A nonlinear evaluation method for horizontal low-frequency characteristics of bracket sets based on automatic contact pair generation strategy, medium

Abstract

The present invention relates to a nonlinear evaluation method and medium for the horizontal low-cycle characteristics of a bracket based on an automatic contact pair generation strategy. The method uses the automatic contact pair generation strategy to determine the contact relationships between various geometric bodies in the bracket structure. Based on the determined contact relationships and in combination with the bracket material properties, the stress-strain relationship is determined. Yield behavior and plastic strain are determined based on plastic mechanics theory and related criteria. Failure modes are determined based on damage mechanics theory, and then a damage evolution equation is defined and damage correction is performed to accurately assess material damage. Based on the analysis results of the material properties, a consistent tangent stiffness matrix and an accordion ratio matrix are obtained to complete the evaluation of the bracket's mechanical properties under horizontal low-cycle characteristics. Compared with existing technologies, the present invention can effectively capture the damage evolution and displacement patterns of the bracket during low-cycle repeated stress. The errors in the hysteretic overall envelope area, secant stiffness error, equivalent viscous damping coefficient, hysteretic energy dissipation, and elastic recovery energy are all small.

Description

Technical Field

[0001] The present invention relates to the field of civil engineering, and in particular to a nonlinear evaluation method for horizontal low-frequency characteristics of bracket sets based on an automatic contact pair generation strategy. Background Art

[0002] The bracket is a world-renowned structural system, widely found in East Asian timber architectural heritage. It is one of the primary load-transmitting components within these structures. Timber architectural heritage often remains in service for hundreds or even thousands of years. Under long-term loads and environmental influences, brackets are susceptible to aging, decay, and insect infestation. Therefore, research on the mechanical performance evaluation of brackets is urgently needed. The complexity of analyzing brackets using solid models primarily stems from two aspects: modeling complexity and computational complexity. With regard to computational complexity, strategies have been developed to address this, thanks to advances in computing power and substructure technology. Regarding modeling complexity, since brackets are complex timber structures with numerous contacting components, the currently common approach is to manually establish contact pairs between relevant contact surfaces. This method is time-consuming and labor-intensive, making it impractical for large-scale deployment. Summary of the Invention

[0003] The present invention aims to overcome the shortcomings of the aforementioned prior art by providing a nonlinear assessment method and medium for the horizontal low-cycle characteristics of bracket sets based on an automatic contact pair generation strategy. This automatic contact pair generation strategy, based on an improved GJK method and a convexification strategy, improves modeling efficiency. Furthermore, an elastic-plastic damage assessment model based on the Hoffman yield criterion and a two-stage damage evolution criterion is established, enhancing assessment accuracy. This invention significantly simplifies the modeling complexity of bracket set hysteretic performance assessment, ensuring assessment accuracy. It also provides methodological support for the horizontal hysteretic characteristic assessment of other structural systems with complex contact relationships.

[0004] The purpose of the present invention can be achieved by the following technical solutions:

[0005] A first aspect of the present invention provides a nonlinear evaluation method for horizontal low-frequency characteristics of bracket sets based on an automatic contact pair generation strategy, comprising the following steps:

[0006] S1: Determine the contact relationship between geometric bodies in the bracket structure through the automatic contact pair generation strategy, including body pair judgment, surface contact determination, and false contact surface elimination;

[0007] S2: Based on the contact relationship determined in S1 and combined with the bracket material properties, the stress-strain relationship is determined. The yield behavior and plastic strain are determined based on plastic mechanics theory and related criteria. The failure mode is determined using the Tsai-Wu criterion based on damage mechanics theory. The damage evolution equation is then defined and the damage is corrected to accurately assess the material damage.

[0008] S3: Based on the analysis results of the material properties in S2, the consistent tangent stiffness matrix and the Accord ratio matrix are obtained to complete the evaluation of the mechanical properties of the bracket under horizontal low-cycle characteristics.

