Uncertain response analysis method, device and equipment of viscoelastic structure and medium

Abstract

The invention discloses an uncertain response analysis method and device for a viscoelastic structure, equipment and a medium, and relates to the technical field of statistics, and the method comprises the steps: obtaining an uncertain variable of the viscoelastic structure and an initial node displacement of a kth time period, determining a mean value of a stiffness matrix of the viscoelastic structure, determining an mth round of recursion term of the k-th time period of the viscoelastic system equation according to the uncertainty variable of the viscoelastic material, the (m-1) th round of recursion term of the k-th time period of the viscoelastic system equation and the initial node displacement of the k-th time period of the viscoelastic structure, and then determining an expansion item coefficient of a nodal displacement mean value of the viscoelastic structure of the mth round of the kth time period of the viscoelastic system equation, determining a mean value of initial nodal displacement of each time period according to the convergence condition and the expansion item coefficient of the nodal displacement mean value of each time period, and performing uncertain response analysis on the viscoelastic structure. According to the method, the calculation result is not influenced by time step length selection, and the uncertainty analysis precision is improved.

Description

Technical Field

[0001] The present application relates to the technical field of statistics, and in particular to an uncertain response analysis method, device, equipment and medium for a viscoelastic structure. Background Art

[0002] In the field of statistical technology, for the calculation of time-related problems, the perturbation analysis method is mainly used to solve the uncertain response of random fields. The uncertain response result can be obtained by solving the deterministic problem only once, but the derivative of the random variable in the time domain needs to be calculated. The existing method for calculating the derivative of random variables in the time domain mainly uses the finite difference method.

[0003] However, the use of the finite difference method for calculations requires the selection of an appropriate time step. The selection of an inappropriate time step will directly affect the calculation accuracy of the derivative. At present, it is relatively difficult to determine the appropriate time step in the existing technology. If it is inaccurate, it will affect the displacement mean and covariance of the random field calculation and will not provide effective guidance for subsequent reliability analysis. Summary of the invention

[0004] The present application provides a method, device, equipment and medium for analyzing uncertain response of viscoelastic structures, which can make the calculation results unaffected by the selection of time step, reduce the error of derivative calculation of random variables in the time domain, and improve the accuracy of uncertainty analysis.

[0005] In order to achieve the above objectives, this application adopts the following technical solutions: In a first aspect, the present application provides a method for analyzing uncertain responses of a viscoelastic structure, the method comprising: Obtain the uncertainty variables of the viscoelastic structure and the initial node displacements at the kth time period; Determining the mean value of the stiffness matrix of the viscoelastic structure according to the uncertainty variables of the viscoelastic structure, and determining the m-th recursive term of the viscoelastic system equation in the kth time period according to the uncertainty variables of the viscoelastic material, the m-1th recursive term of the viscoelastic system equation in the kth time period, and the initial node displacement of the viscoelastic structure in the kth time period; Determine the expansion term coefficient of the mean value of the node displacement of the viscoelastic structure in the mth round of the kth period of the viscoelastic system equation according to the mean value of the stiffness matrix of the viscoelastic structure, the external applied load and boundary conditions of the viscoelastic structure, and the mth round of recursive terms in the kth period of the viscoelastic system equation; Determine whether the expansion term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th period and the expansion term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th period meet the convergence condition; If the expansion term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th period and the expansion term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th period meet the convergence condition; According to the expansion term coefficient of the mean value of the node displacement in each time period, the mean value of the initial node displacement in each time period is determined, and according to the mean value of the initial node displacement in each time period, the uncertain response analysis of the viscoelastic structure is performed.

[0006] In some possible implementations, the method further includes: The covariance of the node displacement is determined according to the initial node displacement of the kth time period; and the uncertainty response analysis of the viscoelastic structure is performed according to the covariance of the initial node displacement of each time period.

[0007] In some possible implementations, the method further includes: If the expanded term coefficients of the mean node displacements of the viscoelastic structure in the first m-1 rounds of the k-th time period and the expanded term coefficients of the mean node displacements of the viscoelastic structure in the m-th round of the k-th time period do not meet the convergence conditions, then the m+1-th round recursive term of the viscoelastic system equation in the k-th time period is determined based on the uncertainty variables of the viscoelastic structure and the m-th round recursive term of the viscoelastic system equation in the k-th time period.

[0008] In some possible implementations, the initial node displacement of the kth time period is obtained by the following method, including: Determine whether k is greater than 1; If k is greater than 1, the initial node displacement of the kth time period is determined according to the sum of the expansion coefficients of the viscoelastic structure node displacements of the first m rounds of the k-1th time period.

[0009] In some possible implementations, the method further includes: If k is not greater than 1, the initial node displacement of the kth time period is determined according to the mean value of the stiffness matrix of the viscoelastic structure and the externally applied load and boundary conditions of the viscoelastic structure.

