finite element algorithm is obtained. All the unit reconstruction equation sets are assembled to obtain the overall reconstruction equation set. The boundary conditions are substituted and the solution is obtained to realize the reconstruction of the global displacement field of the structure.
[0068] Furthermore, step (1) specifically includes:
[0069] Temperature and displacement sensors were deployed on the surface of a large plate structure to record the position coordinates of each sensor on the surface. An experimental system was built to conduct heating experiments. During the heating process, the structure will deform. The sensors collected temperature and displacement data at M moments within the heating period according to the system sampling rate. Based on the strain and temperature data collected by the system, combined with the sensor position coordinates, and using the internal fitting function of Matlab, the temperature and strain data collected by the experimental system were matched one-to-one with the position coordinates of the structure to obtain the temperature field and displacement field of the structure at M moments during the entire heating process.
[0070] Furthermore, step (2) specifically includes:
[0071] The displacement fields at the M time points obtained in step (1) are input into the curvature. With displacement The relationship is used to calculate the curvature field of the structure. The specific form of the relationship is as follows.
[0072]
[0073] in, For the structural curvature field, This represents the curvature of the mid-surface of a large plate in the x-direction after bending. This represents the curvature of the mid-surface of a large plate in the x-direction after bending. This indicates the curvature of the mid-surface of a large plate in the x and y directions after bending. This represents the structural displacement field.
[0074] Furthermore, step (3) specifically includes:
[0075] Based on the temperature fields at M time points obtained from the fitted temperature data in step (1) and the curvature fields at M time points obtained from the curvature displacement relationship in step (2), the temperature and curvature values at each location of the structure at M time points are obtained. A power function is used to fit the temperature and curvature values, where the specific form of the power function is:
[0076]
[0077] in, For the temperature field Temperature values corresponding to discrete points ; , , To characterize the first The fitting coefficients of the power function relating temperature values and curvature at discrete points. The temperature field provides The function represents the temperature value at each location, reflecting the overall structure. The mapping relationship between temperature and curvature at each location, i.e., the structural temperature-curvature model, enables the acquisition of temperature-curvature.
[0078] Taking the first discrete point as an example, the temperature values at M time points during the structural heating process were obtained in step (1), and the curvature values at M time points were obtained in step (2). The temperature values were used as the independent variable of the power function and the curvature values were used as the dependent variable. The fitting coefficients of the temperature-curvature power function relationship at the first discrete point were obtained by fitting the data in Matlab. , , In Matlab The same process is performed at each discrete location to obtain all the fitting coefficients, and then... , , By writing the power function coefficient matrix A, the exponent matrix B, and the constant matrix C, the temperature-curvature model can be obtained.
[0079] Furthermore, step (4) specifically includes:
[0080] Temperature and strain sensors were deployed on the surface of a large plate structure to record the position coordinates of each sensor. An experimental system was built to conduct heating experiments, during which the structure deformed. The sensors collected temperature and strain data at specific moments within the heating period. Based on the collected strain and strain data, combined with the sensor position coordinates, and using a Matlab-based fitting function, the temperature and strain data collected by the experimental system were mapped one-to-one with the structure's position coordinates to obtain the temperature and strain fields at a specific heating moment. Based on the obtained temperature fields, the surface temperature and strain data of the structure were obtained. Temperature values at discrete points , ,Will The temperature value is used as the independent variable of the power function in step (3), and input into the temperature-curvature model to obtain... Curvature values at discrete points That is, the structural curvature field is obtained.
[0081] Furthermore, step (5) specifically includes:
[0082] Substitute the strain field obtained in step (4) and the curvature field obtained through the temperature-curvature model into the structural strain-curvature relationship in elasticity theory. The relationship is determined by linear elasticity theory. For a large plate structure with thickness H, the surface strain is determined by the membrane strain. and structural curvature field Linear representation:
[0083]
[0084] Where h represents the strain of the surface with unknown strain, i.e. the structural surface without strain sensors; c represents the strain of the surface with known strain, i.e. the structural surface with sensors. Depend on and curvature Linear representation:
[0085] (1)
[0086] The single-surface strain field fitted based on measured data in step (4) Substituting the curvature field obtained through the temperature-curvature model into equation (1) above, the strain field on the other side of the structure is calculated. This enables the acquisition of strain on both sides of the structure.
