Structural dynamic analysis method and device containing boundary resistance device

Abstract

The invention relates to a dynamic analysis method and device for a structure containing a boundary resistance device, and the method comprises the steps: calculating a balance damping matrix and a balance load matrix according to the displacement, speed and acceleration of a structure system at a previous moment in a set time step; then combining with a boundary nonlinear dynamic equation of resistance balance to solve the speed of a nonlinear dimension; then the speed of the linear dimension is obtained according to a solution formula of the speed of the linear dimension; according to the speed of the non-linear dimension and the speed of the linear dimension, the displacement, the speed and the acceleration at the current moment are obtained, and according to the characteristics of boundary resistance related to the speed and the inherent characteristics of a boundary non-linear dynamic equation, the dynamic equation which only has the non-linear dimension and is based on boundary resistance balance is used; finally, the displacement, the speed and the acceleration of the structural system at the current moment are calculated, the dimensionality of a nonlinear dynamic equation is greatly reduced, the time consumed by iterative solution is small, and the problem that strong boundary resistance nonlinear iteration is not convergent is solved.

Description

Technical Field

[0001] The present application relates to the field of structural dynamic analysis of bridges containing boundary resistance devices, and in particular to a structural dynamic analysis method and device containing boundary resistance devices. Background Art

[0002] At present, bridge structures are often equipped with friction swing bearings, dampers and other structural systems to improve the structural dynamic performance. The resistance and deformation of friction swing bearings, dampers and other devices show nonlinear characteristics, and the resistance provided is equivalent to changing the boundary constraints of the structure. The structural dynamic analysis with boundary resistance devices is usually called boundary nonlinear dynamic analysis.

[0003] The boundary nonlinear dynamic equation used in boundary nonlinear dynamic analysis is usually expressed as follows:

[0004]

[0005] It can be seen that the boundary nonlinear dynamic equation is a second-order equation, which contains the displacement term u and the velocity term and acceleration term is the boundary nonlinear resistance, which is related to displacement and velocity. Displacement, velocity, acceleration, boundary resistance and external load are all related to time. For simplicity, the following expressions do not have time t. This second-order ordinary differential equation is difficult to solve, and scholars usually need to reduce the order of the above dynamic equation. The reduction method is usually combined with the Newmark-Beta method, that is, the velocity term and acceleration term are converted into displacement terms. The reduced-order boundary nonlinear dynamic equation is as shown in Formula 2.

[0006]

[0007] In the formula To convert stiffness and external load. After the reduction of the order of nonlinear equations, the displacement term is an unknown, and the resistance term contains the displacement term. Although the above nonlinear dynamic equations have been reduced in order, due to the strong nonlinear characteristics of the boundary nonlinear resistance term, the above nonlinear equations generally reach tens of thousands of dimensions, the solution speed is very slow, and it is not easy to converge. The main reason for the non-convergence is that the Jacobian matrix of the boundary resistance contains unknown terms, which is not clear, and the dimensions of the equations are coupled with each other. Summary of the invention

[0008] The embodiments of the present application provide a structural dynamic analysis method and device including a boundary resistance device, so as to solve the problem in the related art that the boundary nonlinear resistance term has a strong nonlinear characteristic, and when the boundary nonlinear dynamic equation is used for analysis, the dimension generally reaches tens of thousands, the solution speed is very slow, and it is not easy to converge.

[0009] In a first aspect, a method for dynamic analysis of a structure including a boundary resistance device is provided, comprising:

[0010] According to the displacement, velocity and acceleration of the structural system at the previous moment in the set time step, the equilibrium damping matrix and the equilibrium load matrix are calculated;

[0011] According to the boundary nonlinear dynamic equation based on resistance balance, in combination with the equilibrium damping matrix and the equilibrium load matrix, the speed of the nonlinear dimension is solved; then, according to the solution formula of the speed of the nonlinear dimension and the speed of the linear dimension, the speed of the linear dimension is obtained;

[0012] According to the velocity of the nonlinear dimension and the velocity of the linear dimension, the displacement, velocity and acceleration of the structural system at the current moment are obtained.