[0010] In some possible implementations, the convergence condition is:

[0011] in, represents the expansion term coefficient of the mean displacement of the viscoelastic structure node of the mth wheel, represents the expansion term coefficient of the mean displacement of the viscoelastic structure node of the jth wheel, represents the factor of the uncertainty variable affecting the viscoelastic material, represents the sum of the expansion coefficients of the mean displacements of the viscoelastic structure nodes of the first m wheels, Represents the convergence threshold.

[0012] In some possible implementations, determining the expansion term coefficient of the mean value of the node displacement of the viscoelastic structure in the mth round of the kth time period of the viscoelastic system equation according to the mean value of the stiffness matrix of the viscoelastic structure, the external applied load and boundary conditions of the viscoelastic structure, and the mth round recursive term in the kth time period of the viscoelastic system equation includes:

[0013] in, represents the mean value of the stiffness matrix of the viscoelastic structure, represents the expansion term coefficient of the mean value of the node displacement of the viscoelastic structure of the mth wheel, Determined by the externally applied loads and boundary conditions of the viscoelastic structure, represents the mth recursive term of the viscoelastic system equation.

[0014] In a second aspect, the present application provides an uncertain response analysis device for a viscoelastic structure, the device comprising: An acquisition module is used to obtain the uncertainty variables of the viscoelastic structure and the initial node displacements of the kth period; A calculation module, for determining the mean value of the stiffness matrix of the viscoelastic structure according to the uncertainty variables of the viscoelastic structure, and determining the m-th recursive term of the viscoelastic system equation in the k-th time period 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 node displacement of the viscoelastic structure in the k-th time period; and determining the expansion term coefficient of the mean value of the node displacement of the viscoelastic structure in the m-th round of the viscoelastic system equation in the k-th time period according to the mean value of the stiffness matrix of the viscoelastic structure, the external 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; A judgment module, used to judge whether the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th time period meet the convergence condition; if the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th time period meet the convergence condition; The analysis module is used to determine the mean of the initial node displacement in each time period according to the expansion term coefficient of the mean of the node displacement in each time period, and perform uncertain response analysis on the viscoelastic structure according to the mean of the initial node displacement in each time period.

[0015] In a third aspect, the present application provides a computing device, including a memory and a processor; One or more computer programs are stored in the memory, and the one or more computer programs include instructions; when the instructions are executed by the processor, the computing device executes the method as described in any one of the first aspects.

[0016] In a fourth aspect, the present application provides a computer-readable storage medium, wherein the computer-readable storage medium is used to store a computer program, and the computer program is used to execute the method as described in any one of the first aspects.

[0017] It can be seen from the above technical solution that the present application has at least the following beneficial effects: In the present application, the processing device first obtains the uncertainty variables of the viscoelastic structure and the initial node displacement of the kth time period; according to the uncertainty variables of the viscoelastic structure, the mean value of the viscoelastic structure stiffness matrix is ​​determined, and then according to the uncertainty variables of the viscoelastic material, the m-1th round recursive term of the viscoelastic system equation in the kth time period and the initial node displacement of the viscoelastic structure in the kth time period, the mth round recursive term of the viscoelastic system equation in the kth time period is determined; then according to the mean value of the viscoelastic structure stiffness matrix, the external applied load and boundary conditions of the viscoelastic structure, and the mth round recursive term of the viscoelastic system equation in the kth time period, the mth round of the viscoelastic system equation in the kth time period is determined. The expanded term coefficient of the mean value of the node displacement of the structure; then determine whether the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the kth period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the mth round of the kth period meet the convergence condition; if the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the kth period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the mth round of the kth period meet the convergence condition, then according to the expanded term coefficient of the mean value of the node displacement of each period, determine the mean value of the initial node displacement of each period, and according to the mean value of the initial node displacement of each period, perform uncertain response analysis on the viscoelastic structure. In the traditional scheme, the perturbation analysis method and the finite difference method are mainly used to perform uncertain response analysis on the viscoelastic structure, but the finite difference method needs to select a suitable time step for calculation. At present, it is difficult to determine a suitable time step in the existing technology. If it is inaccurate, it will affect the inaccuracy of the displacement mean and covariance calculated by the random field, and thus cannot provide effective guidance for subsequent reliability analysis. It can be seen that the present application can make the calculation results unaffected by the selection of the time step, reduce the error of the derivative calculation of the random variable in the time domain, improve the accuracy of uncertainty analysis, and provide effective guidance for subsequent reliability analysis.

