Rapid prediction method for elastic-plastic mechanical property of one-dimensional periodic spiral winding structure
By constructing a reduced-order model and an online incremental algorithm, the problems of large computational load and insufficient accuracy in the elastoplastic analysis of one-dimensional periodic helical winding structures in the existing technology are solved, realizing efficient and accurate prediction of mechanical properties and significantly improving the efficiency of analysis and optimization.
Patent Information
- Application Number
- CN202511897611.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-16
- Publication Date
- 2026-03-20
AI Technical Summary
Existing technologies suffer from high computational complexity and insufficient accuracy in the elastoplastic analysis of one-dimensional periodic helical winding structures, failing to meet the needs of efficient optimization design, and especially struggling to achieve rapid and accurate prediction of mechanical properties under complex working conditions.
A reduced-order model based on K-means clustering and an online incremental algorithm based on the principle of minimum complementary energy are adopted. By constructing a finite element model, extracting the strain condensation tensor, calculating the interaction matrix after dividing it into blocks using the clustering algorithm, and inputting it into the online incremental algorithm, the rapid prediction of the elastoplastic stress-strain curve is achieved.
It improves the efficiency of analysis and optimization of one-dimensional periodic helical winding structures, significantly reduces computation time, and maintains high accuracy with an error of less than 1%.
Smart Images
Figure CN121706479A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of predicting the mechanical properties of helical winding structures, and more particularly to a method for rapidly predicting the elastic-plastic mechanical properties of one-dimensional periodic helical winding structures. BACKGROUND
[0002] One-dimensional periodic helical winding structures are widely used in marine engineering structures, such as umbilical cables, flexible risers, cryogenic pipelines, and wind power dynamic cables. Periodic helical winding design can provide structural flexibility while effectively dispersing and resisting environmental loads, thereby improving the fatigue resistance and tensile properties of the structure. The complex and harsh marine environment can cause one-dimensional periodic helical winding structures to enter a plastic state, and they have a large slenderness ratio, i.e., the axial length is much larger than the cross-sectional dimension, which poses a great challenge to their elastic-plastic analysis.
[0003] Existing theoretical models are based on assumptions and simplifications, such as ignoring interlayer slip and idealizing material behavior as linear elastic. These models do not consider the relative slip between layers in actual applications and the response of materials after entering the plastic state, which can result in unacceptable errors in predicting the structural response. In addition, although high-fidelity finite element analysis can better capture material nonlinearity, geometric nonlinearity, and boundary effects, it can improve the calculation accuracy of the elastic-plastic mechanical properties of one-dimensional periodic helical winding structures, but it often comes with a huge computational cost. Especially when optimization problems are involved, each analysis takes a lot of time, resulting in a long and even impossible optimization process.
[0004] The existing technology often faces the bottleneck of excessive calculation and insufficient accuracy when facing complex working conditions, and cannot meet the needs of efficient elastic-plastic analysis and optimization design. Therefore, it is a problem that needs to be solved by those skilled in the art to propose a method for rapidly predicting the elastic-plastic mechanical properties of one-dimensional periodic helical winding structures to solve the difficulties existing in the prior art. SUMMARY
[0005] Therefore, the present application provides a method for rapidly predicting the elastic-plastic mechanical properties of one-dimensional periodic helical winding structures, which can efficiently and accurately predict the elastic-plastic mechanical properties of one-dimensional periodic helical winding structures, and improve the analysis efficiency and optimization efficiency of one-dimensional periodic helical winding structures.
[0006] To achieve the above purpose, the present application provides the following technical solutions: A method for rapidly predicting the elastic-plastic mechanical properties of one-dimensional periodic helical winding structures, comprising the following steps: S1, constructing a finite element model of a one-dimensional periodic helical winding structure and performing linear elastic analysis on the finite element model to extract a strain concentration tensor; S2, based on the extracted strain concentration tensor, the finite element model is clustered using a clustering algorithm to obtain a block after the reduced order model, and the interaction matrix representing the mechanical relationship between each block in the reduced order model is calculated; S3, the interaction matrix is input into the online incremental algorithm to obtain the elastic-plastic stress-strain curve of the one-dimensional periodic spiral winding structure, and the prediction of the elastic-plastic mechanical properties of the one-dimensional periodic spiral winding structure is realized.
