A plastic damage triggered adaptive model reduction method

Abstract

The application provides a plastic damage trigger adaptive model reduction method.The method realizes nonlinear seismic response analysis of a large complex structure,adopts a modal analysis method for a linear substructure,compared with a traditional finite element method,significantly reduces the calculation requirement and improves the calculation efficiency; meanwhile,for a nonlinear substructure,an order reduction basis constructed by using a tangent stiffness based vibration mode and a constraint mode is used to reduce the degree of freedom,that is,calculation efficiency is further improved and the accuracy of a local nonlinear analysis result is ensured. In addition, the application is not limited to the large complex structure as the analysis object, and the same method can be used for dynamic response analysis of other types of structures.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering technology, and in particular relates to an adaptive model reduction method for plastic damage triggering. Background Technology

[0002] Earthquakes occur relatively frequently in my country, and many densely populated areas are located on seismic belts. Once an earthquake occurs, it can cause incalculable casualties and economic losses. Therefore, the seismic response and seismic resistance assessment of building structures are particularly important. Nonlinear seismic response analysis, as a method for assessing the seismic performance of building structures, needs to resolve the contradiction between simulation accuracy and computational efficiency in the detailed simulation of large and complex structures.

[0003] To efficiently and accurately analyze the seismic response of building structures, there is an urgent need for a computational method that can simultaneously balance simulation precision and computational efficiency. Patent CN108647366A discloses a nonlinear history analysis method for the seismic response of urban building complexes. This method can reflect the seismic damage characteristics of buildings of different heights, but its analysis object is singular and lacks versatility. Patent CN106021824A discloses an application method of deterministic finite element software in the analysis of simple or large complex structures with interval parameters. This method can perform concise and effective analysis of intervals in complex structures, but its computational efficiency is relatively low. Patent CN116451568A discloses a modeling method for a cascaded neural network model to calculate the seismic response of structures. This method can quickly predict the seismic response of structures, but its accuracy for local nonlinear analysis is relatively low. Therefore, to adapt to the seismic response analysis and seismic performance assessment of building structures, it is necessary to propose a general-purpose, computationally efficient, and accurate adaptive model order reduction method triggered by plastic damage. Summary of the Invention

[0004] The purpose of this invention is to address the problems in existing technologies. To address this problem, this invention proposes an adaptive model order reduction method based on plastic damage triggering. This method enables rapid and accurate analysis of the seismic response of large and complex structures.

[0005] This invention is achieved through the following technical solution: This invention proposes an adaptive model order reduction method for plastic damage triggering, the method comprising the following steps:

[0006] Step 1: Characterize the elastoplastic state based on the changes in material stiffness characteristics, and classify it according to plastic deformation, dividing the elastoplastic state into initial elastic, plastic deformation and residual elastic states.

[0007] Step 2: Establish a finite element model of the target structure. Based on the spatial distribution of plastic damage, automatically divide the finite element model of the building structure into linear substructures and nonlinear substructures.

[0008] Step 3: Derive the reduced-order governing equations for each elastoplastic state using the Craig-Bampton method, and perform modal analysis on the linear substructure using modal analysis.

[0009] Step 4: For nonlinear substructures, reduce the degrees of freedom by using reduced-order bases constructed from vibration modes and constraint modes based on tangent stiffness;

[0010] Step 5: If the substructure transitions between two different elastoplastic states, a restart analysis triggered by plastic damage is used.

[0011] Step 6: Summarize the analysis results of the linear substructure and the nonlinear substructure to obtain the seismic response of the target structure.

[0012] Furthermore, the elastoplastic state is introduced as a uniaxial stress-strain relationship. Under the assumption of isotropic material properties, the constitutive relation is written in matrix form to express the elastoplastic state of the finite element. The constitutive relation is written as equation (1).

[0013]

[0014] Where σ and ε represent the stress and strain matrices, D e D p and D re These are the elasticity matrix under the initial elastic state, the plastic deformation matrix under the plastic deformation state, and the elasticity matrix under the residual elastic state, respectively. e E p and E re These represent the elastic modulus of the material under initial elastic conditions, plastic deformation conditions, and residual elastic conditions, respectively. υ is the material's Poisson's ratio, and ε... p and These are plastic strain and plastic strain rate, respectively.

[0015] Furthermore, the elastoplastic state of the structure is regarded as the spatial distribution of component units in different elastoplastic states, and the elastoplastic state in the material properties is associated with the overall stiffness matrix of the structure, as shown in equation (2).

