Structural nonlinear deformation reconstruction method and system based on isogeometry and reduced basis

Abstract

The application discloses a structure nonlinear deformation reconstruction method and system based on isogeometric and reduced basis, and the method comprises the following steps: measuring initial strain data of a ship plate structure surface, constructing a plurality of four-node inverse shell elements of the ship plate based on the initial strain data; assembling the plurality of four-node inverse shell elements to obtain a whole stiffness matrix; reconstructing the whole stiffness matrix based on the measured strain data of the ship plate to obtain a linear reconstruction result of the ship plate; correcting the linear reconstruction result based on the reduced basis, and fusing the correction increment to the linear reconstruction result for nonlinear iteration to complete nonlinear deformation reconstruction. On the basis of the principle of isogeometric analysis, the application combines the inverse finite element method to establish a four-node inverse shell element, realizes high-precision ship structure displacement reconstruction through a small number of strain measuring points, and helps designers to intuitively understand and deeply understand the mechanical properties of the structure and to monitor the safety of the structure in real time.

Description

Technical Field

[0001] This invention belongs to the field of ship structural mechanics technology, specifically relating to a method and system for reconstructing nonlinear structural deformation based on equal geometry and reduced basis. Background Technology

[0002] Ship structures are simultaneously subjected to wave loads under severe sea conditions. This is especially true for ultra-large container ships and large oil tankers, which face complex marine environments during operation. The combined effects of different loads lead to superimposed structural responses, which can easily cause ultimate load-bearing failure of the hull beams.

[0003] The ultimate bearing capacity assessment of ship structures generally employs numerical simulation, standard calculations, and model tests. Model tests are the most important method for obtaining structural mechanical properties and investigating structural failure behavior. However, due to factors such as the number of data acquisition channels, data noise, the difficulty in arranging measurement points caused by the structure itself, and the limited and discrete number of overall samples, the real-time performance and accuracy of test measurement data are difficult to guarantee. It is impossible to obtain data information across the entire field, making it difficult to reveal the mechanism of failure throughout the entire model process.

[0004] The inverse finite element method (iFEM) is mainly used to convert the strain field and displacement field of a structural surface. However, traditional iFEM methods require a precise mesh as support, which is difficult to meet the requirements of large-scale strain measurement point layout in practical engineering. Isogeometric analysis (IGA), similar to FEA, can directly use the geometric model created in mainstream CAD software for numerical analysis without mesh generation. Combining the iFEM method with the isogeometric method to establish an isogeometric reconstruction method can use a smaller number of measurement points while ensuring accuracy.

[0005] The basic principle of the reduced basis method (RBM) is to use nodal displacements related to its own geometric or physical parameters to form the basis of the low-dimensional space, thereby mapping the high-dimensional solution space of the finite element model to a low-dimensional solution space through the Galerkin method. This study focuses on the reconstruction of the nonlinear stress field of ship structural sections, breaking through the key technology of reconstructing stress fields from linear to nonlinear. Based on finite discrete measured data, it obtains the nonlinear stress field distribution of the entire structural domain in real time, fully utilizing limited experimental data to lay a theoretical foundation for exploring the whole-process failure behavior and predicting the overall buckling mode of complex ship structures. Summary of the Invention

[0006] This invention aims to address the shortcomings of existing technologies by proposing a structural nonlinear deformation reconstruction method and system based on isogeometric and reduced basis. By utilizing isogeometric analysis methods, inverse finite element methods, sensor technology, and structural health monitoring technology, a deformation reconstruction technology for ship plate frame structures is constructed. Based on measured data, the displacement deformation and stress field results of the target structure can be obtained.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] The structural nonlinear deformation reconstruction method based on isogeometry and reduced basis includes the following steps:

[0009] Measure the initial strain data of the surface of the ship's plate frame structure, and construct several four-node inverse shell elements of the ship's plate frame based on the initial strain data;

[0010] Assemble several of the four-node inverse shell elements to obtain the overall stiffness matrix;

[0011] The overall stiffness matrix is ​​reconstructed based on the measured strain data of the ship's plate frame to obtain the linear reconstruction result of the ship's plate frame.