[0009] Furthermore, it is characterized in that, in S1, the following steps are specifically included:

[0010] S1-1: Determine the geometric body set of the structure. For each geometric body in the set, calculate its convex hull to obtain a convex hull set. Calculate the minimum Minkowski difference norm between any two convex hulls in the convex hull set, and use this as the approximate distance of the geometric body. Iteratively update the simplex vertex set. When the iteration meets the stopping condition, obtain a set of body pairs with contact relationships.

[0011] S1-2: For each body in the body pair set, all its faces are convexified, and a new body pair is formed with the generated convex hull surface as a variable. The surface distance of each convex surface in these body pairs is calculated. If the surface distance is within the contact sphere, the faces are considered to be in contact.

[0012] S1-3: Eliminate false contact surface relationships.

[0013] Furthermore, in S1-1, the specific process includes:

[0014] Assume that the geometry set of the structure is n v is the number of geometric bodies, for any of them There are nip vertices, geometry V i The convex hull conv(V i (Y)) uses the λ shown in formula (1) j Combined solution:

[0015]

[0016] Convex hull conv(V i The vertex of (Y)) is considered as V i (Y), all the bodies in the geometric body set are processed by formula (1) to obtain the convex hull set: right Any two conv(V i ),conv(V j) Use formula (2) to calculate the minimum Minkowski difference norm between the two:

[0017] MD=min{||y j -y|| i :y i ∈conv(V i ),y j ∈conv(V j )} (2)

[0018] Where MD is the geometry V i and V j The approximate distance of

[0019] Iteratively update the vertex set of the simplex

[0020] is a subset of Minkowski difference, for the three-dimensional case n s =4 represents a tetrahedron, when The iteration stops when the coordinate origin is included or the distance from the coordinate origin cannot be reduced;

[0021] Calculate using formula (3) Distance from the origin:

[0022]

[0023] w is the minimum norm in Minkowski difference, that is, the distance to be calculated, It is the cofactor of the M matrix, representing the deletion of r rows and n s The determinant after the column, is the Cartesian coordinate component of the corresponding vertex in κ;

[0024] According to the process from formula (2) to (3), we can get the set V of body pairs with contact relationship: pair ={(V i ,V j ):V i ,V j ∈V|w ij ≤ε}, where w ij represents the distance between the two bodies calculated by formula (3), and ε represents the sphere for determining contact.

[0025] Furthermore, in S1-2, the specific process includes:

[0026] For V pair Any body V iAll the faces in are convexified using formula (1), and the generated convex hull face is the volume pair of variables, denoted as The surface distances of the convex surfaces in the body pair are calculated using formula (2) and formula (3) one by one. If the distance is within the sphere for determining contact, the surfaces are considered to be in contact.

[0027] In S1-3, the specific process includes: eliminating the following false contact surface relationships: i ,A j ) and (A i ,A k ), A i With A j Initially, there is an approximate parallel relationship, A i With A k Initially there is only one point of contact.

[0028] Furthermore, S2 specifically includes the following steps:

[0029] S2-1: Determine the stress-strain relationship of the bracket material using tensor form;

[0030] S2-2: According to the theory of plastic mechanics, the elastic strain is obtained by eliminating the plastic strain from the overall strain.

[0031] Different criteria are used for bracket materials under tension and compression. Under tension, the behavior is simplified to no yield, while under compression, the Hoffman yield criterion is used to determine the yield behavior. At the same time, the associated flow law is used to determine the plastic strain.

[0032] S2-3: Using the Tsai-Wu criterion applicable to anisotropic materials, the relationship between characteristic points on the stress-strain curve is introduced to determine the relationship between residual characteristic points and limit characteristic points.

[0033] The damage evolution equation is defined and divided into a softening stage and a residual stage. The parabolic equation is used in the softening stage, and the exponential decay equation is used in the residual stage. Considering the problem of non-convergence of the numerical solution caused by stiffness softening, viscosity regularization is used to correct the damage, which involves viscosity regularization parameters and virtual time solution steps, so as to achieve accurate assessment of the material damage.