[0018] It should be understood that the description of technical features, technical solutions, beneficial effects or similar language in this application does not imply that all features and advantages can be realized in any single embodiment. On the contrary, it is understood that the description of features or beneficial effects means that specific technical features, technical solutions or beneficial effects are included in at least one embodiment. Therefore, the description of technical features, technical solutions or beneficial effects in this specification does not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions and beneficial effects described in the present embodiment can also be combined in any appropriate manner. Those skilled in the art will understand that the embodiment can be realized without one or more specific technical features, technical solutions or beneficial effects of a specific embodiment. In other embodiments, additional technical features and beneficial effects can also be identified in a specific embodiment that does not embody all embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A flow chart of an uncertain response analysis method for a viscoelastic structure provided in an embodiment of the present application; Figure 2 A schematic diagram of a viscoelastic plate provided in an embodiment of the present application; Figure 3 A schematic diagram of a random sample of an uncertain variable random field provided in an embodiment of the present application; Figure 4 A schematic diagram of the derivative of the displacement with respect to the random field variable at different time steps provided in an embodiment of the present application; Figure 5 A schematic diagram for comparing the displacement mean calculation results provided in the embodiments of the present application; Figure 6 A schematic diagram for comparing the covariance mean calculation results provided in the embodiments of the present application; Figure 7 A schematic diagram of an uncertain response analysis device for a viscoelastic structure provided in an embodiment of the present application; Figure 8 A schematic diagram of a computing device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0020] The terms "first", "second", "third", etc. in the specification of this application and the accompanying drawings are used to distinguish different objects rather than to limit a specific order.

[0021] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0022] In order to make the description of the following embodiments clear and concise, a brief introduction to the related technology is first given: Viscoelastic structures refer to structures made of materials with viscoelastic properties. Viscoelasticity is a physical property that describes the simultaneous viscous and elastic properties of a material during deformation. Viscoelasticity is a comprehensive property of the viscosity and elasticity of a fluid, involving the viscous and elastic properties of a material. When subjected to external forces, viscoelastic materials can store energy like elastic bodies and consume energy like viscous bodies.

[0023] Mathematical models of viscoelastic structures can be used to describe the strain response of viscoelastic materials under different stress states. These models are usually based on the microstructure and motion state of the material, and the modulus obtained in the experiment is fitted by theoretical analysis or simulation to obtain various parameters in the model.

[0024] Viscoelastic structures have a wide range of applications in practical engineering, especially in situations where both the elastic and viscous properties of materials need to be considered. For example: polymer materials: such as plastics, rubber, etc., these materials often exhibit viscoelastic properties during processing and use; building structures: concrete, foundations, in the design of structures under long-term loads such as bridges and dams, the viscoelastic properties of materials need to be considered to more accurately predict and analyze the deformation and stress relaxation phenomena of materials.

[0025] In view of this, an embodiment of the present application provides an uncertain response analysis method for a viscoelastic structure, which is applied to a processing device. In the method, the processing device first obtains the uncertainty variables of the viscoelastic structure and the initial node displacement of the k-th time period; according to the uncertainty variables of the viscoelastic structure, the mean value of the viscoelastic structure stiffness matrix is ​​determined, and 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 node displacement of the k-th time period of the viscoelastic structure, the m-th recursive term of the viscoelastic system equation in the k-th time period is determined; then, according to the mean value of the viscoelastic structure stiffness matrix, the external applied load and boundary conditions of the viscoelastic structure, and the m-1-th recursive term of the viscoelastic system equation in the k-th time period, the viscoelastic response analysis method for the viscoelastic structure is applied to a processing device. The expanded term coefficient of the mean value of the node displacement of the viscoelastic structure of the mth round of the kth period of the system equation; then determine whether the expanded term coefficient of the mean value of the node displacement of the viscoelastic material of the first m-1 rounds of the kth period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material of the mth round of the kth period meet the convergence condition; if the expanded term coefficient of the mean value of the node displacement of the viscoelastic material of the first m-1 rounds of the kth period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material of the mth round of the kth period meet the convergence condition, then according to the expanded term coefficient of the mean value of the node displacement of each period, determine the mean value of the initial node displacement of each period, and according to the mean value of the initial node displacement of each period, perform uncertain response analysis on the viscoelastic structure. It can be seen that the present application can make the calculation results not affected by the selection of the time step, reduce the error of the derivative calculation of the random variable in the time domain, improve the accuracy of uncertainty analysis, and provide effective guidance for subsequent reliability analysis.

[0026] In order to make the technical solution of the present application clearer and easier to understand, the following describes an uncertain response analysis method for a viscoelastic structure provided by an embodiment of the present application in conjunction with the accompanying drawings. Figure 1 As shown, this figure is a flow chart of an uncertain response analysis method of a viscoelastic structure provided in an embodiment of the present application.

[0027] The uncertain response analysis method of the viscoelastic structure includes: S101. A processing device obtains uncertainty variables of a viscoelastic structure and initial node displacements in a k-th time period.

