A composite explicit time-domain analysis method for vibration response of engineering structures

Abstract

The present invention relates to a composite explicit time-domain analysis method for the vibration response of an engineering structure. The method comprises the following steps: adopting a spatial unit discretization method to obtain a dynamic control model and a structural matrix of the engineering structure to be solved; based on the dynamic control model and the structural matrix, adopting a composite explicit time integration method to perform a three-step iterative solution on the engineering structure to be solved, and determining the dynamic response physical quantity of the engineering structure to be solved in each overall step under a vibration load; the present invention adopts the composite explicit time integration method and performs an iterative solution in three steps, thereby overcoming the technical defects of the existing explicit time integration method in calculating nonlinear problems, and having greatly improved the calculation accuracy and stability compared with the existing explicit time integration method.

Description

Technical Field

[0001] The present invention relates to the technical field of structural dynamics, and in particular to a composite explicit time-domain analysis method and system for vibration response of an engineering structure. Background Art

[0002] With the rapid development of computer technology, direct time integration methods have become widely used to solve the dynamic response of engineering structures. Numerous commercial finite element software packages use direct time integration methods as their core algorithm for solving structural dynamic responses. Therefore, improving the performance of time integration methods is crucial for solving the dynamic response of engineering structures.

[0003] Generally speaking, time integration methods can be categorized as explicit or implicit. Each method has its own advantages and disadvantages and is suitable for different problem-solving applications. Compared to implicit methods, explicit methods are generally conditionally stable, requiring a shorter time step to ensure convergence. However, explicit methods do not require iterative solutions to the equations, resulting in higher single-step computational efficiency than implicit methods. Explicit methods are particularly advantageous when solving large structures or highly nonlinear problems.

[0004] Among existing explicit methods, the central difference method (CD) is the most classic single-step approach, having been applied in renowned commercial finite element software such as ANSYS, ABAQUS, and ADINA. However, the CD method suffers from numerous drawbacks, such as poor numerical dissipation, a short stability interval, and low precision. Numerical dissipation is one of the characteristics that most significantly impacts the algorithm's computational accuracy. Excellent numerical dissipation requires minimizing spurious high-frequency modes caused by finite element discretization while preserving important low-frequency modes as much as possible. This is not easily achieved with explicit methods. To improve numerical dissipation, Noh and Bathe developed a composite time integration method (called the Noh-Bathe method, Noh G, Bathe KJ. An explicit time integration scheme for the analysis of wave propagations. Computers & Structures 2013). This method employs a two-step strategy to achieve superior numerical dissipation and a larger stability interval. This method is a core solution algorithm for transient dynamic response analysis in the ADINA software. However, the Noh-Bathe method has poor stability in solving some nonlinear problems (such as vibration response), is prone to non-convergent calculation results, and has low calculation accuracy.

[0005] In general, the computational accuracy and stability of existing explicit time integration methods in nonlinear problems need to be improved. Summary of the Invention

[0006] The purpose of the present invention is to provide a composite explicit time-domain analysis method and system for the vibration response of engineering structures, so as to improve the accuracy and stability of the dynamic analysis of the vibration response of engineering structures.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] The present invention provides a composite explicit time-domain analysis method for the vibration response of an engineering structure, the method comprising the following steps:

[0009] A spatial unit discretization method is used to obtain a dynamic control model and a structural matrix of the engineering structure to be solved; the structural matrix includes: an overall mass matrix, an overall damping matrix, and an overall stiffness matrix;

[0010] Based on the dynamic control model and the structural matrix, a composite explicit time integration method is used to perform a three-step iterative solution on the engineering structure to be solved, and the dynamic response physical quantities of the engineering structure to be solved in each overall step under the vibration load are determined; the dynamic response physical quantities include a generalized displacement vector, a generalized velocity vector, and a generalized acceleration vector.

