A method for determining multi-point compensation loading positions of a ribbed structure based on stiffness decomposition

Abstract

The application discloses a kind of based on stiffness decomposition's multi-point compensation loading position determination method of containing muscle structure, it includes: S1: target structure is carried out finite element unit division, obtains its overall stiffness matrix K and compliance matrix C;S2: singular value decomposition is carried out to compliance matrix, obtains each sub-compliance matrix;S3: according to singular value determines the corresponding sub-deformation field of sub-compliance matrix, corresponding sub-deformation field is filtered to obtain main deformation field;S4: from each main deformation field obtains corresponding main load field;S5: the influence range of each loading point is set;S6: the loading point set of each main load field is calculated;S7: each main load field is superimposed to obtain superimposed load field, the loading point set of each main load field is summed, and the loading point sequence of overall structure and its in superimposed load field corresponding node load are obtained;According to the loading point sequence of overall structure in superimposed load field corresponding load value, non-maximum suppression method is applied again, and the final loading point set is obtained.

Description

Technical Field

[0001] This invention relates to the fields of mechanics and machinery, and specifically to a method for determining the multi-point compensation loading position of a stiffened structure based on stiffness decomposition. Background Technology

[0002] Large, stiffened structures, as crucial components of heavy equipment, are typically assembled into a unified load-bearing structure using welding. Therefore, the manufacturing precision of stiffened parts significantly impacts the overall structural deviation and accuracy. However, during milling and rolling, residual stresses introduced during machining often lead to warping deformation in the finished parts, severely affecting the welding precision of subsequent components. Due to the presence of stiffeners, deviation compensation for stiffened structures cannot be achieved using a uniform die for stamping loading; instead, localized loading is necessary. Traditional compensation methods, employing reverse displacement to determine loading positions point by point, suffer from low precision and reliance on manual experience, resulting in low compensation efficiency. Furthermore, the majority of deviations in large structures originate from rigid rotation caused by localized stresses, and reverse displacement can easily lead to redistribution of deviations after compensation. Therefore, it is necessary to calculate the loading point selection from a structural mechanics perspective, based on the structural stiffness characteristics theory, to improve the reliability and efficiency of multi-point compensation for large, stiffened structures.

[0003] Currently, the compensation method for large, stiffened structures in heavy equipment uses reverse displacement to determine the loading position point by point. This requires manual clamping tools for local compensation. The compensation accuracy is low, it relies heavily on manual experience, and the compensation efficiency is low. Furthermore, for large structures, the vast majority of deviations are caused by rigid rotation resulting from local stress. Using reverse displacement for local compensation often leads to large-stroke compensation for local deviations caused by rigid rotation, increasing the loading cost of compensation. Summary of the Invention

[0004] The purpose of this invention is to address the problems of traditional compensation methods that use reverse displacement to determine the loading position point by point, which has low accuracy and relies too much on human experience. This invention provides a method for determining the loading position of multi-point compensation for stiffened structures based on stiffness decomposition, thereby improving the accuracy and efficiency of multi-point compensation for large plate structures.

[0005] To achieve the above objectives, this invention provides a method for determining the multi-point compensation loading position of a stiffened structure based on stiffness decomposition, which includes the following steps:

[0006] S1: Perform finite element meshing on the target structure to obtain the mesh nodes of the target structure, as well as the overall stiffness matrix K and flexibility matrix C with constraints, and use the mesh nodes of the compensation surface of the target structure as the loading points to be screened.

[0007] S2: The flexibility matrix is ​​decomposed by singular value decomposition to obtain discrete sub-flexibility matrices.

[0008] S3: Based on the sub-compliance matrices obtained from singular value decomposition, the target deformation field u is decomposed into corresponding sub-deformation fields. The sub-deformation fields are then filtered based on the singular values ​​corresponding to each sub-compliance matrix to obtain the main deformation field u. i ;

[0009] S4: For each principal deformation field, according to F... i =Ku i The corresponding principal load field F is obtained through calculation. i ;

[0010] S5: Set the influence range of each loading point to be filtered according to the actual loading range of the loading tool;

[0011] S6: The set of loading points for each principal load field is calculated using a non-maximum suppression method;

[0012] S7: Superimpose the principal load fields obtained in step S4 to obtain the superimposed load field. The loading point sets of each principal load field obtained in step S6 are joined to obtain the loading point sequence of the overall structure and its corresponding nodal loads in the superimposed load field; based on the loading point sequence of the overall structure in the superimposed load field... The corresponding load values ​​are used to obtain the set of loading points by applying the nonmaximum suppression method.

