Anti-seismic analysis method and system for full-reactor-core assembly of fast reactor and medium

Abstract

The invention relates to an anti-seismic analysis method and system for a full-reactor-core assembly of a fast reactor and a medium, and the method comprises the steps: carrying out the equivalent decomposition of a full-reactor nonlinear multi-assembly system into a series of linear single-assembly vibration systems; based on numerical simulation, calculating an additional mass coefficient of the feature component to simulate the influence of fluid-solid coupling on component vibration; based on an Euler-Bernoulli theory, a connector and an additional mass coefficient, establishing unrelated finite beam unit models of the single reactor core assembly; carrying out dimensionality reduction on a vibration system of the single reactor core assembly to obtain a solution of a single-degree-of-freedom system; calculating vibration response of the single-degree-of-freedom system under modal coordinates by adopting a central difference method, and converting the vibration response into dynamic response under physical coordinates; if the seismic acceleration time history stops, deflection analysis and contact analysis are performed. According to the method, the structural dynamic response under the gap condition is rapidly solved, and the calculation efficiency of the method is greatly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic assessment of fast reactor core structures, and in particular to a seismic analysis method, system and medium for a fast reactor full core assembly. Background Art

[0002] A typical fast reactor core is composed of hundreds of core assemblies, which are arranged in a hexagonal shape and independently inserted into the core support structure. At the same time, the gap between adjacent assemblies is very small, only a few millimeters, so adjacent assemblies will inevitably collide with each other during an earthquake. In addition, since all core assemblies are inserted and connected in the support and surrounded by fluid, the core assembly will vibrate as a whole, and the fluid-solid coupling problem is significant, making internal collisions more complicated. When the intensity of the earthquake becomes higher, the excessive deformation and impact force of the assembly may affect the insertion and extraction of the control rods, resulting in the strength failure of the core assembly and even the risk of nuclear leakage, affecting the safety and reliability of the reactor. Therefore, in the design of fast reactor cores, it is necessary to develop core seismic analysis and evaluation methods.

[0003] In order to evaluate the vibration characteristics of large-scale fast reactor core components, the main evaluation methods currently include: seismic tests and finite element seismic analysis methods. Although seismic tests are more reliable, complete full-scale core seismic tests are rarely carried out due to the high cost of the test. In order to solve this problem, equivalent alternatives are usually used, such as single-component tests, single-row component tests, hexagonal array component tests, and scaled tests. Compared with traditional seismic tests, finite element seismic analysis methods are more economical and efficient. The current common methods include numerical simulation (ABAQUS\ANASYS, etc.) and self-developed methods, such as France's CAST3M and Japan's REVIAN-3D methods. Although the above methods have greatly promoted the evaluation of the seismic performance of reactors, there are still some defects, which are mainly reflected in the following aspects:

[0004] Test plan: Although the alternative test plan has simulated the real component vibration environment as much as possible, there are still many differences between the test setup and the real environment, such as the boundary conditions of the entire core, the influence of fluids, and scale effects.

[0005] Numerical simulation scheme: In order to simulate the seismic response of the entire core assembly, traditional finite element software usually requires a lot of computing time and memory, and has high requirements for computer hardware and software environment.

[0006] Seismic analysis methods: Seismic analysis methods independently developed by various countries mainly use the direct time integration method or corresponding improved versions, with relatively low calculation efficiency. Currently, the above seismic analysis mainly focuses on deformation and displacement response analysis, and lacks in-depth research.

[0007] How to fully consider the actual working conditions of the components in the core when they vibrate, improve the computing efficiency and reduce the computing environment is an urgent problem to be solved. Summary of the invention

[0008] The present invention provides a method, system and medium for seismic analysis of a fast reactor full core assembly, so as to solve the problem of high requirements on computer hardware and software environment and relatively low calculation efficiency.

[0009] To achieve the above-mentioned object, in a first aspect, the present invention provides a method for seismic analysis of a fast reactor core assembly, which is used for seismic analysis and calculation of a core assembly of a fast reactor core in a seismic acceleration time history, wherein pads are arranged between the core assemblies, the core assemblies are fixed by inserting pins into sockets, and a spherical support performs unilateral position limiting on the core assembly, comprising:

[0010] Step 1: Based on numerical simulation, a gap-damping-spring connector for simulating nonlinear collision of core components is obtained, the motion state of each core component and the contact state of each connector are initialized, a full-stack nonlinear multi-component system is obtained, and the full-stack nonlinear multi-component system is equivalently decomposed into a series of linear single-component vibration systems;

[0011] Step 2: Calculate the natural frequency and corresponding mode shape of the selected characteristic component, and calculate the additional mass coefficient of the characteristic component based on numerical simulation to simulate the influence of fluid-solid coupling on the vibration of the component;

[0012] Step 3: Based on the Euler-Bernoulli theory, an equivalent beam model of the core assembly is constructed, and a finite beam unit model of a single core assembly that is independent of each other is established by combining the connector and the additional mass coefficient, wherein the connector is respectively arranged between the core assembly and the core assembly pad, between the core assembly and the spherical support, and between the pin and the socket;

[0013] Step 4: reducing the dimension of the single core assembly vibration system to a single degree of freedom system solution;

[0014] Step 5: Calculate the vibration response of the single-degree-of-freedom system in modal coordinates using a central difference method, and convert the vibration response into a dynamic response in physical coordinates;

[0015] Step 6: Determine whether the earthquake acceleration time history stops. If the earthquake acceleration time history stops, perform deflection analysis and contact analysis.

[0016] Preferably, after determining whether the earthquake acceleration time history has stopped, the method further includes, if the earthquake acceleration time history has not stopped, repeating steps three to five in sequence.

[0017] To achieve the above purpose, in a second aspect, a seismic analysis and calculation of a core assembly of a fast reactor core in a seismic acceleration time history is provided, wherein a spacer is provided between the core assemblies, the core assemblies are fixed by inserting pins into sockets, and a spherical support performs unilateral position limiting on the core assembly, including:

[0018] A single component vibration system generation module is used to obtain a gap-damping-spring connector for simulating nonlinear collision of a core component based on numerical simulation, initialize the motion state of each core component and the contact state of each connector, obtain a full-stack nonlinear multi-component system, and decompose the full-stack nonlinear multi-component system into a series of linear single-component vibration systems;

[0019] An additional mass coefficient calculation module is used to calculate the natural frequency and corresponding modal vibration shape of the selected characteristic component, and based on numerical simulation, calculate the additional mass coefficient of the characteristic component to simulate the influence of fluid-solid coupling on the vibration of the component;

[0020] An equivalent beam model building module is used to build an equivalent beam model of the core assembly based on the Euler-Bernoulli theory, and to establish a finite beam unit model of a single core assembly that is independent of each other by combining the connector and the additional mass coefficient, wherein the connector is respectively arranged between the core assembly and the core assembly pad, between the core assembly and the spherical support, and between the pin and the socket;

[0021] A dimension reduction module, used for reducing the dimension of the single core assembly vibration system to a single degree of freedom system solution;

[0022] A physical response module, used to calculate the vibration response of the single-degree-of-freedom system in modal coordinates by using a central difference method, and convert the vibration response into a dynamic response in physical coordinates;

[0023] The time judgment module is used to judge whether the earthquake acceleration time history has stopped, and if the earthquake acceleration time history has stopped, deflection analysis and contact analysis are performed.