[0011] Optionally, based on the dynamic control model and the structural matrix, a composite explicit time integration method is used to perform a three-step iterative solution on the engineering structure to be solved, and determine the dynamic response physical quantity of the engineering structure to be solved at each overall step under the vibration load, specifically including:

[0012] The following formula is used to determine the dynamic response physical quantity of the engineering structure to be solved in the first sub-step of the i+1th overall step under the vibration load:

[0013]

[0014]

[0015]

[0016]

[0017] Among them, U(t i+p ), and They represent the generalized displacement vector, generalized velocity vector, and generalized acceleration vector of the first sub-step of the i+1th overall step, respectively. U(t i ), and respectively represent the generalized displacement vector, generalized velocity vector, and generalized acceleration vector of the \(i\)-th overall step, \(p\) represents the proportion of a single sub-step in the overall step, where \(0 < p < 1\), and \(\Delta t\) represents the step size of the overall step. represents the intermediate transition vector of the first sub-step of the \((i + 1)\)-th overall step, \(M\) represents the overall mass matrix, \(K\) represents the overall stiffness matrix, \(C\) represents the overall damping matrix, and \(F(t i+p ) represents the vibration load of the first sub-step of the \((i + 1)\)-th overall step;

[0018] According to the dynamic response physical quantities of the engineering structure to be solved in the first sub-step of the \((i + 1)\)-th overall step, use the following formula to determine the dynamic response physical quantities of the engineering structure to be solved in the second sub-step of the \((i + 1)\)-th overall step under the vibration load:

[0019]

[0020]

[0021]

[0022]

[0023] where \(U(t i+2p ), and respectively represent the generalized displacement vector, generalized velocity vector, and generalized acceleration vector of the second sub-step of the \((i + 1)\)-th overall step, represents the unknown coefficient vector in the composite explicit time integration method,, \(F(t i+2p ) represents the vibration load of the second sub-step of the \((i + 1)\)-th overall step;

[0024] According to the dynamic response physical quantities of the engineering structure to be solved in the first and second sub-steps of the \((i + 1)\)-th overall step, use the following formula to determine the dynamic response physical quantities of the engineering structure to be solved in the third sub-step of the \((i + 1)\)-th overall step under the vibration load, as the dynamic response physical quantities of the engineering structure to be solved in the \((i + 1)\)-th overall step under the vibration load:

[0025]

[0026]

[0027]

[0028]

[0029] where, represents the intermediate transition vector of the \((i + 1)\)-th overall step, \(U(t i+1 ), They represent the generalized displacement vector, generalized velocity vector, and generalized acceleration vector of the i+1th overall step, respectively, and α represents In the calculation formula The calculation proportional coefficient, β represents U(t i+1 ) in the calculation formula The proportional coefficients, γ and δ represent In the calculation formula The calculated proportionality coefficient and The calculation proportionality factor, F i+1 Represents the vibration load of the third sub-step of the i+1th overall step.

[0030] Optionally, based on the dynamic control model and the structural matrix, a composite explicit time integration method is used to perform step-by-step iterative solution on the engineering structure to be solved, and the dynamic response physical quantity of the engineering structure to be solved under the vibration load at each overall step is determined, and the method also includes:

[0031] The generalized displacement vector and the generalized velocity vector at the initial moment are used as the initial generalized displacement vector and the initial generalized velocity vector;

[0032] According to the initial generalized displacement vector and the initial generalized velocity vector, the initial generalized acceleration vector of the engineering structure to be solved under the vibration load is solved using the dynamic control model.

[0033] Optionally, based on the dynamic control model and the structural matrix, a composite explicit time integration method is used to perform a three-step iterative solution on the engineering structure to be solved, and a dynamic response physical quantity of the engineering structure to be solved at each overall step under the vibration load is determined, and the method also includes:

[0034] Determine the free parameters of the engineering structure to be solved as:

[0035]

[0036] Optionally, based on the dynamic control model and the structural matrix, a composite explicit time integration method is used to perform a three-step iterative solution on the engineering structure to be solved, and a dynamic response physical quantity of the engineering structure to be solved at each overall step under the vibration load is determined, and the method also includes:

[0037] Solve the equation |K-λM|=0 and obtain multiple characteristic roots;

[0038] The range of the step length of the overall step is determined based on the maximum eigenvalue among the multiple eigenvalues.

[0039]

[0040] Where K represents the overall stiffness matrix, M represents the overall mass matrix, λ represents the characteristic root, and λ max represents the maximum eigenvalue, Δt represents the overall step size, and l represents the stable interval parameter.

[0041] Optionally, l=5.508.