[0013] In some embodiments, calculating the equilibrium damping matrix and the equilibrium load matrix according to the displacement, velocity and acceleration of the structural system at a previous moment in a set time step includes the following steps:

[0014] According to formula 3, combined with the displacement, velocity and acceleration of the structural system at the previous moment in the set time step, the equivalent damping matrix and equivalent load matrix of the structural system are calculated;

[0015] Extracting and splitting the equivalent damping matrix to obtain equivalent damping matrices of different dimensions; splitting the equivalent load array to obtain equivalent load arrays of different dimensions;

[0016] According to the equivalent damping matrices of different dimensions and the equivalent load matrix of the same dimension, and in combination with Formula 4 and Formula 5, a balanced damping matrix and a balanced load matrix are obtained.

[0017] In some embodiments, the displacement, velocity and acceleration of the structural system at the previous moment are u 0 , and

[0018] The formula three is:

[0019]

[0020] Among them, C eq is the equivalent damping matrix, Q eq is the equivalent load array, h is the set time step; 0 , and are the displacement, velocity and acceleration of the previous moment respectively; Q is the load matrix; C is the damping matrix; K is the stiffness matrix; M is the mass matrix.

[0021] In some embodiments, the equivalent damping matrix is ​​extracted and split to obtain equivalent damping matrices of different dimensions; the equivalent load array is split to obtain equivalent load arrays of different dimensions, specifically comprising the following steps:

[0022] From the equivalent damping matrix C eq Extract and split the equivalent damping matrix of l rows and l columns from The equivalent damping matrix with m rows and m columns The equivalent damping matrix with l rows and m columns The equivalent damping matrix with m rows and l columns

[0023] From the equivalent load array Q eq Extract the equivalent load array of l rows from and m rows of equivalent load arrays

[0024] The l is the dimension of boundary resistance, corresponding to the nonlinear dimension; m is the dimension of non-boundary resistance, corresponding to the linear dimension, and the total dimension is n, n=l+m.

[0025] In some embodiments, the formula 4 is:

[0026]

[0027] The formula five is:

[0028]

[0029] in, is the transformation damping matrix with m rows and l columns; is the transformation damping matrix with l rows and l columns; is the velocity transformation matrix with m rows; is the equilibrium damping matrix corresponding to the boundary resistance dimension l, is the equilibrium load matrix corresponding to the boundary resistance dimension l.

[0030] In some embodiments, the boundary nonlinear dynamic equation based on resistance balance is: in, is the equilibrium damping matrix corresponding to the boundary resistance dimension l, D l is the equilibrium resistance array corresponding to the boundary resistance dimension l, is the equilibrium load array corresponding to the boundary resistance dimension l; is the velocity of the nonlinear dimension l;

[0031] The solution formula for the speed of the linear dimension is:

[0032] in, is the speed in linear dimension.

[0033] In some embodiments, the displacement, velocity and acceleration of the structural system at the current moment are obtained according to the velocity of the nonlinear dimension and the velocity of the linear dimension, comprising the following steps:

[0034] By combining the obtained nonlinear dimension speed and linear dimension speed, the speed of the total dimension can be determined to obtain the speed of the structural system at the current moment;

[0035] Then calculate the displacement, velocity and acceleration at the current moment according to formula eight;

[0036] The formula eight is:

[0037]

[0038] in, is the velocity at the current moment; u is the displacement at the current moment; is the acceleration at the current moment.

[0039] In a second aspect, a structural dynamic analysis device including a boundary resistance device is provided, comprising:

[0040] The first module is used to calculate the equilibrium damping matrix and the equilibrium load matrix according to the displacement, velocity and acceleration of the structural system at the previous moment in the set time step;

[0041] The second module is used to solve the nonlinear dimension velocity according to the boundary nonlinear dynamic equation based on the resistance balance and in combination with the equilibrium damping matrix and the equilibrium load matrix; and then obtain the linear dimension velocity according to the solution formula of the nonlinear dimension velocity and the linear dimension velocity;

[0042] The third module is used to obtain the displacement, velocity and acceleration at the current moment according to the velocity of the nonlinear dimension and the velocity of the linear dimension.