[0024] To achieve the above objectives, in a third aspect, the present invention also relates to a computer-readable storage medium, in which instructions are stored, and when the instructions are run, the above-mentioned method for seismic analysis of a full core assembly of a fast reactor is executed.

[0025] The present invention relates to a method, system and medium for seismic analysis of a fast reactor full core assembly, which has the following beneficial effects compared with the prior art:

[0026] The present invention fully considers the actual working conditions of the components in the core when vibrating: nonlinear collision, fluid-solid coupling problems and calculation efficiency problems, proposes a simplified beam unit model, adopts a gap-damper-spring connector to simulate the nonlinear collision between components and components and between components and shrouds, simplifies the influence of fluid-solid coupling into the additional mass of the components, and improves the traditional modal superposition method so that it can accelerate the solution of dynamic response under gap nonlinear conditions, and has stronger engineering applicability.

[0027] The present invention decomposes a complex nonlinear system into an equivalent linear system for calculation, improves the traditional modal superposition method, quickly solves the structural dynamic response under gap conditions, abandons the direct time integration method of traditional large-scale nonlinear systems, and greatly improves the calculation efficiency of the method. Therefore, it will have broad application prospects in the field of seismic analysis of fast reactor core components. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a method flow chart of a method for seismic analysis of a fast reactor full core assembly in Embodiment 1 of the present invention;

[0029] Figure 2 This is a schematic diagram of the main process of a method for seismic analysis of a fast reactor full core assembly in Embodiment 1 of the present invention;

[0030] Figure 3 It is a schematic diagram of calculating the fluid-solid coupling additional mass coefficient of a core assembly of a fast reactor full core assembly seismic analysis method in Embodiment 1 of the present invention;

[0031] Figure 4 It is a schematic diagram of a Central European Bernoulli beam unit of a method for seismic analysis of a full core assembly of a fast reactor in Embodiment 1 of the present invention;

[0032] Figure 5 It is a schematic diagram of a collision model used in a method for seismic analysis of a full core assembly of a fast reactor in Embodiment 1 of the present invention;

[0033] Figure 6 It is a schematic diagram of a simplified beam unit model of a core assembly of a fast reactor full core assembly seismic analysis method in Embodiment 1 of the present invention;

[0034] Figure 7 It is a schematic diagram of an improved modal superposition method of a fast reactor full core assembly seismic analysis method in Embodiment 1 of the present invention;

[0035] Figure 8 is a schematic diagram of earthquake acceleration of Example 1 and Example 2 in Embodiment 1 of the present invention;

[0036] Fig. 9 The calculation results of Example 1 of the first embodiment of the present invention are compared between the seismic analysis method proposed by the present invention and the finite element software ABAQUS;

[0037] Fig.10 The top deflection analysis result of the component of Example 2 of the first embodiment of the present invention is shown in FIG. Figure 1 ;

[0038] Fig.11 The top deflection analysis result of the component of Example 2 of the first embodiment of the present invention is shown in FIG. Figure 2 ;

[0039] Fig.12 The top deflection analysis result of the component of Example 2 of the first embodiment of the present invention is shown in FIG. Figure 3 ;

[0040] Fig.13 The top deflection analysis result of the component of Example 2 of the first embodiment of the present invention is shown in FIG. Figure 4 ;

[0041] Fig.14 Schematic diagram of the component top contact analysis result of Example 2 of Embodiment 1 of the present invention Figure 1 ;

[0042] Fig.15 Schematic diagram of the component top contact analysis result of Example 2 of Embodiment 1 of the present invention Figure 2 ;

[0043] Fig.16 Schematic diagram of the component top contact analysis result of Example 2 of Embodiment 1 of the present invention Figure 3 ;

[0044] Fig.17 Schematic diagram of the component top contact analysis result of Example 2 of Embodiment 1 of the present invention Figure 4 ;

[0045] Fig.18 It is a structural schematic diagram of a fast reactor full core assembly seismic analysis system in Embodiment 2 of the present invention. DETAILED DESCRIPTION

[0046] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention. It should also be noted that, for ease of description, only parts related to the present invention, rather than all structures, are shown in the accompanying drawings.

[0047] Embodiment 1

[0048] A method for seismic analysis of the entire core assembly of a fast reactor, see Figure 1-Figure 2, used for the seismic analysis and calculation of the core assembly of the fast reactor core, in the core system, the core assembly is arranged in a regular hexagon in the shroud, the bottom of the core assembly is inserted into the spherical support, the bottom of all core assemblies are supported by the support, and the top of the edge core assembly will collide with the shroud; in the seismic system, the spherical support and the shroud are regarded as rigid bodies, and their own deformation is ignored. Among them, pads are arranged between the core assemblies, and the core assemblies are fixed by inserting pins into the sockets, and the spherical support performs unilateral positioning of the core assembly, including the following steps: S10 to S60.

[0049] S10: Based on numerical simulation, a gap-damper-spring connector is obtained to simulate the nonlinear collision of core components. The motion state of each core component and the contact state of each connector are initialized to obtain the nonlinear multi-component system of the whole stack. The nonlinear multi-component system of the whole stack is equivalently decomposed into a series of linear single-component vibration systems.

[0050] Among them, the motion state of each core component and the contact state of each connector are initialized to obtain the nonlinear multi-component system of the whole stack, which specifically includes: numerical simulation based on software ABAQUS, when t=0, the initial velocity and displacement of each degree of freedom of each core component are 0, and each connector is in a non-contact state. The dynamic motion equation of the nonlinear multi-component system of the whole stack is expressed as:

[0051]

[0052] Where F(t) represents the external force on the core, which comes from seismic excitation; is the acceleration vector of the multi-component system, is the velocity vector of the multi-component system, U(t) is the displacement vector of the multi-component system, M represents the overall mass matrix of the system, C represents the damping matrix of the system, and K represents the stiffness matrix of the system.