[0042] A composite explicit time-domain analysis system for the vibration response of an engineering structure, the system being applied to the above-mentioned method, comprising:

[0043] A dynamic control model and structural matrix acquisition module is used to obtain the dynamic control model and structural matrix of the engineering structure to be solved using a spatial unit discretization method; the structural matrix includes: an overall mass matrix, an overall damping matrix, and an overall stiffness matrix;

[0044] The dynamic response physical quantity iterative solution module is used to perform a three-step iterative solution on the engineering structure to be solved based on the dynamic control model and the structural matrix using a composite explicit time integration method to determine the dynamic response physical quantity of the engineering structure to be solved at each overall step under the vibration load; the dynamic response physical quantity includes a generalized displacement vector, a generalized velocity vector and a generalized acceleration vector.

[0045] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above method when executing the computer program.

[0046] A computer-readable storage medium stores a computer program, which implements the above method when executed.

[0047] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0048] The present invention discloses a composite explicit time domain analysis method for the vibration response of an engineering structure. The method comprises the following steps: adopting a spatial unit discretization method to obtain a dynamic control model and a structural matrix of the engineering structure to be solved; based on the dynamic control model and the structural matrix, adopting a composite explicit time integration method to perform a three-step iterative solution on the engineering structure to be solved, and determining the dynamic response physical quantity of the engineering structure to be solved in each overall step under a vibration load; the present invention adopts a composite explicit time integration method and performs an iterative solution in three steps, thereby overcoming the technical defects of the existing explicit time integration method in calculating nonlinear problems, and having a significant improvement in calculation accuracy and stability compared with the existing explicit time integration method. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0050] Figure 1 A flow chart of a composite explicit time-domain analysis method for the vibration response of an engineering structure provided by the present invention;

[0051] Figure 2 A schematic diagram of a composite explicit time-domain analysis method for the vibration response of an engineering structure provided by the present invention;

[0052] Figure 3 A schematic diagram of a nonlinear engineering structure in Example 1 provided in an embodiment of the present invention;

[0053] Figure 4 A comparison chart of the calculation results of different algorithms for nonlinear engineering structures in Example 1 provided in an embodiment of the present invention within 0-5 seconds;

[0054] Figure 5 A comparison chart of the calculation results of different algorithms for the nonlinear engineering structure in Example 1 provided in an embodiment of the present invention within 200-205 seconds;

[0055] Figure 6 A schematic diagram of the ten-story shear frame structure in Example 2 provided in an embodiment of the present invention;

[0056] Figure 7 A schematic diagram of the north-south earthquake load on a ten-story shear frame structure in Example 2 provided in an embodiment of the present invention;

[0057] Figure 8 A comparison chart of displacement calculation results obtained by different algorithms when the time step is 0.0091s in Example 2 provided by an embodiment of the present invention;

[0058] Figure 9 A comparison chart of displacement calculation results obtained by different algorithms when the time step is 0.0153s in Example 2 provided by an embodiment of the present invention;

[0059] Figure 10 A comparison chart of displacement calculation results obtained by different algorithms when the time step is 0.001s in Example 2 provided by an embodiment of the present invention;

[0060] Figure 11 A comparison chart of displacement calculation errors of different algorithms when the time step is 0.001s in Example 2 provided by an embodiment of the present invention;

[0061] Figure 12 A schematic diagram of the structure of the transmission tower in Example 3 provided in an embodiment of the present invention;

[0062] Figure 13 A side view of the transmission tower structure in Example 3 provided in an embodiment of the present invention;

[0063] Figure 14 A top view of the transmission tower structure in Example 3 provided in an embodiment of the present invention;

[0064] Figure 15 A schematic diagram of the north-south seismic load on the transmission tower structure in Example 3 provided in an embodiment of the present invention;

[0065] Figure 16 A comparison chart of displacement calculation errors of different algorithms in Example 3 provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0066] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0067] The purpose of the present invention is to provide a composite explicit time domain analysis method and system for the vibration response of an engineering structure, so as to improve the calculation accuracy and efficiency of the explicit time integration method.