[0028] The uncertainty variables of the viscoelastic structure include elastic modulus and viscosity, among which the elastic modulus, also known as "Young's modulus" in elastic mechanics, is a physical quantity that describes the ability of solid materials to resist deformation. The elastic modulus is a proportional coefficient in which the stress and strain of a material are in direct proportion during the elastic deformation stage, and it is also an indicator of the stiffness of the material; viscosity is a physical quantity that represents the internal friction inside the fluid when the fluid flows, and it is the ability of the fluid to resist deformation. In some examples, the viscoelastic structure can be a structure of viscoelastic materials, and the viscoelastic materials include rubber, rubber tires, memory foam, concrete, foundations, etc.

[0029] The processing device obtains the uncertainty variables of the viscoelastic structure through the coordinates of the nodes in the random field and the random events. The specific expression method is shown by formula (1), which is shown as follows:

[0030] in, Expressed as the uncertainty variable of the jth viscoelastic structure, Expressed as the mean value of the uncertainty variable of the viscoelastic structure, Represented as a random event, Represented as coordinates in a random field, is expressed as the i-th eigenvalue of the j-th viscoelastic structure, is represented by the jth viscoelastic structure i feature vectors, is a set of independent standard normal random variables.

[0031] For the initial node displacement of the kth period, the processing device obtains it in the following ways, including: It is determined whether k is greater than 1. If k is greater than 1, the initial node displacement of the kth period is determined according to the sum of the expansion coefficients of the viscoelastic structure node displacements of the first m rounds of the k-1th period. The determination method is shown in formula (2):

[0032] in, is the initial node displacement in the kth period, is the expansion coefficient of the viscoelastic structure node displacement of the first m wheels in the k-1th time period.

[0033] If k is not greater than 1, the initial node displacement at the kth time period is determined according to the mean value of the stiffness matrix of the viscoelastic structure and the external applied load and boundary conditions of the viscoelastic structure. The determination method is shown in formula (3):

[0034] in, is the initial node displacement in the kth period, is the mean value of the stiffness matrix of the viscoelastic structure, Determined by externally applied loads and boundary conditions of the viscoelastic structure.

[0035] S102: The processing device determines a mean value of a stiffness matrix of the viscoelastic structure according to uncertainty variables of the viscoelastic structure.

[0036] The processing device can obtain the mean value of the viscoelastic structure stiffness matrix based on the uncertainty variables of the viscoelastic structure obtained. The specific method of obtaining is the existing method, which will not be repeated here.

[0037] S103. The processing device determines the m-th recursive term of the k-th time period of the viscoelastic system equation according to the uncertainty variable of the viscoelastic material, the m-1-th recursive term of the k-th time period of the viscoelastic system equation, and the initial node displacement of the k-th time period of the viscoelastic structure.

[0038] The method for determining the m-th recursive term of the k-th period of the viscoelastic system equation is shown in formula (4):

[0039] in, represents the mth recursive term of the viscoelastic system equation in the kth period, is expressed as the time step, is the viscosity of the viscoelastic material among the uncertainty variables, is the first parameter of the uncertainty variable of the viscoelastic material, Expressed as the stiffness matrix of the viscoelastic structure, It is expressed as the initial node displacement of the viscoelastic structure at the m-1th round in the kth period, It is expressed as the m-1th recursive term of the kth period of the viscoelastic system equation, is the expansion order.

[0040] The first parameter of the uncertainty variable of viscoelastic materials It can be expressed by formula (5)

[0041] in, is the viscosity of the viscoelastic material among the uncertainty variables, is the first elastic modulus among the uncertainty variables of the viscoelastic material, is the second elastic modulus in the uncertainty variable of the viscoelastic material. , and Depend on Decide.

[0042] S104. The processing device determines the expansion term coefficient of the mean value of the node displacement of the m-th round of the viscoelastic structure in the k-th period of the viscoelastic system equation according to the mean value of the stiffness matrix of the viscoelastic structure, the external applied load and boundary conditions of the viscoelastic structure, and the m-th round of recursive terms in the k-th period of the viscoelastic system equation.

[0043] According to the recursive constitutive equation of the viscoelastic material and the basic theoretical method of finite element, the recursive system equation between the expanded term coefficient of the mean displacement of the viscoelastic structure nodes in the mth round of the kth time period and the expanded term coefficient of the mean displacement of the viscoelastic structure nodes in the m-1th round of the kth time period is determined.

[0044] The probability statistical moment of the response is calculated using the perturbation method based on Taylor expansion. According to the uncertainty variable expression (1) of the viscoelastic structure, the uncertainty variable of the viscoelastic structure can be represented by a series of random variables that obey an independent standard normal distribution: It means that the initial node displacement of the kth period is expressed as the stiffness matrix in (3) and the expansion coefficient of the viscoelastic structure node displacement of the first m wheels Expand to the first-order term at its mean, as shown in formulas (6)-(8): (6) (7) (8) Substituting equations (6)-(8) into equation (3), we can obtain equation (9): (9) Both sides of imperative (9) The coefficients of the same power terms are equal, and we can get formulas (10) and (11):

[0045] (11) in, represents the mean value of the stiffness matrix of the viscoelastic structure, The expansion coefficient representing the mean displacement of the nodes of the viscoelastic structure of the mth wheel, Determined by externally applied loads and boundary conditions of the viscoelastic structure, represents the mth recursive term of the viscoelastic system equation.

