CN114741783A - Inverse finite element deformation reconstruction method based on unit information matrix assembly - Google Patents

Inverse finite element deformation reconstruction method based on unit information matrix assembly Download PDF

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CN114741783A
CN114741783A CN202210312365.2A CN202210312365A CN114741783A CN 114741783 A CN114741783 A CN 114741783A CN 202210312365 A CN202210312365 A CN 202210312365A CN 114741783 A CN114741783 A CN 114741783A
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袁慎芳
董田钰
黄天翔
陈健
吴雯泱
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses an inverse finite element deformation reconstruction method based on unit information matrix assembly, which comprises the following steps: constructing a subunit information matrix; and integrally assembling and solving a global reconstruction equation set. According to the method, the subunit information matrix of each reverse unit is constructed, the full-unit information matrix is obtained by utilizing the sparse matrix to realize the assembly and storage of the subunit information matrices of all the reverse units, the full-unit information matrix in the form of the sparse matrix is converted into the full matrix, the global equivalent stiffness matrix and the global equivalent external force matrix are obtained, the global deformation reconstruction equation set is finally established, the equation set is solved to obtain the node displacement of the global unit, further, the deformation condition of any point in the structure can be obtained by adopting a shape function interpolation method, so that the deformation reconstruction is realized, the data storage amount is small, the reconstruction speed is high, the method can be used for real-time deformation monitoring, and the reconstruction speed is greatly improved while the deformation monitoring requirement of an aerospace structure is met.

Description

Inverse finite element deformation reconstruction method based on unit information matrix assembly
Technical Field
The invention belongs to the technical field of aerospace structure health monitoring, and particularly relates to an inverse finite element deformation reconstruction method based on unit information matrix assembly.
Background
In-orbit operation of a large-size spatial array antenna, complex thermal deformation occurs, and the deformation is more difficult to predict compared with a general aerospace structure, because thermal excitation is caused by severe high-low temperature change and non-uniform temperature distribution, and complex thermal coupling conditions generated by an antenna frame or other structures of a satellite need to be considered. In order to ensure that a large-scale space antenna can work normally, array amplitude-phase errors generated due to structural deformation need to be corrected, array element beams are subjected to feedback control, and real-time and reliable deformation monitoring is the basis of correction and compensation.
In the structural deformation monitoring method based on strain information, the fiber Bragg grating sensor has the characteristics of light weight, small volume, strong anti-interference capability, good electromagnetic insulation performance and the like, and is suitable for deformation monitoring of an on-orbit antenna structure densely covered with electromagnetic sensitive elements. The sensor acquires real-time strain, and can realize the on-line real-time sensing of the aerospace structure by combining advanced signal processing and deformation reconstruction algorithms. In the developed deformation reconstruction algorithm based on the strain information, the reverse finite element algorithm has the advantages of no need of structural materials and load characteristics, high reconstruction precision and the like, and is widely concerned.
However, the method commonly adopted in the unit assembly part by the reverse finite element method at present is to determine the rows and columns of all elements of the equivalent stiffness matrix and the equivalent external force matrix of each unit in the global equivalent stiffness matrix and the equivalent external force matrix respectively, and then to convey the rows and columns to the corresponding positions. When the number of units is large and the assembly time is required, the method is time-consuming and occupies a large data memory, and the real-time performance of deformation reconstruction is influenced.
Disclosure of Invention
In view of the above-mentioned deficiencies of the prior art, the present invention provides an inverse finite element deformation reconstruction method based on unit information matrix assembly, so as to solve the problem of poor real-time reconstruction based on an inverse finite element method in which units are assembled one by one in the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention discloses an inverse finite element deformation reconstruction method based on unit information matrix assembly, which comprises the following steps:
1) constructing a subunit information matrix: dispersing the monitored structure into a plurality of reverse units with unit nodes, and numbering all the reverse units and all the unit nodes respectively; constructing a least square error function of each reverse unit analytic strain field and actual measurement strain and optimizing to obtain an equivalent stiffness matrix and an equivalent external force matrix of each reverse unit, then arranging all coefficients in the obtained equivalent stiffness matrix into a subunit equivalent stiffness information matrix according to node numbers of each reverse unit, arranging all coefficients in the equivalent external force matrix into subunit equivalent external force information matrices in the same way, and forming N subunit equivalent stiffness information matrices and N subunit equivalent external force information matrices;
2) integrally assembling and solving a global reconstruction equation set: sequentially arranging N subunit equivalent stiffness information matrixes and N subunit equivalent external force information matrixes according to the numbers of the reverse units respectively; and the adjacent reverse units have public unit nodes, information with the same unit node number is combined to obtain a full-unit equivalent stiffness information matrix and a full-unit equivalent external force information matrix which are stored in a sparse matrix form, the sparse matrix is converted into a full matrix to construct a global equivalent stiffness matrix and a global equivalent external force matrix to realize integral assembly, and finally a global reconstruction equation set is established to obtain global unit node displacement to realize deformation reconstruction.