[0034] Furthermore, in S2-1, the specific process includes:

[0035] For each contact pair, a symmetric contact pair is established based on the generalized Lagrangian method as shown in formula (4);

[0036]

[0037] K n is the contact normal stiffness, u n is the contact gap, ε c is the penetration tolerance, λi is the Lagrange multiplier of the i-th iteration step;

[0038] The Coulomb model is used for friction, distinguishing between dynamic friction and static friction. The expression of tangential stress f is shown in formula (5):

[0039] f=(1+(R f -1)e -ζ|v| )Pμ d (5)

[0040] where R f is the ratio of static friction to kinetic friction coefficient, ζ is the friction coefficient attenuation coefficient, v is the sliding velocity, μ d is the coefficient of kinetic friction;

[0041] The stress-strain relationship of the bracket material can be expressed in the tensor form as shown in formula (6):

[0042]

[0043] where ε e Represents the elastic strain tensor, E represents the fourth-order stiffness tensor using Voigt notation, Represents the effective stress tensor, the flexibility matrix C = E -1 , σ is the Cauchy stress,

[0044] The expression is as follows:

[0045]

[0046] d represents the damage factor, 1, 2, and 3 are respectively along the grain, radial, and tangential directions. 23,2v Indicates the damage caused by radial shear on the radial-chord surface.

[0047] According to the theory of plasticity, the elastic strain ε e The plastic strain ε can be eliminated from the overall strain ε p , as shown in formula (7):

[0048] ε e =ε-ε p (7)

[0049] Furthermore, in S2-2, the specific process includes:

[0050] The bracket material is simplified to have no yield behavior under tension, and the Hoffman yield criterion is adopted under compression. The Hoffman yield function of isotropic Voce hardening can be written as the general form of formula (8):

[0051]

[0052] Where P and Q are Hoffman plastic matrices, if The radial mapping algorithm is used to pull the stress back to the yield surface. is the equivalent plastic strain, β1 and β2 are hardening parameters, determined based on uniaxial experimental regression;

[0053] The plastic strain is determined by the associated flow rule. The relationship between the total strain increment and the plastic strain increment and the elastic strain increment is shown in formula (9):

[0054]

[0055] where Δλ represents the plasticity multiplier, The gradient of the plastic potential energy and the Kuhn-Tucker conditions for loading and unloading are represents the rate of the plasticity multiplier.

[0056] Furthermore, in S2-3, the specific process includes:

[0057] The failure criterion of bracket materials adopts the Tsai-Wu criterion applicable to anisotropic materials, and eight equations are used to distinguish the eight failure modes of wood, as shown in formula (10):

[0058]

[0059] For f u,i ,f r,i ,ε u,i ε r,i For the characteristic points on the stress-strain curve, the following formula is introduced to determine the relationship between the residual characteristic points and the limit characteristic points:

[0060] The parabolic equation is used in the softening section, and the exponential decay equation is used in the residual section, which gradually decays to approximately 0. The damage evolution equation is defined using formula (11):

[0061]

[0062] When the stiffness softening causes the numerical solution to not converge, the viscosity regularization is used to correct the damage as shown in Equation (12):

[0063]

[0064] Where η is the viscosity regularization parameter and Δt is the virtual time solution step.

[0065] Furthermore, in S3, the specific process includes:

[0066] Construct the consistent tangent stiffness matrix and Jacobian ratio matrix, and the expression is shown in formula (13):

[0067]

[0068] Within the framework of finite element analysis, the consistent tangent stiffness matrix and the Jacobian ratio matrix are applied to solve the equilibrium equations of the bracket arch during horizontal low-cycle loading. At each loading step, these matrices are used to calculate the increments of node displacements, stresses, and strains based on the current deformation state and material properties, thereby gradually tracking the mechanical response history of the bracket arch structure under horizontal low-cycle repeated loading.

[0069] The consistent tangent stiffness matrix is ​​used to reflect the stiffness characteristics of the material in the current deformation state. Combined with the Accord ratio matrix, key mechanical performance indicators such as the structural internal force distribution, deformation mode, and energy dissipation during loading, unloading, and repeated loading are calculated.

[0070] A second aspect of the present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, is used to perform the nonlinear evaluation method of the horizontal low-frequency characteristics of bracket sets based on the automatic contact pair generation strategy as described above.