[0007] Optionally, in S1, a finite element model of the one-dimensional periodic spiral winding structure is constructed, and linear elastic analysis is performed on the finite element model, and the specific content of the strain concentration tensor is: A finite element model of a representative volume element of the one-dimensional periodic spiral winding structure is constructed, wherein the axial length of the representative volume element is a unit pitch; Periodic boundary conditions are applied to the nodes of two cross sections of the finite element model, and characteristic strains in the axial direction are applied to all elements; Linear elastic analysis is performed on the finite element model, and the strain concentration tensor is extracted.
[0008] Optionally, in S2, the K-means clustering algorithm is used to cluster the finite element model to obtain a block after the reduced order model.
[0009] Optionally, the K-means clustering algorithm is used to cluster different components.
[0010] Optionally, in S3, the interaction matrix is input into the online incremental algorithm to obtain the elastic-plastic stress-strain curve of the one-dimensional periodic spiral winding structure, and the prediction of the elastic-plastic mechanical properties of the one-dimensional periodic spiral winding structure is realized. The specific content is: The minimum complementary energy principle suitable for one-dimensional periodic boundary conditions is derived; The interaction matrix is input into the online incremental algorithm to realize fast prediction of the elastic-plastic stress-strain curve.
[0011] Optionally, the specific process of the online incremental algorithm includes: Strain is applied to each block in the reduced order model, the average stress of each block is calculated according to elastic analysis, and it is judged whether the yield stress is reached; If all blocks do not enter the yield state, continue to increase the strain and maintain the elastic analysis; If some blocks enter the yield state, the blocks that enter the yield state are calculated according to plasticity, and the other blocks are calculated according to elasticity; If all blocks enter the yield state, they are all analyzed according to plasticity; Continue to increase the strain until the maximum loading strain is reached.
[0012] Via the technical solution, compared with the prior art, the application provides a one-dimensional periodic spiral winding structure elastic-plastic mechanical property fast prediction method, which has the following beneficial effects: (1) The application takes the equivalent elastic-plastic mechanical property of the one-dimensional periodic spiral winding structure as the research target, establishes a reduced-order model based on the K-means clustering algorithm, and an online incremental algorithm based on the minimum complementary energy principle, and uses the results of direct numerical simulation as a comparison, which shows the high accuracy and high efficiency of the application. (2) The application can efficiently and accurately predict the elastic-plastic mechanical property of the one-dimensional periodic spiral winding structure, and improve the analysis efficiency and optimization efficiency of the one-dimensional periodic spiral winding structure. BRIEF DESCRIPTION OF DRAWINGS
[0013] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are only a part of the embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of the provided drawings.
[0014] Figure 1 A one-dimensional periodic spiral winding structure elastic-plastic mechanical property fast prediction method flow chart is provided for the application. Figure 2 A finite element model selection method for establishing a representative volume element (RVE) is provided for the application. Figure 3 A one-dimensional periodic spiral winding structure schematic diagram is provided for the application. Figure 4 A comparison diagram of the method and the direct numerical simulation (DNS) method is provided for the application. Figure 5 A clustering block model schematic diagram is provided for the application. Figure 6 A comparison diagram of the calculation results of the method and the direct numerical simulation (DNS) method is provided for the application. DETAILED DESCRIPTION
[0015] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only a part of the embodiments of the application, not all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the application.
[0016] Referring to Figure 1As shown, the present application discloses a one-dimensional periodic spiral winding structure elastic-plastic mechanical property rapid prediction method, comprising the following steps: S1, construct a finite element model of one-dimensional periodic spiral winding structure, and perform linear elastic analysis on the finite element model to extract strain concentration tensor; S2, based on the extracted strain concentration tensor, use clustering algorithm to cluster the finite element model, obtain the reduced model after blocking, and calculate the interaction matrix representing the mechanical relationship between each block in the reduced model; S3, input the interaction matrix into the online incremental algorithm to obtain the elastic-plastic stress-strain curve of the one-dimensional periodic spiral winding structure, and realize the prediction of the elastic-plastic mechanical property of the one-dimensional periodic spiral winding structure.