[0012] The linear reconstruction result is corrected based on the reduction basis, and the correction increment is fused into the linear reconstruction result for nonlinear iteration to complete the nonlinear deformation reconstruction.

[0013] Preferably, the initial strain data includes: structural plane strain and bending strain;

[0014] The plane strain of the structure is:

[0015] ;

[0016] The bending strain is:

[0017] ;

[0018] in, Within the unit x , y Normal strain in the direction and bending strain in the xy plane, These are the upper and lower surfaces of the strain measurement point, respectively.

[0019] Preferably, the four-node inverse shell unit includes:

[0020]

[0021] in, The real-time strain of the cross section. This is the explicit form of the strain matrix. For the positive weighting constant of the plane strain of the structure, For positive weighting constants of bending strain, h For unit thickness, n The number of strain measurement points, For the components of theoretical membrane strain, This represents the component of the theoretical bending strain.

[0022] Preferably, the assembly method includes: converting the four-node inverse shell element into a global stiffness matrix using a transformation matrix, and integrating the global stiffness matrix to obtain the overall stiffness matrix.

[0023]

[0024] Where 0 is 3 The zero vector of 3, and T is the transformation matrix.

[0025] Preferably, the reconstruction method includes:

[0026] Obtain the measured strain data;

[0027] Solve for the least-squares functional error function of the theoretical strain and measured strain data within the four-node inverse shell element, i.e., the linear reconstruction result:

[0028]

[0029] in, It is a vector containing the degrees of freedom of the nodes; These are the surface strain, bending strain, and transverse shear strain components, respectively. These are the weighting coefficients related to the surface strain, bending strain, and transverse shear strain components, respectively. Input strain field.

[0030] The present invention also provides a structural nonlinear deformation reconstruction system based on isogeometry and reduced basis, the system being applied to the method described in any of the above, comprising: a unit construction module, a matrix assembly module, a reconstruction module, and a correction iteration module;

[0031] The unit construction module is used to measure the initial strain data of the surface of the ship plate frame structure, and to construct several four-node inverse shell units of the ship plate frame based on the initial strain data.

[0032] The matrix assembly module is used to assemble several of the four-node inverse shell units to obtain the overall stiffness matrix.

[0033] The reconstruction module is used to reconstruct the overall stiffness matrix based on the measured strain data of the ship plate frame, so as to obtain the linear reconstruction result of the ship plate frame.

[0034] The correction iteration module is used to correct the linear reconstruction result based on the reduction basis, and to fuse the correction increment into the linear reconstruction result for nonlinear iteration to complete the nonlinear deformation reconstruction.

[0035] Preferably, the initial strain data includes: structural plane strain and bending strain;

[0036] The plane strain of the structure is:

[0037] ;

[0038] The bending strain is:

[0039] ;

[0040] in, Within the unit x , y Normal strain in the direction and bending strain in the xy plane, These are the upper and lower surfaces of the strain measurement point, respectively.

[0041] Preferably, the four-node inverse shell unit includes:

[0042]

[0043] in, The real-time strain of the cross section. This is the explicit form of the strain matrix. For the positive weighting constant of the plane strain of the structure, For positive weighting constants of bending strain, h For unit thickness, n The number of strain measurement points, For the components of theoretical membrane strain, This represents the component of the theoretical bending strain.

[0044] Preferably, the workflow of the matrix assembly module includes: converting the four-node inverse shell element into a global stiffness matrix using a transformation matrix, and integrating the global stiffness matrix to obtain the overall stiffness matrix.

[0045]

[0046] Where 0 is 3 The zero vector of 3, and T is the transformation matrix.