Further, the process of constructing the subunit information matrix in step 1) specifically includes:
11) dispersing the monitored structure into N reverse units, forming M unit nodes according to the types of the reverse units, numbering the reverse units and the unit nodes respectively, constructing a least square error function of each reverse unit analytical strain field and actual measurement strain, and optimizing to obtain a node displacement array a of each reverse unit when the analytical strain and the actual measurement strain error are minimumeIs full ofThe equation set for foot:
ken·ae＝fen,n＝1,2...N
wherein, kenAnd fenRespectively an equivalent stiffness matrix and an equivalent external force matrix of the nth reverse unit;
12) generating a global number of the freedom degree of each reverse unit node according to the unit node numbers; each reverse unit has a plurality of unit nodes, and assuming that the serial number of the j-th unit node of the nth (N-1 … … N) reverse unit is M (M-1 … … M), and the degree of freedom of each unit node is dof, the serial numbers of all the degrees of freedom of the unit node are dof- (M-1) +1, dof- (M-1) +2 … … dof · M, and the degree of freedom of all the unit nodes of the nth (N-1 … … N) reverse unit is obtained by traversing all the unit nodes of the reverse unit and is used as the equivalent stiffness matrix ke of the nth reverse unitnAnd an equivalent external force matrix fenThe position index of the element row and column;
13) will be equivalent stiffness matrix kenSubscripts corresponding to all elements store an inline index vector Ike-nAnd column index vector Jke-nAnd an equivalent stiffness matrix kenData vector Vke-n，[Ike-n Jke-n Vke-n]The equivalent stiffness information matrix of the subunit is obtained; the equivalent external force matrix fe is obtained by the same methodnSubscripts corresponding to all elements store an inline index vector Ife-nAnd column index vector Jfe-nAnd an equivalent external force matrix fenData vector Vfe-n，[Ife-n Jfe-n Vfe-n]The equivalent external force information matrix of the subunit is obtained; and traversing all the reverse units to obtain N subunit equivalent stiffness information matrixes and N subunit equivalent external force information matrixes.
Further, the overall assembling and solving of the global reconstruction equation set in the step 2) specifically includes:
21) sequentially arranging all the subunit equivalent stiffness information matrixes according to the reverse unit numbers to obtain a full-unit equivalent stiffness information splicing matrix [ I ]ke Jke Vke]All the subunits are arranged in sequence according to the reverse unit numbers in the same wayObtaining an equivalent external force information matrix to obtain a full-unit equivalent external force information splicing matrix [ I ]fe Jfe Vfe]：
Figure BDA0003567572620000031
Figure BDA0003567572620000032
22) Splicing all-unit equivalent stiffness information into a matrix [ I ]ke Jke Vke]Having the same row index IkeAnd column index JkeV of positionkeThe elements are accumulated to construct a full-unit equivalent stiffness information matrix S in the form of a sparse matrixkeSimilarly, the full-unit equivalent external force information is spliced into a matrix [ I ]fe Jfe Vfe]Having the same row index IfeAnd column index JfeV of positionfeThe elements are accumulated to construct a full-unit equivalent external force information matrix S in a sparse matrix formfe；
23) Whole-unit equivalent stiffness information matrix SkeAnd full-unit equivalent external force information matrix SfeThe full-cell equivalent stiffness information and the full-cell equivalent external force information are compressed and stored for a sparse matrix; converting the sparse matrix into a full matrix by supplementing zero elements to obtain a global equivalent stiffness matrix K and a global equivalent external force matrix F, and establishing a global reconstruction equation set:
K·U＝F
and supplementing a structural constraint condition solution equation to obtain global unit node displacement U, and further obtaining the deformation condition of any point in the monitored structure by adopting a shape function interpolation method, thereby realizing deformation reconstruction.