[0068] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0069] Example 1

[0070] like Figure 1 and Figure 2 As shown, embodiment 1 of the present invention provides a composite explicit time domain analysis method for the vibration response of an engineering structure, the method comprising the following steps:

[0071] Step 101: A spatial unit discretization method is used to obtain a dynamic control model and a structural matrix of the engineering structure to be solved; the structural matrix includes an overall mass matrix, an overall damping matrix, and an overall stiffness matrix.

[0072] Step 101 of the embodiment of the present invention belongs to the preparation process of algorithm pre-processing, and derives the calculation formula of the structural response.

[0073] The specific calculation process of determining the process motion equation:

[0074] Finite element discretization is performed on the structure, that is, the structure is divided into a finite number of small units (assumed) connected at the nodes, and then the shape function assumed in each unit is used to piecewise approximate the unknown field function on the entire solution domain, that is, the displacement a of any point in the unit e i The n nodes of the unit can be displaced u iI (t) means:

[0075] a i (x,y,z,t)=N1(x,y,z)u iI (t) (1)

[0076] Among them, N1(x,y,z) is the unit shape function, which is a known function that depends on the unit type. The above formula is written in matrix form

[0077] a=Nu e (2)

[0078] in

[0079] N=[N1 N2…N n ] (3)

[0080] Where a is the unit displacement field, N is the unit shape function matrix, and u e is the unit node displacement.

[0081] Then the element strain matrix is

[0082] ε=Bu e (4)

[0083] in

[0084] B=LN (5)

[0085]

[0086] L is the operator matrix, and B is the strain-displacement relationship matrix of the geometric equation of elasticity, also known as the strain matrix.

[0087] The element stress matrix is

[0088] σ=DBu e (7)

[0089] in

[0090]

[0091] in D is the relationship matrix between stress and strain in the physical equation of elastic mechanics, also known as the elastic matrix, ν is the Poisson's ratio, and E is the elastic modulus.

[0092] Through various methods, such as the principle of minimum potential energy, Galerkin method, etc., the internal and external virtual work of the engineering structure is

[0093]

[0094] Among them, K e , F e are the element stiffness matrix and the element equivalent node load vector, respectively, expressed as

[0095] K e =∫B T DXF e (10)

[0096]

[0097] The unit node displacement vector can be expressed as

[0098] u e =G e U (12)

[0099] Among them, U=[u 11 u 21 u 31 …u 1N u 2N u 3N ] T is the structural node displacement vector composed of the displacement of each node of the structure, N is the total number of nodes of the structure, G e is a selection matrix composed of 1 and 0. For example, for a plane triangle element (the node numbers of the three nodes of the element are I, J, and M respectively)

[0100]

[0101] Substituting formula (12) into formula (9), we can get

[0102]

[0103] Among them, K is the overall stiffness matrix, F is the overall load vector of the structure, which are expressed as

[0104]

[0105]

[0106] The kinetic energy of the structure is

[0107]

[0108] Where ρ is the engineering structure density, for A,U e, the result of the time derivative of U; M, M e They are the overall mass matrix and unit mass matrix of the engineering structure respectively. The overall mass matrix M can be obtained from the unit mass matrix M e Assembled, it can be expressed as

[0109]

[0110]

[0111] The virtual work of the viscosity force is

[0112]

[0113] Among them, C, C e are the overall damping matrix and unit damping matrix of the structure, respectively, expressed as

[0114]

[0115]

[0116] Hamilton's principle formula is

[0117]

[0118] Among them, t1~t2 is the time interval of the engineering structure response to be sought

[0119] Substitute the above equations into equation (23) and perform partial integration to obtain

[0120]

[0121] The value of the displacement vector U at time t1 and t2 is given, that is, Considering the arbitrariness of δU, we have

[0122]

[0123] So far, the motion equation of the structure is obtained.

[0124] For seismic response analysis, the external load can be expressed as

[0125]

[0126] in, is the earthquake load acceleration vector; R is the influence vector, which defines the displacement generated in the structure when the foundation produces a static unit displacement in the direction of the load excitation.

[0127] Substituting Equation (26) into Equation (25), we obtain the motion equation of the structure under seismic load:

[0128]

[0129] Step 102: Based on the dynamic control model and the structural matrix, a composite explicit time integration method is used to perform a three-step iterative solution on the engineering structure to be solved, and the dynamic response physical quantities of the engineering structure to be solved under the vibration load at each overall step are determined; the dynamic response physical quantities include a generalized displacement vector, a generalized velocity vector, and a generalized acceleration vector.