[0043] The beneficial effects of the technical solution provided by this application include:

[0044] The embodiment of the present application provides a structural dynamic analysis method and device including a boundary resistance device, wherein a balanced damping matrix and a balanced load matrix are calculated according to the displacement, velocity and acceleration of the structural system at the previous moment in a set time step; the velocity of the nonlinear dimension is solved according to the boundary nonlinear dynamic equation based on resistance balance and in combination with the balanced damping matrix and the balanced load matrix; then the velocity of the linear dimension is obtained according to the solution formula of the velocity of the linear dimension; the displacement, velocity and acceleration at the current moment are obtained according to the velocity of the nonlinear dimension and the velocity of the linear dimension. The above utilizes the characteristics of the boundary resistance related to the velocity and the inherent characteristics of the boundary nonlinear dynamic equation, and uses the dynamic equation with only nonlinear dimension and based on boundary resistance balance to finally calculate the displacement, velocity and acceleration of the structural system at the current moment, the dimension of the nonlinear dynamic equation is greatly reduced, the time consumption of the nonlinear iterative solution is very small, the calculation solution is greatly improved, and the problem of non-convergence of nonlinear iteration of strong boundary resistance is solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0046] Figure 1 A schematic diagram of the general flow of the structural dynamic analysis method including the boundary resistance device provided in the embodiment of the present application. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0048] The boundary nonlinear dynamic equation used in boundary nonlinear dynamic analysis is usually expressed as follows:

[0049]

[0050] It can be seen that the boundary nonlinear dynamic equation is a second-order equation, which contains the displacement term u and the velocity term and acceleration term is the boundary nonlinear resistance, which is related to displacement and velocity. Displacement, velocity, acceleration, boundary resistance and external load are all related to time. This second-order ordinary differential equation is difficult to solve, and scholars usually need to reduce the order of the above dynamic equation. The reduction method is usually combined with the Newmark-Beta method, that is, the velocity term and acceleration term are converted into displacement terms. The boundary nonlinear dynamic equation after reduction is as shown in Formula 2.

[0051]

[0052] In the formula To convert stiffness and external load. After the reduction of the order of nonlinear equations, the displacement term is an unknown, and the resistance term contains the displacement term. Although the above nonlinear dynamic equations have been reduced in order, due to the strong nonlinear characteristics of the boundary nonlinear resistance term, the above nonlinear equations generally reach tens of thousands of dimensions, the solution speed is very slow, and it is not easy to converge. The main reason for the non-convergence is that the Jacobian matrix of the boundary resistance contains unknown terms, which is not clear, and the dimensions of the equations are coupled with each other.

[0053] Therefore, in order to solve the problem that existing methods are difficult to achieve, such as slow solution and non-convergence of boundary nonlinear dynamic equations, the embodiments of the present application provide a structural dynamic analysis method, device, equipment and medium containing a boundary resistance device, so as to solve the problem in the related technology that due to the strong nonlinear characteristics of the boundary nonlinear resistance term, the dimension when using the boundary nonlinear dynamic equation for analysis generally reaches tens of thousands, the solution speed is very slow, and it is not easy to converge.

[0054] See also Figure 1 In a first aspect, a method for dynamic analysis of a structure including a boundary resistance device is provided, comprising:

[0055] Step 100, calculating a balanced damping matrix and a balanced load matrix according to the displacement, velocity and acceleration of the structural system at a previous moment in a set time step;

[0056] Step 101, according to the boundary nonlinear dynamic equation based on resistance balance, combined with the balanced damping matrix and the balanced load matrix, the speed of the nonlinear dimension is solved; then according to the solution formula of the speed of the nonlinear dimension and the speed of the linear dimension, the speed of the linear dimension is obtained; the nonlinear dimension corresponds to the boundary resistance device;

[0057] Step 102: derive the displacement, velocity and acceleration of the structural system at the current moment according to the velocity of the nonlinear dimension and the velocity of the linear dimension.