The invention has the beneficial effects that:
according to the method, the subunit information matrix of each reverse unit is constructed, the full-unit information matrix is obtained by utilizing the sparse matrix to realize the assembly and storage of the subunit information matrices of all the reverse units, the full-unit information matrix in the form of the sparse matrix is converted into the full matrix, the global equivalent stiffness matrix and the global equivalent external force matrix are obtained, the global deformation reconstruction equation set is finally established, the equation set is solved to obtain the node displacement of the global unit, further, the deformation condition of any point in the structure can be obtained by adopting a shape function interpolation method, so that the deformation reconstruction is realized, the data storage amount is small, the reconstruction speed is high, the method can be used for real-time deformation monitoring, and the reconstruction speed is greatly improved while the deformation monitoring requirement of an aerospace structure is met.
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FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of a composite material honeycomb sandwich panel structure and a position of a clamp used in the embodiment.
Fig. 3 is a schematic diagram of reverse element division.
Fig. 4a is a schematic diagram of a simulated strain field of positive strain of the upper surface of the honeycomb sandwich panel along the X-axis direction as an algorithm input of the inverse finite element method.
Fig. 4b is a schematic diagram of a simulated strain field of positive strain of the upper surface of the honeycomb sandwich panel along the Y-axis direction as an algorithm input of the inverse finite element method.
Fig. 4c is a schematic diagram of a simulated strain field of shear strain of the upper surface of the honeycomb sandwich panel in the XY plane as an algorithm input of the inverse finite element method.
FIG. 5a is a schematic diagram of a simulated strain field of positive strain along the X-axis direction of the lower surface of the honeycomb sandwich panel input as an algorithm of an inverse finite element method.
FIG. 5b is a schematic diagram of a simulated strain field of positive strain along the Y-axis direction of the lower surface of the honeycomb sandwich panel as the algorithm input of the inverse finite element method.
Fig. 5c is a simulation strain field diagram of shear strain of the lower surface of the honeycomb sandwich panel in the XY plane, which is input as an algorithm of an inverse finite element method.
Fig. 6a is a schematic view of a simulated displacement field of the honeycomb sandwich panel in a direction perpendicular to the panel surface.
Fig. 6b is a schematic diagram of a reconstructed displacement field perpendicular to the plate surface direction, which is obtained by performing deformation reconstruction on the honeycomb sandwich plate by using an inverse finite element method.
Fig. 6c is a schematic diagram of error distribution of the reconstructed displacement field and the simulated displacement field.
Detailed Description
In order to facilitate understanding of those skilled in the art, the present invention will be further described with reference to the following examples and drawings, which are not intended to limit the present invention.
Referring to fig. 1, the reverse finite element deformation reconstruction method based on element information matrix assembly according to the present invention includes the following steps:
1) constructing a subunit information matrix: dispersing the monitored structure into a plurality of reverse units with unit nodes, and numbering all the reverse units and all the unit nodes respectively; constructing a least square error function of each reverse unit analytic strain field and actual measurement strain and optimizing to obtain an equivalent stiffness matrix and an equivalent external force matrix of each reverse unit, then arranging all coefficients in the obtained equivalent stiffness matrix into a subunit equivalent stiffness information matrix according to node numbers of each reverse unit, arranging all coefficients in the equivalent external force matrix into subunit equivalent external force information matrices in the same way, and forming N subunit equivalent stiffness information matrices and N subunit equivalent external force information matrices;
specifically, the process of constructing the subunit information matrix in step 1) specifically includes:
11) dispersing a monitored structure into N reverse units, forming M unit nodes according to the types of the reverse units, numbering the reverse units and the unit nodes respectively, constructing a least square error function of an analytic strain field and an actual measurement strain of each reverse unit, and optimizing to obtain a node displacement array a of each reverse unit when the analytic strain error and the actual measurement strain error are minimumeThe system of equations satisfied:
ken·ae＝fen,n＝1,2...N
therein, kenAnd fenRespectively an equivalent stiffness matrix and an equivalent external force matrix of the nth reverse unit;
12) generating a global number of the degree of freedom of each reverse unit node according to the unit node numbers; each inverseThe method comprises the steps that a cell is provided with a plurality of cell nodes, the number of the j (th) cell node of the N (N is 1 … … N) th reverse cell is M (M is 1 … … M), the degree of freedom of each cell node is dof, the number of all degrees of freedom of the cell node is dof (M-1) +1, dof (M-1) +2 … … dof M, the degrees of freedom of all cell nodes of the N (N is 1 … … N) th reverse cell are obtained by traversing all cell nodes of the reverse cell, and the degrees of freedom are used as an equivalent stiffness matrix ke of the N (th) reverse cellnAnd an equivalent external force matrix fenThe position index of the element row and column;
13) will be equivalent stiffness matrix kenSubscripts corresponding to all elements store an inline index vector Ike-nAnd column index vector Jke-nAnd an equivalent stiffness matrix kenData vector Vke-n，[Ike-n Jke-n Vke-n]The equivalent stiffness information matrix of the subunit is obtained; the equivalent external force matrix fe is obtained by the same methodnSubscripts corresponding to all elements store an inline index vector Ife-nAnd column index vector Jfe-nAnd an equivalent external force matrix fenData vector Vfe-n，[Ife-n Jfe-n Vfe-n]The equivalent external force information matrix of the subunit is obtained; and traversing all the reverse units to obtain N subunit equivalent stiffness information matrixes and N subunit equivalent external force information matrixes.