[0071] Compared with the prior art, the present invention has the following beneficial effects:

[0072] 1) The nonlinear evaluation method for the horizontal low-cycle characteristics of bracket sets based on the automatic contact pair generation strategy proposed in the present invention brings significant advantages from a technical perspective. In terms of modeling, its unique automatic contact pair generation strategy can quickly determine the contact relationship based on the set of structural geometries through a series of rigorous calculations (such as convex hull processing, Minkowski difference norm calculation, etc.). The entire process does not require manual intervention and adjustment, which not only greatly improves the modeling efficiency, but also ensures the accuracy of the model in contact simulation. This efficient and accurate modeling method provides a solid and reliable foundation for subsequent analysis, so that the contact behavior of the bracket structure under complex stress conditions can be more realistically reflected, thereby effectively improving the reliability of the evaluation of the overall mechanical properties of the bracket set.

[0073] 2) The elastic-plastic damage assessment model based on the two-stage damage evolution criterion proposed in the present invention is of great technical significance. The model fully considers the characteristics of the bracket material in different stress stages. By carefully dividing the damage evolution stages (softening stage and residual stage) and combining precise equation definitions (such as parabolic equations and exponential decay equations), it can more accurately track the damage development process of the material under horizontal low-cycle characteristics. In the calculation process, a variety of factors are comprehensively considered, such as stress-strain relationship, yield criterion, failure mode, etc., so that the damage assessment results are more in line with the actual situation and the accuracy of the calculation is effectively improved. This not only helps to deeply understand the damage mechanism of brackets under repeated loads, but also provides a more targeted and scientific basis for the structural design, maintenance and reinforcement of brackets. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 1 is a schematic flow chart of a nonlinear evaluation method for horizontal low-frequency characteristics of bracket sets based on an automatic contact pair generation strategy in the present invention;

[0075] Figure 2 To verify the example, the finite element model diagram is automatically generated based on the solid model by calling the pymapdl package;

[0076] Figure 3 For verification purposes, elastic recovery energy (ER) and hysteresis energy (EH) are used to examine the error between calculation and experiment. DETAILED DESCRIPTION

[0077] Overall, the present invention discloses a nonlinear evaluation method for the horizontal low-cycle characteristics of bracket sets based on an automatic contact pair generation strategy. First, an automatic contact pair generation strategy based on the improved GJK method and the convexification strategy is proposed, and an elastic-plastic damage evaluation model based on the Hoffman yield criterion and the two-stage damage evolution criterion is established. The method proposed in the present invention can effectively capture the damage evolution and displacement pattern of bracket sets during low-cycle repeated stress. In addition, compared with the test results, the overall hysteresis envelope area, secant stiffness error, equivalent viscous damping coefficient, hysteretic energy dissipation and elastic recovery energy errors are all small. The present invention can greatly simplify the modeling complexity in the process of bracket set hysteretic performance evaluation, ensure the evaluation accuracy, and also provide method support for the horizontal hysteretic characteristics evaluation of other structural systems with complex contact relationships.

[0078] This paper proposes a nonlinear assessment method for the horizontal low-cycle characteristics of bracket sets based on an automatic contact pair generation strategy. This method allows for the rapid creation of a bracket set finite element model that accounts for contact behavior, eliminating the need for manual adjustments and significantly improving modeling efficiency. Furthermore, an elastic-plastic damage assessment model based on a two-stage damage evolution criterion is proposed to enhance computational accuracy.

[0079] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. Component models, material names, connection structures, control methods, algorithms, and other features not explicitly described in this technical solution are considered common technical features disclosed in the prior art.

[0080] Example 1

[0081] This embodiment discloses a method for nonlinear evaluation of horizontal low-cycle characteristics of bracket sets based on an automatic contact pair generation strategy. Figure 1 , including the following steps:

[0082] Assume that the geometry set of the structure is n v is the number of geometric bodies. Then for any geometric body There are n ip vertices. Then the geometry V i The convex hull conv(V i (Y)) can be expressed as λ shown in formula (1) j Combination solution.