[0058] By utilizing the characteristics of boundary resistance being related to velocity and the inherent characteristics of boundary nonlinear dynamic equations, a boundary nonlinear dynamic equation with only nonlinear dimension and based on boundary resistance balance was established and used. Compared with conventional technologies, the technical advantages of the present invention are: (1) The dimension of the nonlinear dynamic equation is greatly reduced, the time consumption of nonlinear iterative solution is very small, the computational solution is greatly improved, and the problem of non-convergence of strong resistance nonlinear iteration is solved. For example, the dimension of the structure is usually hundreds of thousands, while the dimension of the nonlinear boundary resistance is only dozens. Compared with conventional equations, the computational solution time is improved by more than 20 times. (2) The present invention is first proposed to be based on resistance balance. The boundary nonlinear resistance is mainly related to velocity, and the displacement is secondary. Conventional equations are established based on displacement balance. Nonlinear iterative solution is not direct and requires data conversion, resulting in poor iterative solution performance.

[0059] The above utilizes the characteristics of boundary resistance and velocity correlation and the inherent characteristics of boundary nonlinear dynamic equations, and uses a dynamic equation with only nonlinear resistance dimension and based on boundary resistance balance to finally calculate the displacement, velocity and acceleration of the structural system at the current moment. The dimension of the nonlinear dynamic equation is greatly reduced, the iterative solution is time-saving, and the problem of non-convergence of nonlinear iteration of strong boundary resistance is solved.

[0060] In some preferred embodiments, step 100 specifically includes the following steps:

[0061] Step 1001, according to formula 3, and in combination with the displacement, velocity and acceleration of the structural system at the previous moment in the set time step, calculate the equivalent damping matrix and equivalent load matrix of the full dimension of the structural system; the displacement, velocity and acceleration of the structural system at the previous moment are u 0 , and

[0062] Formula three is:

[0063]

[0064] Among them, C eq is the equivalent damping matrix, Q eq is the equivalent load array, h is the set time step; u 0 , and are the displacement, velocity and acceleration of the previous moment respectively; Q is the load matrix; C is the damping matrix; K is the stiffness matrix; and M is the mass matrix.

[0065] Step 1002: extract and split the equivalent damping matrix to obtain equivalent damping matrices of different dimensions; split the equivalent load array to obtain equivalent load arrays of different dimensions; specifically:

[0066] From the equivalent damping matrix C eq Extract and split the equivalent damping matrix of l rows and l columns from The equivalent damping matrix with m rows and m columns The equivalent damping matrix with l rows and m columns The equivalent damping matrix with m rows and l columns That is, from C eq Extract the elements at the intersection of rows and columns corresponding to the resistance dimension to form an equivalent damping matrix with l rows and l columns. From C eq Delete the elements at the intersection of the row and column corresponding to the resistance dimension, and the remaining elements form an equivalent damping matrix with m rows and m columns From C eq Extract the elements of the row position corresponding to the resistance dimension, and delete the elements of the column position corresponding to the resistance dimension to form an equivalent damping matrix with l rows and m columns. From C eq Extract the elements of the column position corresponding to the resistance dimension, and delete the elements of the row position corresponding to the resistance dimension to form an equivalent damping matrix with m rows and l columns.

[0067] From the equivalent load array Q eq Extract the equivalent load array of l rows from and m rows of equivalent load arrays That is, from Q eq Extract the row elements corresponding to the resistance dimension to form an equivalent load array of l rows From Q eq Extract the row elements corresponding to the non-resistance dimension to form an m-row equivalent load array

[0068] l is the dimension of boundary resistance, corresponding to the nonlinear dimension; m is the dimension of non-boundary resistance, corresponding to the linear dimension, so the total dimension is n, n=l+m.

[0069] Step 1003: Based on the equivalent damping matrix of different dimensions and the equivalent load matrix of the same dimension, and in combination with Formula 4 and Formula 5, the equilibrium damping matrix and the equilibrium load matrix are obtained. That is, the transformation matrix based on resistance balance is determined, and the transformation damping matrix with m rows and l columns is The transformation damping matrix with l rows and l columns and the velocity transformation matrix with m rows

[0070] Formula 4 is:

[0071]

[0072] Formula 5 is:

[0073]

[0074] in, is the transformation damping matrix with m rows and l columns; is the transformation damping matrix with l rows and l columns; is the velocity transformation matrix with m rows; is the equilibrium damping matrix corresponding to the boundary resistance dimension l, is the equilibrium load matrix corresponding to the boundary resistance dimension l.

