A method, device, equipment and medium for analyzing uncertain response of a viscoelastic structure

Abstract

The application discloses a kind of uncertain response analysis method, device, equipment and medium of viscoelastic structure, it is related to statistical technique field, the method includes: obtaining the initial node displacement of the uncertainty variable and the k time period of viscoelastic structure, determine the mean value of the stiffness matrix of viscoelastic structure, according to the uncertainty variable of viscoelastic material, the k time period of the m-1 round recursive term of viscoelastic system equation and the initial node displacement of the k time period of viscoelastic structure, determine the m round recursive term of the k time period of viscoelastic system equation, then determine the expansion term coefficient of the mean value of the node displacement of the k time period of viscoelastic system equation in the m round of viscoelastic structure, according to convergence condition and the expansion term coefficient of the mean value of each time period node displacement, determine the mean value of the initial node displacement of each time period, carry out uncertain response analysis to viscoelastic structure.The method can make that calculation result is not influenced by time step selection, improve uncertainty analysis precision.

Description

Technical Field

[0001] This application relates to the field of statistical technology, and in particular to a method, apparatus, equipment and medium for analyzing the uncertain response of viscoelastic structures. Background Technology

[0002] In the field of statistical technology, the calculation of time-related problems mainly uses perturbation analysis to solve the uncertain response of random fields. Only one deterministic problem needs to be solved to obtain the result of the uncertain response. However, it is necessary to calculate the derivative of the random variable in the time domain. The existing methods for calculating the derivative of the random variable in the time domain mainly use the finite difference method.

[0003] However, the finite difference method requires the selection of an appropriate time step. An inappropriate time step will directly affect the accuracy of the derivative calculation. Currently, it is quite difficult to determine an appropriate time step in existing technologies. If it is inaccurate, it will affect the accuracy of the displacement mean and covariance of the random field calculation, thus failing to provide effective guidance for subsequent reliability analysis. Summary of the Invention

[0004] This application provides a method, apparatus, device, and medium for analyzing the uncertain response of viscoelastic structures, which enables the calculation results to be unaffected by the selection of the time step, reduces the error in calculating the derivative of random variables in the time domain, and improves the accuracy of uncertainty analysis.

[0005] To achieve the above objectives, this application adopts the following technical solution:

[0006] In a first aspect, this application provides a method for analyzing the uncertain response of a viscoelastic structure, the method comprising:

[0007] Obtain the uncertainty variables of the viscoelastic structure and the initial nodal displacements in the k-th time period;

[0008] Based on the uncertainty variables of the viscoelastic structure, the mean value of the stiffness matrix of the viscoelastic structure is determined. Based on the uncertainty variables of the viscoelastic material, the (m-1)th recursive term of the kth time period of the viscoelastic system equation, and the initial nodal displacement of the viscoelastic structure in the kth time period, the mth recursive term of the viscoelastic system equation in the kth time period is determined.

[0009] Based on the mean value of the stiffness matrix of the viscoelastic structure, the externally applied load and boundary conditions of the viscoelastic structure, and the recursive term of the mth round of the kth time period of the viscoelastic system equation, determine the expansion term coefficients of the mean nodal displacement of the viscoelastic structure in the mth round of the kth time period of the viscoelastic system equation.

[0010] Determine whether the expansion coefficients of the mean nodal displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacement of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition.

[0011] If the expansion coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition;

[0012] Based on the expansion coefficients of the mean nodal displacements in each time period, the mean initial nodal displacements in each time period are determined. Based on the mean initial nodal displacements in each time period, an uncertain response analysis is performed on the viscoelastic structure.

[0013] In some possible implementations, the method further includes:

[0014] Based on the initial node displacements in the k-th time period, the covariance of the node displacements is determined; based on the covariance of the initial node displacements in each time period, an uncertainty response analysis is performed on the viscoelastic structure.

[0015] In some possible implementations, the method further includes:

[0016] If the expansion coefficients of the mean nodal displacements of the viscoelastic structure in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic structure in the m-th round of the k-th time period do not meet the convergence condition, then the recursive term of the (m+1)-th round of the viscoelastic system equation in the k-th time period is determined based on the uncertainty variables of the viscoelastic structure and the recursive term of the m-th round of the viscoelastic system equation in the k-th time period.

[0017] In some possible implementations, the initial node displacement of the k-th time period is obtained in the following ways:

[0018] Determine if k is greater than 1;

[0019] If k is greater than 1, the initial node displacement of the k-th time period is determined by the sum of the expansion coefficients of the nodal displacements of the viscoelastic structure in the first m rounds of the (k-1)-th time period.

[0020] In some possible implementations, the method further includes:

[0021] If k is not greater than 1, the initial nodal displacement in the k-th time period is determined based on the mean of the stiffness matrix of the viscoelastic structure and the externally applied load and boundary conditions of the viscoelastic structure.

