Workshop floor response spectrum calculation method and system adopting substructure analysis

Abstract

The invention provides a workshop floor response spectrum calculation method adopting substructure analysis, and the method comprises the steps: solving a site response problem of a free field through a semi-analytical method based on the modulus and damping of the free field, and obtaining transmission boundary information; respectively calculating foundation impedance matrixes of transmission boundary information through a flexible volume method; calculating an upper structure matrix according to the foundation impedance matrix; the upper structure matrix comprises an upper stiffness matrix, an upper mass matrix and an upper damping matrix; constructing a motion equation according to the foundation impedance matrix and the upper structure matrix, and solving to obtain a frequency domain displacement response transfer function; and performing interpolation calculation on the frequency domain displacement response transfer function to obtain seismic response. According to the method, the calculation of the reaction spectrum is realized through a substructure analysis method for decomposing a linear soil-junction interaction analysis problem into a series of relatively simple subproblems, the calculation efficiency is improved, and the model construction period is shortened.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of response spectrum calculation, in particular to a plant floor response spectrum calculation method and system using substructure analysis. BACKGROUND

[0002] Response spectrum analysis is a widely used method in structural dynamics analysis, especially in the field of earthquake engineering. Its main purpose is to estimate the maximum response of a structure under seismic action through response spectrum. Response spectrum represents the maximum response that a structure with different natural periods (or frequencies) may experience under a specific seismic action, such as displacement, velocity, and acceleration. Through this analysis method, the response characteristics of a structure when facing short and uncertain transient dynamic events (such as earthquakes and impacts) can be evaluated. One of the notable features of response spectrum analysis is that it is applicable to situations where the time history of the load is unknown, and transient analysis cannot be performed. The duration of such events is usually short and cannot be considered as ergodic (or "stationary") processes, so the random response analysis method is not applicable. In this context, the response spectrum method achieves analysis through a special type of modal superposition. The basic idea is to provide an input that limits the response of the modal characteristics of a structure with specific natural frequencies and damping under such event excitation.

[0003] Currently, floor response spectrum calculation mainly uses the finite element method, which is an approximate method for discretizing continuous bodies. Its theoretical basis is the variational principle, continuum subdivision, and piecewise interpolation technology. That is, first find the variational representation of the mathematical physics problem to be solved, which is the total energy representation for solid mechanics problems. Then, the problem domain is divided into a finite set of elements, and the distribution of physical functions is represented by piecewise interpolation within the element. Solve the discrete algebraic equations to obtain the numerical solution of the physical function.

[0004] The essence of finite element floor response spectrum is to establish a linear model of the structure using the finite element method, calculate the acceleration response time history of the structure at a specific location (floor) through time history analysis, and then perform spectral analysis (calculate the maximum response of single degree of freedom system) on these time history data. Finally, the acceleration response spectrum curve representing the severity of the seismic environment (amplitude and frequency characteristics) at this location is generated. However, if the input parameters of a part of the structure change, this traditional finite element analysis method still needs to calculate the response of the complete model, which is a waste of time and cost for engineers who need to quickly obtain the response of the structure. Therefore, it is necessary to design a plant floor response spectrum calculation method and system using substructure analysis. SUMMARY

[0005] The application aims to provide a plant floor response spectrum calculation method and system using substructure analysis, which realizes the calculation of the response spectrum through a substructure analysis method of decomposing a linear soil-structure interaction analysis problem into a series of relatively simple subproblems, so as to improve the calculation efficiency and shorten the model construction period.

[0006] To achieve the above-mentioned purpose, the application provides the following scheme:

[0007] A plant floor response spectrum calculation method using substructure analysis, comprising the following steps:

[0008] Based on the modulus and damping of the free field, the field response problem of the free field is solved by a semi-analytical method to obtain transmission boundary information; the transmission boundary information includes P-SV-Rayleigh waves and SH-LOVE waves;

[0009] The foundation impedance matrix of the transmission boundary information is calculated by a flexible volume method;

[0010] The upper structure matrix is calculated according to the foundation impedance matrix; the upper structure matrix includes an upper stiffness matrix, an upper mass matrix and an upper damping matrix;

[0011] The motion equation is constructed according to the foundation impedance matrix and the upper structure matrix and is solved to obtain a frequency domain displacement response transfer function;

[0012] The frequency domain displacement response transfer function is calculated by interpolation to obtain a seismic response.