[0075] In some preferred embodiments, in step 101: the boundary nonlinear dynamic equation based on resistance balance, i.e., Formula 6, is used to perform nonlinear numerical iterative solution to determine the speed of the nonlinear dimension, and Formula 7 can be used to determine the speed of the non-resistance dimension.

[0076] The boundary nonlinear dynamic equation based on resistance balance is: Corresponding to formula 6; where, is the equilibrium damping matrix corresponding to the boundary resistance dimension l, D l is the equilibrium resistance array corresponding to the boundary resistance dimension l, is the equilibrium load array corresponding to the boundary resistance dimension l; is the velocity of the nonlinear dimension l;

[0077] The solution formula for the speed of linear dimension is: Corresponding formula 7.

[0078] in, is the speed in linear dimension.

[0079] In some preferred embodiments, step 102 includes:

[0080] By combining the obtained nonlinear dimension speed and linear dimension speed, the speed of the total dimension can be determined to obtain the speed at the current moment;

[0081] Then calculate the displacement, velocity and acceleration at the current moment according to formula eight;

[0082] Formula 8 is:

[0083]

[0084] in, is the velocity at the current moment; u is the displacement at the current moment; is the acceleration at the current moment.

[0085] In a second aspect, a structural dynamic analysis device including a boundary resistance device is provided, comprising:

[0086] The first module is used to calculate the equilibrium damping matrix and the equilibrium load matrix according to the displacement, velocity and acceleration of the structural system at the previous moment in the set time step;

[0087] The second module is used to solve the nonlinear dimension velocity according to the boundary nonlinear dynamic equation based on the resistance balance and in combination with the equilibrium damping matrix and the equilibrium load matrix; and then obtain the linear dimension velocity according to the solution formula of the nonlinear dimension velocity and the linear dimension velocity;

[0088] The third module is used to obtain the displacement, velocity and acceleration at the current moment according to the velocity of the nonlinear dimension and the velocity of the linear dimension.

[0089] In a third aspect, an electronic device is provided, comprising:

[0090] Processor, memory, communication interface;

[0091] The memory is used to store executable instructions executable by the processor;

[0092] The processor is configured to perform a structural dynamic analysis method including a boundary resistance device by executing executable instructions.

[0093] In a fourth aspect, a readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, a structural dynamic analysis method containing a boundary resistance device is implemented.

[0094] In the above, the memory can be either independent or integrated with the processor. Optionally, when the memory is a device independent of the processor, the electronic device may further include: a bus for connecting the above devices. The electronic device is used to execute the technical solution in any of the above method embodiments, and its implementation principle and technical effect are similar, which will not be repeated here.

[0095] A readable storage medium stores a computer program, which implements the technical solution provided by any of the above embodiments when executed by a processor.

[0096] Those skilled in the art can understand that all or part of the steps of implementing the above-mentioned method embodiments can be completed by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, the steps of the above-mentioned method embodiments are executed; and the aforementioned storage medium includes: ROM, RAM, disk or optical disk and other media that can store program codes.

[0097] In the description of the present application, it should be noted that the terms "upper", "lower", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application. Unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be a connection between the two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to the specific circumstances.

[0098] It should be noted that, in this application, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0099] The above description is only a specific implementation of the present application, so that those skilled in the art can understand or implement the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest range consistent with the principles and novel features applied for herein.

Claims

1. A structural dynamic analysis method including a boundary resistance device, characterized in that: It includes: According to the displacement, velocity and acceleration of the structural system at the previous moment in the set time step, the equilibrium damping matrix and the equilibrium load matrix are calculated; According to the boundary nonlinear dynamic equation based on resistance balance, in combination with the equilibrium damping matrix and the equilibrium load matrix, the speed of the nonlinear dimension is solved; then, according to the solution formula of the speed of the nonlinear dimension and the speed of the linear dimension, the speed of the linear dimension is obtained; According to the velocity of the nonlinear dimension and the velocity of the linear dimension, the displacement, velocity and acceleration of the structural system at the current moment are obtained.