[0022] In some possible implementations, the convergence condition is:

[0023]

[0024] in, The coefficient of the expansion term representing the mean displacement of the viscoelastic structure nodes in the m-th round is given. The coefficient of the expansion term representing the mean displacement of the viscoelastic structural nodes in the j-th round is given. Factors representing uncertainties affecting the viscoelastic material. The sum of the coefficients of the expanded terms representing the mean displacement of the viscoelastic structural nodes in the first m wheels. This represents the convergence threshold.

[0025] In some possible implementations, the expansion coefficients of the mean nodal displacements of the viscoelastic structure in the m-th cycle of the k-th time period of the viscoelastic system equations are determined based on the mean of the stiffness matrix of the viscoelastic structure, the externally applied loads and boundary conditions of the viscoelastic structure, and the recursive terms of the m-th cycle of the k-th time period of the viscoelastic system equations. These coefficients include:

[0026]

[0027] in, This represents the mean value of the stiffness matrix of the viscoelastic structure. The coefficient of the expansion term representing the mean nodal displacement of the viscoelastic structure in the m-th round is given. The conditions are determined by the externally applied load and boundary conditions of the viscoelastic structure. This represents the m-th recursive term in the equations of the viscoelastic system.

[0028] Secondly, this application provides an uncertain response analysis device for viscoelastic structures, the device comprising:

[0029] The acquisition module is used to acquire the uncertainty variables of the viscoelastic structure and the initial nodal displacements in the k-th time period;

[0030] The calculation module is used to determine the mean value of the stiffness matrix of the viscoelastic structure based on the uncertainty variables of the viscoelastic structure; to determine the m-th recursive term of the viscoelastic system equation in the k-th time period based on the uncertainty variables of the viscoelastic material, the (m-1)-th recursive term of the viscoelastic system equation in the k-th time period, and the initial nodal displacement of the viscoelastic structure in the k-th time period; and to determine the expansion coefficient of the mean nodal displacement of the viscoelastic structure in the m-th time period of the viscoelastic system equation based on the mean value of the stiffness matrix of the viscoelastic structure, the externally applied load and boundary conditions of the viscoelastic structure, and the m-th recursive term of the viscoelastic system equation in the k-th time period.

[0031] The judgment module is used to determine whether the expansion coefficients of the mean nodal displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacement of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition; if the expansion coefficients of the mean nodal displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacement of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition;

[0032] The analysis module is used to determine the mean of the initial nodal displacements for each time period based on the expansion term coefficients of the mean nodal displacements for each time period, and to perform uncertain response analysis on the viscoelastic structure based on the mean of the initial nodal displacements for each time period.

[0033] Thirdly, this application provides a computing device, including a memory and a processor;

[0034] The memory stores one or more computer programs, the one or more computer programs including instructions; when the instructions are executed by the processor, the computing device performs the method as described in any one of the first aspects.

[0035] Fourthly, this application provides a computer-readable storage medium for storing a computer program for performing the method as described in any one of the first aspects.

[0036] As can be seen from the above technical solution, this application has at least the following beneficial effects:

[0037] In this application, the processing device first obtains the uncertainty variables of the viscoelastic structure and the initial nodal displacements in the k-th time period; based on the uncertainty variables of the viscoelastic structure, it determines the mean of the stiffness matrix of the viscoelastic structure; then, based on the uncertainty variables of the viscoelastic material, the (m-1)th recursive term of the viscoelastic system equation in the k-th time period, and the initial nodal displacements of the viscoelastic structure in the k-th time period, it determines the m-th recursive term of the viscoelastic system equation in the k-th time period; next, based on the mean of the stiffness matrix of the viscoelastic structure, the externally applied load and boundary conditions of the viscoelastic structure, and the m-th recursive term of the viscoelastic system equation in the k-th time period, it determines the viscoelasticity of the m-th recursive term in the k-th time period of the viscoelastic system equation. The expansion coefficients of the mean nodal displacements of the structure are calculated. Then, it is determined whether the expansion coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition. If the expansion coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition, the mean initial nodal displacements of each time period are determined based on the expansion coefficients of the mean nodal displacements of each time period. Based on the mean initial nodal displacements of each time period, an uncertain response analysis is performed on the viscoelastic structure. In traditional schemes, perturbation analysis and finite difference methods are mainly used to perform uncertain response analysis on viscoelastic structures. However, the calculation using the finite difference method requires the selection of an appropriate time step. Currently, determining an appropriate time step is quite difficult in existing technologies. If it is inaccurate, it will affect the accuracy of the displacement mean and covariance calculated by the random field, thus failing to provide effective guidance for subsequent reliability analysis. As can be seen, this application enables the calculation results to be unaffected by the selection of the time step, reduces the error in the calculation of the derivative of random variables in the time domain, improves the accuracy of uncertainty analysis, and provides effective guidance for subsequent reliability analysis.