[0053] In this system, the spring force of the connector is the internal force of the system. In order to solve the collision force, the entire dynamic equation needs to be solved. However, the huge number of degrees of freedom of the above system matrix will make the calculation time and the required memory too large, resulting in a huge calculation burden. At the same time, due to the presence of nonlinear connectors inside the system, this brings a lot of nonlinear calculation difficulties to the multi-component system. Therefore, it is very uneconomical to directly solve the dynamic equations of the above multi-component system. In order to solve this difficulty, the present invention decomposes the multi-component system with significant nonlinearity and is equivalent to a series of linear single-component vibration systems. At this time, the spring force of the connector becomes the external force of a single component, and it changes with time.

[0054] Among them, the whole stack nonlinear multi-component system is equivalently decomposed into a series of linear single-component vibration systems, including:

[0055] The full stack nonlinear multi-component system is decomposed through the connector. At a certain moment, the single-component vibration system is a linear single-component vibration system, and its dynamic motion equation is:

[0056]

[0057] Among them, f(t) represents the external force of the component, which comes from the spring force of the connector; represents the acceleration vector of a single component, represents the velocity vector of a single component, u(t) represents the displacement vector of a single component, m represents the overall mass matrix of the core assembly, c represents the damping matrix of the core assembly, and k represents the stiffness matrix of the core assembly, where the seismic excitations received by the core assembly in the full-reactor nonlinear multi-component system are all converted into the spring force of the connector.

[0058] S20: Calculate the natural frequency and corresponding modal vibration shape of the selected characteristic component, and calculate the additional mass coefficient of the characteristic component based on numerical simulation to simulate the influence of fluid-solid coupling on the vibration of the component.

[0059] After the above system decomposition, we get a series of vibration systems with similar components. For the convenience of subsequent calculations, we need to select characteristic components and perform modal analysis to obtain the natural frequency and modal vibration shape of the components. During modal analysis, the free vibration equation of the system without considering the influence of damping is solved, that is,

[0060]

[0061] Assume that the solution is in the form: u(t) = φsinω(tt 0 ), we get a generalized eigenvalue problem, namely:

[0062] kυ-ω 2 mφ=0

[0063] Among them, φ is an n-order vector, ω is the vibration frequency of vector φ, t is the time variable, t 0 is the time constant determined by the initial conditions. According to the characteristic analysis, n characteristic solutions can be obtained, namely According to the orthogonality and regularity of the natural vibration modes, we can get:

[0064]

[0065] That is: Φ T mΦ=I,Φ T kΦ=Ω, Φ and Ω represent the natural vibration mode matrix and the natural frequency matrix respectively.

[0066] Among them, the additional mass coefficient of the characteristic component is calculated to simulate the influence of fluid-solid coupling on the vibration of the component. Specifically, the additional mass coefficient of the characteristic component is calculated based on the numerical simulation of the software ABAQUS to approximately simulate the influence of fluid-solid coupling on the vibration of the component.

[0067] Since the core assembly of a fast reactor is immersed in the coolant, the gap between the two assemblies is very small. When an earthquake occurs, the coolant has a significant effect on the movement and deformation of the core assembly structure, making the structural vibration exhibit strong nonlinearity. Therefore, the fluid-solid coupling effect is crucial to the seismic analysis of the core of a fast reactor. In order to quantify the effect of fluid on structural movement, the traditional potential flow theory is heavily dependent on the shape of the assembly and is not suitable for the development of seismic analysis programs for large-scale assembly groups. The present invention combines the full-scale acoustic-solid coupling model of the finite element software ABAQUS to determine the additional mass coefficient of the beam unit model, and includes steps: S21 to S24.

[0068] S21: Based on the Euler-Bernoulli beam theory, the real core assembly is simplified into a beam unit model, and the typical characteristic beam model boundary conditions are selected: the bottom edge is fixed and the upper end is a free end.

[0069] S22: The concentrated additional mass is evenly distributed along the axial direction of the core assembly to equivalently simulate the influence of the fluid on the vibration of the assembly.

[0070] S23: In the Abaqus numerical simulation, the first-order natural frequency of the core assembly is adjusted by changing the additional mass coefficient of the cross section of the beam unit model so that the natural frequency of the core assembly is equal to the wet frequency of the assembly in the coolant.

[0071] S24: The damping effect of the fluid on the core assembly is equivalently simulated by an additional damping coefficient, which is determined by the vibration test results.

[0072] S30: Based on the Euler-Bernoulli theory, an equivalent beam model of the core assembly is constructed. Combined with the connector and the additional mass coefficient, a finite beam unit model of a single core assembly that is independent of each other is established, wherein the connector is respectively arranged between the core assembly and the core assembly pad, between the core assembly and the spherical support, and between the pin and the socket.

[0073] Among them, based on the Euler-Bernoulli theory, an equivalent beam model of the core assembly is constructed, and a finite beam unit model of a single core assembly that is independent of each other is established by combining the gap-damping-spring connector and the additional mass coefficient, which specifically includes steps: S31 to S36.

[0074] S31: Based on the Euler-Bernoulli beam theory, under the 2D plane assumption, the finite element equations of the general plane beam unit are derived. In the local coordinate system, each node of the general plane beam unit has three degrees of freedom, namely the deflection in the Y direction, the axial displacement in the X direction, and the rotation angle in the plane.

[0075] Each beam unit has 6 degrees of freedom, among which the deformation and stress states of tension, compression and bending of the straight beam unit in the beam unit are not coupled with each other, and the axial stiffness is directly superimposed, which is equivalent to the simple superposition of the axial force rod unit and the beam unit, that is, superimposing the stiffness matrices of the two.

[0076] Beam element node displacement q e , beam unit node force P e It is expressed as:

[0077]

[0078] In the formula, u 1 , ν 1 and θ 1 represents the plane displacement and rotation of the first node in the beam element, u 2 , ν 2 and θ 2 represents the plane displacement and rotation of the second node in the beam element; P u1 , P ν1 and M 1 represents the nodal force and bending moment at the first node in the beam element, P u2 , P ν2 and M 2 represents the nodal force and moment at the second node in the beam element.

[0079] The element stiffness matrix K of the beam element e and the mass matrix M of the beam element e It is expressed as:

[0080]

[0081]

[0082] In the formula, E represents the Young's modulus of the material in the beam unit, ρ represents the material density of the material in the beam unit, A represents the cross-sectional area of ​​the material in the beam unit, l represents the unit length of the material in the beam unit and I represents the moment of inertia of the material in the beam unit; ∈ is taken as 0.0001.