2. The structural dynamic analysis method including the boundary resistance device according to claim 1, characterized in that: According to the displacement, velocity and acceleration of the structural system at the previous moment in the set time step, the equilibrium damping matrix and the equilibrium load matrix are calculated, including the following steps: According to formula 3, combined with the displacement, velocity and acceleration of the structural system at the previous moment in the set time step, the equivalent damping matrix and equivalent load matrix of the structural system are calculated; Extracting and splitting the equivalent damping matrix to obtain equivalent damping matrices of different dimensions; splitting the equivalent load array to obtain equivalent load arrays of different dimensions; According to the equivalent damping matrices of different dimensions and the equivalent load matrix of the same dimension, and in combination with Formula 4 and Formula 5, a balanced damping matrix and a balanced load matrix are obtained.

3. The structural dynamic analysis method including the boundary resistance device according to claim 2, characterized in that: The displacement, velocity and acceleration of the structural system at the previous moment are u0, and The formula three is: Among them, C eq is the equivalent damping matrix, Q eq is the equivalent load array, h is the set time step; u0, and are the displacement, velocity and acceleration of the previous moment respectively; Q is the load matrix; C is the damping matrix; K is the stiffness matrix; M is the mass matrix.

4. The structural dynamic analysis method including the boundary resistance device according to claim 3 is characterized in that: The equivalent damping matrix is ​​extracted and split to obtain equivalent damping matrices of different dimensions; the equivalent load array is split to obtain equivalent load arrays of different dimensions, specifically comprising the following steps: From the equivalent damping matrix C eq Extract and split the equivalent damping matrix of l rows and l columns from The equivalent damping matrix with m rows and m columns The equivalent damping matrix with l rows and m columns The equivalent damping matrix with m rows and l columns From the equivalent load array Q eq Extract the equivalent load array of l rows from and m rows of equivalent load arrays The l is the dimension of boundary resistance, corresponding to the nonlinear dimension; m is the dimension of non-boundary resistance, corresponding to the linear dimension, and the total dimension is n, n=l+m.

5. The structural dynamic analysis method including the boundary resistance device according to claim 4, characterized in that: The formula 4 is: The formula five is: in, is the transformation damping matrix with m rows and l columns; is the transformation damping matrix with l rows and l columns; is the velocity transformation matrix with m rows; is the equilibrium damping matrix corresponding to the boundary resistance dimension l, is the equilibrium load matrix corresponding to the boundary resistance dimension l.

6. The structural dynamic analysis method including the boundary resistance device according to claim 5, characterized in that: The boundary nonlinear dynamic equation based on resistance balance is: in, is the equilibrium damping matrix corresponding to the boundary resistance dimension l, D l is the equilibrium resistance array corresponding to the boundary resistance dimension l, is the equilibrium load array corresponding to the boundary resistance dimension l; is the velocity of the nonlinear dimension l; The solution formula for the speed of the linear dimension is: in, is the speed in linear dimension.

7. The structural dynamic analysis method including the boundary resistance device according to claim 4, characterized in that: According to the velocity of the nonlinear dimension and the velocity of the linear dimension, the displacement, velocity and acceleration of the structural system at the current moment are obtained, including the following steps: By combining the obtained nonlinear dimension speed and linear dimension speed, the speed of the total dimension can be determined to obtain the speed of the structural system at the current moment; Then calculate the displacement, velocity and acceleration at the current moment according to formula eight; The formula eight is: in, is the velocity at the current moment; u is the displacement at the current moment; is the acceleration at the current moment.

8. A structural dynamic analysis device including a boundary resistance device, characterized in that: It includes: The first module is used to calculate the equilibrium damping matrix and the equilibrium load matrix according to the displacement, velocity and acceleration of the structural system at the previous moment in the set time step; The second module is used to solve the nonlinear dimension velocity according to the boundary nonlinear dynamic equation based on the resistance balance and in combination with the equilibrium damping matrix and the equilibrium load matrix; and then obtain the linear dimension velocity according to the solution formula of the nonlinear dimension velocity and the linear dimension velocity; The third module is used to obtain the displacement, velocity and acceleration at the current moment according to the velocity of the nonlinear dimension and the velocity of the linear dimension.

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