[0038] It should be understood that the descriptions of technical features, technical solutions, beneficial effects, or similar language in this application do not imply that all features and advantages can be achieved in any single embodiment. Rather, it is understood that the description of a feature or beneficial effect means that a specific technical feature, technical solution, or beneficial effect is included in at least one embodiment. Therefore, the descriptions of technical features, technical solutions, or beneficial effects in this specification do not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions, and beneficial effects described in this embodiment can be combined in any suitable manner. Those skilled in the art will understand that embodiments can be implemented without one or more specific technical features, technical solutions, or beneficial effects of a particular embodiment. In other embodiments, additional technical features and beneficial effects may be identified in specific embodiments that do not embody all embodiments. Attached Figure Description

[0039] Figure 1 A flowchart illustrating an uncertain response analysis method for a viscoelastic structure provided in this application embodiment;

[0040] Figure 2 A schematic diagram of a viscoelastic flat plate provided in an embodiment of this application;

[0041] Figure 3 A schematic diagram of a random sample of an uncertain variable random field provided in an embodiment of this application;

[0042] Figure 4 A schematic diagram illustrating the derivatives of displacement with respect to random field variables at different time steps, as provided in the embodiments of this application;

[0043] Figure 5 A schematic diagram comparing the displacement mean calculation results provided in the embodiments of this application;

[0044] Figure 6 A schematic diagram comparing the covariance mean calculation results provided in the embodiments of this application;

[0045] Figure 7 A schematic diagram of an uncertain response analysis device for a viscoelastic structure provided in an embodiment of this application;

[0046] Figure 8 This is a schematic diagram of a computing device provided in an embodiment of this application. Detailed Implementation

[0047] The terms "first," "second," and "third," etc., used in this application specification and accompanying drawings are used to distinguish different objects, not to limit a specific order.

[0048] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0049] To ensure clarity and conciseness in the description of the following embodiments, a brief introduction to the related technologies is given first:

[0050] Viscoelastic structures refer to structures composed of materials exhibiting viscoelastic properties. Viscoelasticity describes the physical property of a material that simultaneously exhibits viscous and elastic characteristics during deformation. It is a combined property of the viscosity and elasticity of fluids, involving both the viscous and elastic properties of materials. When subjected to external forces, viscoelastic materials can store energy like an elastic body and dissipate energy like a viscous body.

[0051] Mathematical models of viscoelastic structures can be used to describe the strain response of viscoelastic materials under different stress states. These models are typically based on the material's microstructure and motion state, and obtain the parameters in the model by fitting the modulus obtained from experiments through theoretical analysis or simulation.

[0052] Viscoelastic structures have wide applications in practical engineering, especially in situations where the elastic and viscous properties of materials need to be considered simultaneously. For example, polymer materials such as plastics and rubber often exhibit viscoelastic properties during processing and use; building structures such as concrete and foundations, and in the design of structures under long-term loads such as bridges and dams, the viscoelastic properties of the materials need to be considered to more accurately predict and analyze material deformation and stress relaxation phenomena.

[0053] In view of this, embodiments of this application provide an uncertain response analysis method for viscoelastic structures, applied to a processing device. In this method, the processing device first obtains the uncertain variables of the viscoelastic structure and the initial nodal displacements in the k-th time period; based on the uncertain variables of the viscoelastic structure, it determines the mean of the stiffness matrix of the viscoelastic structure; then, based on the uncertain variables of the viscoelastic material, the (m-1)th recursive term of the viscoelastic system equation in the k-th time period, and the initial nodal displacements of the viscoelastic structure in the k-th time period, it determines the m-th recursive term of the viscoelastic system equation in the k-th time period; finally, based on the mean of the stiffness matrix of the viscoelastic structure, the externally applied loads and boundary conditions of the viscoelastic structure, and the m-th recursive term of the viscoelastic system equation in the k-th time period, it determines the viscoelastic... The system equations are analyzed by first determining the expansion coefficients of the mean nodal displacements of the viscoelastic structure in the m-th round of the k-th time period; then, it is determined whether the expansion coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition; if the expansion coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition, then the mean initial nodal displacements of each time period are determined based on the expansion coefficients of the mean nodal displacements of each time period, and the uncertain response analysis of the viscoelastic structure is performed based on the mean initial nodal displacements of each time period. It is evident that this application enables the calculation results to be unaffected by the selection of the time step, reduces the error in calculating the derivatives of random variables in the time domain, improves the accuracy of uncertainty analysis, and provides effective guidance for subsequent reliability analysis.

[0054] To make the technical solution of this application clearer and easier to understand, the following describes, in conjunction with the accompanying drawings, an uncertain response analysis method for a viscoelastic structure provided by an embodiment of this application. Figure 1 As shown in the figure, this is a flowchart of an uncertain response analysis method for a viscoelastic structure provided in an embodiment of this application.

[0055] The uncertain response analysis method for this viscoelastic structure includes:

[0056] S101, The processing equipment obtains the uncertainty variables of the viscoelastic structure and the initial nodal displacements in the k-th time period.