[0083] S32: The gap-damping-spring connector is arranged between the core assembly and the core assembly pad, between the core assembly and the spherical support, between the pin and the socket, and between the connectors between the core assembly and the shroud, wherein the core assembly is arranged in a regular hexagon in the shroud, and the top of the core assembly at the edge will collide with the shroud.

[0084] In the attached Figure 5In the figure, a is a schematic diagram of the collision position, b is a schematic diagram of the connector and nonlinear spring stiffness, and c is a schematic diagram of the collision force analysis of the upper boss and pin of the component. Due to the compact arrangement characteristics of the hexagonal components in the fast reactor core, such as Figure 5 As shown in the figure, under earthquake conditions, nonlinear collisions will occur between the pads of the upper boss of the core assembly or between the pads of the middle boss of the core assembly, between the spherical support and the assembly, and between the pin and the socket. Therefore, it is very important to simulate the gap and collision force between the pads and the pin sockets; at the same time, the ball seat support plays a unilateral limit role for the assembly. In order to perform nonlinear collision analysis of the assembly, the analysis process is as follows:

[0085] Gap-damping-spring connectors are set between the core assembly and the core assembly pad, between the core assembly and the spherical support, and between the pin and the socket to simulate the real gap, and the collision force at this location is approximately calculated by the deformation of the spring. δ and k represent the gap value and collision stiffness of the connector, respectively.

[0086] S33: The collision stiffness of the equivalent gap-damping-spring connector and the damping coefficient of the gap-damping-spring connector are measured through collision tests; the gap value of the gap-damping-spring connector is determined by the gap between the core assemblies and the gap between the core assembly and the shroud.

[0087] S34: In the vertical direction, since the ball seat support plays a unilateral limiting role on the core assembly, a unilateral equivalent spring needs to be set at the spherical seat position to simulate the vertical collision.

[0088] S35: The connectors between the core assembly and the core assembly pads and the connectors between the core assembly and the shroud are single-sided connectors, while the connectors between the core assembly and the spherical support and the connectors between the pins and the sockets are double-sided connectors.

[0089] The connectors between the core assembly and the core assembly pads and the connectors between the core assembly and the shroud are single-sided connectors, that is, only the compression state of the spring is considered, and the spring force is not considered in the extension state; the connectors between the core assembly and the spherical support and the connectors between the pins and the sockets are double-sided connectors, that is, the compression and extension states of the spring are considered, with extension being positive and compression being negative.

[0090] S36: Calculation of core assembly collision force: The top collision force of the core assembly is represented by the collision force between the core assemblies in six directions around the core assembly. The collision force between the core assembly and the spherical support and between the pin and the support are directly calculated by the bilateral connectors in the XY direction. Figure 5As shown in the figure, taking the force analysis of the top of component 3 as an example, the collision forces of the components in the six directions are synthesized into collision forces in the X / Y directions and applied to the finite element analysis model; the collision force in the X / Y horizontal direction of the pin position of component 3 can be directly calculated by the bilateral connector. Based on the above Euler Bernoulli theory, collision model and fluid-solid coupling additional mass, a simplified beam unit model of the full core component is established, as shown in Figure 6 shown.

[0091] S40: Reduce the dimension of a single core assembly vibration system to a single degree of freedom system.

[0092] Specifically, based on the natural frequency and corresponding modal vibration shape of the characteristic components of S10, the modal superposition method is used to solve the dynamic response of the system, and the dynamic response of the system in physical coordinates is converted into the dynamic response in modal coordinates to achieve dimensionality reduction.

[0093] In the specific example: the modal superposition method is further improved so that it can approximate the dynamic response solution of the structure under the condition of gap simulation, reduce the dimension of the single component vibration system to the solution of the single degree of freedom system, and improve the calculation efficiency. Based on the natural frequency and natural vibration mode of the component in step 1, the modal superposition method is used to solve the dynamic response of the system, and the dynamic response of the system in physical coordinates is converted into the dynamic response in modal coordinates:

[0094]

[0095] Where q(t)=[q 1 (t) q 2 (t) q 3 (t) … q n (t)] T The meaning of the above transformation is to regard u(t) as φ i The linear combination of i can be regarded as a generalized displacement basis vector, q i It is a generalized displacement value. Mathematically, it is the transformation of the displacement vector u(t) from the n-dimensional space with the node displacement of the finite element system as the basis vector (also known as the physical coordinate) to the n-dimensional space with φ i is the n-dimensional space of basis vectors (also called vibration shape coordinates or modal coordinates). At the same time, the linear superposition of a small number of modal vibration shapes is used to approximate the dynamic response under physical coordinates to achieve dimensionality reduction.

[0096] Substitute the above transformation into the equation of motion and multiply both ends by Φ T , we can get the equation of motion in the new basis vector space:

[0097]

[0098] The above equation can be converted into m mutually uncoupled single-degree-of-freedom second-order ordinary differential equations:

[0099]

[0100] Due to the nonlinear boundary conditions of large-scale core components such as gaps and collisions, the deformation of fast reactor core components mainly includes the linear superposition of component rigid body translation and modal vibration shapes. Therefore, in order to make the modal superposition method suitable for approximate simulation of component deformation with rigid body translation components, such as Figure 7 As shown, the dynamic response of the present invention in modal coordinates is Add the component of rigid body translation: φ 1 ,φ 2 and φ 3 They represent the vertical translation, horizontal translation and rotational translation of the component respectively, φ 4 ,φ 5 and φ 6 The first three modal vibration shapes of the cantilever beam are shown in sequence. It is worth noting that φ 1 ~φ 3 The rigid body translation component of also needs to be regularized by mass matrix to keep the numerical dimension consistent.

[0101] S50: The vibration response of the single-degree-of-freedom system in modal coordinates is calculated using the central difference method, and the vibration response is converted into the dynamic response in physical coordinates.