[0087] Furthermore, the least squares optimization in step (6) specifically involves:
[0088] Converting biplane strain into structural neutral plane strain and curvature:
[0089]
[0090]
[0091] in, These represent the surface strain field and curvature field of the structure, respectively. and It is a two-sided strain;
[0092] Construct the error function between all measured strains and theoretical strains within the inverse element of the structure:
[0093]
[0094] in, The displacement field to be determined for the structure is... For weighting coefficients, For the strain field of the inverse element theory, The structure is respectively The measured strain and curvature field of each element, where H is the structural thickness. For the first The area of each unit, where n represents the area of the structure divided into n discrete reverse units;
[0095] Take the partial derivative of the error function and set it to zero:
[0096]
[0097] The system of equations satisfied by the nodal displacements of the reverse element of the structure is as follows:
[0098]
[0099] in, The displacement field to be determined for the structure is... These are the coefficient matrix and coefficient vector of the above system of equations, respectively;
[0100] By assembling this system of equations and substituting the boundary conditions, the global displacement field of the structure can be reconstructed.
[0101] The following examples further illustrate the solution proposed in this application.
[0102] The deformation and reconstruction object in this embodiment is a large antenna plate structure with dimensions of 3125mm × 1500mm × 20mm (length × width × thickness). A heating element is installed on the lower surface. During the experiment, the antenna plate is continuously heated. Due to the temperature gradient along the thickness direction of the antenna plate during heating, warping deformation occurs. Firstly, in this experiment, a fiber optic grating temperature sensor is placed on the side of the structure without the heating element to collect temperature data. Figure 2 As shown, a fiber optic strain sensor is used to collect strain data, as follows. Figure 3As shown, a laser displacement sensing system was set up to collect displacement data. During the entire experiment, the antenna plate structure was continuously heated for 10 minutes, and temperature and displacement data were collected throughout the heating process.
[0103] Measured data from 10 time points (minute 1, minute 2, ..., minute 10) during heating were selected to train the temperature-curvature model. Figure 4 The figure shows the displacement results at the 10th minute. The temperature and displacement data at each moment are fitted together, and then the curvature field at 10 moments is calculated using the displacement, as shown below. Figures 5a-5c The figure shows the curvature field at 10 minutes.
[0104] Using the cold surface temperature of each unit as the independent variable, and the curvature in the x-direction as the independent variable... curvature in the y direction and the torque in the x and y directions For the dependent variable, a power function is used for fitting, specifically in the form of:
[0105]
[0106] in, For the temperature field Temperature values corresponding to discrete points , , The fitting coefficients for the power function are 20493, representing the 20493 discrete temperature values provided for the antenna plate structure. This function reflects the mapping relationship between temperature and curvature at 20493 locations throughout the structure, i.e., the temperature curvature model. Figure 6 As shown.
[0107] The temperature-curvature model has been constructed above. This model will be used to realize online real-time deformation reconstruction of the antenna sub-plate structure based on single-surface strain. Taking the displacement field at the 10-minute heating time as an example, based on... Figure 2 and Figure 3 A fiber optic grating sensor layout was used to acquire single-surface temperature and strain data of the structure at 10-minute intervals. The discrete data were then fitted to obtain the single-surface temperature and strain fields of the structure at 10-minute intervals, as shown below. Figure 7 , Figures 8a-8c As shown.
[0108] The single-sided temperature field is input into the temperature-curvature model to obtain the structural curvature field. Using the relationship between curvature and strain, the structural curvature field and the single-sided strain field are input as the following equation to obtain the strain field of the antenna sub-plate's hot surface, such as... Figure 9 As shown;
[0109]
[0110] in, The temperature field of the surface without heating elements. The curvature field calculated using the temperature curvature model.
[0111] The cold surface strain and hot surface strain were used as inputs to the inverse finite element algorithm to verify the displacement reconstruction effect; the deformation reconstruction results after 10 minutes of heating are as follows: Figures 10a-10c As shown. The maximum reconstruction error of the measured displacement minus the reconstructed displacement is 0.49 mm, accounting for 8.1% of the maximum displacement of 6.05 mm. In summary, the temperature curvature model-inverse finite element deformation reconstruction method for large plate structures under thermal load proposed in this invention can achieve deformation reconstruction under single-surface strain measurement conditions.