[0047] Preferably, the workflow of the reconstruction module includes:

[0048] Obtain the measured strain data, and solve the least-squares functional error function of the theoretical strain and measured strain data within the four-node inverse shell element, i.e., the linear reconstruction result:

[0049]

[0050] in, It is a vector containing the degrees of freedom of the nodes; These are the surface strain, bending strain, and transverse shear strain components, respectively. These are the weighting coefficients related to the surface strain, bending strain, and transverse shear strain components, respectively. Input strain field.

[0051] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0052] Based on the principles of isogeometric analysis and combined with the inverse finite element method, this invention establishes a four-node inverse shell element. This allows for high-precision displacement reconstruction of ship structures with a smaller number of strain measurement points, assisting designers in intuitively understanding and deeply analyzing the mechanical properties of structures and monitoring structural safety in real time. Real-time acquisition of structural displacement distribution provides effective support for structural safety design and assessment. Besides assisting engineering designers, this invention can also be used to supplement courses in universities, improving students' understanding and mastery of professional theoretical knowledge. Attached Figure Description

[0053] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0055] Figure 2 This is a schematic diagram of the fast calculation process for reduced basis according to an embodiment of the present invention;

[0056] Figure 3 This is a schematic diagram illustrating the linear incremental iteration principle of an embodiment of the present invention. Detailed Implementation

[0057] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0059] Example 1

[0060] In this embodiment, as Figure 1 As shown, the structural nonlinear deformation reconstruction method based on isogeometry and reduced basis includes the following steps:

[0061] S1. Measure the initial strain data of the surface of the ship's plate frame structure, and construct several four-node inverse shell elements of the ship's plate frame based on the initial strain data.

[0062] Each strain measurement point is arranged on the upper and lower surfaces at the inverse element centroid. The measured initial strain data include: plane strain and bending strain of the structure; the relationship between the discrete strain of the structural surface and the plane strain and bending strain of the structure can be expressed as:

[0063] The plane strain of the structure is:

[0064] ;

[0065] The bending strain is:

[0066] ;

[0067] in, Within the unit x , y Normal strain in the direction and bending strain in the xy plane, These are the upper and lower surfaces of the strain measurement point, respectively.

[0068] The four-node inverse shell element includes:

[0069]

[0070] in, The real-time strain of the cross section. This is the explicit form of the strain matrix. For the positive weighting constant of the plane strain of the structure, For positive weighting constants of bending strain, h For unit thickness, n The number of strain measurement points, For the components of theoretical membrane strain, This represents the component of the theoretical bending strain.

[0071] S2. Assemble several four-node inverse shell elements to obtain the overall stiffness matrix.

[0072] The assembly method includes: converting the four-node inverse shell element into a global stiffness matrix through a transformation matrix, and integrating the global stiffness matrix to obtain the overall stiffness matrix;

[0073] In this embodiment, in order to analyze the overall structure, it is necessary to convert the stiffness matrix equation of the four-node plate inverse finite element in the local coordinate system into the stiffness matrix equation in the global coordinate system, and integrate the element stiffness matrix into the overall stiffness matrix.

[0074] The unit normal vector *n* of the face in a four-node inverse shell element, and the unit vectors *p* and *l* along the y-axis and x-axis of the local coordinate system. The transformation matrix of the nodal degrees of freedom of a four-node plate inverse finite element from the local coordinate system to the global coordinate system can be defined as:

[0075]

[0076] Where 0 is 3 The zero vector of 3, T, is the coordinate transformation matrix from the local coordinate system to the global coordinate system. Integrating the stiffness matrix equations of the discrete structure yields the global stiffness matrix equation of the structure.

[0077] S3. Based on the measured strain data of the ship's plate frame, the overall stiffness matrix is ​​reconstructed to obtain the linear reconstruction result of the ship's plate frame.