[0013] Optionally, based on the modulus and damping of the free field, the field response problem of the free field is solved by a semi-analytical method to obtain transmission boundary information, which includes:

[0014] The displacement of the free field is linearly analyzed according to the modulus and damping to obtain a displacement harmonic response;

[0015] The dynamic equation of a discrete layered system is constructed according to the displacement harmonic response and the eigenvalue is solved to obtain P-SV-Rayleigh waves;

[0016] The soil layer and viscous boundary of variable thickness are simulated according to the displacement harmonic response to obtain SH-LOVE waves.

[0017] Optionally, the foundation impedance matrix of the transmission boundary information is calculated by a flexible volume method, which includes:

[0018] The element mass matrix and the central stiffness matrix are obtained by a finite element method in the central region;

[0019] The layered mass matrix and the layered stiffness matrix are obtained by a generalized Rayleigh damping modal superposition method in the layered region.

[0020] Assembling the unit mass matrix, the center stiffness matrix, the layered mass matrix and the layered stiffness matrix to obtain a foundation mass and stiffness matrix;

[0021] Inverting the foundation mass and stiffness matrix to obtain a foundation impedance matrix.

[0022] Optionally, calculating an upper structure matrix according to the foundation impedance matrix, comprising:

[0023] Calculating an upper stiffness matrix according to the foundation mass and stiffness matrix;

[0024] Calculating an upper mass matrix according to the unit mass matrix;

[0025] Calculating an upper damping matrix according to the upper mass matrix.

[0026] Optionally, constructing a motion equation according to the foundation impedance matrix and the upper structure matrix and solving the motion equation to obtain a frequency domain displacement response transfer function, comprising:

[0027] Obtaining a free field displacement amplitude according to the foundation impedance matrix and the upper structure matrix;

[0028] Forming a complex stiffness matrix according to the free field displacement amplitude and the upper structure matrix;

[0029] Constructing a motion equation according to the free field displacement amplitude and the complex stiffness matrix;

[0030] Solving the motion equation and performing an FFT inverse transform to obtain the frequency domain displacement response transfer function.

[0031] Optionally, performing interpolation calculation on the frequency domain displacement response transfer function to obtain a seismic response, comprising:

[0032] Calculating the motion equation of the selected frequency in the entire frequency band within the cutoff frequency range;

[0033] Dividing the selected frequency in the frequency band so that each frequency band contains 5 selected frequencies;

[0034] In the frequency band, interpolating the motion equation according to the frequency response function of the two-degree-of-freedom system to obtain a complex constant;

[0035] Calculating the seismic response according to the complex constant.

[0036] Optionally, performing interpolation calculation on the frequency domain displacement response transfer function to obtain a seismic response, further comprising: if there are less than 5 selected frequencies in the last frequency band obtained by division, adding the selected frequencies in the previous frequency band to the last frequency band.

[0037] A plant floor response spectrum calculation system using substructure analysis comprises:

[0038] A free field analysis module is configured to solve a site response problem of a free field based on modulus and damping of the free field by a semi-analytical method to obtain transmission boundary information; the transmission boundary information comprises P-SV-Rayleigh waves and SH-LOVE waves.

[0039] A foundation impedance analysis module is configured to calculate a foundation impedance matrix of the transmission boundary information by a flexible volume method.

[0040] An upper structure calculation module is configured to calculate an upper structure matrix based on the foundation impedance matrix; the upper structure matrix comprises an upper stiffness matrix, an upper mass matrix and an upper damping matrix.

[0041] A motion equation solving module is configured to construct a motion equation based on the foundation impedance matrix and the upper structure matrix and solve the motion equation to obtain a frequency domain displacement response transfer function.

[0042] A seismic response analysis module is configured to perform interpolation calculation on the frequency domain displacement response transfer function to obtain a seismic response.

[0043] According to the embodiments of the present application, the following technical effects are achieved: the plant floor response spectrum calculation method using substructure analysis comprises: solving a site response problem of a free field based on modulus and damping of the free field by a semi-analytical method to obtain transmission boundary information; the transmission boundary information comprises P-SV-Rayleigh waves and SH-LOVE waves; calculating a foundation impedance matrix of the transmission boundary information by a flexible volume method; calculating an upper structure matrix based on the foundation impedance matrix; the upper structure matrix comprises an upper stiffness matrix, an upper mass matrix and an upper damping matrix; constructing a motion equation based on the foundation impedance matrix and the upper structure matrix and solving the motion equation to obtain a frequency domain displacement response transfer function; performing interpolation calculation on the frequency domain displacement response transfer function to obtain a seismic response. The method realizes the calculation of the response spectrum by decomposing the linear soil-structure interaction analysis problem into a series of relatively simple sub-problems by the substructure analysis method, improves the calculation efficiency and shortens the model construction period. BRIEF DESCRIPTION OF DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0045] Figure 1This is a flowchart of the method for calculating the floor reaction spectrum of a factory building according to an embodiment of the present invention;