[0130] From the equation of motion (25), we know that to solve the displacement, velocity and acceleration vectors of the finite element system, the first step is to determine the mass matrix, damping matrix, stiffness matrix and load vector of the finite element system. As mentioned above, the stepwise time integration method also needs to determine the initial generalized displacement vector U0, generalized velocity vector And the generalized acceleration vector is calculated by formula (25): For a single degree of freedom system, the above matrices and vectors degenerate into scalars.

[0131] Determine the time step Δt according to the type of dynamic problem of the specific engineering structure and the algorithm stability interval; determine the five free parameters p, α, β, r and δ. <p<1。

[0132] (1) To obtain high calculation accuracy, the relationship needs to be limited

[0133]

[0134] (2) Method for finding the stable interval of the algorithm: Solve the frequency equation |K-λM|=0, and we can get n characteristic roots λ i (i=n), take the maximum value λ max , then the maximum system frequency The range of the stable interval Δt can be written as:

[0135]

[0136] l is the stability interval parameter of the new method, which is determined by the value of parameter p and can reach a maximum of 6.0. The p value recommended by this algorithm is The stable interval parameter is l=5.508.

[0137] After the above initialization, step 102 is to perform a three-step iterative solution on the engineering structure to be solved using a composite explicit time integration method based on the dynamic control model and the structural matrix to determine the dynamic response physical quantity of the engineering structure to be solved at each overall step under the vibration load, specifically including:

[0138] Calculate the generalized displacement vector U(t i+p ), generalized velocity vector Generalized acceleration vector Calculate successively according to the following formula:

[0139]

[0140]

[0141]

[0142]

[0143] where, U(t i+p ), and represent the generalized displacement vector, generalized velocity vector and generalized acceleration vector of the first sub-step of the (i + 1)-th global step respectively, U(t i ), and represent the generalized displacement vector, generalized velocity vector and generalized acceleration vector of the i-th global step respectively, p represents the proportion of a single sub-step in the global step, 0 < p < 1, Δt represents the step size of the global step, represents the intermediate transition vector of the first sub-step of the (i + 1)-th global step, M represents the global mass matrix, K represents the global stiffness matrix, C represents the global damping matrix, F(t i+p ) represents the vibration load of the first sub-step of the (i + 1)-th global step;

[0144] Calculate the generalized displacement vector U(t i+2p ), generalized velocity vector generalized acceleration vector successively according to the following formula:

[0145]

[0146]

[0147]

[0148]

[0149] where, U(t i+2p ), and represent the generalized displacement vector, generalized velocity vector and generalized acceleration vector of the second sub-step of the (i + 1)-th global step respectively, represents the unknown coefficient vector in the composite explicit time integration method, F(t i+2p [[ID=6​​​i+1 ), generalized velocity vector Generalized acceleration vector Calculate in sequence using the following formulas:

[0151]

[0152]

[0153]

[0154]

[0155] in, represents the intermediate transition vector of the i+1th overall step, U(t i+1 ), They represent the generalized displacement vector, generalized velocity vector, and generalized acceleration vector of the i+1th overall step, respectively, and α represents In the calculation formula The calculation proportional coefficient, β represents U(t i+1 ) in the calculation formula The proportional coefficients, γ and δ represent In the calculation formula The calculated proportionality coefficient and The calculation proportionality factor, F i+1 Represents the vibration load of the third sub-step of the i+1th overall step.

[0156] The algorithm performs iterative calculations (replacing the structural parameters of the current moment with the structural parameters of the initial moment / previous moment until all structural parameters of all moments are determined, and then outputting all structural parameters). The calculated results are stored and Figure 2 The iterative strategy shown performs progressive calculations and storage on all time steps, and finally obtains the calculation results of all time points, which are then applied to the calculation and post-processing analysis of other physical quantities.