[0057] The uncertainties in viscoelastic structures include the elastic modulus and viscosity. The elastic modulus, also known as Young's modulus in elasticity mechanics, is a physical quantity describing the ability of a solid material to resist deformation. It is a proportionality constant that directly correlates stress and strain during the elastic deformation stage of a material, and is also an indicator of material stiffness. Viscosity is a physical quantity representing the internal friction that occurs within a fluid during flow, and is the fluid's ability to resist deformation. In some examples, the viscoelastic structure can be a structure made of viscoelastic materials, including rubber, rubber tires, memory foam, concrete, and foundations.

[0058] The processing device obtains the uncertainty variables of the viscoelastic structure through the coordinates of the nodes and random events in the random field. The specific representation method is shown by formula (1), which is as follows:

[0059]

[0060] in, Let the uncertainty variable be represented by the j-th viscoelastic structure. This represents the mean of the uncertainty variables of the viscoelastic structure. Represented as a random event, Represented as coordinates in a random field. Let represent the i-th eigenvalue of the j-th viscoelastic structure. Represented as the j-th viscoelastic structure i 1 eigenvector It is a set of independent standard normal random variables.

[0061] The initial node displacement for the k-th time period is obtained by the processing device in the following ways:

[0062] Determine if k is greater than 1. If k is greater than 1, determine the initial node displacement of the k-th time period based on the sum of the expansion coefficients of the nodal displacements of the viscoelastic structure in the first m rounds of the (k-1)-th time period. The determination method is shown in formula (2):

[0063]

[0064] in, Let be the initial node displacement in the k-th time period. , where is the expansion term coefficient of the nodal displacement of the viscoelastic structure in the first m rounds of the (k-1)th time period.

[0065] If k is not greater than 1, the initial nodal displacement in the k-th time period is determined based on the mean of the stiffness matrix of the viscoelastic structure and the external load and boundary conditions applied to the viscoelastic structure. The determination method is shown in formula (3):

[0066]

[0067] in, Let be the initial node displacement in the k-th time period. Let be the mean of the stiffness matrix of the viscoelastic structure. The conditions are determined by the externally applied loads and boundary conditions of the viscoelastic structure.

[0068] S102. The processing equipment determines the mean value of the stiffness matrix of the viscoelastic structure based on the uncertainty variables of the viscoelastic structure.

[0069] Based on the obtained uncertainties of the viscoelastic structure, the processing equipment can obtain the mean value of the viscoelastic structure stiffness matrix. The specific method used to obtain it is the existing method, and will not be elaborated here.

[0070] S103. The processing equipment determines the m-th recursive term of the k-th time period of the viscoelastic system equation based on the uncertainty variables of the viscoelastic material, the (m-1)-th recursive term of the k-th time period of the viscoelastic system equation, and the initial nodal displacement of the viscoelastic structure in the k-th time period.

[0071] The method for determining the m-th recursive term of the k-th time period of the viscoelastic system equation is shown in formula (4):

[0072]

[0073] in, This represents the m-th recursive term in the k-th time interval of the viscoelastic system equations. Represented as time step, For viscoelastic materials, viscosity is an uncertain variable. For viscoelastic materials, the first parameter is the uncertainty variable. Represented as the stiffness matrix of a viscoelastic structure. This represents the initial nodal displacements of the viscoelastic structure in the (m-1)th cycle of the k-th time period. This is represented as the (m-1)th recursive term in the k-th time period of the viscoelastic system equations. Let be the order of the expansion.

[0074] The first parameter of the uncertainty variable of viscoelastic materials It can be expressed by formula (5)

[0075]

[0076] in, For viscoelastic materials, viscosity is an uncertain variable. Let be the first elastic modulus among the uncertainties of viscoelastic materials. Let be the second elastic modulus among the uncertainties of viscoelastic materials. , and Depend on Decide.

[0077] S104. The processing equipment determines the expansion coefficients of the mean nodal displacement of the viscoelastic structure in the mth round of the kth time period of the viscoelastic system equation based on the mean value of the stiffness matrix of the viscoelastic structure, the external load and boundary conditions of the viscoelastic structure, and the recursive term of the mth round of the kth time period of the viscoelastic system equation.

[0078] Based on the recursive constitutive equation of the viscoelastic material and the basic finite element theory method, the recursive system equation between the expansion term coefficients of the mean nodal displacements of the viscoelastic structure in the m-th round of the k-th time period and the expansion term coefficients of the mean nodal displacements of the viscoelastic structure in the (m-1)-th round of the k-th time period is determined.

[0079] The probabilistic statistical moments of the response are calculated using the perturbation method based on Taylor expansion. According to the expression for the uncertainty variables of a viscoelastic structure (1), the uncertainty variables of a viscoelastic structure can be represented by a series of random variables following an independent standard normal distribution. This indicates that the stiffness matrix in the initial nodal displacement method (3) for the k-th time period is... The expansion term coefficients of the viscoelastic structural nodal displacements of the front m wheels Expanding to the first-order terms at its mean, as shown in formulas (6)-(8):

[0080] (6)

[0081] (7)

[0082] (8)

[0083] Substituting equations (6)-(8) into equation (3) yields equation (9).