[0102] Among them, the central difference method is used to calculate the vibration response of the single-degree-of-freedom system in modal coordinates, and the vibration response is converted into the dynamic response in physical coordinates, including:

[0103] The acceleration and speed Use displacement q i (t) means:

[0104]

[0105]

[0106] In order to solve the displacement q at time t+Δt i (t+Δt), substituting the above velocity and acceleration into the motion equation of the multi-degree-of-freedom system, we can obtain the recursive formula of the central difference method, that is,

[0107]

[0108] When t = 0, we can get q i (-Δt), that is

[0109]

[0110] where q i (0) and can be obtained from the given initial conditions, and Then we can use the equation of motion at t = 0 to get:

[0111]

[0112] At this point, the algorithm steps for solving the equation of motion step by step using the central difference method can be summarized as follows:

[0113] 1) Initial calculation

[0114] · Forming stiffness Mass 1 and damping 2ω i ξ i ;

[0115] Given q i (0) and

[0116] Choose a time step Δt, where Δt < Δt cr , and calculate the integration constant c 2 =2c 0 and c 3 =1 / c 2 ;

[0117] ·calculate

[0118] ·Form effective quality

[0119] Triangular decomposition

[0120] 2) For each time step (t=0, Δt, 2Δt, ...)

[0121] Calculate the payload at time t

[0122]

[0123] Solve for the displacement at time t+Δt

[0124]

[0125] S60: Determine whether the earthquake acceleration time history stops. If the earthquake acceleration time history stops, perform deflection analysis and contact analysis. If the earthquake acceleration time history does not stop, repeat S30 to S50.

[0126] Among them, performing deflection analysis and contact analysis specifically includes: obtaining a maximum deflection distribution diagram and a fitting curve of the component top under different component gap conditions and a maximum collision force distribution diagram and a fitting curve of the component top under different component gap conditions.

[0127] Two examples are given below to further illustrate the present invention. Figure 7 The acceleration time history of the earthquake (Northridge earthquake record) is shown. Steel is selected as an example of the material, with a Poisson's ratio of 0.3, a Young's modulus of E=210GPa, and a material density of 7800kg / m^3.

[0128] (1) Example 1: This example uses a seven-component structural model to demonstrate the effectiveness of a proposed efficient seismic analysis method for fast reactor core components. Fig. 9 The calculation results of the seismic analysis method proposed in the present invention and the finite element software ABAQUS are compared, where a shows the comparison of the motion trajectory of the top of the component, and b shows the time history diagram of the collision force at the top of the component. Fig. 9 As shown in part a of FIG. 1 , the motion trajectory of the component top calculated by the method proposed in the present invention and the ABAQUS software is very similar, and the motion range error in the X / Y direction is very small; Fig. 9 As shown in part b, the time history of the collision force at the top of the assembly obtained by the two methods is compared. Obviously, the distribution of the collision force is very similar, and the maximum collision force is 3493.04N and 3305.99N, respectively, with an error of only 6.37%. However, in terms of computational efficiency, the calculation time of the method proposed in the present invention is 100.49s, and the calculation time of ABAQUS software under parallel computing conditions is close to 30h, and the computational efficiency is improved by 3 orders of magnitude. Therefore, this example verifies that the seismic analysis method proposed in the present invention can efficiently calculate the seismic response of the core assembly.

[0129] Example 2: This example further analyzes the effect of model parameters (number of component layers and component gap) on the deformation and contact of the full core component. In the deflection analysis, Figure 10-13 The distribution diagram and fitting curve of the maximum deflection of the component top under different component layer conditions are shown. As the number of component layers increases, the maximum and minimum deflections of the components in the core and the maximum deflection of the central component increase. This is mainly because the large scale of the components makes the core have a greater inertia effect, resulting in an increase in the top deformation level; at the same time, the deformation degree at the center of the core is significantly smaller than that of the edge components. Figure 10-13 As shown, Fig.10 is the distribution diagram of the maximum deflection of the component top under different component layer numbers (number of core components), Fig.11 is the fitting curve of the maximum deflection of the component top under different component layer numbers (number of core components), Fig.12Represents the maximum deflection distribution of the component top under different gap conditions, Fig.13 Fitted curves representing the maximum deflection of the component top under different clearance conditions. Fig.10 The maximum deflection distribution diagram and fitting curve of the component top under different component gap conditions are shown. Obviously, as the component gap increases, the deformation level of the core component top increases linearly; when the gap is less than 2mm, the deformation level inside the core is lower than that of the edge component; however, when the gap is too large, the deflection level of the edge component top drops significantly, and a large number of local deformation phenomena occur.

[0130] In contact analysis, Figure 13-14 The figure below shows the bar graph of the maximum collision force at the top of each component layer and the distribution graph of the maximum collision force of each component under different component layers (number of core components). Figure 16-17 They represent the maximum collision force distribution diagram and fitting curve of the component top under different gap conditions respectively. Figure 13-14 The maximum collision force distribution diagram and bar graph of the component top under different component layer conditions are shown in Figure 2. When the number of component layers remains unchanged, the closer the component position in the core is to the center, the smaller the maximum collision force of the component is. This phenomenon is mainly because the outer component has a larger movement space and greater energy. When the component position remains unchanged, as the number of component layers (component scale) continues to increase, the maximum collision force of the component at this position continues to rise. This is mainly because the inertia of the core is greater. Figure 16-17 The maximum impact force distribution diagram and fitting curve of the component top under different component gap conditions are shown in Figure 1. Obviously, as the component gap increases, the impact strength at the top of the core component increases linearly; the impact force level inside the core is lower than that of the edge components.

[0131] Embodiment 2

[0132] A fast reactor full core assembly seismic analysis system is used for seismic analysis and calculation of core assemblies of a fast reactor core in the time history of earthquake acceleration, wherein pads are arranged between core assemblies, core assemblies are fixed by inserting pins into sockets, and ball supports are used to limit the core assemblies on one side, such as Fig.18 As shown, it includes a single-component vibration system generation module 71, an additional mass coefficient calculation module 72, an equivalent beam model construction module 73, a dimensionality reduction module 74, a physical response module 75 and a time judgment module 76.

[0133] A single component vibration system generation module 71 is used to obtain a gap-damping-spring connector for simulating nonlinear collision of core components based on numerical simulation, initialize the motion state of each core component and the contact state of each connector, obtain a full-core nonlinear multi-component system, and decompose the full-core nonlinear multi-component system into a series of linear single-component vibration systems;

[0134] An additional mass coefficient calculation module 72 is used to calculate the natural frequency and corresponding mode vibration shape of the selected characteristic component, and based on numerical simulation, calculate the additional mass coefficient of the characteristic component to simulate the influence of fluid-solid coupling on the vibration of the component;

[0135] An equivalent beam model building module 73 is used to build an equivalent beam model of a core assembly based on the Euler-Bernoulli theory, and to establish a finite beam unit model of a single core assembly that is independent of each other by combining a connector and an additional mass coefficient, wherein the connector is respectively provided between the core assembly and the core assembly pad, between the core assembly and the spherical support, and between the pin and the socket;

[0136] A dimension reduction module 74 is used to reduce the dimension of a single core assembly vibration system to a single degree of freedom system solution;

[0137] A physical response module 75 is used to calculate the vibration response of the single-degree-of-freedom system in modal coordinates by using a central difference method, and to convert the vibration response into a dynamic response in physical coordinates;

[0138] The time judgment module 76 is used to judge whether the earthquake acceleration time history has stopped. If the earthquake acceleration time history has stopped, deflection analysis and contact analysis are performed.