[0017] Further, the specific content of S1, constructing a finite element model of one-dimensional periodic spiral winding structure, and performing linear elastic analysis on the finite element model to extract strain concentration tensor, is: Construct a finite element model of a representative volume element of one-dimensional periodic spiral winding structure, wherein the axial length of the representative volume element is a unit pitch; Apply periodic boundary conditions to the nodes of two cross sections of the finite element model, and apply characteristic strain in the axial direction to all elements; Perform linear elastic analysis on the finite element model to extract strain concentration tensor.
[0018] Further, in S2, K-means clustering algorithm is used to cluster the finite element model to obtain the reduced model after blocking.
[0019] Further, K-means clustering algorithm clusters different components respectively.
[0020] Specifically, the specific process of constructing a reduced model in the offline stage includes: Establish a finite element model of a representative volume element (RVE); Apply 6 sets of orthogonal eigenstrains and perform linear elastic analysis; Calculate the strain concentration tensor; Construct a reduced model based on K-means clustering algorithm; Calculate the interaction matrix.
[0021] Specifically, the selection method of RVE is as shown in Figure 2 Wherein is the actual axial length of the one-dimensional periodic spiral winding structure, is the axial length of the RVE, is the cross-sectional diameter, is the diameter of the spiral winding monofilament, is the winding angle of the monofilament.
[0022] Furthermore, in S3, the interaction matrix is input into the online incremental algorithm to obtain the elastoplastic stress-strain curve of the one-dimensional periodic helical winding structure. The specific content of predicting the elastoplastic mechanical properties of the one-dimensional periodic helical winding structure is as follows: Derive the minimum complementary energy principle applicable to one-dimensional periodic boundary conditions; By inputting the interaction matrix into an online incremental algorithm, rapid prediction of elastoplastic stress-strain curves can be achieved.
[0023] Furthermore, the specific process of the online incremental algorithm includes: Strain is applied to each block in the reduced-order model, and the average stress of each block is calculated according to elastic analysis to determine whether the yield stress has been reached. If none of the blocks have reached the yield state, continue to increase the strain and maintain the elasticity analysis; If some blocks enter the yielding state, the blocks that enter the yielding state are calculated according to plasticity, while the other blocks are analyzed according to elasticity. If all blocks reach the yield state, then they are all analyzed according to plasticity. Continue increasing the strain until the maximum loading strain is reached.
[0024] Specifically, the elastoplastic analysis process based on the principle of minimum complementary energy is as follows: For a one-dimensional periodic helical winding structure, the total residual energy of its Reverse Energy Vessel (RVE) can be expressed as: (1) in, Indicates the intrinsic strain components, Represents stress components, This represents the total volume of the RVE. Represents the residual energy density. , Specifically: (2) (3) in, Indicates elastic strain. This represents the inverse function of the constitutive equation for inelastic materials. Indicates built-in variables; The total residual energy is represented in block form: (4) in, Indicates the number of blocks. Indicates the first Each block, Indicates the first The residual energy density of each block, Indicates the first The volume of each block Indicates the first The average stress components of each block; In clustering order reduction algorithms, stress and strain are averaged across each block, which is equivalent to assuming that the stress in each block is equal to the average stress across the block. Its mean stress can be used Approximately, based on this assumption, the total complementary energy can be expressed as: (5) in, For the first The residual energy density of the block; During the elastic phase, Represented as: (6) in, Indicates the first Average stress of each block Indicates the transpose symbol. Indicates the first The compliance matrix of each block; The total surplus energy can be represented in block form as follows: (7) in, This represents the diagonal matrix representing the volume of each block. This represents the compliance matrix of each block. Indicates intrinsic strain; Once the RVE enters the plastic state, the incremental form of the minimum complementary energy principle is used to linearize the nonlinear calculation process. The incremental form of the minimum complementary energy principle is expressed as: (8) in, Represents the interaction matrix. The matrix represents the unknown quantity to be solved. The linear combination coefficients of the provided self-balancing stress basis vectors; Equation (8) states that, among all statically permitted block stress fields, the “actual” block stress field (both balanced and compatible) minimizes the total block residual energy of the RVE. The statically permitted block stress field is the interaction matrix using the ROM. Constructed according to formula (9); (9) In one specific embodiment, in order to verify the performance of the method provided by the embodiments of the present invention, Figure 3 Taking the one-dimensional periodic helical winding structure shown as an example, the geometric and material parameters are shown in Tables 1 and 2, respectively. A finite element model is established as follows: Figure 4We selected the Direct Numerical Simulation (DNS) method for comparison.