[0013] A further improvement of the present invention is that, in step S1, the process of obtaining the overall stiffness matrix K and the flexibility matrix C with constraints specifically includes: solving for the equivalent force vector F, F = Ku, on the nodes of the structural finite element based on the target deformation field u of all mesh nodes; and, for the stiffness matrix K containing constraints, using the method of setting the diagonal elements of the corresponding nodes to large numbers to obtain the structural stiffness matrix K considering deformation constraints and the corresponding flexibility matrix C, where C = K -1 And satisfy u = CF.

[0014] A further improvement of the present invention is that step S2 specifically includes: performing singular value decomposition on the flexibility matrix C to obtain the sub-flexibility matrices C of each order. i Its expression is:

[0015]

[0016] Where S is the singular value σ of the matrix i The diagonal matrices formed are U and V, which are unitary matrices generated by singular value decomposition, and n is the dimension of the flexibility matrix C; U i Let V be the i-th column of the unitary matrix U.i Let be the i-th column of the unitary matrix V.

[0017] A further improvement of the present invention is that step S3 specifically includes: decomposing the target deformation field u into various candidate deformation fields u according to the sub-compliance matrix. i The expression for the candidate deformation field is:

[0018] u i =C i F = σ i U i V i T F

[0019] Wherein, the sub-compliance matrix C i The sub-deformation fields are sorted according to the magnitude of their corresponding singular values. The top k candidate deformation fields with a cumulative singular value contribution of over 90% are obtained. Candidate deformation fields with a standard deviation of nodal deformation less than a deviation threshold are then removed, resulting in m principal deformation fields u. i Wherein: the cumulative singular value contribution is calculated as follows:

[0020]

[0021] A further improvement of the present invention is that step S6 uses the non-maximum suppression method to screen candidate loading points. The steps include: taking the mesh nodes obtained by finite element division as loading points to be screened; for mesh node i, calculating the intersection-union ratio of other mesh nodes with mesh node i according to the loading range; if interference occurs, retaining mesh node i with a larger force value, deleting mesh node j, and merging the load of mesh node j with the load of mesh node i; traversing all mesh nodes in the sequence in turn, and finally obtaining the set of loading points of the current main load field.

[0022] The solution provided by this invention has the following technical advantages: The purpose of this invention is to solve the problems of low accuracy and over-reliance on manual experience associated with traditional compensation methods that use reverse displacement to determine the loading position point by point. This invention provides a method for determining the loading position of multi-point compensation in stiffened structures based on stiffness decomposition. This algorithm selects singular value decomposition (SVD) to decompose the flexibility matrix of the structure, obtaining the sub-deformation fields corresponding to each sub-flexibility matrix. SVD decomposes the globally continuous deformation field into locally continuous deformation fields, thus facilitating the solution of discrete loading points. Furthermore, the main load field is solved for the selected main deformation field, using load rather than displacement as the criterion for determining whether a node is a loading point. This is because for a node, the larger the load required to produce the corresponding target deviation, the more likely it is to be a loading point. Finally, nodes are filtered using the load amount as the criterion to obtain the final set of loading points for the overall structure. The algorithm determines the loading point position from the stiffness matrix, overcoming the problems of deformation transfer and ambiguous position points caused by the traditional point-by-point loading method with reverse displacement. It can calculate reasonable loading point positions for the multi-point deviation compensation process of stiffened structures under arbitrary deviations. Attached Figure Description

[0023] Figure 1 This is a target deformation field in this method embodiment;

[0024] Figure 2 The example shows the principal deformation field obtained by SVD decomposition and standard deviation screening of the target deformation field.

[0025] Figure 3 This is the set of loading points obtained by screening the main load field and the non-maximum suppression method in the example.