[0016]

[0017] In the initial elastic state, the overall stiffness matrix of the structure consists only of the element stiffness matrices. Composition; Under plastic deformation, the overall stiffness matrix of the structure includes the stiffness matrices of all elements. Or includes element stiffness matrix and Under residual elastic conditions, the overall stiffness matrix of the structure also includes the element stiffness matrix. and Excluding element stiffness matrix

[0018] Furthermore, the nonlinear governing equation for the elastoplastic state is represented by equation (3):

[0019]

[0020] Where M g C g and K g These are the mass matrix, damping matrix, and stiffness matrix, respectively; u g , and These are the displacement vector, velocity vector, and acceleration vector, respectively; f g It is the external force vector, R(u) g ) is the nonlinear restoring force vector corresponding to plastic deformation or residual elastic state; stiffness matrix K g It is determined by the element stiffness Composition, and corresponding to R(u) g The stiffness of a ) is determined by the element stiffness. or element stiffness Composition; the subscript g indicates the overall structure;

[0021] The overall structure is divided into linear substructures, nonlinear substructures, and linear-nonlinear interfaces; the displacement vectors are correspondingly divided into subvectors, i.e. The subscripts l, b, and n represent the linear substructure, the linear-nonlinear interface, and the nonlinear substructure, respectively; therefore, equation (3) is reformulated as equation (4).

[0022]

[0023] Furthermore, according to the Craig-Bampton method, the linear substructure reduces its degrees of freedom by using a set of reduced-order bases constructed with a small number of vibration modes and constraint modes, while the nonlinear substructure and the linear-nonlinear interface remain unchanged; in the residual elastic state, the nonlinear substructure exhibits elastic deformation, and its seismic response is represented by the superposition of multiple vibration modes based on tangent stiffness; the degrees of freedom of the nonlinear substructure are reduced in the same way as those of the linear substructure, by using a set of reduced-order bases constructed with vibration modes and constraint modes based on tangent stiffness; the reduced-order governing equations in both the plastic deformation and residual elastic states are established by modal matrix transformation, as shown in equations (5) and (6);

[0024]

[0025]

[0026] in These are the vibration modes of a linear substructure, determined based on the eigenvalue problem (K... ll -Ω l M ll )Φ l =0 is calculated; here, It is based on the effective interface quality from Φ l The few feature vectors selected from them The constrained modes of the linear substructure are determined using the Guyan condensation method. Accordingly, and These are the vibration modes and constraint modes of the nonlinear substructure based on tangent stiffness, respectively; all modes of the nonlinear substructure are calculated based on the tangent stiffness matrix.

[0027] Substituting equations (5) and (6) into equation (4), and multiplying equation (4) by the transposed modal matrix, the reduced-order control equations under plastic deformation and residual elastic states are expressed as equations (7) and (8), respectively.

[0028]

[0029] in

[0030]

[0031]

[0032]

[0033]

[0034]

[0035] in

[0036]

[0037]

[0038]

[0039]

[0040] in, and These are the displacement vectors represented in the mixed coordinate space under plastic deformation and residual elastic states, respectively; the subscript h indicates the mixed coordinate space.

[0041] In nonlinear time-history analysis, the reduced-order control equation is solved incrementally, as shown in equation (9).

[0042]

[0043] Among them, u t+Δt and f t+Δt These are the displacement vector and the external force vector at time step t+Δt, respectively.

[0044] Furthermore, the Newmark-beta integration method is used to establish the relationship between the displacement vector, velocity vector, and acceleration vector;

[0045]

[0046] The unknown variables of the reduced-order governing equations are simplified to displacement vectors u. t+Δt Therefore, the Newton-Raphson method is used to iteratively solve the reduced-order governing equations.

[0047]

[0048] Substituting equation (9) into equation (12), the equivalent equilibrium equation is expressed in equation (13) as follows:

[0049]

[0050] in, It is the generalized stiffness matrix. It is a generalized force vector;

[0051] The incremental iterative solution process is represented by equations (9)-(13). This series of equations is expressed in a generalized form. For a given elastoplastic state, by substituting the corresponding matrices and vectors into equation (13), the reduced-order equivalent equilibrium equation is obtained.

[0052] Furthermore, the reduced-order governing equations are solved in an incremental iteration process from the initial elastic state to the plastic deformation and residual elastic states; the plastic deformation state and the residual elastic state alternate until the seismic excitation ends; when the elastoplastic state remains unchanged between time steps t and t-Δt, the incremental iterative analysis will step backward to the next time step t+Δt; however, when the elastoplastic state changes between time steps t and t-Δt, the displacement solution will not be submitted at time step t; the incremental iterative analysis returns to time step t-Δt, updates the substructure modeling mode, establishes the reduced-order governing equations accordingly, and reanalyzes the current time step t.