[0046] S105. The processing device determines whether the expanded term coefficient of the mean value of the node displacement of the viscoelastic material of the first m-1 rounds in the kth time period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material of the mth round in the kth time period meet the convergence condition.

[0047] The convergence condition is shown in formula (12):

[0048] in, represents the expansion term coefficient of the mean displacement of the viscoelastic structure node of the mth wheel, represents the expansion term coefficient of the mean displacement of the viscoelastic structure node of the jth wheel, represents the factor of the uncertainty variable affecting the viscoelastic material, represents the sum of the expansion coefficients of the mean displacements of the viscoelastic structure nodes of the first m wheels, Represents the convergence threshold.

[0049] If the norm of the expanded term coefficient of the mean nodal displacement of the viscoelastic material in the first m-1 rounds of the kth period divided by the norm of the expanded term coefficient of the mean nodal displacement of the viscoelastic material in the mth round of the kth period is less than or equal to the convergence threshold , then the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th period are considered to meet the convergence conditions; if the norm of the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th period divided by the norm of the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th period is greater than the convergence threshold , it is considered that the expanded term coefficient of the mean value of the nodal displacement of the viscoelastic material in the first m-1 rounds of the k-th period and the expanded term coefficient of the mean value of the nodal displacement of the viscoelastic material in the m-th round of the k-th period do not meet the convergence conditions.

[0050] If the expansion term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th period and the expansion term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th period meet the convergence condition, execute S106; If the expansion term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the kth period and the expansion term coefficient of the mean value of the node displacement of the viscoelastic material in the mth round of the kth period do not meet the convergence condition, execute S109.

[0051] S106. The processing device determines the mean of the initial node displacements in each time period according to the expansion term coefficient of the mean of the node displacements in each time period, and performs uncertain response analysis on the viscoelastic structure according to the mean of the initial node displacements in each time period.

[0052] The processing device obtains the expansion term coefficient of the mean value of the node displacement in each period through the above steps, and obtains the mean value of the initial node displacement in each period according to the expansion term coefficient of the mean value of the node displacement in each period. In the first period, that is, when k=1, the mean value of the initial node displacement is shown in formula (13), and when k>1, the mean value of the initial node displacement is shown in formula (14): (13)

[0053] in, is the mean value of the initial node displacement in the first period, is the inverse matrix of the stiffness matrix of the viscoelastic structure, Determined by externally applied loads and boundary conditions of the viscoelastic structure, is the mean value of the initial node displacement in the kth period, is the expansion coefficient of the viscoelastic structure node displacement of the first m wheels in the k-1th time period.

[0054] According to the mean value of the initial node displacement in each time period, the uncertain response analysis of the viscoelastic structure is performed. This analysis method is an existing method and will not be described in detail here.

[0055] S107: The processing device determines the covariance of the node displacement according to the initial node displacement in the kth time period.

[0056] According to the initial node displacement of the kth time period, the derivative of the node displacement expansion term coefficient of the kth time period is determined, and the covariance of the node displacement is determined based on the derivative of the node displacement expansion term coefficient, as shown in formula (15):

[0057] in, is the covariance of the node displacement in the kth period, is the initial node displacement in the kth period, is a set of independent standard normal random variables, is the transpose of the matrix.

[0058] S108. The processing device performs uncertainty response analysis on the viscoelastic structure according to the covariance of the initial node displacements in each time period.

[0059] The processing device performs uncertainty response analysis on the viscoelastic structure according to the covariance of the initial node displacements in each time period. This analysis method is an existing method and will not be described in detail here.

[0060] S109, the processing device determines the (m+1)th recursive term of the kth time period of the viscoelastic system equation according to the uncertainty variable of the viscoelastic structure and the (m)th recursive term of the kth time period of the viscoelastic system equation.

[0061] In some embodiments, to verify the effectiveness of the present invention, a viscoelastic plate is used as an example. Figure 2 As shown in FIG. 1 , the figure is a schematic diagram of a viscoelastic plate provided in an embodiment of the present application, wherein 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 obeys a normal distribution, the mean and standard deviation of the uncertainty variable are shown in the following formula (16):

[0062] (16) in, The mean value of the first elastic modulus of the uncertainty variable representing the viscoelastic structure, The mean value of the second elastic modulus of the uncertainty variable representing the viscoelastic structure, The mean value of the viscosity of the uncertainty variable representing the viscoelastic structure, The covariance of the first elastic modulus of the uncertainty variable representing the viscoelastic structure, The covariance of the second elastic modulus of the uncertainty variable representing the viscoelastic structure, Covariance of the viscosity of the uncertainty variable representing the viscoelastic structure.