[0139] In this embodiment, the time judgment module 76 is also used to determine whether the earthquake acceleration time history has stopped. If the earthquake acceleration time history has not stopped, the equivalent beam model construction module 73, the dimensionality reduction module 74 and the physical response module 75 are repeatedly executed in sequence.

[0140] In some embodiments, the motion state of each core assembly and the contact state of each connector are initialized.

[0141] The full stack nonlinear multi-component system is obtained, including:

[0142] Based on the numerical simulation of ABAQUS software, at t = 0, the initial velocity and displacement of each degree of freedom of each core component are 0, and each connector is in a non-contact state. The dynamic motion equation of the whole reactor nonlinear multi-component system is expressed as:

[0143]

[0144] Where F(t) represents the external force on the core, which comes from seismic excitation; is the acceleration vector of the multi-component system, is the velocity vector of the multi-component system, U(t) is the displacement vector of the multi-component system, M represents the overall mass matrix of the system, C represents the damping matrix of the system, and K represents the stiffness matrix of the system;

[0145] The whole stack nonlinear multi-component system is equivalently decomposed into a series of linear single-component vibration systems, including:

[0146] The full stack nonlinear multi-component system is decomposed through the connector. At a certain moment, the single-component vibration system is a linear single-component vibration system, and its dynamic motion equation is:

[0147]

[0148] Among them, f(t) represents the external force of the component, which comes from the spring force of the connector; represents the acceleration vector of a single component, represents the velocity vector of a single component, u(t) represents the displacement vector of a single component, m represents the overall mass matrix of the core assembly, c represents the damping matrix of the core assembly, and k represents the stiffness matrix of the core assembly, where the seismic excitations received by the core assembly in the full-reactor nonlinear multi-component system are all converted into the spring force of the connector.

[0149] In some embodiments, the additional mass coefficient of the characteristic component is calculated to simulate the effect of fluid-solid coupling on the vibration of the component. Specifically, the additional mass coefficient of the beam unit model is determined by combining the full-scale acoustic-solid coupling model of the finite element software ABAQUS. The steps are as follows:

[0150] Based on the Euler-Bernoulli beam theory, the real core assembly is simplified into a beam unit model, and the typical characteristic beam model boundary conditions are selected: the bottom edge is fixed and the upper end is a free end;

[0151] The concentrated additional mass is evenly distributed along the axial direction of the core assembly to equivalently simulate the effect of fluid on the vibration of the assembly;

[0152] In the Abaqus numerical simulation, the first-order natural frequency of the core assembly is adjusted by changing the additional mass coefficient of the cross section of the beam unit model so that the natural frequency of the core assembly is equal to the wet frequency of the assembly in the coolant;

[0153] The damping effect of the fluid on the core assembly is equivalently simulated by an additional damping coefficient, which is determined by the vibration test results.

[0154] In some embodiments, based on the Euler-Bernoulli theory, an equivalent beam model of the core assembly is constructed, and a finite beam unit model of a single core assembly that is independent of each other is established by combining a gap-damping-spring connector and an additional mass coefficient, specifically including:

[0155] Based on the Euler-Bernoulli beam theory, the finite element equation of the general plane beam element is derived under the 2D plane assumption. In the local coordinate system, each node of the general plane beam element has three degrees of freedom, namely, the deflection in the Y direction, the axial displacement in the X direction, and the rotation angle in the plane.

[0156] Each beam element has 6 degrees of freedom, among which the deformation and stress states of tension, compression and bending of the straight beam element in the beam element are not coupled with each other, and the axial stiffness is directly superimposed;

[0157] Beam element node displacement q e , beam unit node force P e It is expressed as:

[0158]

[0159] In the formula, u 1 and ν 1 represents the in-plane displacement of the first node in the beam element, θ 1 represents the rotation angle of the first node in the beam element, u 2 and ν 2 represents the in-plane displacement of the second node in the beam element, θ 2 represents the rotation angle of the second node in the beam element;

[0160] P u1 and P ν1 represents the nodal force at the first node in the beam element, M 1 represents the bending moment at the first node in the beam element, P u2 and P ν2 represents the nodal force at the second node in the beam element, M 2 Represents the bending moment at the second node in the beam element.

[0161] The element stiffness matrix K of the beam element e and the mass matrix M of the beam element e It is expressed as:

[0162]

[0163]

[0164] Wherein, E represents the Young's modulus of the material in the beam unit, ρ represents the material density of the material in the beam unit, A represents the cross-sectional area of ​​the material in the beam unit, l represents the unit length of the material in the beam unit and I represents the moment of inertia of the material in the beam unit; ∈ is taken as 0.0001;

[0165] Gap-damping-spring connectors are arranged between the core assembly and the core assembly pad, between the core assembly and the spherical support, between the pin and the socket, and between the connectors between the core assembly and the shroud, wherein the core assembly is arranged in a regular hexagon in the shroud, and the top of the core assembly at the edge will collide with the shroud.

[0166] The collision stiffness of the equivalent gap-damping-spring connector and the damping coefficient of the gap-damping-spring connector are measured by collision tests; the gap value of the gap-damping-spring connector is determined by the gap between the core assemblies and the gap between the core assembly and the spherical support;

[0167] In the vertical direction, since the ball seat support plays a unilateral limiting role on the core assembly, a unilateral equivalent spring needs to be set at the spherical seat position to simulate the vertical collision;

[0168] The connectors between the core assembly and the core assembly pads and between the core assembly and the shroud are single-sided connectors, while the connectors between the core assembly and the spherical support and between the pins and the sockets are double-sided connectors;

[0169] Calculation of core assembly collision force: The top collision force of the core assembly is represented by the resultant collision force between the core assemblies in six directions around the core assembly. The collision force between the core assembly and the spherical support and between the pin and the support are both directly calculated by the bilateral connectors in the XY directions.

[0170] In some embodiments, reducing the dimension of a single-component vibration system to a solution of a single-degree-of-freedom system includes:

[0171] Based on the natural frequency and corresponding modal vibration shape of the characteristic component in step one, the modal superposition method is used to solve the dynamic response of the system, and the dynamic response of the system in physical coordinates is converted into the dynamic response in modal coordinates to achieve dimensionality reduction.