[0046] Figure 2 This is a system structure diagram of the factory floor response spectrum calculation method according to an embodiment of the present invention. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0049] like Figure 1 As shown, this embodiment of the invention provides a method for calculating the floor response spectrum of a factory building using substructure analysis, including the following steps:

[0050] Step 100: Based on the modulus and damping of the free field, solve the field response problem of the free field using a semi-analytical method to obtain the transmission boundary information; the transmission boundary information includes: P-SV-Rayleigh wave and SH-LOVE wave;

[0051] Step 200: Calculate the ground impedance matrix of the transmission boundary information using the flexible volume method;

[0052] Step 300: Calculate the superstructure matrix based on the foundation impedance matrix; the superstructure matrix includes: superstructure stiffness matrix, superstructure mass matrix, and superstructure damping matrix;

[0053] Step 400: Construct and solve the motion equations based on the foundation impedance matrix and the superstructure matrix to obtain the frequency domain displacement response transfer function;

[0054] Step 500: Interpolate the frequency domain displacement response transfer function to obtain the seismic response.

[0055] In step 100 of this embodiment, when calculating the free-field motion, it is assumed that the site before foundation excavation is a horizontally layered site covering a rigid base or elastic half-space. The layered soil is assumed to be an elastic or viscoelastic homogeneous isotropic medium, and its modulus and damping are represented by complex modulus. Then, a semi-analytical method is used to solve the site response problem, that is, the finite element discretization method is used in the vertical direction, and the analytical method is used in the horizontal direction. Specifically, if a P-wave or SV-wave is incident on the surface of the bedrock half-space, assuming that the displacement in each layer of the free field changes linearly, then for a simple plane wave propagating along the x-direction with a frequency of ω, the displacement of each point in the layered foundation can also be expressed as a simple harmonic response with a certain amplitude and a corresponding frequency of ω, as expressed in the following expression:

[0056] δ x =αU x (z)e i(ωt-kx)

[0057] δ z =iαU z (z)e i(ωt-kx) ;

[0058] Where α is the modal participation coefficient, determined by the motion of the control points. For z j-1 <z<z j+1 Control points, have U 2j-1 and U 2j The two degrees of freedom correspond to displacements in the x and z directions, respectively, U 2j+1 and U 2j+2 The two degrees of freedom correspond to the displacements in the x and z directions, respectively, h j U represents the thickness of soil layer j; x (z) and U z (z) are interconnected and can be normalized. The wave number k is a complex number, and its real part represents the wave velocity V. a =ω / Re(k), where the imaginary part represents the attenuation factor exp(-Im(k)x).

[0059] Specifically, in obtaining the P-SV-Rayleigh wave, the top of each soil layer has two degrees of freedom of displacement (one horizontal and one vertical). Substituting the displacement expression for each layer into the differential equation of motion, and combining the stiffness and mass matrices of each soil layer, the dynamic equation of the discrete layered system is obtained, expressed as: in

[0060] P b Let A be the interaction force vector at the interface between the soil system and the half-space, and U be the displacement vector. [G] and [M] are both band-symmetric matrices. The harmonic response of the layer surface or the nodes in the layer is obtained by solving the eigenvalue of the dynamic equation, i.e. P-SV-Rayleigh wave.

[0061] In the process of obtaining SH-LOVE wave, the method used is similar to that of P-SV-Rayleigh wave problem. This embodiment takes the SH wave incident from the base to the semi-infinite layered system as an example. For the semi-infinite space at the bottom of the layered base, a variable-thickness soil layer and a viscous boundary are added to simulate the process, in which only the displacement in the y direction exists, and the expression is: y = αU y (z)e i(ωt-kx) .

[0062] The step 200 of this embodiment is based on the flexible volume method to solve the flexibility matrix coefficient of each node in the excavation body under each frequency harmonic wave excitation in the transmission boundary information, so as to assemble the flexibility matrix, and then obtain the impedance matrix by inverting the flexibility matrix.