[0053] Assuming the structure changes its elastoplastic state at time step t, this means the structure exists in two different elastoplastic states at time step t-Δt and time step t. The displacement solution at time step t will be cancelled, and the incremental iterative analysis will revert to the submission state at time step t-Δt. For the initial elastic, plastic deformation, and residual elastic states, the submitted seismic response vectors are respectively... and The displacement vector is represented in modal coordinate space; the displacement vector in mixed coordinate space is... and The displacement vector is transformed from modal coordinates or mixed coordinates to physical coordinates in one of the following three equations:

[0054]

[0055]

[0056]

[0057] Where, Φ d It is the principal mode matrix of the entire structure. and These are the displacement vectors in the physical coordinates of the initial elastic, plastic deformation, and residual elastic states, respectively.

[0058] Furthermore, in the restart analysis, the displacement vector at time step t is determined by assuming... or To initialize; the initialization of these displacement vectors refers to three pairs of possible restart analysis sequences: a sequence from the initial elastic state to the plastic deformation state, a sequence from the plastic deformation state to the residual elastic state, and a sequence from the residual elastic state to the plastic deformation state; only one of these restart analysis sequences is implemented as a restart analysis program; displacement vectors and Divided into and The initial displacement vector is transformed from physical coordinates to hybrid coordinates in one of the following two equations; therefore, a reduction in degrees of freedom occurs at time step t.

[0059]

[0060] in

[0061] and

[0062] in, and These are the vibration modes and constraint modes of the linear substructure, respectively. and These are the vibration modes and constraint modes of the nonlinear substructure; the governing equations can be expressed as equations (19) and (20);

[0063]

[0064]

[0065] Solving equations (19) and (20) yields the seismic response of the structure under plastic deformation and residual elastic states, respectively; equations (19) and (20) are solved iteratively before the end of the seismic excitation.

[0066] This invention proposes an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the adaptive model reduction method triggered by plastic damage.

[0067] This invention proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the adaptive model reduction method triggered by plastic damage.

[0068] The beneficial effects of this invention are:

[0069] This invention proposes an adaptive model reduction method triggered by plastic damage. This method enables nonlinear seismic response analysis of large and complex structures. For linear substructures, modal analysis is employed, which significantly reduces computational requirements and improves computational efficiency compared to the traditional finite element method. Simultaneously, for nonlinear substructures, the traditional finite element method is used, ensuring the accuracy of local nonlinear analysis results. Furthermore, this invention is not limited to large and complex structures; the same method can be used for dynamic response analysis of other types of structures. Attached Figure Description

[0070] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0071] Figure 1 A schematic diagram of the structural stiffness matrix under different elastoplastic states;

[0072] Figure 2 A flowchart illustrating the restart analysis implementation method between two different elastoplastic states;

[0073] Figure 3Flowchart of the model order reduction method for plastic damage triggering. Detailed Implementation

[0074] 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.

[0075] This invention proposes an adaptive model reduction method for plastic damage triggering. The implementation process involves: the model's elastoplastic state, reduced-order control equations based on substructure modeling, and a restart analysis method for solving the reduced-order control equations. The elastoplastic state of the model is used to divide the target structure into linear and nonlinear substructures; the reduced-order control equations based on substructure modeling are used to reduce the degrees of freedom of linear and nonlinear substructures; and the restart analysis method for solving the reduced-order control equations is used to perform restart analysis for plastic damage triggering between two different elastoplastic states.

[0076] Specifically, in combination Figures 1-3 This invention proposes an adaptive model order reduction method for plastic damage triggering, the method comprising the following steps:

[0077] Step 1: Characterize the elastoplastic state based on the changes in material stiffness characteristics, and classify it according to plastic deformation, dividing the elastoplastic state into initial elastic, plastic deformation and residual elastic states.

[0078] Step 2: Establish a finite element model of the target structure. Based on the spatial distribution of plastic damage, automatically divide the finite element model of the building structure into linear substructures and nonlinear substructures.

[0079] Step 3: Derive the reduced-order governing equations for each elastoplastic state using the Craig-Bampton method, and perform modal analysis on the linear substructure using modal analysis.

[0080] Step 4: For nonlinear substructures, reduce the degrees of freedom by using reduced-order bases constructed from vibration modes and constraint modes based on tangent stiffness;

[0081] Step 5: If the substructure transitions between two different elastoplastic states, a restart analysis triggered by plastic damage is used.

[0082] Step 6: Summarize the analysis results of the linear substructure and the nonlinear substructure to obtain the seismic response of the target structure.

[0083] The elastoplastic state is introduced as a uniaxial stress-strain relationship. Under the assumption of isotropic material properties, the constitutive relation is written in matrix form to express the elastoplastic state of the finite element. The constitutive relation is written as equation (1).

[0084]

[0085] Where σ and ε represent the stress and strain matrices, D e D p and D re These are the elasticity matrix under the initial elastic state, the plastic deformation matrix under the plastic deformation state, and the elasticity matrix under the residual elastic state, respectively. e E p and E re These represent the elastic modulus of the material under the initial elastic state, the plastic modulus of the material under the plastic deformation state, and the elastic modulus of the material under the residual elastic state, respectively. v is the Poisson's ratio, and ε is the elastic modulus of the material. p and These are plastic strain and plastic strain rate, respectively. For concrete, E e =E c E p =α c E c And E re =d c E c For steel materials, E e =E s E p =α s E s And E re =E s .