[0112] This invention acquires the real-time temperature and curvature fields of a large plate structure during the heating process, providing a foundation for establishing a temperature-curvature model. It also establishes the relationship between temperature and deformation of the large plate through the temperature-curvature model. Furthermore, it improves the inverse finite element method (IFM) by acquiring the strain on the other side of the structure based on single-sided strain, reducing the number of sensors required. The acquired strain on both sides of the structure is used as the measured strain input in the error function of the inverse finite element method to participate in least-squares optimization, completing the entire deformation reconstruction process and realizing the deformation reconstruction of the structure.
[0113] The method of this invention generally reduces the number of sensors required for the inverse finite element algorithm, improves the feasibility of the inverse finite element algorithm in structural deformation reconstruction, enhances the applicability of the inverse finite element algorithm under different working conditions, and plays a positive role in promoting the research on deformation reconstruction of large plate structures.
[0114] Many specific details have been set forth in the foregoing description to provide a thorough understanding of the present invention. However, the above description is merely a preferred embodiment of the present invention, and the present invention can be implemented in many other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed above. Furthermore, any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention, or modify them into equivalent embodiments, using the methods and techniques disclosed above, without departing from the scope of the present invention. Any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the content of the present invention, shall still fall within the protection scope of the present invention.
Claims
1. A method for reconstructing the temperature-curvature model of a large plate under thermal load using inverse finite element deformation, characterized by: Includes the following steps: S1. Apply thermal load to a large plate to conduct a thermal deformation experiment. By arranging temperature and displacement sensors on the structure, acquire temperature and displacement data at M moments during the entire heating period. Based on the acquired data, fit the temperature field and displacement field of the structure at M moments during the entire heating process. S2, the displacement field input curvature and displacement at the M time points obtained in S1. The relationship is used to obtain the curvature field of the structure at M time points. ; S3, based on the temperature field at M time points obtained in S1 and the curvature field of the structure at M time points obtained in S2, uses a power function to fit the temperature and curvature values at each position of the structure at M time points, obtains the temperature-curvature power function fitting coefficients at each position, and obtains the temperature-curvature model of the structure. S4. When performing real-time online deformation monitoring of the structure, acquire the temperature data collected by the temperature sensor and the strain data collected by the strain sensor on the structure at a certain moment, fit the data to obtain the temperature field and single-plane strain field of the structure, and use the fitted temperature field as the input of the temperature curvature-model in S3 to further obtain the curvature field of the structure at that moment. S5. Input the single-plane strain field and curvature field obtained in S4 into the structural strain-curvature relationship in the theory of elasticity to calculate the strain field of the other plane of the structure, so as to obtain the double-plane strain of the structure. S6 uses the measured strain obtained in S5 as the error function of the inverse finite element algorithm to participate in the least squares optimization, and obtains the unit reconstruction equation set of each element under the inverse finite element algorithm. All unit reconstruction equation sets are assembled to obtain the overall reconstruction equation set. The boundary conditions are substituted and solved to realize the reconstruction of the global displacement field of the structure.
2. The inverse finite element deformation reconstruction method for a large plate under thermal load according to claim 1, characterized in that: S1 includes: Temperature and displacement sensors were deployed on the surface of a large plate structure to record the position coordinates of each sensor on the surface. An experimental system was built to conduct heating experiments. During the heating process, the structure will deform. The sensors collected temperature and displacement data at M moments within the heating period according to the system sampling rate. Based on the strain and temperature data collected by the system, combined with the sensor position coordinates, and using the internal fitting function of Matlab, the temperature and strain data collected by the experimental system were matched one-to-one with the position coordinates of the structure to obtain the temperature field and displacement field of the structure at M moments during the entire heating process.
3. The inverse finite element deformation reconstruction method for a large plate under thermal load according to claim 1, characterized in that: S2 includes: The displacement field at the M time points obtained in S1 is input curvature. With displacement The relationship is used to calculate the curvature field of the structure. The specific form of the relationship is as follows: ， in, For the structural curvature field, This represents the curvature of the mid-surface of a large plate in the x-direction after bending. This represents the curvature of the mid-surface of a large plate in the x-direction after bending. This indicates the curvature of the mid-surface of a large plate in the x and y directions after bending. This represents the structural displacement field.