[0026] Figure 4 For the example Figure 1 The set of final loading points corresponding to the target deformation field.

[0027] Figure 5 This refers to the overall methodology and process. Detailed Implementation

[0028] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0029] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the illustrations only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0030] Some exemplary embodiments of the invention have been described for illustrative purposes. It should be understood that the invention may be implemented in other ways not specifically shown in the accompanying drawings.

[0031] like Figure 5 As shown, an embodiment of the present invention includes a method for determining the multi-point compensation loading position of a stiffened structure based on stiffness decomposition. This embodiment requires the flat plate structure to be compensated to a certain extent through multi-point compensation. Figure 1 The diagram shows a plate-like structure with a certain curvature. In this case, the constrained parts of the part are the two sides in the width direction, and the constraint type is simply supported. Specifically, it includes:

[0032] Step 1: Perform finite element meshing on the target structure to obtain the mesh nodes and the overall stiffness matrix K and flexibility matrix C with constraints. Use the mesh nodes of the compensation surface of the target structure as the loading points to be selected. During the process of obtaining the flexibility matrix C, solve for the equivalent force vector on the finite element nodes of the structure based on the target deformation field u of all mesh nodes: F = Ku. For the stiffness matrix with constraints, use the method of setting the diagonal elements of the corresponding nodes to larger numbers (usually multiplied by 10). 10 (On the order of magnitude of numbers) thus yields the structural stiffness matrix K and flexibility matrix C = K considering deformation constraints. -1 And satisfying u = CF. In this embodiment, the above structure is divided using two-dimensional shell elements.

[0033] Step 2: Decompose the flexibility matrix C based on singular value decomposition. It is represented as:

[0034]

[0035] Where S is the singular value σ of the matrix i The diagonal matrices formed are U and V, which are unitary matrices generated by singular value decomposition, and n is the dimension of the flexibility matrix C. i Let V be the i-th column of the unitary matrix U. i Let be the i-th column of the unitary matrix V.

[0036] Step 3: Based on the sub-compliance matrices obtained in Step 2, decompose the target deformation field u into corresponding sub-deformation fields. Then, filter the sub-deformation fields according to the singular values ​​of each sub-compliance matrix to obtain the main deformation field u. iSpecifically, the calculation expression for the candidate deformation field is u. i =C i F = σ i U i V i T F. Wherein, the sub-compliance matrix C i The sub-deformation fields are sorted according to the magnitude of their corresponding singular values. The top k candidate deformation fields with a cumulative singular value contribution of over 90% are obtained. Candidate deformation fields with a standard deviation of nodal deformation less than a deviation threshold are then removed, resulting in m principal deformation fields u. i The cumulative singular value contribution is calculated as follows:

[0037]

[0038] The main deformation field is obtained as follows Figure 2 As shown.

[0039] Step 4: Based on the obtained principal deformation field, it is necessary to further solve for the principal deformation load field. For each principal deformation field u i According to F i =Ku i The corresponding principal load field F is obtained through calculation. i .

[0040] Step 5: Further adjust the influence range of each loading point to be screened based on the actual loading range of the loading tool, in order to calculate the interference between loading points. The interference is evaluated using the intersection-union ratio of the loading ranges (a greater than zero indicates interference).

[0041] Step 6: Calculate the set of loading points for each principal load field using a non-maximum suppression method. Specifically, after obtaining the current principal load field F... i Then, non-maximum suppression (NMS) was used to calculate the principal load field F. i Loading points: The mesh nodes obtained from finite element analysis are used as the loading points to be screened; for mesh node i, the spatial intersection-union ratio of other mesh nodes and mesh node i is calculated according to the loading range; if interference occurs, mesh node i with a larger force value is retained, mesh node j is deleted, and the load of mesh node j is merged with the load of mesh node i; all mesh nodes in the sequence are traversed in turn, and finally the set of loading points of the current main load field is obtained. Figure 3 This is a schematic diagram of a set of loading points.