[0083]

[0084] Convex hull conv(V i The vertex of (Y)) can be regarded as V i (Y) is a subset of the set. Then all the bodies in the geometric body set are processed with the formula (1) to obtain the convex hull set: right Any two conv(V i ),conv(V j ) Use formula (2) to calculate the minimum Minkowski difference norm between the two.

[0085] MD=min{||y j -y|| i :y i ∈conv(V i ),y j ∈conv(V j )} (2)

[0086] MD can be regarded as a geometric body V i and V j The approximate distance. In actual calculation, the computational cost of directly solving the Minkowski difference set is extremely high. Instead of directly calculating the Minkowski difference set, we iteratively update the vertex set called the simplex is a subset of Minkowskidifference, for the three-dimensional case ns =4 represents a tetrahedron. The iteration stops when the coordinate origin is included or the distance from the coordinate origin cannot be reduced. The former means that the two bodies are in contact, and the latter means that the two bodies are not in contact. Distance from the origin.

[0087]

[0088] Where w is the minimum norm of the Minkowski difference, that is, the distance to be calculated. is the cofactor of the M matrix, representing the deletion of r rows and n s The determinant after the column. are the Cartesian coordinate components of the corresponding vertex in κ.

[0089] According to the process of formula (2)-(3), we can get the set V of body pairs with contact relationship: pair ={(V i ,V j ):V i ,V j ∈V|w ij ≤ε}, where w ij = is the distance between the two bodies calculated by formula (3). ε is the sphere for determining contact. Then for V pair Any body V i All the faces in are convexified using formula (1), and the volume pairs with the generated convex hull faces as variables can be written as:

[0090] The distance between the convex surfaces in the body pair is calculated using formulas (2)-(3). If the distance is within the sphere for determining contact, the surfaces are considered to be in contact. In actual operation, the above algorithm may produce a false contact surface relationship, that is, the contact surface (A i ,A j ) and (A i ,A k ), A i With A j Initially, there is an approximate parallel relationship, and A i With A k Initially, there is only one point of contact. In the repeated analysis and calculation of the low-cycle bracket, it is rare to see A i With A k There are more point contacts in the subsequent deformation. At the same time, the contact surface (A i ,A j ) and (A i ,A k) When such contact pairs exist simultaneously, unbalanced forces are likely to occur in finite element analysis, resulting in non-convergence of the calculation. Therefore, the surface contact pairs should be eliminated.

[0091] For each contact surface pair, a symmetric contact pair is established based on the generalized Lagrangian method as shown in Equation (4).

[0092]

[0093] Kn is the contact normal stiffness, un is the contact gap. c is the penetration tolerance. i is the Lagrange multiplier of the i-th iteration step. The Coulomb model is used for friction, distinguishing between dynamic friction and static friction, and the expression of the tangential stress f is shown in Equation (5).

[0094] f=(1+(R f -1)e -ζ|v| )Pμ d (5)

[0095] where R f is the ratio of static friction to kinetic friction coefficient, ζ is the friction coefficient attenuation coefficient, v is the sliding velocity, μ d is the coefficient of kinetic friction.

[0096] Furthermore, the nonlinear evaluation adopts the following process.

[0097] The stress-strain relationship of the bracket material can be expressed in the tensor form as shown in formula (6):

[0098]

[0099] where ε e represents the elastic strain tensor. E represents the fourth-order stiffness tensor using Voigt notation. Represents the effective stress tensor. The flexibility matrix C = E -1 σ is the Cauchy stress. Then The expression can be written as follows. d represents the damage factor, 1, 2, and 3 are the longitudinal, radial, and tangential directions, respectively. 23,2v Indicates radial shear damage on the chordal surface.

[0100]

[0101] According to the theory of plasticity, the elastic strain ε e The plastic strain ε can be eliminated from the overall strain ε p , as shown in formula (7).

[0102] ε e =ε-ε p (7)

[0103] The bracket material is simplified to have no yield behavior in the tensile state, while the Hoffman yield criterion is adopted in the compressive state. The Hoffman yield function of isotropic Voce hardening can be written as the general form of Equation (8):

[0104]

[0105] Where P and Q are Hoffman plastic matrices. The stress is pulled back to the yield surface through the radial mapping algorithm. is the equivalent plastic strain. β1 and β2 are hardening parameters, which are determined based on uniaxial experimental regression.