[0064] Assuming a plane stress problem, the autocorrelation function of the random field is exponential, the correlation length along the x direction is 0.5m, and the correlation length along the y direction is 1m. This application gives a random sample of the random field of uncertain variables, such as Figure 3 As shown, this figure is a schematic diagram of a random sample of an uncertain variable random field provided by an embodiment of the present application, wherein the units of the horizontal and vertical axes are meters, and the calculation stability of the derivatives under different time steps is compared and analyzed, such as Figure 4 As shown in FIG. 1 , this figure is a schematic diagram of the derivative of displacement to uncertainty variables at different time steps provided by the embodiment of the present application. The calculation accuracy of the algorithm proposed in the present application is not affected by the size of the time step. On this basis, the mean and covariance of the structural displacement uncertainty response are calculated and compared with the Monte Carlo method, as shown in FIG. Figure 5 As shown in FIG. 1 , this figure is a schematic diagram of the comparison of the displacement mean calculation results provided in the embodiment of the present application, that is, Figure 2 The comparison chart of the position of point B in the middle is as follows: Figure 6As shown in FIG. 1 , this figure is a schematic diagram of the comparison of the covariance mean calculation results provided in the embodiment of the present application, that is, Figure 2 The comparison diagram of the position of point B in the figure shows that the algorithm proposed in this application has high calculation accuracy.

[0065] Based on the above content, the processing device first obtains the uncertainty variables of the viscoelastic structure and the initial node displacement of the kth time period; according to the uncertainty variables of the viscoelastic structure, the mean value of the viscoelastic structure stiffness matrix is ​​determined, and then according to the uncertainty variables of the viscoelastic material, the m-1th round recursive term of the viscoelastic system equation in the kth time period and the initial node displacement of the viscoelastic structure in the kth time period, the mth round recursive term of the viscoelastic system equation in the kth time period is determined; then according to the mean value of the viscoelastic structure stiffness matrix, the external applied load and boundary conditions of the viscoelastic structure, and the mth round recursive term of the viscoelastic system equation in the kth time period, the mth round of the viscoelastic system equation in the kth time period is determined. The expanded term coefficient of the mean value of the node displacement of the structure; then determine whether the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th period meet the convergence condition; if the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th period meet the convergence condition, then determine the mean value of the initial node displacement of each period according to the expanded term coefficient of the mean value of the node displacement of each period, and perform uncertain response analysis on the viscoelastic structure according to the mean value of the initial node displacement of each period. It can be seen that the present application can make the calculation results not affected by the selection of the time step, reduce the error of the derivative calculation of the random variable in the time domain, improve the accuracy of uncertainty analysis, and provide effective guidance for subsequent reliability analysis.

[0066] Combination of the above Figures 1 to 6 A method for analyzing uncertain responses of a viscoelastic structure provided in an embodiment of the present application is introduced in detail. The device and apparatus provided in the embodiment of the present application will be introduced below in conjunction with the accompanying drawings.

[0067] like Figure 7 As shown, this figure is a schematic diagram of an uncertain response analysis device for a viscoelastic structure provided in an embodiment of the present application, the device comprising: An acquisition module 701 is used to acquire the uncertainty variables of the viscoelastic structure and the initial node displacement of the kth time period; The calculation module 702 is used to determine the mean value of the stiffness matrix of the viscoelastic structure according to the uncertainty variables of the viscoelastic structure, determine the m-th recursive term of the viscoelastic system equation in the k-th time period 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 node displacement of the viscoelastic structure in the k-th time period; determine the expansion term coefficient of the mean value of the node displacement of the viscoelastic structure in the m-th round of the viscoelastic system equation in the k-th time period according to the mean value of the stiffness matrix of the viscoelastic structure, the external 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 703 is used to judge whether the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th time period meet the convergence condition; if the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th time period meet the convergence condition; The analysis module 704 is used to determine the mean of the initial node displacements in each time period according to the expansion term coefficient of the mean of the node displacements in each time period, and perform uncertain response analysis on the viscoelastic structure according to the mean of the initial node displacements in each time period.

[0068] In some possible implementations, the analysis module 704 is further configured to determine the covariance of the node displacement according to the initial node displacement in the kth time period; and perform uncertainty response analysis on the viscoelastic structure according to the covariance of the initial node displacement in each time period.

[0069] In some possible implementations, the device further includes: A determination module is used to determine the m+1th round recursive term of the viscoelastic system equation in the kth time period according to the uncertainty variables of the viscoelastic structure and the mth round recursive term of the viscoelastic system equation in the kth time period if the expanded term coefficients of the mean value of the node displacement of the viscoelastic structure in the first m-1 rounds of the kth time period and the expanded term coefficients of the mean value of the node displacement of the viscoelastic structure in the mth round of the kth time period do not meet the convergence conditions.