2) Integrally assembling and solving a global reconstruction equation set: sequentially arranging N subunit equivalent stiffness information matrixes and N subunit equivalent external force information matrixes according to the reverse unit numbers respectively; the adjacent reverse units have public unit nodes, information with the same unit node number is combined to obtain a full-unit equivalent stiffness information matrix and a full-unit equivalent external force information matrix which are stored in a sparse matrix form to realize integral assembly, the sparse matrix is converted into a full matrix to construct a global equivalent stiffness matrix and a global equivalent external force matrix, and finally a global reconstruction equation set is established to obtain global unit node displacement to realize deformation reconstruction;
specifically, the overall assembling and solving of the global reconstruction equation set in step 2) specifically includes:
21) according to the inverseSequentially arranging all the subunit equivalent stiffness information matrixes to the unit numbers to obtain a full-unit equivalent stiffness information splicing matrix [ I ]ke Jke Vke]Arranging all the subunit equivalent external force information matrixes in sequence according to the reverse unit numbers in the same way to obtain a full-unit equivalent external force information splicing matrix [ Ife Jfe Vfe]：
Figure BDA0003567572620000051
Figure BDA0003567572620000052
22) Splicing all-unit equivalent stiffness information into a matrix Ike Jke Vke]Having the same row index IkeAnd column index JkeV of positionkeThe above elements are accumulated to construct a full-unit equivalent stiffness information matrix S in the form of a sparse matrixkeSimilarly, the full-unit equivalent external force information is spliced into a matrix [ I ]fe Jfe Vfe]Having the same row index IfeAnd column index JfeV of positionfeThe elements are accumulated to construct a full-unit equivalent external force information matrix S in a sparse matrix formfe；
23) Whole-unit equivalent stiffness information matrix SkeAnd full-unit equivalent external force information matrix SfeThe full-cell equivalent stiffness information and the full-cell equivalent external force information are compressed and stored for a sparse matrix; converting the sparse matrix into a full matrix by supplementing zero elements to obtain a global equivalent stiffness matrix K and a global equivalent external force matrix F, and establishing a global reconstruction equation set:
K·U＝F
and (3) supplementing a structural constraint condition solution equation to obtain global unit node displacement U, and further obtaining the deformation condition of any point in the monitored structure by adopting a shape function interpolation method, thereby realizing deformation reconstruction.
The deformation reconstruction object of the embodiment is a composite material honeycomb sandwich plate structure, as shown in fig. 2, the dimension is 3125mm × 1500mm × 20mm (length × width × thickness), the lower surface is provided with a heating element, and a temperature gradient exists in the thickness direction during heating, so that the honeycomb sandwich plate generates buckling deformation. The honeycomb sandwich plate is divided into 29 x 23 four-node reverse shell units according to the gradient of simulation displacement of 1mm, as shown in fig. 3, each unit has 4 nodes, and each node has 6 degrees of freedom. Strain field distribution of positive strain and shear strain of the upper surface and the lower surface of the honeycomb sandwich panel is shown in fig. 4 a-4 c and fig. 5 a-5 c, a least square error function is constructed by extracting the simulated strain and the analytic strain field of each reverse unit, and an equivalent stiffness matrix ke and an equivalent external force matrix fe of each reverse unit are obtained, wherein the matrix size of the equivalent stiffness matrix ke is 24 × 24, and the matrix size of the equivalent external force matrix fe is 24 × 1.