[0063] Specifically, each column of the flexibility matrix is obtained by applying a unit load on the corresponding interaction node degree of freedom of the column to calculate the displacement on the interaction node, so that each column element of the flexibility matrix involves a point load solution. In the case of applying a horizontal load, the expression of displacement in the flexibility matrix is:

[0064] u x = u H ;

[0065]

[0066] wherein u H and u V are the displacements in the horizontal direction and the vertical direction in the load model, denotes the horizontal distance between the load point A on the center line and the interaction point B outside the boundary.

[0067] The symmetric finite element model of the impedance matrix obtained by inverting the flexibility matrix includes two areas, i.e. a cylindrical central area with a radius R composed of axisymmetric elements and a layered area outside the central area. In this embodiment, the finite element method is used to form the element mass matrix and the stiffness matrix in the cylindrical central area, and the mass matrix and the stiffness matrix are formed in the layered area in the form of generalized Rayleigh damping modal superposition, and the mass and stiffness matrices of the entire foundation are assembled together by the matrices of the central area and the layered area. In this embodiment, the stiffness matrix expression of the jth layer of soil is: wherein ξ is the size of x direction after conversion to cylindrical coordinate system, B is the strain matrix, and D is the elastic matrix. The calculation formula of the element mass matrix is: Where, p is the material density of the soil layer, and h is the thickness of the soil layer.

[0068] It should be noted that in the matrix generation process of the central region, a specific frequency harmonic load with a unit amplitude is also applied to each degree of freedom on the nodes of the central region, so as to obtain the displacement amplitude of the nodes in the central region and the interface nodes between the central region and the layered region, and then the displacement amplitude of the nodes in the layered region is derived by the horizontal distance of the nodes in the layered region from the interface. The specific frequency harmonic load of the embodiment can be divided into two cases:

[0069] (1) Vertical load, the expression is:

[0070] (2) Horizontal load, the expression is:

[0071] Where θ is the angle between the radial direction of the cylindrical coordinate system and the x direction of the coordinate system and respectively represent the displacements of r, z and θ directions at r a in the coordinate system. The displacement amplitudes of the nodes in the central region and the layered region are assembled into the flexibility matrix of the foundation, and the inverse is obtained to obtain the stiffness matrix and the impedance matrix of the foundation, and the expression is: Where F f is the flexibility matrix, is the inverse of the flexibility matrix F f . The calculation process of each column element in the flexibility matrix is: the displacement response of all degrees of freedom of the interaction nodes is obtained by applying a unit harmonic load on the degree of freedom related to the column. In actual calculation, the load point is the point on the central axis, and the response point can be on the central axis and the boundary, or outside the boundary, depending on the size of the central region. The displacement of all points is obtained by solving the displacement vector and the modal participation coefficient:

[0072]

[0073] Where U c and U ρ are the displacement vectors of the nodes on the central axis and the displacement vectors of the nodes on the boundary, which are converted to the global Cartesian coordinate system to obtain the flexibility matrix.

[0074] The calculation formula of the upper stiffness matrix in step 300 of the embodiment is: The calculation formula of the upper mass matrix is: Where N is the element shape function matrix. The calculation formula of the upper damping matrix is: Where μ is the element damping coefficient.

[0075] The step 400 of the embodiment first solves the free-field displacement amplitude at the interaction point in the seismic excitation according to the ground impedance matrix and the superstructure matrix. The solving process is the same as the harmonic response in the step 100. In some embodiments, the flexible volume method and the substructure reduction method are also used for solving. The expressions of the solving results are and where the free-field displacement vector of each frequency is a function of a specific wave field and the input control point position of the free-field ground. For the external load excitation case, the free-field displacement does not need to be solved. Specifically, the motion equation is composed of a load vector and a complex stiffness matrix. The load vector is obtained by solving the impedance matrix through the flexible volume method and the substructure reduction method. For the seismic excitation, the expression of the load vector is: where i is the ground and structure ground degree of freedom, and w is the internal degree of freedom of the excavated soil. For other external load excitations, the load vector is generated in the conventional finite element manner, and the expression is: where F i and F s are the external forces acting on the structure and soil body boundary and the remaining part, and are the displacements of the ground and structure interface and the internal part of the excavated soil, respectively. The complex stiffness matrix is obtained by merging the coefficient matrices generated by the flexible volume method and the substructure reduction method, and the expression is: where and are the complex stiffness matrices of the ground and structure interface of the substructure II and the substructure III, respectively, and are the complex stiffness matrices of the ground and structure interface and the internal part of the excavated soil of the substructure II and the substructure III, and the complex stiffness matrix of the remaining part of the structure and the ground and structure interface, respectively, s is the degree of freedom of the remaining part of the structure, and u i , u w and u s are the displacements of the ground and structure interface, the internal part of the excavated soil, and the remaining part of the structure, respectively, is the complex stiffness matrix of the remaining part of the structure. Finally, the motion equation is constructed, and the equation is solved, and the frequency domain displacement response transfer function is obtained through the FFT inverse transformation.