[0078] The reconstruction method includes: acquiring measured strain data; solving the least-squares functional error function of theoretical and measured strain data within a four-node inverse shell element, including plane strain, bending strain, and transverse shear strain; and defining the input strain field. With numerical formula The difference comparison method, the error functional of the iFEM of the i-th cell, i.e. the linear reconstruction result, can be expressed as:

[0079]

[0080] in, It is a vector containing the degrees of freedom of the nodes; These are the surface strain, bending strain, and transverse shear strain components, respectively. These are the weighting coefficients related to the surface strain, bending strain, and transverse shear strain components, respectively.

[0081] S4. Based on the reduction basis, the linear reconstruction result is corrected, and the correction increment is fused into the linear reconstruction result for nonlinear iteration to complete the nonlinear deformation reconstruction.

[0082] In the nonlinear analysis of structural ultimate strength, the configuration changes continuously, so the configuration at any given time is unknown, making it impossible to directly solve the virtual internal energy equation. Theoretically, any configuration at a known time can be used as a reference configuration. This embodiment uses the complete Lagrangian configuration at time 0 and the updated Lagrangian configuration at time t as reference configurations. The IGA-RB combined approximation method is used to accurately calculate the linear response of the structure in real time. In the solution of each force application step, unlike the traditional full analysis method that solves the N×N (assuming the original degrees of freedom are N) full equations, a tolerance is given. The affected degrees of freedom are labeled (assumed to be S). The IGA discrete equations are solved, reduced to only S degrees of freedom, where S is much smaller than N. This greatly improves the efficiency of the analysis while ensuring accuracy. Then, based on the reduced basis, the real-time analysis completes the correction of the stress field reconstruction for each load step.

[0083] In this embodiment, as Figure 2 As shown, the reduction basis method is used to correct the results of each deformation reconstruction. The implementation steps of this method are as follows:

[0084] 1) Obtain the current stiffness matrix at time t using the linear reconstruction method. and load column matrix For each iteration, initialization is performed to establish the mathematical relationship between the displacement U increment;

[0085] 2) Based on load step increment The strain increments obtained are used to select the degrees of freedom for the reduced basis weight analysis, and basis vectors are constructed to establish the reduced basis equations. The reduced basis equations are then solved.

[0086] 3) Substitute the results of the reduced basis solution into the mathematical relationship of the displacement increment U to obtain... ;

[0087] The core is to establish the mathematical relationship between the measured strain and the change of nodal degrees of freedom for each load step, thereby obtaining the stiffness matrix under the current state, obtaining the increment of current displacement and stress by solving the equations, and approximating the nonlinear deformation field and stress field of large deformation through multiple iterations.

[0088] In this embodiment, as Figure 3 As shown, drawing on the Newton-Raphson solution process of the nonlinear finite element method, a method using the iFEM incremental procedure is proposed to approximate the nonlinear stress field under large deformation. The implementation steps of this method are as follows:

[0089] 1) Construct inverse shell elements and establish the topological relationship between discrete inverse shell elements to lay the foundation for stiffness matrix assembly; establish displacement-strain relationship through equal geometric high-order continuous basis functions, and at the same time establish mathematical calculation relationship between the strain on the upper and lower surfaces and the strain in the middle section of the same inverse shell element.

[0090] 2) Strain sensors are placed at the center of the inverse shell unit. Through isogeometric numerical simulation and experimental measurement, a relationship model between theoretical strain and measured strain is established. A weighted least squares functional is constructed to establish a mathematical model for linear displacement deformation and stress field reconstruction.

[0091] 3) The stiffness of the reconstruction iteration process is corrected by reducing the basis method. At each load step in the nonlinear stage, the displacement and stress fields are corrected. For each modification involving the standard linear inverse analysis process, the linear iFEM is used for the load step increment. The deformation increments of each load step are summed to determine the final nonlinear displacement field and stress field of the structure.

[0092] 4) Verify whether the nonlinear reconstruction results match the nonlinear numerical simulation results.