Generating a global number of the freedom degree of each reverse unit node according to the unit node numbers; assuming that the four cell node numbers of the nth reverse cell are i, j, k, s, the global number of the degree of freedom of the reverse cell node is (6 xi-5 … 6 xi, 6 xi-5 … 6 xi, 6 xi-5 … 6 xi, 6 xs-5 … 6 xs), the equivalent stiffness matrix ke is respectivelynSubscripts corresponding to all elements store an inline index vector Ike-nAnd column index vector Jke-nAnd a data vector Vke-nHere, the sizes of the row index vector, the column index vector and the data vector are all 576 × 1, and a subunit equivalent stiffness information matrix [ I ] is obtainedke-n Jke-n Vke-n](ii) a The equivalent external force matrix fe is treated by the same methodnSubscripts corresponding to all elements store an inline index vector Ife-nAnd column index vector Jfe-nAnd a data vector Vfe-nHere, the size of the row index vector, the column index vector and the data vector is 24 × 1, and a subunit equivalent external force information matrix [ I ] is obtainedfe-n Jfe-n Vfe-n]。
Sequentially arranging all 667 reverse unit equivalent stiffness information matrixes according to the reverse unit numbers to obtain a full-unit equivalent stiffness information splicing matrix [ I ]ke Jke Vke]The matrix size is 384192 × 3; arranged in sequenceObtaining a full-unit equivalent external force information splicing matrix [ I ] from the subunit equivalent external force information matrixes of the 667 reverse unitsfe Jfe Vfe]The matrix size is 16008 × 3.
Will have the same row index IkeAnd column index JkeData vector V at locationkeThe elements are accumulated to obtain a full-unit equivalent stiffness information matrix SkeThe same will have the same row index IfeAnd column index JfeData vector V at locationfeThe elements are accumulated to obtain a full-unit equivalent external force information matrix Sfe。
SkeAnd SfeThe compression storage and the unit integral assembly of each element and the corresponding position in the equivalent stiffness matrix and the equivalent external force matrix of all the reverse units are respectively realized in a sparse matrix form.
At SkeAnd SfeSupplementing zero elements to the vacant positions to realize conversion from the sparse matrix to the full matrix, respectively obtaining a global equivalent stiffness matrix K with the size of 4320 multiplied by 4320 and a global equivalent external force matrix F with the size of 4320 multiplied by 1, and establishing a global reconstruction equation set:
K·U＝F
the global unit node displacement U can be obtained by supplementing the structural constraint conditions and solving the equation set, and further, the deformation condition of any point in the structure can be obtained by adopting a shape function interpolation method, so that the deformation reconstruction is realized, and the reconstruction result is shown in fig. 6 a-6 c.
The result of comparing the reconstruction precision and the assembly speed based on the unit information matrix assembly and the unit one-by-one superposition shows that the results of the reconstruction displacement calculated by the two unit assembly modes are equal on the precision of 0.01mm, the reconstruction error of the maximum error position is 8.86 percent, the assembly time based on the unit information matrix is 28.43ms, and the unit one-by-one superposition assembly time is 52.94 ms. Therefore, the speed can be increased by more than 40% based on the whole assembly of the unit information matrix, and the deformation reconstruction real-time performance is effectively improved.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims (3)

1. An inverse finite element deformation reconstruction method based on unit information matrix assembly is characterized by comprising the following steps:
1) constructing a subunit information matrix: dispersing the monitored structure into a plurality of reverse units with unit nodes, and numbering all the reverse units and all the unit nodes respectively; constructing a least square error function of each reverse unit analytic strain field and actual measurement strain and optimizing to obtain an equivalent stiffness matrix and an equivalent external force matrix of each reverse unit, then sorting all coefficients in the obtained equivalent stiffness matrix into a subunit equivalent stiffness information matrix according to node numbers of each reverse unit, and similarly sorting all coefficients in the equivalent external force matrix into subunit equivalent external force information matrices to form N subunit equivalent stiffness information matrices and N subunit equivalent external force information matrices;
2) integrally assembling and solving a global reconstruction equation set: sequentially arranging N subunit equivalent stiffness information matrixes and N subunit equivalent external force information matrixes according to the numbers of the reverse units respectively; and the adjacent reverse units have public unit nodes, information with the same unit node number is combined to obtain a full-unit equivalent stiffness information matrix and a full-unit equivalent external force information matrix which are stored in a sparse matrix form, the sparse matrix is converted into a full matrix, a global equivalent stiffness matrix and a global equivalent external force matrix can be constructed to realize integral assembly, and a global reconstruction equation set is established to obtain global unit node displacement to realize deformation reconstruction.