[0076] The specific steps of the step 500 of the embodiment include:

[0077] The motion equation of the selected frequency is calculated in the entire frequency band within the cutoff frequency range, and the expression of the motion equation is as described above;

[0078] The selected frequency is divided into frequency bands, so that each frequency band contains 5 selected frequencies;

[0079] In the frequency band, the motion equation is interpolated and calculated according to the frequency response function of the two-degree-of-freedom system, and five complex constants are obtained; the expression of the frequency response function of the two-degree-of-freedom system is: Wherein the subscript 1 and the subscript 2 respectively represent the code of the two-degree-of-freedom system, K * Indicate the stiffness matrix, M indicates the mass matrix, ω indicates the frequency, and P indicates the load. The expression of the interpolation calculation process is:

[0080] Wherein ω1, ω2, ω3, ω4 and ω5 are all frequency constants, and U1, U2, U3, U4 and U5 are displacements corresponding to the five frequency points. The seismic response of the intermediate frequency in each frequency band is calculated according to the complex constant, and the expression is: Wherein the superscript i is the i th frequency band, c is the complex constant, and ω is the frequency.

[0081] Specifically, if the last frequency band is less than 5 selected frequencies in step 500, the selected frequencies in the previous frequency band are added to the last frequency band, and the seismic response in the overlapping frequency is averaged.

[0082] As Figure 2 shown, the embodiment of the present application also provides a plant floor response spectrum calculation system using substructure analysis, comprising:

[0083] A free field analysis module is configured to solve the site response problem of the free field based on the modulus and damping of the free field by a semi-analytical method to obtain transmission boundary information; the transmission boundary information includes P-SV-Rayleigh wave and SH-LOVE wave.

[0084] A foundation impedance analysis module is configured to calculate the foundation impedance matrix of the transmission boundary information by a flexible volume method.

[0085] An upper structure calculation module is configured to calculate an upper structure matrix according to the foundation impedance matrix; the upper structure matrix includes an upper stiffness matrix, an upper mass matrix and an upper damping matrix.

[0086] A motion equation solving module is configured to construct and solve the motion equation according to the foundation impedance matrix and the upper structure matrix to obtain a frequency domain displacement response transfer function.

[0087] A seismic response analysis module is configured to interpolate and calculate the frequency domain displacement response transfer function to obtain the seismic response.

[0088] The beneficial effects of the present application are as follows:

[0089] 1) The traditional whole finite element analysis is decomposed into five independent parts, when the input parameters (such as soil layer data, seismic wave input, etc.) of a part change, only the affected part and the subsequent part need to be recalculated, avoiding repeated processing of unchanged parts, reducing redundant calculation, greatly reducing the calculation time and resource consumption, and significantly improving the calculation efficiency;

[0090] 2) The parametric modeling method is adopted, local recalculation can be performed by quickly adjusting the model parameters (such as soil layer properties, seismic input, etc.), which greatly shortens the model modification and verification period, and can adapt to the rapid design change requirements;

[0091] 3) The substructure technology such as flexible volume method and substructure reduction method is adopted, which can handle different boundary conditions and wave propagation problems, and improves the applicability and flexibility in complex engineering environment;

[0092] 4) Through the semi-analytical method, frequency domain motion equation solving, transfer function interpolation and other technologies, the accuracy of the calculation results in the aspect of dynamics response is ensured, the calculation precision is improved, and the engineering safety is also guaranteed.

[0093] The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the difference from other embodiments, and the same or similar parts between various embodiments can be referred to each other.