[0086] The elastoplastic state of a structure is considered as the spatial distribution of component elements in different elastoplastic states. Plastic deformation mainly affects the reduction of stiffness and can be used to distinguish the different elastoplastic states mentioned above. The elastoplastic state in the material properties is associated with the overall stiffness matrix of the structure. The stiffness matrix of the structure only considers the material nonlinearity and does not consider the geometric nonlinearity, as shown in equation (2).

[0087]

[0088] Figure 1 The structural stiffness matrices are shown for different elastoplastic states. In the initial elastic state, the overall structural stiffness matrix consists only of the element stiffness matrices. Composition; Under plastic deformation, the overall stiffness matrix of the structure includes the stiffness matrices of all elements. Or includes element stiffness matrix and Under residual elastic conditions, the overall stiffness matrix of the structure also includes the element stiffness matrix. and Excluding element stiffness matrix

[0089] The nonlinear governing equation for the elastoplastic state is represented by equation (3):

[0090]

[0091] Where M g C g and K g These are the mass matrix, damping matrix, and stiffness matrix, respectively; u g , and These are the displacement vector, velocity vector, and acceleration vector, respectively; f g It is the external force vector, R(u) g ) is the nonlinear restoring force vector corresponding to plastic deformation or residual elastic state; stiffness matrix K g It is determined by the element stiffness Composition, and corresponding to R(u) g The stiffness of a ) is determined by the element stiffness. or element stiffness Composition; the subscript g indicates the overall structure;

[0092] In each specific time step of the nonlinear time history analysis, the spatial distribution of plastic damage can be determined by incremental plastic strain. For a given plastic damage distribution, the mixed coordinate CMS method is used to reduce the model order of structures with sparse plastic damage distribution. The mixed coordinate CMS method has been validated to provide sufficient numerical accuracy for structures with local nonlinearities when a suitable set of reduced-order bases is constructed. In the mixed coordinate CMS method, the overall structure is divided into linear substructures, nonlinear substructures, and linear-nonlinear interfaces; the displacement vectors are correspondingly divided into subvectors, i.e. The subscripts l, b, and n represent the linear substructure, the linear-nonlinear interface, and the nonlinear substructure, respectively; therefore, equation (3) is reformulated as equation (4).

[0093]

[0094] According to the Craig-Bampton method, the linear substructure reduces its degrees of freedom by using a reduced-order basis constructed with a small number of vibration modes and constraint modes, while the nonlinear substructure and the linear-nonlinear interface remain unchanged. This MOR method is suitable for establishing reduced-order governing equations under plastic deformation. Under residual elastic conditions, the nonlinear substructure exhibits elastic deformation, and its seismic response is represented by a superposition of multiple vibration modes based on tangent stiffness. The degrees of freedom of the nonlinear substructure are reduced in the same way as those of the linear substructure, by using a reduced-order basis constructed with a set of vibration modes and constraint modes based on tangent stiffness. The reduced-order governing equations under both plastic deformation and residual elastic conditions are established by modal matrix transformation, as shown in equations (5) and (6).

[0095]

[0096] in These are the vibration modes of a linear substructure, determined based on the eigenvalue problem (K... ll -Ω l M ll )Φ l =0 is calculated; here, It is based on the effective interface quality from Φ l The few feature vectors selected from them The constrained modes of the linear substructure are determined using the Guyan condensation method. Accordingly, and These are the vibration modes and constraint modes of the nonlinear substructure based on tangent stiffness, respectively; all modes of the nonlinear substructure are calculated based on the tangent stiffness matrix.

[0097] Substituting equations (5) and (6) into equation (4), and multiplying equation (4) by the transposed modal matrix, the reduced-order control equations under plastic deformation and residual elastic states are expressed as equations (7) and (8), respectively.

[0098]

[0099] in

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] in

[0106]

[0107]

[0108]

[0109]

[0110] in, and These are the displacement vectors represented in the mixed coordinate space under plastic deformation and residual elastic states, respectively; the subscript h indicates the mixed coordinate space.

[0111] In the reduced-order governing equation (7), the seismic response of the linear substructure is obtained by superimposing the principal modes, while the linear-nonlinear interface and the nonlinear substructure remain in the physical coordinate space without any reduction in degrees of freedom. This MOR method will significantly improve computational efficiency during the plastic deformation stage, especially when the proportion of linear degrees of freedom is large and the number of substructures is small.