[0084] (9)

[0085] Both sides of the formula (9) Since the coefficients of terms with the same power are equal, we can obtain formulas (10) and (11):

[0086] (11)

[0087] in, This represents the mean value of the stiffness matrix of the viscoelastic structure. The coefficient of the expansion term representing the mean nodal displacement of the viscoelastic structure in the m-th cycle. The conditions are determined by the externally applied loads and boundary conditions of the viscoelastic structure. This represents the m-th recursive term in the equations for a viscoelastic system.

[0088] S105. The processing device determines whether the expansion coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition.

[0089] The convergence condition is shown in formula (12):

[0090]

[0091] in, The coefficient of the expansion term representing the mean displacement of the viscoelastic structure nodes in the m-th round is given. The coefficient of the expansion term representing the mean displacement of the viscoelastic structural nodes in the j-th round is given. Factors representing uncertainties affecting the viscoelastic material. The sum of the coefficients of the expanded terms representing the mean displacement of the viscoelastic structural nodes in the first m wheels. This represents the convergence threshold.

[0092] If the norm of the expanded term coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period is less than or equal to the convergence threshold... Then, it is considered that the expansion coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition; if the norm of the expansion coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period divided by the norm of the expansion coefficients of the mean nodal displacements of the viscoelastic material in the m-th round of the k-th time period is greater than the convergence threshold. If the expansion coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic material in the m-th round of the k-th time period do not satisfy the convergence condition.

[0093] If the expansion coefficients of the mean nodal displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacement of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition, then execute S106.

[0094] If the expansion coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic material in the m-th round of the k-th time period do not meet the convergence condition, then execute S109.

[0095] S106. The processing equipment determines the mean value of the initial nodal displacement for each time period based on the expansion term coefficient of the mean nodal displacement for each time period, and performs uncertain response analysis on the viscoelastic structure based on the mean value of the initial nodal displacement for each time period.

[0096] The processing device obtains the expansion coefficients of the mean node displacements for each time period through the above steps, and obtains the mean of the initial node displacements for each time period based on the expansion coefficients of the mean node displacements for each time period. For the first time period, when k=1, the mean of the initial node displacements is shown in formula (13). When k>1, the mean of the initial node displacements is shown in formula (14).

[0097] (13)

[0098]

[0099] in, This represents the mean of the initial nodal displacements in the first time period. It is the inverse of the stiffness matrix of the viscoelastic structure. The conditions are determined by the externally applied loads and boundary conditions of the viscoelastic structure. Let be the mean of the initial node displacements in the k-th time period. , where is the expansion term coefficient of the nodal displacement of the viscoelastic structure in the first m rounds of the (k-1)th time period.

[0100] Uncertain response analysis is performed on the viscoelastic structure based on the average initial nodal displacements at each time period. This analysis method is an existing method and will not be elaborated here.

[0101] S107. The processing equipment determines the covariance of the node displacement based on the initial node displacement in the k-th time period.

[0102] Based on the initial node displacement of the k-th time period, the derivative of the coefficients of the expanded term of the node displacement in the k-th time period is determined, and the covariance of the node displacement is determined based on the derivative of the coefficients of the expanded term of the node displacement, as shown in formula (15):

[0103]

[0104] in, Let be the covariance of the nodal displacements in the k-th time period. Let be the initial node displacement in the k-th time period. It is a set of independent standard normal random variables. It is the transpose of the matrix.

[0105] S108. The processing equipment performs uncertainty response analysis on the viscoelastic structure based on the covariance of the initial node displacements at each time period.

[0106] The processing equipment performs uncertainty response analysis on the viscoelastic structure based on the covariance of the initial node displacements at each time period. This analysis method is an existing method and will not be described in detail here.

[0107] S109. The processing equipment then determines the (m+1)th recursive term of the viscoelastic system equation in the kth time period based on the uncertainty variables of the viscoelastic structure and the mth recursive term of the kth time period of the viscoelastic system equation.

[0108] In some embodiments, to verify the effectiveness of the present invention, a viscoelastic plate is used as an example, such as... Figure 2 As shown in the figure, this is a schematic diagram of a viscoelastic plate provided in an embodiment of this application. The length of the viscoelastic plate is l2, the width of the viscoelastic plate is l1, and the length of the crack is l3. Assuming that the uncertainty variable of the viscoelastic structure is a random field variable that follows a normal distribution, the mean and standard deviation of the uncertainty variable are shown in the following formula (16):

[0109]

[0110] (16)

[0112] in, The mean of the first elastic modulus represents the uncertainty variable of the viscoelastic structure. The mean of the second elastic modulus, representing the uncertainty variable of the viscoelastic structure. The mean viscosity represents the uncertainty variable of the viscoelastic structure. The covariance of the first elastic modulus represents the uncertainty variable of the viscoelastic structure. The covariance of the second elastic modulus represents the uncertainty variable of the viscoelastic structure. The covariance of viscosity represents the uncertainty variable of a viscoelastic structure.