[0157] Compared with the CD method and the classic Bathe method that have been commercially applied, the method of the present invention has a larger stability range and higher precision characteristics. Especially for nonlinear dynamic problems, calculation results with significantly better stability and calculation accuracy can be obtained. A series of case tests verified the effectiveness, stability and high precision of the new invention method for solving structural response calculation problems. The three cases compared the new method with the CD method and the Noh-Bathe method. The following is a further explanation with examples, drawings and implementation process. Each algorithm uses the same time step. The reference solution of all cases uses a time step of Δt = 1×10 -6 Obtained by implicit Bathe algorithm of s.

[0158] Calculation example 1

[0159] Example 1 is a standard example for verifying the feasibility of nonlinear analysis, which mainly tests the feasibility, stability and calculation accuracy of the present invention in nonlinear analysis. Figure 3 As shown, the system is a spring pendulum with two degrees of freedom. The dynamic equation of this nonlinear system is expressed as

[0160]

[0161]

[0162] Where θ represents the angular displacement, r represents the radial displacement, m represents the mass of the pendulum, g represents the acceleration due to gravity, L0 represents the length of the spring when it is not deformed, and k represents the elastic constant of the spring. The initial conditions of the system are

[0163] r(0)=r0,θ(0)=θ0,

[0164] Let m = 1 kg, g = 9.81 m / s 2 , L0=0.5m,k s =98.1N / m, r0=0.25m, and The time step of each algorithm is 0.02s.

[0165] Figure 4 The calculation results of the radial displacement r in the range of 0-5s are given. As shown in the figure, compared with the reference solution, the calculation results of the CD method show a large deviation and non-convergence, while the calculation results of the Noh-Bathe method and the new invention method have higher accuracy. Figure 5 The calculation results for the radial displacement r in the range of 200-205 s are given. It can be seen that the error of the Noh-Bathe method is significantly greater than that of the new method. Overall, the new method is more accurate than both the CD method and the Noh-Bathe method in calculating nonlinear problems.

[0166] Calculation example 2

[0167] Example 2 is a standard basic example for feasibility verification of earthquake response analysis, which mainly tests the feasibility, stability and calculation accuracy of the method of the present invention in structural dynamics problems. Figure 6 The ten-story shear frame structure shown was subjected to the 1940 El Centro north-south earthquake loads (e.g. Figure 7The structure adopts an interlayer shear model and a rigid layer assumption. Finite element rod elements are used for discretization, with N = 8 elements and a total of 8 degrees of freedom. The initial displacements and velocities of all floors are set to 0. The top floor displacement is selected for analysis. Figure 8 The displacement calculation results when the time step is 0.0091s (time period 0.5-1.5s) are given. Figure 8 It can be seen that at this time step, the calculation results of the CD method do not converge, while the calculation results of the Noh-Bathe method and the method of the present invention are in good agreement with the reference solution. Figure 9 The displacement calculation results when the time step is 0.0153s (time period 0.5-1.5s) are given. Figure 9 It can be seen that at this time step, the calculation results of the Noh-Bathe method do not converge, while the calculation results of the method of the present invention are in good agreement with the reference solution. Figure 10 The displacement calculation results (time period 28-30s) with a time step of 0.001s are given. As can be seen from the figure, all the calculation results are in good agreement with the reference solution. Figure 11 The displacement error when the time step is 0.001s (time period 29.5-30s) is given. The displacement error E0(t) is calculated by the following formula

[0168]

[0169] Among them, u e (t) is the reference solution at time t, and u(t) is the calculated value at time t. As can be seen from the figure, the computational accuracy of the new method is greater than that of the CD method and the Bathe method. In summary, the stability and computational accuracy of the new method are superior to those of the CD method and the Bathe method.

[0170] Calculation example 3

[0171] Example 3 is a typical example to verify the calculation accuracy of the time integration method for general structures, mainly testing the feasibility and calculation accuracy of the method of the present invention in engineering structures. Figure 12 The transmission tower structure shown was subjected to the 1971 San Fernando north-south earthquake loads (e.g. Figure 15 ) function. The side view and top view of the structure are respectively Figure 13 and Figure 14 The structure uses three-dimensional Euler-Bernoulli beam elements. The total number of elements in the system is 249, and the elements are connected by rigid nodes. The system is fixed to the ground. The density of all elements is 7850 kg / m 2 , the elastic modulus is assumed to be 2×10 7Pa, the cross section is circular with a radius of 0.05m, and the Poisson's ratio is 0.2. The initial displacements and velocities for all degrees of freedom are 0. A time step of 0.001s is used for the numerical simulation. The displacement response of node A in the Y direction is selected for analysis. Figure 16 The displacement calculation errors of the three methods are given (time period 9.5-10s). As can be seen from the figure, the calculation accuracy of the new invention method is higher than that of the CD method and the Noh-Bathe method.