[0112] In the reduced-order governing equation (8), the seismic response of the linear substructure is obtained using modal superposition based on the initial stiffness, while the nonlinear substructure is simulated by modal superposition based on the tangent stiffness. Only the linear-nonlinear interface remains in the physical coordinate space without any reduction in degrees of freedom. This MOR method will significantly reduce the degrees of freedom in the residual elastic state until new plastically deformable structural components appear, or existing residual elastic structural components return to the plastically deformable state. Equations (7) and (8) will be solved iteratively until the seismic excitation ends.

[0113] In nonlinear time-history analysis, the reduced-order control equation is solved incrementally, as shown in equation (9).

[0114]

[0115] Among them, u t+Δt and f t+Δt These are the displacement vector and the external force vector at time step t+Δt, respectively.

[0116] The Newmark-beta integration method is used to establish the relationship between the displacement vector, velocity vector, and acceleration vector;

[0117]

[0118]

[0119] The unknown variables of the reduced-order governing equations are simplified to displacement vectors u. t+ΔtTherefore, the Newton-Raphson method is used to iteratively solve the reduced-order governing equations.

[0120]

[0121] Substituting equation (9) into equation (12), the equivalent equilibrium equation is expressed in equation (13) as follows:

[0122]

[0123] in, It is the generalized stiffness matrix. It is a generalized force vector;

[0124] The incremental iterative solution process is represented by equations (9)-(13). This series of equations is expressed in a generalized form. For a given elastoplastic state, by substituting the corresponding matrices and vectors into equation (13), the reduced-order equivalent equilibrium equation is obtained.

[0125] The reduced-order governing equations are solved in an incremental iteration process from the initial elastic state to the plastic deformation and residual elastic states; the plastic deformation state and the residual elastic state alternate until the seismic excitation ends; when the elastoplastic state remains unchanged between time steps t and t-Δt, the incremental iterative analysis will step backward to the next time step t+Δt; however, when the elastoplastic state changes between time steps t and t-Δt, the displacement solution will not be submitted at time step t; the incremental iterative analysis returns to time step t-Δt, updates the substructure modeling mode, establishes the reduced-order governing equations accordingly, and reanalyzes the current time step t.

[0126] Assuming the structure changes its elastoplastic state at time step t, this means the structure exists in two different elastoplastic states at time step t-Δt and time step t. The displacement solution at time step t will be cancelled, and the incremental iterative analysis will revert to the submission state at time step t-Δt. For the initial elastic, plastic deformation, and residual elastic states, the submitted seismic response vectors are respectively... and The displacement vector is represented in modal coordinate space; the displacement vector in mixed coordinate space is... and The displacement vector is transformed from modal coordinates or mixed coordinates to physical coordinates in one of the following three equations:

[0127]

[0128]

[0129]

[0130] Where, Φ d It is the principal mode matrix of the entire structure. and These are the displacement vectors in the physical coordinates of the initial elastic, plastic deformation, and residual elastic states, respectively. The elastoplastic state at time step t-Δt should be one of the three elastoplastic states; therefore, only one coordinate transformation of equations (14), (15), and (16) can be performed.

[0131] In the restart analysis, the displacement vector at time step t is determined by the assumption... or To initialize; the initialization of these displacement vectors refers to three pairs of possible restart analysis sequences: a sequence from the initial elastic state to the plastic deformation state, a sequence from the plastic deformation state to the residual elastic state, and a sequence from the residual elastic state to the plastic deformation state; only one of these restart analysis sequences is implemented as a restart analysis program; displacement vectors and Divided into and The initial displacement vector is transformed from physical coordinates to hybrid coordinates in one of the following two equations; therefore, a reduction in degrees of freedom occurs at time step t.

[0132]

[0133]

[0134] in

[0135] and

[0136] in, and These are the vibration modes and constraint modes of the linear substructure, respectively. and These are the vibration modes and constraint modes of the nonlinear substructure; the governing equations can be expressed as equations (19) and (20);

[0137]

[0138]

[0139] Solving equations (19) and (20) yields the seismic response of the structure under plastic deformation and residual elastic states, respectively; equations (19) and (20) are solved iteratively before the end of the seismic excitation.

[0140] The method described in this invention is logically rigorous and has a clear principle. It can divide large and complex structures into linear and nonlinear substructures and analyze them using different methods, providing an effective analytical tool for the nonlinear seismic response analysis of large and complex structures.