[0113] Assuming a plane stress problem, the autocorrelation function of the random field is exponential, with a correlation length of 0.5m along the x-direction and 1m along the y-direction. This application provides a random sample of the uncertain variable random field, such as... Figure 3As shown in the figure, this is a schematic diagram of a random sample of an uncertain variable random field provided in an embodiment of this application. The units of the horizontal and vertical axes are meters. The calculation stability of the derivative under different time steps is compared and analyzed. Figure 4 As shown in the figure, this diagram illustrates the derivatives of displacement with respect to uncertainties at different time steps according to embodiments of this application. The computational accuracy of the algorithm proposed in this application is not affected by the size of the time step. Based on this, the mean and covariance of the structural displacement uncertainty response were calculated and compared with the Monte Carlo method, as shown below. Figure 5 As shown, this figure is a schematic diagram comparing the displacement mean calculation results provided in the embodiments of this application, that is, Figure 2 A comparison diagram of the location of point B in the middle, as shown below. Figure 6 As shown, this figure is a schematic diagram comparing the covariance mean calculation results provided in the embodiments of this application, that is, Figure 2 The comparison diagram of point B shows that the algorithm proposed in this application has high calculation accuracy.

[0114] Based on the above, the processing device first obtains the uncertainty variables of the viscoelastic structure and the initial nodal displacements in the k-th time period; according to the uncertainty variables of the viscoelastic structure, it determines the mean of the stiffness matrix of the viscoelastic structure; then, according to the uncertainty variables of the viscoelastic material, the (m-1)th recursive term of the viscoelastic system equation in the k-th time period, and the initial nodal displacements of the viscoelastic structure in the k-th time period, it determines the m-th recursive term of the viscoelastic system equation in the k-th time period; next, according to the mean of the stiffness matrix of the viscoelastic structure, the externally applied load and boundary conditions of the viscoelastic structure, and the m-th recursive term of the viscoelastic system equation in the k-th time period, it determines the viscoelasticity in the m-th round of the viscoelastic system equation in the k-th time period. The expansion coefficients of the mean nodal displacements of the structure are calculated. Then, it is determined whether the expansion coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition. If the expansion coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition, the mean initial nodal displacements of each time period are determined based on the expansion coefficients of the mean nodal displacements of each time period. Based on the mean initial nodal displacements of each time period, an uncertain response analysis is performed on the viscoelastic structure. It is evident that this application enables the calculation results to be unaffected by the selection of the time step, reduces the error in calculating the derivatives of random variables in the time domain, improves the accuracy of uncertainty analysis, and provides effective guidance for subsequent reliability analysis.

[0115] The above text combined Figures 1 to 6This application provides a detailed description of an uncertain response analysis method for viscoelastic structures. The apparatus and equipment provided in this application will be described below with reference to the accompanying drawings.

[0116] like Figure 7 As shown in the figure, this is a schematic diagram of an uncertain response analysis device for a viscoelastic structure provided in an embodiment of this application. The device includes:

[0117] The acquisition module 701 is used to acquire the uncertainty variables of the viscoelastic structure and the initial nodal displacements in the k-th time period;

[0118] The calculation module 702 is used to determine the mean value of the stiffness matrix of the viscoelastic structure based on the uncertainty variables of the viscoelastic structure; to determine the m-th recursive term of the k-th time period of the viscoelastic system equation based on the uncertainty variables of the viscoelastic material, the (m-1)-th recursive term of the k-th time period of the viscoelastic system equation, and the initial nodal displacement of the viscoelastic structure in the k-th time period; and to determine the expansion coefficient of the mean nodal displacement of the viscoelastic structure in the m-th time period of the viscoelastic system equation based on the mean value of the stiffness matrix of the viscoelastic structure, the externally applied load and boundary conditions of the viscoelastic structure, and the m-th recursive term of the k-th time period of the viscoelastic system equation.

[0119] The judgment module 703 is used to determine whether the expansion coefficients of the mean nodal displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacement of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition; if the expansion coefficients of the mean nodal displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacement of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition;

[0120] The analysis module 704 is used to determine the mean value of the initial nodal displacement in each time period based on the expansion term coefficient of the mean nodal displacement in each time period, and to perform uncertain response analysis on the viscoelastic structure based on the mean value of the initial nodal displacement in each time period.

[0121] In some possible implementations, the analysis module 704 is further configured to determine the covariance of the node displacements based on the initial node displacements of the k-th time period; and to perform uncertainty response analysis on the viscoelastic structure based on the covariances of the initial node displacements of each time period.

[0122] In some possible implementations, the device further includes:

[0123] The determination module is used to determine the (m+1)th round recursive term of the viscoelastic system equation in the k-th time period if the expansion coefficients of the mean nodal displacements of the viscoelastic structure in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic structure in the m-th round of the k-th time period do not meet the convergence condition.