[0070] In some possible implementations, the initial node displacement of the kth time period is obtained by the following method, including: Determine whether k is greater than 1; If k is greater than 1, the initial node displacement of the kth time period is determined according to the sum of the expansion coefficients of the viscoelastic structure node displacements of the first m rounds of the k-1th time period.

[0071] In some possible implementations, the device further includes: If k is not greater than 1, the initial node displacement of the kth time period is determined according to the mean value of the stiffness matrix of the viscoelastic structure and the externally applied load and boundary conditions of the viscoelastic structure.

[0072] In some possible implementations, the convergence condition is:

[0073] in, represents the expansion term coefficient of the mean displacement of the viscoelastic structure node of the mth wheel, represents the expansion term coefficient of the mean displacement of the viscoelastic structure node of the jth wheel, represents the factor of the uncertainty variable affecting the viscoelastic material, represents the sum of the expansion coefficients of the mean displacements of the viscoelastic structure nodes of the first m wheels, Represents the convergence threshold.

[0074] In some possible implementations, determining the expansion term coefficient of the mean value of the node displacement of the viscoelastic structure in the mth round of the kth time period of the viscoelastic system equation according to the mean value of the stiffness matrix of the viscoelastic structure, the external applied load and boundary conditions of the viscoelastic structure, and the mth round recursive term in the kth time period of the viscoelastic system equation includes:

[0075] in, represents the mean value of the stiffness matrix of the viscoelastic structure, represents the expansion term coefficient of the mean value of the node displacement of the viscoelastic structure of the mth wheel, Determined by the externally applied loads and boundary conditions of the viscoelastic structure, represents the mth recursive term of the viscoelastic system equation.

[0076] According to an uncertain response analysis device for a viscoelastic structure according to an embodiment of the present application, the method described in the embodiment of the present application may be executed correspondingly, and the above-mentioned other operations and / or functions of each module / unit of the uncertain response analysis device for a viscoelastic structure are respectively to realize Figure 1 For the sake of brevity, the corresponding processes of each method in the illustrated embodiment are not described in detail here.

[0077] An embodiment of the present application also provides a computing device.

[0078] like Figure 8As shown, this figure is a schematic diagram of a computing device provided by an embodiment of the present application, and 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 through the bus 801.

[0079] The bus 801 may be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 8 Only one thick line is used in the diagram, but this does not mean that there is only one bus or only one type of bus.

[0080] The processor 802 may be any one or more of a central processing unit (CPU), a graphics processing unit (GPU), a microprocessor (MP), or a digital signal processor (DSP).

[0081] The communication interface 803 is used for communicating with the outside.

[0082] The memory 804 may include a volatile memory, such as a random access memory (RAM). The memory 804 may also include a non-volatile memory, such as a read-only memory (ROM), a flash memory, a hard disk drive (HDD), or a solid state drive (SSD).

[0083] The memory 804 stores executable codes, and the processor 802 executes the executable codes to perform the aforementioned uncertain response analysis method of the viscoelastic structure.

[0084] Specifically, in implementing Figure 7 In the case of the embodiment shown, and Figure 7 When each module or unit of the uncertain response analysis device for a viscoelastic structure described in the embodiment is implemented by software, the execution Figure 7The software or program code required for the functions of each module / unit in the system may be partially or completely stored in the memory 804. The processor 802 executes the program code corresponding to each unit stored in the memory 804 to perform the uncertain response analysis method of the viscoelastic structure.

[0085] The embodiment of the present application also provides a computer-readable storage medium. The computer-readable storage medium can be any available medium that can be stored by a computing device or a data storage device such as a data center containing one or more available media. The available medium can be a magnetic medium (such as a floppy disk, a hard disk, a tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid-state hard disk). The computer-readable storage medium includes instructions that instruct the computing device to execute the above-mentioned uncertain response analysis method of a viscoelastic structure.

[0086] The embodiment of the present application further provides a computer program product, which includes one or more computer instructions. When the computer instructions are loaded and executed on a computing device, the process or function described in the embodiment of the present application is generated in whole or in part.

[0087] The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. 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, optical fiber, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0088] When the computer program product is executed by a computer, the computer executes any one of the aforementioned methods for analyzing uncertain responses of viscoelastic structures. The computer program product may be a software installation package, and when any one of the aforementioned methods for analyzing uncertain responses of viscoelastic structures needs to be used, the computer program product may be downloaded and executed on a computer.

[0089] The descriptions of the processes or structures corresponding to the above-mentioned figures have different emphases. For parts that are not described in detail in a certain process or structure, please refer to the relevant descriptions of other processes or structures.

[0090] The above description is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions within the technical scope disclosed in the present application should be included in the protection scope of the present application.