[0141] Example:

[0142] like Figure 2 This example operates according to the flowchart of the technical solution, where Γ state These are parameters used to identify the elastoplastic state. Furthermore, Γ state =1 indicates that the elastic-plastic state changes at time step t, while Γ state =0 indicates that the elastic-plastic state remains unchanged. Variable Θ state,t Θ is a fundamental parameter defining the elastoplastic state at time step t, used to distinguish between the three elastoplastic states. state,t =1,Θ state,t =2 and Θ state,t =3 represents the initial elastic, plastic deformation, and residual elastic states, respectively. The process includes the following steps:

[0143] Step 1: Input

[0144] Step 2: If the elastic-plastic state changes at time step t, i.e. Γ state When Θ = 1, determine the variable Θ. state,t-Δt Numerical value, if Θ state,t-Δt =1, then proceed to step 3; if Θ state,t-Δt =2, then proceed to step 4; if Θ state,t-Δt =3, then proceed to step 5; if Γ state =0, then proceed directly to step 18;

[0145] Step 3: Let Division Proceed to step 4;

[0146] Step 4: Let Division Proceed to step 5;

[0147] Step 5: Let Division Proceed to step 6;

[0148] Step 6: Convert the matrix (M) g ,K g ) block into matrix (M) ll ,K ll ),(M bb ,K bb ), and (M nn ,K nn );

[0149] Step 7: Solve (M) ll ,K ll ) t The eigenvalues ​​are used to obtain the eigenvectors of the linear substructure;

[0150] Step 8: Construct a reduced basis based on the eigenvectors of the linear substructure.

[0151] Step 9: Construct a reduced basis using Guyan's order reduction method

[0152] Step 10: Determine the variable Θ state,t Numerical value, if Θ state,t =3, then proceed to step 11; otherwise, proceed directly to step 14;

[0153] Step 11: Solve (M) nn ,K nn ) t The eigenvalues ​​are used to obtain the eigenvectors of the nonlinear substructure, and then proceed to step 12.

[0154] Step 12: Construct a reduced basis based on the eigenvectors of the nonlinear substructure. Proceed to step 13;

[0155] Step 13: Construct a reduced basis using Guyan's order reduction method Proceed to step 14;

[0156] Step 14: Determine the judgment variable Θ state,t Numerical value, if Θ state,t =2, then proceed to step 15; if Θ state,t =3, then proceed to step 16; if Θ state,t =1, then proceed directly to step 17;

[0157] Step 15: Construct the transpose matrix initialization Calculate using equations (10) and (11) and Proceed to step 16;

[0158] Step 16: Construct the transpose matrix initialization Calculate using equations (10) and (11) and Proceed to step 17;

[0159] Step 17: Let Γ state =0, proceed to step 21;

[0160] Step 18: Determine the variable Θstate,t Numerical value, if Θ state,t =2, then proceed to step 19; if Θ state,t =3, then proceed to step 20; if Θ state,t =1, then proceed directly to step 21;

[0161] Step 19: Let Calculate using equations (10) and (11) and Proceed to step 20;

[0162] Step 20: Let Calculate using equations (10) and (11) and Proceed to step 21;

[0163] Step 21: Output

[0164] like Figure 3 This example follows the flowchart of the technical solution and includes the following steps:

[0165] Step 1: Enter M g C g K g f g ,β,γ,Δt,n step i max , ε;

[0166] Step 2: Initialize parameters t = 0, j step =1,Γ state =0,Θs tate =1,

[0167] Step 3: Determine j step <n step If the condition is met, proceed to step 4; otherwise, proceed directly to step 27.

[0168] Step 4: Determine Γ state Check if the condition = 0 is true. If it is true, proceed to step 5; if it is not true, proceed to step 6.

[0169] Step 5: Move to the next time step, t = j step ×Δt, proceed to step 7;

[0170] Step 6: j step =j step -1, t=j step ×Δt, transpose the displacement vector, proceed to step 7;

[0171] Step 7: Determine the variable Θstate，t Numerical value, if Θ state，t =1, then proceed to step 8; if Θ state，t =2, then proceed to step 9; if Θ state，t =3, then proceed to step 10;

[0172] Step 8: Reduce the displacement vector in the initial elastic state, then proceed to step 9;

[0173] Step 9: Go to Figure 2 In the algorithm shown, proceed to step 10;

[0174] Step 10: Go to Figure 2 In the algorithm shown, let i = 1, η convergence =0, proceed to step 11;

[0175] Step 11: Determine if i < i max &η convergence Check if the condition = 0 is true. If it is true, proceed to step 12; if it is not true, proceed to step 16.

[0176] Step 12: Determine the variable Θ state，t The value of Θ, if state，t =1, then proceed to step 13; if Θ state，t =2, then proceed to step 14; if Θ state，t =3, then proceed to step 15;

[0177] Step 13: Solve the governing equations under the initial elastic state, then proceed to Step 14;

[0178] Step 14: Solve the governing equation: Equation (19), proceed to step 15;

[0179] Step 15: Solve the governing equation: Equation (20), proceed to step 16;

[0180] Step 16: Determine If the condition is met, proceed to step 17; otherwise, proceed directly to step 18.

[0181] Step 17: Let η convergence =1, proceed to step 18;

[0182] Step 18: Let i = i + 1, then return to step 11;

[0183] Step 19: Determine η convergence Check if the equation = 1 is true. If it is true, proceed to step 20; if it is false, proceed to step 21.