[0106] The plastic strain is determined by the associated flow rule. The relationship between the total strain increment and the plastic strain increment and the elastic strain increment is shown in formula (9).

[0107]

[0108] where Δλ represents the plasticity multiplier, represents the gradient of the plastic potential energy. The Kuhn-Tucker conditions for loading and unloading are represents the rate of the plasticity multiplier.

[0109] The failure criterion of bracket materials adopts the Tsai-Wu criterion applicable to anisotropic materials, and eight equations are used to distinguish the eight failure modes of wood, as shown in formula (10).

[0110]

[0111] For f u,i ,f r,i ,ε u,i ε r,i For the characteristic points on the stress-strain curve, the following formula is introduced to determine the relationship between the residual characteristic points and the limit characteristic points:

[0112] The damage evolution equation is defined as two stages: the softening stage and the residual stage. The softening stage adopts a parabolic equation, and the residual stage adopts an exponential decay equation, which gradually decays to approximately 0. The damage evolution equation is defined using Equation (11):

[0113]

[0114] Stiffness softening will lead to non-convergence of the numerical solution. Viscous regularization can be used to correct the damage as shown in Equation (12).

[0115]

[0116] Where η is the viscosity regularization parameter and Δt is the virtual time step. Based on the consistency condition of the discrete problem, the consistent tangent stiffness matrix and the Jacobian ratio matrix can be derived, as shown in Equation (13).

[0117]

[0118] Afterwards, within the finite element analysis framework, the consistent tangent stiffness matrix and the Jacobian ratio matrix were applied to solve the equilibrium equations of the bracket set during horizontal low-cycle loading. In each loading step, these matrices were used to calculate the increments of node displacement and stress and strain according to the current deformation state and material properties, thereby gradually tracing the mechanical response process of the bracket set structure under horizontal low-cycle repeated loading.

[0119] The consistent tangent stiffness matrix is ​​used to reflect the stiffness characteristics of the material in the current deformation state. Combined with the Accord ratio matrix, key mechanical performance indicators such as the structural internal force distribution, deformation mode, and energy dissipation during loading, unloading, and repeated loading are calculated.

[0120] This embodiment also proposes a computer-readable storage medium, wherein the storage medium stores computer instructions, and the computer instructions are used to enable a computer to execute the above-mentioned nonlinear evaluation method of the horizontal low-frequency characteristics of the bracket based on the automatic contact pair generation strategy. The storage medium can be an electronic medium, a magnetic medium, an optical medium, an electromagnetic medium, an infrared medium or a semiconductor system or a propagation medium. The storage medium can also include a semiconductor or solid-state memory, a magnetic tape, a removable computer disk, a random access memory (RAM), a read-only memory (ROM), a hard disk and an optical disk. The optical disk can include a compact disk - read-only memory (CD-ROM), a compact disk - read / write (CD-RW) and a DVD.

[0121] Verification Example 1

[0122] To evaluate the benefits of this invention, the following validation example can be used. This case study uses horizontal low-cycle repeated experiments on brackets in southern China. Analysis is conducted on the seven-bracket-type bracket-type (DGBCL), the column-type bracket-type (DGOCL), and the corner bracket-type (DGBCN).

[0123] Rhino 6.0 was used to build the solid model of the bracket, and the proposed automatic contact pair generation strategy was implemented on the Jupyter notebook based on Python 3.8. At the same time, the pymapdl package was called to automatically generate the following based on the solid model: Figure 2The finite element model shown in the figure uses Solid187 elements to simulate the mechanical behavior of the wood and aluminum alloy frame. Contact174 and Tartget170 elements are used to simulate the friction between the wood and the aluminum alloy, and Combin39 spring elements are used to simulate the restraint behavior of the upper aluminum alloy frame. The elastic modulus of the aluminum alloy is 60,000 MPa, the Poisson's ratio is 0.3, and the friction coefficient between the aluminum alloy and the wood is 0.45. The friction coefficient between the wood and the aluminum alloy is 0.35. The ratio of static to kinetic friction coefficients is 1.25, and the friction coefficient attenuation factor is 3. For the inter-ply paving, 118,233 nodes and 94,158 elements are created, with 306 contact pairs automatically generated. For the column head paving, 103,175 nodes and 92,510 elements are created, with 451 contact pairs automatically generated. For the corner paving, 167,748 nodes and 142,671 elements are created, with 722 contact pairs automatically generated.