[0172] In some embodiments, deflection analysis and contact analysis are performed, specifically including: obtaining a maximum deflection distribution diagram and a fitting curve of the component top under different component gap conditions and a maximum collision force distribution diagram and a fitting curve of the component top under different component gap conditions.

[0173] In some embodiments, the vibration response of the single-degree-of-freedom system in modal coordinates is calculated using a central difference method, and the vibration response is converted into a dynamic response in physical coordinates, including:

[0174] The acceleration and speed Use displacement q i (t) means:

[0175]

[0176]

[0177] The above acceleration and speed Substituting into the motion equation of the multi-degree-of-freedom system, we can obtain the recursive formula of the central difference method, namely:

[0178]

[0179] When t = 0, we can get q i (t-Δt), Δt is the time step:

[0180]

[0181] Among them, the initial displacement q i (t0) and initial velocity can be obtained from the given initial conditions, and Then we can use the equation of motion at t = 0 to get:

[0182]

[0183] The central difference method is used to gradually solve the motion equation at t = 0, and the stiffness is obtained as The mass is unit mass and the damping is 2ω i ξ i ;

[0184] Where Δt<Δt cr , and calculate the integration constant c 2 =2c 0 and c 3 =1 / c 2 , forming effective quality

[0185] Calculate the effective load at each time t of the earthquake acceleration time history Where t=0,Δt,2Δt,…

[0186]

[0187] Based on the effective mass and effective load, solve for the displacement q at time t+Δt i (t+Δt):

[0188] The implementation process, method and effect of a seismic analysis system for a fast reactor full core assembly in this embodiment are the same as those of a seismic analysis method for a fast reactor full core assembly described in the first embodiment, and will not be described in detail here.

[0189] Embodiment 3

[0190] The present invention relates to a computer-readable storage medium, in which instructions are stored. When the instructions are executed, a method for seismic analysis of a full core assembly of a fast reactor is executed. The process method and effect of the method for seismic analysis of a full core assembly of a fast reactor are the same as those described in Example 1, and are not described in detail here.

[0191] It should be noted that, in this article, the terms "include", "comprises" or any other variations 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, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0192] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for seismic analysis of a fast reactor core assembly, characterized in that: The method is used for seismic analysis and calculation of core assemblies of a fast reactor core in the time history of earthquake acceleration, wherein pads are arranged between the core assemblies, the core assemblies are fixed by inserting pins into sockets, and the spherical support performs unilateral position limiting on the core assemblies, including: Step 1: Based on numerical simulation, a gap-damping-spring connector for simulating nonlinear collision of core components is obtained, the motion state of each core component and the contact state of each connector are initialized, a full-stack nonlinear multi-component system is obtained, and the full-stack nonlinear multi-component system is equivalently decomposed into a series of linear single-component vibration systems; Step 2: Calculate the natural frequency and corresponding mode shape of the selected characteristic component, and calculate the additional mass coefficient of the characteristic component based on numerical simulation to simulate the influence of fluid-solid coupling on the vibration of the component; Step 3: Based on the Euler-Bernoulli theory, an equivalent beam model of the core assembly is constructed, and a finite beam unit model of a single core assembly that is independent of each other is established by combining the connector and the additional mass coefficient, wherein the connector is respectively arranged between the core assembly and the core assembly pad, between the core assembly and the spherical support, and between the pin and the socket; Step 4: reducing the dimension of the single core assembly vibration system to a single degree of freedom system solution; Step 5: Calculate the vibration response of the single-degree-of-freedom system in modal coordinates using a central difference method, and convert the vibration response into a dynamic response in physical coordinates; Step 6: Determine whether the earthquake acceleration time history stops. If the earthquake acceleration time history stops, perform deflection analysis and contact analysis.

2. A fast reactor full core assembly seismic analysis method according to claim 1, characterized in that: The step of judging whether the earthquake acceleration time history has stopped further includes, if the earthquake acceleration time history has not stopped, repeating steps three to five in sequence.

3. The method for seismic analysis of a fast reactor core assembly according to claim 1, characterized in that: Initializing the motion state of each core component and the contact state of each connector to obtain a full-core nonlinear multi-component system specifically includes: Based on the numerical simulation of the software ABAQUS, at the moment t=0, the initial velocity and displacement of each degree of freedom of each core component are 0, and each of the connectors is in a non-contact state. The dynamic motion equation of the full-stack nonlinear multi-component system is expressed as: Where F(t) represents the external force on the core, which comes from seismic excitation; is the acceleration vector of the multi-component system, is the velocity vector of the multi-component system, U(t) is the displacement vector of the multi-component system, M represents the overall mass matrix of the system, C represents the damping matrix of the system, and K represents the stiffness matrix of the system; The equivalent decomposition of the full stack nonlinear multi-component system into a series of linear single-component vibration systems specifically includes: The full stack nonlinear multi-component system is decomposed through the connector. At a certain moment, the single-component vibration system is a linear single-component vibration system, and its dynamic motion equation is: Wherein, f(t) represents the external force of the component, which comes from the spring force of the connector; represents the acceleration vector of a single component, represents the velocity vector of a single component, u(t) represents the displacement vector of a single component, m represents the overall mass matrix of the core assembly, c represents the damping matrix of the core assembly and k represents the stiffness matrix of the core assembly, wherein in the full-core nonlinear multi-component system, the seismic excitations received by the core assembly are all converted into the spring force of the connector.

4. A fast reactor full core assembly seismic analysis method according to claim 1, characterized in that: The additional mass coefficient of the characteristic component is calculated to simulate the influence of fluid-solid coupling on the vibration of the component, specifically: combining the full-scale acoustic-solid coupling model of the finite element software ABAQUS, and determining the additional mass coefficient of the beam unit model, the steps are: Based on the Euler-Bernoulli beam theory, the actual core assembly is simplified into a beam unit model, and the typical characteristic beam model boundary conditions are selected: the bottom edge is fixed and the upper end is a free end; uniformly distributing concentrated additional mass along the axial direction of the core assembly to equivalently simulate the influence of fluid on assembly vibration; In the Abaqus numerical simulation, the first order natural frequency of the core assembly is adjusted by changing the additional mass coefficient of the cross section of the beam unit model so that the natural frequency of the core assembly is equal to the wet frequency of the assembly in the coolant; The damping effect of the fluid on the core assembly is equivalently simulated by an additional damping coefficient, and the additional damping coefficient is measured by vibration test results.