[0172] Example 2

[0173] Embodiment 2 of the present invention provides a composite explicit time-domain analysis system for the vibration response of an engineering structure. The system is applied to the method of embodiment 1, and the system includes:

[0174] The dynamic control model and structural matrix acquisition module is used to obtain the dynamic control model and structural matrix of the engineering structure to be solved using the spatial unit discretization method. The structural matrix includes the overall mass matrix, the overall damping matrix, and the overall stiffness matrix.

[0175] The dynamic response physical quantity iterative solution module is used to perform a three-step iterative solution on the engineering structure to be solved based on the dynamic control model and the structural matrix using a composite explicit time integration method to determine the dynamic response physical quantity of the engineering structure to be solved at each overall step under the vibration load; the dynamic response physical quantity includes a generalized displacement vector, a generalized velocity vector and a generalized acceleration vector.

[0176] The specific implementation method of the functions of each module in Example 2 of the present invention is the same as the specific steps in Example 1, and will not be repeated here.

[0177] Example 3

[0178] Embodiment 3 of the present invention provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned method when executing the computer program.

[0179] In addition, when the computer program in the above-mentioned memory is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory, a random access memory, a magnetic disk or an optical disk.

[0180] Example 4

[0181] Embodiment 4 of the present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed, the above method is implemented.

[0182] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0183] The present invention adopts a spatial unit discretization method to obtain a dynamic control model and a structural matrix of an engineering structure to be solved; based on the dynamic control model and the structural matrix, a composite explicit time integration method is adopted to perform a three-step iterative solution on the engineering structure to be solved, and determine the dynamic response physical quantity of the engineering structure to be solved in each overall step under a vibration load; the present invention adopts a composite explicit time integration method and performs an iterative solution in three steps, thereby overcoming the technical defects of the existing explicit time integration method in calculating nonlinear problems, and has greatly improved the calculation accuracy and stability compared with the existing explicit time integration method.

[0184] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0185] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A composite explicit time-domain analysis method for the vibration response of an engineering structure, characterized in that: The method comprises the following steps: A spatial unit discretization method is used to obtain a dynamic control model and a structural matrix of the engineering structure to be solved; the structural matrix includes: an overall mass matrix, an overall damping matrix, and an overall stiffness matrix; Based on the dynamic control model and the structural matrix, a composite explicit time integration method is used to perform a three-step iterative solution on the engineering structure to be solved, and the dynamic response physical quantities of the engineering structure to be solved at each overall step under the vibration load are determined; the dynamic response physical quantities include a generalized displacement vector, a generalized velocity vector, and a generalized acceleration vector, specifically including: The following formula is used to determine the dynamic response physical quantity of the engineering structure to be solved in the first sub-step of the i+1th overall step under the vibration load: Among them, U(t i+p ), and respectively represent the generalized displacement vector, generalized velocity vector and generalized acceleration vector of the first sub-step of the (i + 1)-th global step. U(t i ), and respectively represent the generalized displacement vector, generalized velocity vector and generalized acceleration vector of the i-th global step. p represents the proportion of a single sub-step in a global step, where 0 < p < 1. Δt represents the step size of a global step. represents the intermediate transition vector of the first sub-step of the (i + 1)-th global step. M represents the global mass matrix, K represents the global stiffness matrix, C represents the global damping matrix, and F(t i+p ) represents the vibration load of the first sub-step of the (i + 1)-th global step; According to the dynamic response physical quantity of the engineering structure to be solved in the first sub-step of the i+1th overall step, the dynamic response physical quantity of the engineering structure to be solved in the second sub-step of the i+1th overall step under the vibration load is determined using the following formula: Among them, U(t i+2p ), and They represent the generalized displacement vector, generalized velocity vector, and generalized acceleration vector of the second sub-step in the (i+1)th overall step, respectively. represents the unknown coefficient vector in the composite explicit time integration method, F(t i+2p ) represents the vibration load of the second sub-step of the i+1th overall step.