Claims

1. A method for analyzing uncertain response of viscoelastic structures, characterized in that: The method comprises: Obtain the uncertainty variables of the viscoelastic structure and the initial node displacements at the kth time period; Determining the mean value of the stiffness matrix of the viscoelastic structure according to the uncertainty variables of the viscoelastic structure, and determining the m-th recursive term of the viscoelastic system equation in the kth time period according to the uncertainty variables of the viscoelastic material, the m-1th recursive term of the viscoelastic system equation in the kth time period, and the initial node displacement of the viscoelastic structure in the kth time period; Determine the expansion term coefficient of the mean value of the node displacement of the viscoelastic structure in the mth round of the kth period of the viscoelastic system equation according to the mean value of the stiffness matrix of the viscoelastic structure, the external applied load and boundary conditions of the viscoelastic structure, and the mth round of recursive terms in the kth period of the viscoelastic system equation; Determine whether the expansion term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th period and the expansion term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th period meet the convergence condition; If the expansion term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th period and the expansion term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th period meet the convergence condition; According to the expansion term coefficient of the mean value of the node displacement in each time period, the mean value of the initial node displacement in each time period is determined, and according to the mean value of the initial node displacement in each time period, the uncertain response analysis of the viscoelastic structure is performed.

2. The method according to claim 1, characterized in that The method further comprises: Determining the covariance of the node displacement according to the initial node displacement of the kth time period; According to the covariance of the initial node displacements in each time period, uncertainty response analysis is performed on the viscoelastic structure.

3. The method according to claim 2, characterized in that The method further comprises: If the expanded term coefficients of the mean node displacements of the viscoelastic structure in the first m-1 rounds of the k-th time period and the expanded term coefficients of the mean node displacements of the viscoelastic structure in the m-th round of the k-th time period do not meet the convergence conditions, then the m+1-th round recursive term of the viscoelastic system equation in the k-th time period is determined based on the uncertainty variables of the viscoelastic structure and the m-th round recursive term 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 kth time period is obtained by the following method, including: Determine whether k is greater than 1; If k is greater than 1, the initial node displacement of the kth time period is determined according to the sum of the expansion coefficients of the viscoelastic structure node displacements of the first m rounds of the k-1th time period.

5. The method according to claim 4, characterized in that The method further comprises: If k is not greater than 1, the initial node displacement of the kth time period is determined according to the mean value 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, represents the expansion term coefficient of the mean displacement of the viscoelastic structure node of the mth wheel, represents the expansion term coefficient of the mean displacement of the viscoelastic structure node of the jth wheel, represents the factor of the uncertainty variable affecting the viscoelastic material, represents the sum of the expansion coefficients of the mean displacements of the viscoelastic structure nodes of the first m wheels, Represents the convergence threshold.

7. The method according to claim 1, characterized in that Determining the expansion term coefficient of the mean value of the node displacement of the viscoelastic structure in the mth round of the kth period of the viscoelastic system equation according to the mean value of the stiffness matrix of the viscoelastic structure, the external applied load and boundary conditions of the viscoelastic structure, and the mth round recursive term in the kth period of the viscoelastic system equation comprises: in, represents the mean value of the stiffness matrix of the viscoelastic structure, represents the expansion term coefficient of the mean value of the node displacement of the viscoelastic structure of the mth wheel, Determined by the externally applied loads and boundary conditions of the viscoelastic structure, represents the mth recursive term of the viscoelastic system equation.

8. An uncertain response analysis device for a viscoelastic structure, characterized in that: The device comprises: An acquisition module is used to obtain the uncertainty variables of the viscoelastic structure and the initial node displacements of the kth period; A calculation module, for determining the mean value of the stiffness matrix of the viscoelastic structure according to the uncertainty variables of the viscoelastic structure, and determining the m-th recursive term of the viscoelastic system equation in the k-th time period 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 node displacement of the viscoelastic structure in the k-th time period; and determining the expansion term coefficient of the mean value of the node displacement of the viscoelastic structure in the m-th round of the viscoelastic system equation in the k-th time period according to the mean value of the stiffness matrix of the viscoelastic structure, the external 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; A judgment module, used to judge whether the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th time period meet the convergence condition; if the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the first m-1 rounds of the k-th time period and the expanded term coefficient of the mean value of the node displacement of the viscoelastic material in the m-th round of the k-th time period meet the convergence condition; The analysis module is used to determine the mean of the initial node displacement in each time period according to the expansion term coefficient of the mean of the node displacement in each time period, and perform uncertain response analysis on the viscoelastic structure according to the mean of the initial node displacement in each time period.

9. A computing device, characterized in that including memory and processor; One or more computer programs are stored in the memory, and the one or more computer programs include instructions; when the instructions are executed by the processor, the computing device executes the method as claimed 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, and the computer program is used to execute the method according to any one of claims 1 to 7.

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