[0025] Table 1 Model Geometric Parameters
[0026] Table 2 Model Material Parameters
[0027] Based on the method disclosed in this invention, a clustering block model of the structure is obtained, such as... Figure 5 As shown. The results of this method are compared with those of DNS calculation, for example... Figure 6 As shown, the average relative error calculated by equation (10) is 0.62%, which shows that the method has extremely high accuracy.
[0028] (10)
[0029] in, This represents the average relative error. Indicates the number of loading steps. Indicates the first The stress results calculated by FCA (the method proposed in this invention) under each loading step, Indicates the first The stress results calculated by DNS under each loading step.
[0030] In addition, the computation time of FCA and DNS was calculated, as shown in Table 3. Compared with DNS, the computation time of FCA was reduced by -98.13%.
[0031] Table 3 Comparison of Calculation Time
[0032] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.
[0033] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for rapid prediction of the elastoplastic mechanical properties of a one-dimensional periodic helical winding structure, characterized in that, Includes the following steps: S1. Construct a finite element model of a one-dimensional periodic helical winding structure, and perform linear elastic analysis on the finite element model to extract the strain condensation tensor; S2. Based on the extracted strain condensed tensor, the finite element model is clustered using a clustering algorithm to obtain a block-based reduced-order model. The interaction matrix representing the mechanical relationship between the blocks in the reduced-order model is then calculated. S3. Input the interaction matrix into the online incremental algorithm to obtain the elastoplastic stress-strain curve of the one-dimensional periodic helical winding structure, thereby realizing the prediction of the elastoplastic mechanical properties of the one-dimensional periodic helical winding structure.
2. The method for rapid prediction of the elastoplastic mechanical properties of a one-dimensional periodic helical winding structure according to claim 1, characterized in that, In S1, a finite element model of a one-dimensional periodic helical winding structure is constructed, and linear elastic analysis is performed on the finite element model to extract the specific contents of the strain concentration tensor: A finite element model of a one-dimensional periodic helical winding structure representing a volume element is constructed, where the axial length of the volume element is a unit pitch. Periodic boundary conditions are applied to the nodes of the two sections of the finite element model, and characteristic strain in the axial direction is applied to all elements; Linear elastic analysis was performed on the finite element model to extract the strain condensation tensor.
3. The method for rapid prediction of the elastoplastic mechanical properties of a one-dimensional periodic helical winding structure according to claim 1, characterized in that, In S2, the K-means clustering algorithm is used to cluster the finite element model to obtain the reduced-order model after block division.
4. The method for rapid prediction of the elastoplastic mechanical properties of a one-dimensional periodic helical winding structure according to claim 3, characterized in that, The K-means clustering algorithm clusters different components separately.
5. The method for rapid prediction of the elastoplastic mechanical properties of a one-dimensional periodic helical winding structure according to claim 1, characterized in that, In S3, the interaction matrix is input into the online incremental algorithm to obtain the elastoplastic stress-strain curve of the one-dimensional periodic helical winding structure. The specific content of predicting the elastoplastic mechanical properties of the one-dimensional periodic helical winding structure is as follows: Derive the minimum complementary energy principle applicable to one-dimensional periodic boundary conditions; By inputting the interaction matrix into an online incremental algorithm, rapid prediction of elastoplastic stress-strain curves can be achieved.
6. The method for rapid prediction of the elastoplastic mechanical properties of a one-dimensional periodic helical winding structure according to claim 5, characterized in that, The specific process of the online incremental algorithm includes: Strain is applied to each block in the reduced-order model, and the average stress of each block is calculated according to elastic analysis to determine whether the yield stress has been reached. If none of the blocks have reached the yield state, continue to increase the strain and maintain the elasticity analysis; If some blocks enter the yielding state, the blocks that enter the yielding state are calculated according to plasticity, while the other blocks are analyzed according to elasticity. If all blocks reach the yield state, then they are all analyzed according to plasticity. Continue increasing the strain until the maximum loading strain is reached.