[0094] In the present application, specific examples are applied to illustrate the principles and implementation modes of the present application, and the above embodiment description is only used to help understand the method and core idea of the present application; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation mode and application range will also be changed. In summary, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A method for calculating a response spectrum of a plant floor using substructure analysis, characterized by, The method comprises the following steps: Solving the site response problem of the free field based on the modulus and damping of the free field by a semi-analytical method to obtain transmission boundary information; the transmission boundary information comprises P-SV-Rayleigh waves and SH-LOVE waves; Calculating the foundation impedance matrix of the transmission boundary information by a flexible volume method; Calculating the superstructure matrix according to the foundation impedance matrix; the superstructure matrix comprises a super stiffness matrix, a super mass matrix and a super damping matrix; Building a motion equation according to the foundation impedance matrix and the superstructure matrix and solving the motion equation to obtain a frequency domain displacement response transfer function; Performing interpolation calculation on the frequency domain displacement response transfer function to obtain a seismic response.

2. The method for calculating the plant floor response spectrum using substructure analysis according to claim 1, wherein, Solving the site response problem of the free field based on the modulus and damping of the free field by a semi-analytical method to obtain transmission boundary information, comprising: Performing linear analysis on the displacement of the free field according to the modulus and the damping to obtain a displacement harmonic response; Building a discrete layered system dynamic equation according to the displacement harmonic response and solving the characteristic value to obtain the P-SV-Rayleigh waves; Performing variable-thickness soil layer and viscous boundary simulation according to the displacement harmonic response to obtain the SH-LOVE waves.

3. The method for calculating the plant floor response spectrum using substructure analysis according to claim 1, wherein, Calculating the foundation impedance matrix of the transmission boundary information by a flexible volume method, comprising: Obtaining an element mass matrix and a central stiffness matrix by a finite element method in a central region; Obtaining a layered mass matrix and a layered stiffness matrix by a generalized Rayleigh damping modal superposition method in a layered region; Performing matrix assembly on the element mass matrix, the central stiffness matrix, the layered mass matrix and the layered stiffness matrix to obtain a foundation mass and stiffness matrix; Performing an inverse operation on the foundation mass and stiffness matrix to obtain the foundation impedance matrix.

4. The method for calculating the plant floor response spectrum using substructure analysis according to claim 3, characterized by, Calculating the superstructure matrix according to the foundation impedance matrix, comprising: Calculating the super stiffness matrix according to the foundation mass and stiffness matrix; Calculating the super mass matrix according to the element mass matrix; Calculating the super damping matrix according to the super mass matrix.

5. The method for calculating the plant floor response spectrum using substructure analysis according to claim 1, wherein, Building a motion equation according to the foundation impedance matrix and the superstructure matrix and solving the motion equation to obtain a frequency domain displacement response transfer function, comprising: Obtaining a free field displacement amplitude according to the foundation impedance matrix and the superstructure matrix; Forming a complex stiffness matrix according to the free field displacement amplitude and the superstructure matrix; Building the motion equation according to the free field displacement amplitude and the complex stiffness matrix; Solving the motion equation and performing FFT inverse transformation to obtain the frequency domain displacement response transfer function.

6. The method for calculating a plant floor response spectrum using substructure analysis according to claim 1, wherein, Performing interpolation calculation on the frequency domain displacement response transfer function to obtain a seismic response, comprising: Calculating the motion equation of selected frequencies in the entire frequency band in a cutoff frequency range; Dividing the selected frequencies in a frequency band so that each of the frequency bands contains five selected frequencies; Performing interpolation calculation on the motion equation according to the frequency response function of a two-degree-of-freedom system in the frequency band to obtain a complex constant; Calculating the seismic response according to the complex constant.

7. The method for calculating the plant floor response spectrum using substructure analysis according to claim 6, wherein, The interpolation calculation of the frequency domain displacement response transfer function obtains the seismic response, and further comprises: if there are less than 5 selected frequencies in the last frequency band obtained by the division, the selected frequencies in the previous frequency band are added to the last frequency band.

8. A plant floor response spectrum calculation system using substructure analysis, characterized by, Comprise: A free field analysis module, configured to solve a site response problem of a free field based on modulus and damping of the free field by a semi-analytical method to obtain transmission boundary information; The transmission boundary information comprises P-SV-Rayleigh waves and SH-LOVE waves; A foundation impedance analysis module, configured to calculate a foundation impedance matrix of the transmission boundary information by a flexible volume method respectively; An upper structure calculation module, configured to calculate an upper structure matrix according to the foundation impedance matrix; the upper structure matrix comprises an upper stiffness matrix, an upper mass matrix and an upper damping matrix; A motion equation solving module, configured to construct a motion equation according to the foundation impedance matrix and the upper structure matrix and solve the motion equation to obtain a frequency domain displacement response transfer function; A seismic response analysis module, configured to perform interpolation calculation on the frequency domain displacement response transfer function to obtain a seismic response.

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