5. The method for seismic analysis of a fast reactor core assembly according to claim 1, characterized in that: The equivalent beam model of the core assembly is constructed based on the Euler-Bernoulli theory, and a finite beam unit model of a single core assembly that is independent of each other is established by combining the gap-damping-spring connector and the additional mass coefficient, which specifically includes: Based on the Euler-Bernoulli beam theory, under the 2D plane assumption, the finite element equation of the general plane beam unit is derived. In the local coordinate system, each node of the general plane beam unit has three degrees of freedom, namely, the deflection in the Y direction, the axial displacement in the X direction, and the rotation angle in the plane. Each beam element has 6 degrees of freedom, among which the deformation and stress states of tension, compression and bending of the straight beam element in the beam element are not coupled with each other, and the axial stiffness is directly superimposed; The beam element node displacement q e , the beam unit node force P e It is expressed as: Wherein, u1 and ν1 represent the plane displacement of the first node in the beam element, θ1 represents the rotation angle of the first node in the beam element, u2 and ν2 represent the plane displacement of the second node in the beam element, and θ2 represents the rotation angle of the second node in the beam element; P u1 and P ν1 represents the node force of the first node in the beam element, M1 represents the bending moment of the first node in the beam element, and P u2 and P ν2 represents the nodal force of the second node in the beam element, and M2 represents the bending moment of the second node in the beam element. The element stiffness matrix K of the beam element e and the mass matrix M of the beam element e It is expressed as: Wherein, E represents the Young's modulus of the material in the beam unit, ρ represents the material density of the material in the beam unit, A represents the cross-sectional area of ​​the material in the beam unit, l represents the unit length of the material in the beam unit and I represents the moment of inertia of the material in the beam unit; ∈ is taken as 0.0001; The gap-damping-spring connector is arranged between the core assembly and the core assembly spacer, between the core assembly and the spherical support, between the pin and the socket, and between the connectors between the core assembly and the shroud, wherein the core assembly is arranged in a regular hexagon in the shroud, and the top of the core assembly at the edge will collide with the shroud; The collision stiffness of the equivalent gap-damping-spring connector and the damping coefficient of the gap-damping-spring connector are measured by a collision test; the gap value of the gap-damping-spring connector is determined by the gap between the core assemblies and the gap between the core assembly and the shroud; In the vertical direction, since the ball seat support plays a unilateral limiting role on the core assembly, a unilateral equivalent spring needs to be set at the spherical seat position to simulate the vertical collision; The connectors between the core assembly and the core assembly pads and between the core assembly and the shroud are single-sided connectors, while the connectors between the core assembly and the spherical support and between the pins and the sockets are double-sided connectors; Calculation of core assembly collision force: The top collision force of the core assembly is represented by the resultant collision force between the core assemblies in six directions around the core assembly. The collision force between the core assembly and the spherical support and between the pin and the support are both directly calculated by the bilateral connectors in the XY directions.

6. A fast reactor full core assembly seismic analysis method according to claim 1, characterized in that : The method of reducing the dimension of the single-component vibration system to a single-degree-of-freedom system comprises: Based on the natural frequency and corresponding modal vibration shape of the characteristic component in step one, the modal superposition method is used to solve the dynamic response of the system, and the dynamic response of the system in physical coordinates is converted into the dynamic response in modal coordinates to achieve dimensionality reduction.

7. The method for seismic analysis of a fast reactor core assembly according to claim 1, characterized in that: The execution of deflection analysis and contact analysis specifically includes: obtaining a maximum deflection distribution diagram and a fitting curve of the component top under different component gap conditions, and a maximum collision force distribution diagram and a fitting curve of the component top under different component gap conditions.

8. The method for seismic analysis of a fast reactor core assembly according to claim 1, characterized in that: The method of using the central difference method to calculate the vibration response of the single-degree-of-freedom system in modal coordinates and converting the vibration response into a dynamic response in physical coordinates includes: The acceleration and speed Expressed in terms of displacement qi(t): The above acceleration and speed Substituting into the motion equation of the multi-degree-of-freedom system, we can obtain the recursive formula of the central difference method, namely: When t = 0, we can get q i (-Δt), Δt is the time step: Among them, the initial displacement qi(0) and the initial velocity can be obtained from the given initial conditions, and Then we can use the equation of motion at t = 0 to get: The central difference method is used to gradually solve the motion equation at t = 0, and the stiffness is obtained as The mass is unit mass and the damping is 2ω i ξ i ; Where Δt<Δt cr , and calculate the integration constant c2=2c0 and c3=1 / c2, forming the effective mass Calculate the effective load at each time t of the earthquake acceleration time history Where t = 0, Δt, 2Δt, ... Based on the effective mass and the effective load, solve for the displacement q at time t+Δt i (t+Δt):

9. A fast reactor full core assembly seismic analysis system, characterized in that: The method is used for seismic analysis and calculation of core assemblies of a fast reactor core in the time history of earthquake acceleration, wherein pads are arranged between the core assemblies, the core assemblies are fixed by inserting pins into sockets, and the spherical support performs unilateral position limiting on the core assemblies, including: A single component vibration system generation module is used to obtain a gap-damping-spring connector for simulating nonlinear collision of a core component based on numerical simulation, initialize the motion state of each core component and the contact state of each connector, obtain a full-stack nonlinear multi-component system, and decompose the full-stack nonlinear multi-component system into a series of linear single-component vibration systems; An additional mass coefficient calculation module is used to calculate the natural frequency and corresponding modal vibration shape of the selected characteristic component, and based on numerical simulation, calculate the additional mass coefficient of the characteristic component to simulate the influence of fluid-solid coupling on the vibration of the component; An equivalent beam model building module is used to build an equivalent beam model of the core assembly based on the Euler-Bernoulli theory, and to establish a finite beam unit model of a single core assembly that is independent of each other by combining the connector and the additional mass coefficient, wherein the connector is respectively arranged between the core assembly and the core assembly pad, between the core assembly and the spherical support, and between the pin and the socket; A dimension reduction module, used for reducing the dimension of the single core assembly vibration system to a single degree of freedom system solution; A physical response module, used to calculate the vibration response of the single-degree-of-freedom system in modal coordinates by using a central difference method, and convert the vibration response into a dynamic response in physical coordinates; The time judgment module is used to judge whether the earthquake acceleration time history has stopped, and if the earthquake acceleration time history has stopped, deflection analysis and contact analysis are performed.

10. A computer-readable storage medium, characterized in that: The storage medium stores instructions, which, when executed, execute a fast reactor full core assembly seismic analysis method as described in any one of claims 1-8.

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