[0093] Example 2

[0094] In this embodiment, the structural nonlinear deformation reconstruction system based on isogeometry and reduced basis includes: a unit construction module, a matrix assembly module, a reconstruction module, and a correction iteration module;

[0095] The element construction module is used to measure the initial strain data of the surface of the ship's plate frame structure, and to construct several four-node inverse shell elements of the ship's plate frame based on the initial strain data.

[0096] Each strain measurement point is arranged on the upper and lower surfaces at the inverse element centroid. The measured initial strain data include: plane strain and bending strain of the structure; the relationship between the discrete strain of the structural surface and the plane strain and bending strain of the structure can be expressed as:

[0097] The plane strain of the structure is:

[0098] ;

[0099] The bending strain is:

[0100] ;

[0101] in, Within the unit x , y Normal strain in the direction and bending strain in the xy plane, These are the upper and lower surfaces of the strain measurement point, respectively.

[0102] The four-node inverse shell element includes:

[0103]

[0104] in, The real-time strain of the cross section. This is the explicit form of the strain matrix. For the positive weighting constant of the plane strain of the structure, For positive weighting constants of bending strain, h For unit thickness, n The number of strain measurement points, For the components of theoretical membrane strain, This represents the component of the theoretical bending strain.

[0105] The matrix assembly module is used to assemble several four-node inverse shell elements to obtain the overall stiffness matrix.

[0106] The matrix assembly module's workflow includes: converting the four-node inverse shell element into a global stiffness matrix using a transformation matrix, and then integrating the global stiffness matrices to obtain the overall stiffness matrix.

[0107]

[0108] Where 0 is 3 The zero vector of 3, and T is the transformation matrix. By using the transformation matrix, the stiffness matrix equation of the element in the local coordinate system can be transformed into the stiffness matrix equation in the global coordinate system. Then, the stiffness matrix equations of the discrete structure can be integrated to obtain the overall stiffness matrix equation of the structure.

[0109] The reconstruction module is used to reconstruct the overall stiffness matrix based on the measured strain data of the ship's plate frame, and obtain the linear reconstruction result of the ship's plate frame.

[0110] The workflow of the reconstruction module includes: acquiring measured strain data, solving the least-squares functional error function of theoretical strain and measured strain data within a four-node inverse shell element, including three parts: plane strain, bending strain, and transverse shear strain. The input strain field is then defined. With numerical formula The difference comparison method, the error functional of the iFEM of the i-th cell, i.e. the linear reconstruction result, can be expressed as:

[0111]

[0112] in, It is a vector containing the degrees of freedom of the nodes; These are the surface strain, bending strain, and transverse shear strain components, respectively. These are the weighting coefficients related to the surface strain, bending strain, and transverse shear strain components, respectively.

[0113] The correction iteration module is used to correct the linear reconstruction result based on the reduction basis, and to integrate the correction increment into the linear reconstruction result for nonlinear iteration, thereby completing the nonlinear deformation reconstruction.

[0114] In the nonlinear analysis of structural ultimate strength, the configuration changes continuously, so the configuration at any given time is unknown, making it impossible to directly solve the virtual internal energy equation. Theoretically, any configuration at a known time can be used as a reference configuration. This embodiment uses the complete Lagrangian configuration at time 0 and the updated Lagrangian configuration at time t as reference configurations. The IGA-RB combined approximation method is used to accurately calculate the linear response of the structure in real time. In the solution of each force application step, unlike the traditional full analysis method that solves the N×N (assuming the original degrees of freedom are N) full equations, a tolerance is given. The affected degrees of freedom are labeled (assumed to be S). The IGA discrete equations are solved, reduced to only S degrees of freedom, where S is much smaller than N. This greatly improves the efficiency of the analysis while ensuring accuracy. Then, based on the reduced basis, the real-time analysis completes the correction of the stress field reconstruction for each load step.