2. The method for reconstructing inverse finite element deformation based on element information matrix assembly according to claim 1, wherein the constructing sub-element information matrix in step 1) specifically comprises:
11) dispersing the monitored structure into N reverse units, forming M unit nodes according to the types of the reverse units, and respectively aligning the reverse units and the unit nodesNumbering, constructing a least square error function of the analytic strain field and the measured strain of each reverse unit, and optimizing to obtain a node displacement array a of each reverse unit when the analytic strain and the measured strain have the minimum erroreThe system of equations satisfied:
ken·ae＝fen,n＝1,2...N
therein, kenAnd fenRespectively an equivalent stiffness matrix and an equivalent external force matrix of the nth reverse unit;
12) generating a global number of the freedom degree of each reverse unit node according to the unit node numbers; each reverse unit is provided with a plurality of unit nodes, if the number of the j-th unit node of the nth reverse unit is M, M is 1 … … M, and the degree of freedom of each unit node is dof, the numbers of all the degrees of freedom of the unit node are dof (M-1) +1, dof (M-1) +2 … … dof M, all the unit nodes of the reverse unit are traversed to obtain the number of the degrees of freedom of all the unit nodes of the nth reverse unit, and the number is used as the equivalent stiffness matrix ke of the nth reverse unitnAnd an equivalent external force matrix fenThe position index of the element row and column;
13) will be equivalent stiffness matrix kenSubscripts corresponding to all elements store an inline index vector Ike-nAnd column index vector Jke-nAnd an equivalent stiffness matrix kenData vector Vke-n，[Ike-n Jke-n Vke-n]The equivalent stiffness information matrix of the subunit is obtained; the equivalent external force matrix fe is treated by the same methodnSubscripts corresponding to all elements store an inline index vector Ife-nAnd column index vector Jfe-nAnd an equivalent external force matrix fenData vector Vfe-n，[Ife-n Jfe-n Vfe-n]The equivalent external force information matrix of the subunit is obtained; and traversing all the reverse units to obtain N subunit equivalent stiffness information matrixes and N subunit equivalent external force information matrixes.
3. The method for reconstructing inverse finite element deformation based on element information matrix assembly according to claim 1, wherein the overall assembly and solving of the global reconstruction equation set process in the step 2) specifically comprises:
21) sequentially arranging all the subunit equivalent stiffness information matrixes according to the reverse unit numbers to obtain a full-unit equivalent stiffness information splicing matrix [ I ]ke Jke Vke]Arranging all the subunit equivalent external force information matrixes in sequence according to the reverse unit numbers in the same way to obtain a full-unit equivalent external force information splicing matrix [ Ife Jfe Vfe]：
Figure FDA0003567572610000021
Figure FDA0003567572610000022
22) Splicing all-unit equivalent stiffness information into a matrix Ike Jke Vke]Having the same row index IkeAnd column index JkeV of positionkeThe above elements are accumulated to construct a full-unit equivalent stiffness information matrix S in the form of a sparse matrixkeSimilarly, the full-unit equivalent external force information is spliced into a matrix [ I ]fe Jfe Vfe]Having the same row index IfeAnd column index JfeV of positionfeThe elements are accumulated to construct a full-unit equivalent external force information matrix S in a sparse matrix formfe；
23) Whole-unit equivalent stiffness information matrix SkeAnd full-unit equivalent external force information matrix SfeThe full-cell equivalent stiffness information and the full-cell equivalent external force information are compressed and stored for a sparse matrix; converting the sparse matrix into a full matrix by supplementing zero elements to obtain a global equivalent stiffness matrix K and a global equivalent external force matrix F, and establishing a global reconstruction equation set:
K·U＝F
and supplementing a structural constraint condition solution equation to obtain global unit node displacement U, and further obtaining the deformation condition of any point in the monitored structure by adopting a shape function interpolation method, thereby realizing deformation reconstruction.
CN202210312365.2A 2022-03-28 2022-03-28 Inverse finite element deformation reconstruction method based on unit information matrix assembly Pending CN114741783A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115854245A (en) * 2022-12-08 2023-03-28 大连理工大学 For pressure vessels inner surface strain reconstruction method

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115854245A (en) * 2022-12-08 2023-03-28 大连理工大学 For pressure vessels inner surface strain reconstruction method

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