[0184] Step 20: Submit the displacement vector at the current time step. Proceed to step 22;

[0185] Step 21: Go to the end and report condensation failure, then proceed to Step 22;

[0186] Step 22: Check the elastoplastic state of the overall structure;

[0187] Step 23: Let Θ statec，t =1, 2, and 3 represent the initial elastic, plastic deformation, and residual elastic states, respectively;

[0188] Step 24: Determine Θ state，t ≠Θ state，t-Δt If the condition is met, proceed to step 25; otherwise, proceed to step 26.

[0189] Step 25: Let Γ state =1, proceed to step 26;

[0190] Step 26: Let j step =j step +1, return to step 3;

[0191] Step 27: Output

[0192] This invention proposes an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the adaptive model reduction method triggered by plastic damage.

[0193] This invention proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the adaptive model reduction method triggered by plastic damage.

[0194] The memory in this application embodiment can be volatile memory or non-volatile memory, or it can include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memory used in the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0195] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., high-density digital video discs (DVDs)), or semiconductor media (e.g., solid-state disks (SSDs)).

[0196] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0197] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as being executed by a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0198] The above provides a detailed description of the adaptive model order reduction method for plastic damage triggering proposed in this invention. Specific examples have been used to illustrate the principle and implementation of this invention. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A plasticity damage triggered adaptive model reduction method, characterized in that, The method comprises the following steps: Step 1: the elastic-plastic state is characterized according to the change of the material stiffness characteristic, and is classified according to the plastic deformation, and the elastic-plastic state is divided into initial elasticity, plastic deformation and residual elasticity state; Step 2: a finite element model of the target structure is established, and the finite element model of the building structure is automatically divided into linear substructures and nonlinear substructures according to the spatial distribution of the plastic damage; Step 3: the Craig-Bampton method is used to derive the reduced-order control equation under each elastic-plastic state, and the modal analysis method is used to analyze the modal of the linear substructure; Step 4: for the nonlinear substructure, the reduced-order basis constructed by the tangent stiffness-based vibration mode and the constraint mode is used to reduce the degrees of freedom; Step 5: if the substructure is converted between two different elastic-plastic states, the plastic damage triggered restart analysis is used; Step 6: the analysis results of the linear substructure and the analysis results of the nonlinear substructure are summarized to obtain the seismic response of the target structure.

2. The method of claim 1, wherein, The elastic-plastic state is introduced into the uniaxial stress-strain relationship, and under the assumption of isotropic material characteristics, the constitutive relationship is written in the form of a matrix, which is used to express the elastic-plastic state of the finite element, and the constitutive relationship is written in equation (1) where σ and ε represent the stress and strain matrices, D e , D p , and D re are the elastic matrix in the initial elastic state, the plastic matrix in the plastic deformation state, and the elastic matrix in the residual elastic state, respectively, E e , E p , and E re are the material elastic modulus in the initial elastic state, the material plastic modulus in the plastic deformation state, and the material elastic modulus in the residual elastic state, respectively, υ is the material Poisson's ratio, ε p , and are the plastic strain and the plastic strain rate, respectively.

3. The method of claim 2, wherein, The elastic-plastic state of the structure is regarded as the spatial distribution of the component units in different elastic-plastic states, and the elastic-plastic state in the material characteristics is associated with the overall stiffness matrix of the structure, as shown in equation (2); In the initial elastic state, the global stiffness matrix of the structure is composed only of the element stiffness matrices In the plastic deformation state, the global stiffness matrix of the structure contains all the element stiffness matrices or contains the element stiffness matrices and In the residual elastic state, the global stiffness matrix of the structure contains both the element stiffness matrices and and does not contain the element stiffness matrices 4. The method of claim 3, wherein, The nonlinear control equation of the elastic-plastic state is represented by equation (3): where M g , g and K g are mass, damping and stiffness matrices, respectively; u g , and are displacement, velocity and acceleration vectors, respectively; f g is an external force vector, and R(u g ) is a nonlinear restoring force vector corresponding to plastic deformation or residual elastic state; the stiffness matrix K g is composed of element stiffness , while the stiffness corresponding to R(u g ) is composed of element stiffness or element stiffness ; the subscript g indicates the global structure; The global structure is divided into linear substructures, nonlinear substructures and linear-nonlinear interfaces; the displacement vector is correspondingly divided into sub-vectors, i.e. The subscripts l, b and n represent linear substructures, linear-nonlinear interfaces and nonlinear substructures, respectively; therefore, equation (3) is re-expressed as equation (4); 5. The method of claim 4, wherein, According to the Craig-Bampton method, the linear substructure is reduced in degrees of freedom by a set of reduced-order bases constructed using a small number of vibration modes and constraint modes, while the nonlinear substructure and the linear-nonlinear interface remain unchanged; in the residual elastic state, the nonlinear substructure is in elastic deformation mode, and its seismic response is represented by the superposition combination of multiple tangent stiffness-based vibration modes; the degrees of freedom of the nonlinear substructure are reduced in the same way as the linear substructure, that is, by a set of reduced-order bases constructed by tangent stiffness-based vibration modes and constraint modes; the reduced-order control equations in the plastic deformation and residual elastic states are established by modal matrix transformation, as shown in equations (5) and (6); where is the vibration mode of the linear substructure, which is calculated from the eigenvalue problem (K ll -Ω l M ll )Φ l = 0; here, is the few eigenvectors selected from Φ l according to the effective interface mass, is the constraint mode of the linear substructure, which is determined by the Guyan condensation method Correspondingly, and are the tangent stiffness-based vibration mode and constraint mode of the nonlinear substructure, respectively; all the modes of the nonlinear substructure are calculated based on the tangent stiffness matrix; Substitute equations (5) and (6) into equation (4), and left multiply equation (4) by the transpose modal matrix, the reduced-order control equations in the plastic deformation and residual elastic states are represented as equations (7) and (8) respectively; Wherein Wherein wherein, and are the displacement vectors in the hybrid coordinate space under plastic deformation and residual elastic state, respectively; subscript h denotes the hybrid coordinate space; The reduced-order control equation is solved in incremental form in nonlinear time history analysis, as shown in equation (9) where u t+Δt and f t+Δt are the displacement and external force vectors at time step t + Δt, respectively.