2. The composite explicit time domain analysis method for engineering structure vibration response according to claim 1, characterized in that: The method further includes: performing a three-step iterative solution on the engineering structure to be solved by using a composite explicit time integration method based on the dynamic control model and the structural matrix to determine the dynamic response physical quantity of the engineering structure to be solved at each overall step under the vibration load; According to the dynamic response physical quantities of the first sub-step and the second sub-step of the engineering structure to be solved in the i+1th overall step, the dynamic response physical quantity of the third sub-step of the engineering structure to be solved in the i+1th overall step under the vibration load is determined using the following formula as the dynamic response physical quantity of the engineering structure to be solved in the i+1th overall step under the vibration load: in, represents the intermediate transition vector of the i+1th overall step, U(t i+1 ), They represent the generalized displacement vector, generalized velocity vector, and generalized acceleration vector of the i+1th overall step, respectively, and α represents In the calculation formula The calculation proportional coefficient, β represents U(t i+1 ) in the calculation formula The proportional coefficients, γ and δ represent In the calculation formula The calculated proportionality coefficient and The calculation proportionality factor, F i+1 Represents the vibration load of the third sub-step of the i+1th overall step.

3. The composite explicit time domain analysis method for engineering structure vibration response according to claim 1, characterized in that: Based on the dynamic control model and the structural matrix, a composite explicit time integration method is used to perform step-by-step iterative solution on the engineering structure to be solved, and the dynamic response physical quantity of the engineering structure to be solved at each overall step under the vibration load is determined, and the above also includes: The generalized displacement vector and the generalized velocity vector at the initial moment are used as the initial generalized displacement vector and the initial generalized velocity vector; According to the initial generalized displacement vector and the initial generalized velocity vector, the initial generalized acceleration vector of the engineering structure to be solved under the vibration load is solved using the dynamic control model.

4. The composite explicit time domain analysis method for engineering structure vibration response according to claim 2, characterized in that: Based on the dynamic control model and the structural matrix, a composite explicit time integration method is used to perform a three-step iterative solution on the engineering structure to be solved, and the dynamic response physical quantity of the engineering structure to be solved at each overall step under the vibration load is determined, which also includes: Determine the free parameters of the engineering structure to be solved as:

5. The composite explicit time domain analysis method for engineering structure vibration response according to claim 1, characterized in that: Based on the dynamic control model and the structural matrix, a composite explicit time integration method is used to perform a three-step iterative solution on the engineering structure to be solved, and the dynamic response physical quantity of the engineering structure to be solved at each overall step under the vibration load is determined, which also includes: Solve the equation |K-λM|=0 and obtain multiple characteristic roots; The range of the step length of the overall step is determined based on the maximum eigenvalue among the multiple eigenvalues. Where K represents the overall stiffness matrix, M represents the overall mass matrix, λ represents the characteristic root, and λ max represents the maximum eigenvalue, Δt represents the overall step size, and l represents the stable interval parameter.

6. The composite explicit time domain analysis method for engineering structure vibration response according to claim 5, characterized in that: l＝5.508。 7. A composite explicit time-domain analysis system for the vibration response of engineering structures, characterized in that: The system is applied to the method according to any one of claims 1 to 6, and the system includes: A dynamic control model and structural matrix acquisition module is used to obtain the dynamic control model and structural matrix of the engineering structure to be solved using a spatial unit discretization method; the structural matrix includes: an overall mass matrix, an overall damping matrix, and an overall stiffness matrix; The dynamic response physical quantity iterative solution module is used to perform a three-step iterative solution on the engineering structure to be solved based on the dynamic control model and the structural matrix using a composite explicit time integration method to determine the dynamic response physical quantity of the engineering structure to be solved at each overall step under the vibration load; the dynamic response physical quantity includes a generalized displacement vector, a generalized velocity vector and a generalized acceleration vector.

8. An electronic device, characterized in that: The method comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method according to any one of claims 1 to 6 when executing the computer program.

9. A computer-readable storage medium, characterized in that The storage medium stores a computer program, which implements the method according to any one of claims 1 to 6 when executed.

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