[0124] In some possible implementations, the initial node displacement of the k-th time period is obtained in the following ways:

[0125] Determine if k is greater than 1;

[0126] If k is greater than 1, the initial node displacement of the k-th time period is determined by the sum of the expansion coefficients of the nodal displacements of the viscoelastic structure in the first m rounds of the (k-1)-th time period.

[0127] In some possible implementations, the device further includes:

[0128] If k is not greater than 1, the initial nodal displacement in the k-th time period is determined based on the mean of the stiffness matrix of the viscoelastic structure and the externally applied load and boundary conditions of the viscoelastic structure.

[0129] In some possible implementations, the convergence condition is:

[0130]

[0131] in, The coefficient of the expansion term representing the mean displacement of the viscoelastic structure nodes in the m-th round is given. The coefficient of the expansion term representing the mean displacement of the viscoelastic structural nodes in the j-th round is given. Factors representing uncertainties affecting the viscoelastic material. The sum of the coefficients of the expanded terms representing the mean displacement of the viscoelastic structural nodes in the first m wheels. This represents the convergence threshold.

[0132] In some possible implementations, the expansion coefficients of the mean nodal displacements of the viscoelastic structure in the m-th cycle of the k-th time period of the viscoelastic system equations are determined based on the mean of the stiffness matrix of the viscoelastic structure, the externally applied loads and boundary conditions of the viscoelastic structure, and the recursive terms of the m-th cycle of the k-th time period of the viscoelastic system equations. These coefficients include:

[0133]

[0134] in, This represents the mean value of the stiffness matrix of the viscoelastic structure. The coefficient of the expansion term representing the mean nodal displacement of the viscoelastic structure in the m-th round is given. The conditions are determined by the externally applied load and boundary conditions of the viscoelastic structure. This represents the m-th recursive term in the equations of the viscoelastic system.

[0135] An uncertain response analysis apparatus for a viscoelastic structure according to an embodiment of this application can correspond to the execution of the method described in the embodiment of this application, and the other operations and / or functions of each module / unit of the uncertain response analysis apparatus for a viscoelastic structure are respectively for implementing Figure 1 For the sake of brevity, the corresponding processes of each method in the illustrated embodiments will not be described in detail here.

[0136] This application also provides a computing device.

[0137] like Figure 8 As shown in the figure, this is a schematic diagram of a computing device provided in an embodiment of this application. The computing device 800 includes a bus 801, a processor 802, a communication interface 803, and a memory 804. The processor 802, the memory 804, and the communication interface 803 communicate with each other via the bus 801.

[0138] The 801 bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 8 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0139] The processor 802 can be any one or more of the following processors: central processing unit (CPU), graphics processing unit (GPU), microprocessor (MP), or digital signal processor (DSP).

[0140] The communication interface 803 is used for external communication.

[0141] Memory 804 may include volatile memory, such as random access memory (RAM). Memory 804 may also include non-volatile memory, such as read-only memory (ROM), flash memory, hard disk drive (HDD), or solid state drive (SSD).

[0142] The memory 804 stores executable code, and the processor 802 executes the executable code to perform the aforementioned uncertain response analysis method for viscoelastic structures.

[0143] Specifically, in achieving Figure 7 In the case of the illustrated embodiment, and Figure 7 When the modules or units of the uncertain response analysis device for a viscoelastic structure described in the embodiments are implemented by software, the following steps are performed: Figure 7 The software or program code required for the functions of each module / unit can be partially or entirely stored in memory 804. Processor 802 executes the program code corresponding to each unit stored in memory 804, and performs the aforementioned uncertain response analysis method for viscoelastic structures.

[0144] This application also provides a computer-readable storage medium. The computer-readable storage medium can be any available medium that a computing device can store, or a data storage device such as a data center containing one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state drive). The computer-readable storage medium includes instructions that instruct a computing device to execute the aforementioned method for analyzing the uncertain response of a viscoelastic structure.

[0145] This application also provides a computer program product comprising one or more computer instructions. When the computer instructions are loaded and executed on a computing device, all or part of the processes or functions described in this application are generated.

[0146] The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions may be transmitted from one website, computer, or data center to another website, computer, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0147] When the computer program product is executed by a computer, the computer performs any of the aforementioned methods for uncertain response analysis of viscoelastic structures. The computer program product can be a software installation package; when any of the aforementioned methods for uncertain response analysis of viscoelastic structures is required, the computer program product can be downloaded and executed on the computer.

[0148] The descriptions of the processes or structures corresponding to the above figures each have their own emphasis. For parts of a process or structure that are not described in detail, please refer to the relevant descriptions of other processes or structures.

[0149] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions within the technical scope disclosed in this application should be covered within the scope of protection of this application.