[0042] Step 7: Superimpose the principal load fields obtained in Step 4 to obtain the superimposed load field. The loading point sets of each principal load field obtained in step 6 are joined to obtain the loading point sequence of the overall structure and its corresponding nodal loads in the superimposed load field; based on the loading point sequence of the overall structure in the superimposed load field... The corresponding load values ​​are used to obtain the set of loading points by applying the non-maximum suppression method, such as... Figure 4 As shown.

[0043] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in the present invention should still be covered by the claims of the present invention.

Claims

1. A method for determining the multi-point compensation loading position of a stiffened structure based on stiffness decomposition, characterized in that... Includes the following steps: S1: Perform finite element meshing on the target structure to obtain the mesh nodes of the target structure, as well as the overall stiffness matrix K and flexibility matrix C with constraints, and use the mesh nodes of the compensation surface of the target structure as the loading points to be screened. S2: The flexibility matrix is ​​decomposed by singular value decomposition to obtain discrete sub-flexibility matrices. S3: Based on the sub-compliance matrices obtained from singular value decomposition, the target deformation field u is decomposed into corresponding sub-deformation fields. The sub-deformation fields are then filtered based on the singular values ​​corresponding to each sub-compliance matrix to obtain the main deformation field u. i ; S4: For each principal deformation field, according to F... i =Ku i The corresponding principal load field F is obtained through calculation. i ; S5: Set the influence range of each loading point to be filtered according to the actual loading range of the loading tool; S6: The set of loading points for each principal load field is calculated using a non-maximum suppression method; S7: Superimpose the principal load fields obtained in step S4 to obtain the superimposed load field. The loading point sets of each principal load field obtained in step S6 are joined to obtain the loading point sequence of the overall structure and its corresponding nodal loads in the superimposed load field; based on the loading point sequence of the overall structure in the superimposed load field... The corresponding load values ​​are used to obtain the set of loading points by applying the nonmaximum suppression method.

2. The method for determining the multi-point compensation loading position of a stiffened structure based on stiffness decomposition according to claim 1, characterized in that... In step S1, the process of obtaining the overall stiffness matrix K and flexibility matrix C with constraints specifically includes: solving for the equivalent force vector F, F = Ku, on the nodes of the structural finite element based on the target deformation field u of all mesh nodes; and using the method of setting the diagonal elements of the corresponding nodes to large numbers to obtain the structural stiffness matrix K and the corresponding flexibility matrix C considering deformation constraints, where C = K -1 And satisfy u = CF.

3. The method for determining the multi-point compensation loading position of a stiffened structure based on stiffness decomposition according to claim 2, characterized in that... Step S2 specifically includes: performing singular value decomposition on the flexibility matrix C to obtain the corresponding sub-flexibility matrices C of each order. i Its expression is: Where S is the singular value σ of the matrix i The diagonal matrices formed are U and V, which are unitary matrices generated by singular value decomposition, and n is the dimension of the flexibility matrix C; U i Let V be the i-th column of the unitary matrix U. i Let be the i-th column of the unitary matrix V.

4. The method for determining the multi-point compensation loading position of a stiffened structure based on stiffness decomposition according to claim 3, characterized in that... Step S3 specifically includes: decomposing the target deformation field u into various candidate deformation fields u according to the sub-compliance matrix. i The expression for the candidate deformation field is: u i =C i F=σ i U i V i T F Wherein, the sub-compliance matrix C i The sub-deformation fields are sorted according to the magnitude of their corresponding singular values. The top k candidate deformation fields with a cumulative singular value contribution of over 90% are obtained. Candidate deformation fields with a standard deviation of nodal deformation less than a deviation threshold are then removed, resulting in m principal deformation fields u. i Wherein: the cumulative singular value contribution is calculated as follows:

5. The method for determining the multi-point compensation loading position of a stiffened structure based on stiffness decomposition according to claim 1, characterized in that, Step S6 uses the non-maximum suppression method to screen candidate loading points. The steps include: taking the mesh nodes obtained from finite element analysis as loading points to be screened; for mesh node i, calculating the intersection-union ratio of other mesh nodes with mesh node i based on the loading range; if interference occurs, retaining mesh node i with a larger force value, deleting mesh node j, and merging the load of mesh node j with the load of mesh node i; traversing all mesh nodes in the sequence in turn, and finally obtaining the set of loading points for the current main load field.

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