4. The inverse finite element deformation reconstruction method for a large plate under thermal load according to claim 1, characterized in that: S3 includes: Based on the temperature fields obtained from the fitted temperature data in S1 at M time points, and the curvature fields obtained from the curvature-displacement relationship in S2 at M time points, the temperature and curvature values at each location of the structure at M time points are obtained. A power function is then used to fit the temperature and curvature values, where the specific form of the power function is: ， in, For the temperature field Temperature values corresponding to discrete points , , To characterize the first The fitting coefficients of the power function relating temperature values and curvature at discrete points. The temperature field provides The function represents the temperature value at each location, reflecting the overall structure. The mapping relationship between temperature and curvature at each location, i.e., the structural temperature-curvature model, enables the acquisition of temperature-curvature. Taking the first discrete point as an example, temperature values at M time points during the structural heating process are obtained in S1, and curvature values at M time points are obtained in S2. Using the temperature values as the independent variable and the curvature values as the dependent variable, a fitting operation is performed in Matlab to obtain the fitting coefficients for the temperature-curvature power function relationship at the first discrete point. , , In Matlab The same process is performed at each discrete location to obtain all the fitting coefficients, and then... , , By writing the power function coefficient matrix A, the exponent matrix B, and the constant matrix C, the temperature-curvature model can be obtained.
5. The inverse finite element deformation reconstruction method for a large plate under thermal load according to claim 1, characterized in that: S4 includes: Temperature and strain sensors were deployed on the surface of a large plate structure to record the position coordinates of each sensor. An experimental system was built to conduct heating experiments, during which the structure deformed. The sensors collected temperature and strain data at specific moments within the heating period. Based on the collected strain and strain data, combined with the sensor position coordinates, and using a Matlab-based fitting function, the temperature and strain data collected by the experimental system were mapped one-to-one with the structure's position coordinates to obtain the temperature and strain fields at a specific heating moment. Based on the obtained temperature fields, the surface temperature and strain data of the structure were obtained. Temperature values at discrete points , ,Will A temperature value is used as the independent variable of the power function in S3, and input into the temperature-curvature model to obtain... Curvature values at discrete points That is, the structural curvature field is obtained.
6. The method for reconstructing the temperature-curvature model of a large plate under thermal load using inverse finite element deformation according to claim 1, characterized in that: S5 includes: The strain field obtained in S4 and the curvature field obtained through the temperature-curvature model are substituted into the structural strain-curvature relationship in elasticity theory. The relationship is determined by linear elasticity theory. For a large plate structure with thickness H, the surface strain is determined by the membrane strain. and structural curvature field Linear representation: ， Where h represents the strain of the surface with unknown strain, i.e., the structural surface without strain sensors; c represents the strain of the surface with known strain, i.e., the structural surface with sensors. Depend on and curvature Linear representation: ， The single-surface strain field in S4 is fitted based on measured data. Substituting the curvature field obtained through the temperature-curvature model into the above equation, the strain field on the other side of the structure can be calculated. This enables the acquisition of strain on both sides of the structure.
7. The inverse finite element deformation reconstruction method for a large plate under thermal load according to claim 1, characterized in that: The least squares optimization in S6 is as follows: Converting biplane strain into structural neutral plane strain and curvature: ， ， in, These represent the surface strain field and curvature field of the structure, respectively. and It is a two-sided strain; Construct the error function between all measured strains and theoretical strains within the inverse element of the structure: ， in, The displacement field to be determined for the structure is... For weighting coefficients, For the strain field of the inverse element theory, The structure is respectively The measured strain and curvature field of each element, where H is the structural thickness. For the first The area of each unit, where n represents the area of the structure divided into n discrete reverse units; Take the partial derivative of the error function and set it to 0: ， The system of equations satisfied by the nodal displacements of the reverse element of the structure is as follows: ， in, The displacement field to be determined for the structure is... These are the coefficient matrix and coefficient vector of the above system of equations, respectively; By assembling this system of equations and substituting the boundary conditions, the global displacement field of the structure can be reconstructed.