Claims

1. A method for analyzing the uncertain response of a viscoelastic structure, characterized in that, The method includes: Obtain the uncertainty variables of the viscoelastic structure and the initial nodal displacements in the k-th time period; Based on the uncertainty variables of the viscoelastic structure, the mean value of the stiffness matrix of the viscoelastic structure is determined. Based on the uncertainty variables of the viscoelastic material, the (m-1)th recursive term of the kth time period of the viscoelastic system equation, and the initial nodal displacement of the viscoelastic structure in the kth time period, the mth recursive term of the viscoelastic system equation in the kth time period is determined. Based on the mean value of the stiffness matrix of the viscoelastic structure, the externally applied load and boundary conditions of the viscoelastic structure, and the recursive term of the mth round of the kth time period of the viscoelastic system equation, determine the expansion term coefficients of the mean nodal displacement of the viscoelastic structure in the mth round of the kth time period of the viscoelastic system equation. Determine whether the expansion coefficients of the mean nodal displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacement of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition. If the expansion coefficients of the mean nodal displacements of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition; Based on the expansion coefficients of the mean nodal displacements in each time period, the mean initial nodal displacements in each time period are determined. Based on the mean initial nodal displacements in each time period, an uncertain response analysis is performed on the viscoelastic structure.

2. The method according to claim 1, characterized in that, The method further includes: Based on the initial node displacements in the k-th time period, determine the covariance of the node displacements; Uncertainty response analysis is performed on the viscoelastic structure based on the covariance of the initial node displacements at each time period.

3. The method according to claim 2, characterized in that, The method further includes: If the expansion coefficients of the mean nodal displacements of the viscoelastic structure in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacements of the viscoelastic structure in the m-th round of the k-th time period do not meet the convergence condition, then the recursive term of the (m+1)-th round of the viscoelastic system equation in the k-th time period is determined based on the uncertainty variables of the viscoelastic structure and the recursive term of the m-th round of the viscoelastic system equation in the k-th time period.

4. The method according to claim 3, characterized in that, The initial node displacement of the k-th time period is obtained through the following methods: Determine if k is greater than 1; If k is greater than 1, the initial node displacement of the k-th time period is determined by the sum of the expansion coefficients of the nodal displacements of the viscoelastic structure in the first m rounds of the (k-1)-th time period.

5. The method according to claim 4, characterized in that, The method further includes: If k is not greater than 1, the initial nodal displacement in the k-th time period is determined based on the mean of the stiffness matrix of the viscoelastic structure and the externally applied load and boundary conditions of the viscoelastic structure.

6. The method according to claim 1, characterized in that, The convergence condition is: in, The coefficient of the expansion term representing the mean displacement of the viscoelastic structure nodes in the m-th round is given. The coefficient of the expansion term representing the mean displacement of the viscoelastic structural nodes in the j-th round is given. Factors representing uncertainties affecting the viscoelastic material. The sum of the coefficients of the expanded terms representing the mean displacement of the viscoelastic structural nodes in the first m wheels. This represents the convergence threshold.

7. The method according to claim 1, characterized in that, Based on the mean of the stiffness matrix of the viscoelastic structure, the externally applied load and boundary conditions of the viscoelastic structure, and the recursive term of the m-th iteration of the k-th time period of the viscoelastic system equations, determine the expansion coefficients of the mean nodal displacements of the viscoelastic structure in the m-th iteration of the k-th time period of the viscoelastic system equations, including: in, This represents the mean value of the stiffness matrix of the viscoelastic structure. The coefficient of the expansion term representing the mean nodal displacement of the viscoelastic structure in the m-th round is given. The conditions are determined by the externally applied load and boundary conditions of the viscoelastic structure. This represents the m-th recursive term in the equations of the viscoelastic system.

8. An uncertain response analysis device for a viscoelastic structure, characterized in that, The device includes: The acquisition module is used to acquire the uncertainty variables of the viscoelastic structure and the initial nodal displacements in the k-th time period; The calculation module is used to determine the mean value of the stiffness matrix of the viscoelastic structure based on the uncertainty variables of the viscoelastic structure; to determine the m-th recursive term of the viscoelastic system equation in the k-th time period based on the uncertainty variables of the viscoelastic material, the (m-1)-th recursive term of the viscoelastic system equation in the k-th time period, and the initial nodal displacement of the viscoelastic structure in the k-th time period; and to determine the expansion coefficient of the mean nodal displacement of the viscoelastic structure in the m-th time period of the viscoelastic system equation based on the mean value of the stiffness matrix of the viscoelastic structure, the externally applied load and boundary conditions of the viscoelastic structure, and the m-th recursive term of the viscoelastic system equation in the k-th time period. The judgment module is used to determine whether the expansion coefficients of the mean nodal displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacement of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition; if the expansion coefficients of the mean nodal displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expansion coefficients of the mean nodal displacement of the viscoelastic material in the m-th round of the k-th time period satisfy the convergence condition; The analysis module is used to determine the mean of the initial nodal displacements for each time period based on the expansion term coefficients of the mean nodal displacements for each time period, and to perform uncertain response analysis on the viscoelastic structure based on the mean of the initial nodal displacements for each time period.

9. A computing device, characterized in that, Including memory and processor; The memory stores one or more computer programs, the one or more computer programs including instructions; when the instructions are executed by the processor, the computing device performs the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store a computer program for performing the method as described in any one of claims 1 to 7.

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