6. The method of claim 5, wherein, The relationship between the displacement vector and the velocity vector and the acceleration vector is established by using the Newmark-beta integration method; The unknown variables of the reduced-order control equation are simplified as a displacement vector u t+Δt ; therefore, the Newton-Raphson method is used to iteratively solve the reduced-order control equation; Substitute equation (9) into equation (12), and the equivalent equilibrium equation is expressed in equation (13) as follows: wherein, is the generalized stiffness matrix, is the generalized force vector; The incremental iteration solving process is represented by equations (9)-(13), which are expressed in a generalized form, and for a specified elastic-plastic state, the corresponding matrices and vectors are substituted into equation (13) to obtain the reduced-order equivalent equilibrium equation.

7. The method of claim 6, wherein, The reduced-order governing equations are solved in an incremental iterative procedure from the initial elastic state to the plastic deformation and residual elastic state; the plastic deformation state and the residual elastic state are alternately interchanged until the end of the seismic excitation; When the elastoplastic state remains unchanged between the time steps t and t-Δt, the incremental iterative analysis will step backward to the next time step t+Δt; however, when the elastoplastic state changes between the time steps t and t-Δt, the displacement solution will not be submitted at the time step t; the incremental iterative analysis returns to the time step t-Δt, updates the substructure modeling mode, establishes the reduced-order governing equations accordingly, and reanalyzes the current time step t; Assuming the structure changes the elastoplastic state at time step t, which means the structure is in two different elastoplastic states at time step t-At and time step t; the displacement solution at time step t will be canceled, and the incremental iterative analysis will go back to the committed state at time step t-At; for the initial elastic, plastic deformation and residual elastic state, the committed seismic response vector is and is the displacement vector expressed in modal coordinate space; the displacement vector in mixed coordinate space is and The displacement vector is converted from modal coordinates or mixed coordinates to physical coordinates in one of the following three equations: where Φ d is the principal mode matrix of the whole structure, and are the displacement vectors in the physical coordinates of the initial elastic, plastic deformation and residual elastic state, respectively.

8. The method of claim 7, wherein, In the restart analysis, the displacement vectors at time step t are initialized by assuming or These displacement vector initializations refer to three pairs of possible restart analysis sequences, namely, a sequence from the initial elastic state to the plastic deformation state, a sequence from the plastic deformation state to the residual elastic state, and a sequence from the residual elastic state to the plastic deformation state; where only one of the reanalysis sequences is implemented as a reanalysis program; displacement vector and are partitioned into and The initialized displacement vector is converted from physical coordinates to mixed coordinates in one of the following two equations; thus, a reduction in degrees of freedom occurs at time step t; wherein and where and are the vibration modes and the constrained modes of the linear substructure, respectively, and are the vibration modes and the constrained modes of the nonlinear substructure; the governing equations can be expressed as equations (19) and (20); Solving the equations (19) and (20) respectively obtains the seismic response of the structure in the plastic deformation and residual elastic state; The equations (19) and (20) are alternately solved before the end of the seismic excitation. 9.An electronic device comprising a memory and a processor, the memory storing a computer program, wherein, The processor executes the computer program to implement the steps of the method of any one of claims 1-8.

10. A computer readable storage medium for storing computer instructions, characterized in that, The computer instructions are executed by the processor to implement the steps of the method of any one of claims 1-8.

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