[0115] In this embodiment, as Figure 2 As shown, the reduction basis method is used to correct the results of each deformation reconstruction. The implementation steps of this method are as follows:

[0116] 1) Obtain the current stiffness matrix at time t using the linear reconstruction method. and load column matrix For each iteration, initialization is performed to establish the mathematical relationship between the displacement U increment;

[0117] 2) Based on load step increment The strain increments obtained are used to select the degrees of freedom for the reduced basis weight analysis, and basis vectors are constructed to establish the reduced basis equations. The reduced basis equations are then solved.

[0118] 3) Substitute the results of the reduced basis solution into the mathematical relationship of the displacement increment U to obtain... ;

[0119] The core is to establish the mathematical relationship between the measured strain and the change of nodal degrees of freedom for each load step, thereby obtaining the stiffness matrix under the current state, obtaining the increment of current displacement and stress by solving the equations, and approximating the nonlinear deformation field and stress field of large deformation through multiple iterations.

[0120] In this embodiment, as Figure 3As shown, drawing on the Newton-Raphson solution process of the nonlinear finite element method, a method using the iFEM incremental procedure is proposed to approximate the nonlinear stress field under large deformation. The implementation steps of this method are as follows:

[0121] 1) Construct inverse shell elements and establish the topological relationship between discrete inverse shell elements to lay the foundation for stiffness matrix assembly; establish displacement-strain relationship through equal geometric high-order continuous basis functions, and at the same time establish mathematical calculation relationship between the strain on the upper and lower surfaces and the strain in the middle section of the same inverse shell element.

[0122] 2) Strain sensors are placed at the center of the inverse shell unit. Through isogeometric numerical simulation and experimental measurement, a relationship model between theoretical strain and measured strain is established. A weighted least squares functional is constructed to establish a mathematical model for linear displacement deformation and stress field reconstruction.

[0123] 3) The stiffness of the reconstruction iteration process is corrected by reducing the basis method. At each load step in the nonlinear stage, the displacement and stress fields are corrected. For each modification involving the standard linear inverse analysis process, the linear iFEM is used for the load step increment. The deformation increments of each load step are summed to determine the final nonlinear displacement field and stress field of the structure.

[0124] 4) Verify whether the nonlinear reconstruction results match the nonlinear numerical simulation results.

[0125] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A structural nonlinear deformation reconstruction method based on isogeometric and reduced basis, characterized in that, Includes the following steps: Measure the initial strain data of the surface of the ship's plate frame structure, and construct several four-node inverse shell elements of the ship's plate frame based on the initial strain data; Assemble several of the four-node inverse shell elements to obtain the overall stiffness matrix; The overall stiffness matrix is ​​reconstructed based on the measured strain data of the ship's plate frame to obtain the linear reconstruction result of the ship's plate frame. The linear reconstruction result is corrected based on the reduction basis, and the correction increment is fused into the linear reconstruction result for nonlinear iteration to complete the nonlinear deformation reconstruction. The methods for making corrections include: 1) Obtain the current stiffness matrix at time t using the linear reconstruction method. and load column matrix For each iteration, initialization is performed to establish the mathematical relationship between the displacement U increment; 2) Based on load step increment The strain correction increments obtained are used to select the degrees of freedom for the reduced basis weight analysis, and basis vectors are constructed to establish the reduced basis equations, and the reduced basis equations are solved. 3) Substitute the results of the reduced basis solution into the mathematical relationship of the displacement increment U to obtain... ; The core is to establish the mathematical relationship between the measured strain and the change of nodal degrees of freedom for each load step, thereby obtaining the stiffness matrix under the current state, obtaining the correction increment of the current displacement and stress by solving the equations, and approximating the nonlinear deformation field and stress field of large deformation through multiple iterations.

2. The structural nonlinear deformation reconstruction method based on isogeometric and reduced basis according to claim 1, characterized in that, The initial strain data includes: structural plane strain and bending strain; The plane strain of the structure is: ； The bending strain is: ； in, Within the unit x , y Normal strain in the direction and bending strain in the xy plane, These are the upper and lower surfaces of the strain measurement point, respectively.