[0124] The following table shows the pseudo code of the algorithm used in this verification example:

[0125]

[0126] During the calculation, the elastic recovery energy (ER) and hysteresis energy (EH) were used to check the error between the calculation and the experiment. The calculation results are shown in the following table. Figure 3 As shown in the figure, (a) is the ER and EH of DGBCL, (b) is the ER and EH of DGOCL, and (c) is the ER and EH of DGBCN. The calculation results show that the method of the present invention can accurately evaluate the horizontal low-cycle energy consumption characteristics of the bracket.

[0127] The above description of the embodiments is intended to facilitate understanding and use of the invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to these embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above-described embodiments. Improvements and modifications made by those skilled in the art based on the disclosure of the present invention, without departing from the scope of the present invention, should be within the scope of protection of the present invention.

Claims

1. A nonlinear evaluation method for horizontal low-frequency characteristics of bracket sets based on an automatic contact pair generation strategy, characterized in that: The following steps are involved: S1: Determine the contact relationship between geometric bodies in the bracket structure through the automatic contact pair generation strategy, including body pair judgment, surface contact determination, and false contact surface elimination; S2: Based on the contact relationship determined in S1 and combined with the bracket material properties, the stress-strain relationship is determined. The yield behavior and plastic strain are determined based on plastic mechanics theory and related criteria. The failure mode is determined using the Tsai-Wu criterion based on damage mechanics theory. The damage evolution equation is then defined and the damage is corrected to accurately assess the material damage. S3: Based on the analysis results of material properties in S2, obtain the consistent tangent stiffness matrix and the Accord ratio matrix to complete the evaluation of the mechanical properties of the bracket under horizontal low-cycle characteristics; S1 specifically includes the following steps: S1-1: Determine the set of geometric bodies in the structure. For each geometric body in the set, calculate its convex hull to obtain a convex hull set. Calculate the minimum Minkowski difference norm between any two convex hulls in the convex hull set, using this as the approximate distance between the geometric bodies. Iterate and update the simplex vertex set. When the iteration meets the stopping condition, obtain a set of body pairs with contact relationships. S1-2: For each body in the body pair set, all its faces are convexified, and a new body pair is formed with the generated convex hull surface as a variable. The surface distance of each convex surface in these body pairs is calculated. If the surface distance is within the contact sphere, the faces are considered to be in contact. S1-3: Eliminate false contact surface relationships; S2 specifically includes the following steps: S2-1: Determine the stress-strain relationship of the bracket material using tensor form; S2-2: According to the theory of plastic mechanics, the elastic strain is obtained by eliminating the plastic strain from the overall strain. Different criteria are used for bracket materials under tension and compression. Under tension, the behavior is simplified to no yield, while under compression, the Hoffman yield criterion is used to determine the yield behavior. At the same time, the associated flow law is used to determine the plastic strain. S2-3: Using the Tsai-Wu criterion applicable to anisotropic materials, the relationship between characteristic points on the stress-strain curve is introduced to determine the relationship between residual characteristic points and limit characteristic points. The damage evolution equation is defined and divided into a softening stage and a residual stage. The parabolic equation is used in the softening stage, and the exponential decay equation is used in the residual stage. Considering the problem of non-convergence of the numerical solution caused by stiffness softening, viscosity regularization is used to correct the damage, which involves viscosity regularization parameters and virtual time solution steps, so as to achieve accurate assessment of the material damage.

2. A storage medium containing computer-executable instructions, characterized in that: When the computer executable instruction storage medium is executed by a computer processor, it is used to perform the nonlinear evaluation method of the horizontal low-frequency characteristics of bracket sets based on the automatic contact pair generation strategy as claimed in claim 1.

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