3. The structural nonlinear deformation reconstruction method based on isogeometric and reduced basis according to claim 2, characterized in that, The four-node inverse shell unit includes: in, The real-time strain of the cross section. This is the explicit form of the strain matrix. For the positive weighting constant of the plane strain of the structure, For positive weighting constants of bending strain, h For unit thickness, n The number of strain measurement points, For the components of theoretical membrane strain, This represents the component of the theoretical bending strain.

4. The structural nonlinear deformation reconstruction method based on isogeometric and reduced basis according to claim 1, characterized in that, The assembly method includes: converting the four-node inverse shell element into a global stiffness matrix using a transformation matrix, and integrating the global stiffness matrix to obtain the overall stiffness matrix. Where 0 is 3 The zero vector of 3, and T is the transformation matrix.

5. The structural nonlinear deformation reconstruction method based on isogeometric and reduced basis according to claim 1, characterized in that, The reconstruction method includes: Obtain the measured strain data; Solve for the least-squares functional error function of the theoretical strain and measured strain data within the four-node inverse shell element, i.e., the linear reconstruction result: in, It is a vector containing the degrees of freedom of the nodes; , and These are the surface strain, bending strain, and transverse shear strain components, respectively. These are the weighting coefficients related to the surface strain, bending strain, and transverse shear strain components, respectively. , and Input strain field.

6. A structural nonlinear deformation reconstruction system based on isogeometry and reduced basis, said system being applied to the method described in any one of claims 1-5, characterized in that, include: Unit construction module, matrix assembly module, reconstruction module, and correction iteration module; The unit construction module is used to measure the initial strain data of the surface of the ship plate frame structure, and to construct several four-node inverse shell units of the ship plate frame based on the initial strain data. The matrix assembly module is used to assemble several of the four-node inverse shell units to obtain the overall stiffness matrix. The reconstruction module is used to reconstruct the overall stiffness matrix based on the measured strain data of the ship plate frame, so as to obtain the linear reconstruction result of the ship plate frame. The correction iteration module is used to correct the linear reconstruction result based on the reduction basis, and to fuse the correction increment into the linear reconstruction result for nonlinear iteration to complete the nonlinear deformation reconstruction.

7. The structural nonlinear deformation reconstruction system based on isogeometric and reduced basis according to claim 6, characterized in that, The initial strain data includes: structural plane strain and bending strain; The plane strain of the structure is: ； The bending strain is: ； in, Within the unit x , y Normal strain in the direction and bending strain in the xy plane, These are the upper and lower surfaces of the strain measurement point, respectively.

8. The structural nonlinear deformation reconstruction system based on isogeometry and reduced basis according to claim 6, characterized in that, The four-node inverse shell unit includes: in, The real-time strain of the cross section. This is the explicit form of the strain matrix. For the positive weighting constant of the plane strain of the structure, For positive weighting constants of bending strain, h For unit thickness, n The number of strain measurement points, For the components of theoretical membrane strain, This represents the component of the theoretical bending strain.

9. The structural nonlinear deformation reconstruction system based on isogeometry and reduced basis according to claim 6, characterized in that, The workflow of the matrix assembly module includes: converting the four-node inverse shell element into a global stiffness matrix using a transformation matrix, and integrating the global stiffness matrix to obtain the overall stiffness matrix. Where 0 is 3 The zero vector of 3, and T is the transformation matrix.

10. The structural nonlinear deformation reconstruction system based on isogeometry and reduced basis according to claim 6, characterized in that, The workflow of the reconstruction module includes: Obtain the measured strain data, and solve the least-squares functional error function of the theoretical strain and measured strain data within the four-node inverse shell element, i.e., the linear reconstruction result: in, It is a vector containing the degrees of freedom of the nodes; , and These are the surface strain, bending strain, and transverse shear strain components, respectively. These are the weighting coefficients related to the surface strain, bending strain, and transverse shear strain components, respectively. , and Input strain field.

Images