Simulation solving method for elastic dynamic problem of engineering structure

Abstract

The invention provides an engineering structure elastodynamic problem simulation solving method, which comprises the following steps: writing a corresponding elastodynamic problem control equation in a defined bounded domain, and solving a computational domain integral; dispersing boundaries into elements through a linear integration method of domain integration, obtaining LIM by using background cells, and applying IIMLS to an estimated node value to obtain a shape function; and through a discretization formula, time response is obtained by adopting NewMarkscheme, so that the function of simulating and solving the elastic power problem of the engineering structure is realized. According to the method, the position of the integral point on an integral line does not need to be judged by adopting an out-of-domain approximation integral point method; the method is applied to analyzing and optimizing the problems of dynamic response, deformation and the like of the engineering structure, the accuracy and the effectiveness of a solving result are high, then the structural dynamics problem in actual engineering is analyzed, the problems of dynamic response, deformation and the like of the engineering structure are controlled, and the safety and the reliability of the engineering structure are ensured.

Description

Technical Field

[0001] The invention belongs to the technical field of elastic dynamics problems, and in particular relates to a simulation and solution method for elastic dynamics problems of engineering structures. Background Art

[0002] With the continuous development of computers, it is becoming more and more important to use numerical methods to solve engineering problems. The two most popular numerical methods are the finite element method and the boundary element method. The finite element method is suitable for various irregular geometric shapes and complex boundary conditions, and requires the area to be meshed, but it may cause serious distortion when dealing with some large and complex problems; the boundary element method divides the boundary of the problem domain into many small boundary elements, and performs mathematical modeling and calculations on each boundary element. It only needs to discretize the boundary, avoiding internal discretization, reducing the dimension of the problem, and can automatically meet the boundary conditions at infinity. It has higher accuracy for solving problems in infinite and semi-infinite domains.

[0003] Boundary Element Method (BEM) is a new calculation method that emerged in the 1970s. It takes the generalized displacement and generalized force on the boundary as independent variables and uses the singular function that satisfies the field equation as the weighting function. It is a special format of weighted residual method.

[0004] The boundary element method only needs to divide the boundary of the solution domain into units, so the dimension of the problem to be solved becomes lower. For problems that only need to find boundary values, the physical quantities in the region are not calculated to improve efficiency. In addition, the boundary element method can automatically meet the boundary conditions at infinity, which is suitable for solving problems in infinite and semi-infinite domains, and has higher solution accuracy. BEM only requires boundary discretization, and has the advantages of dimensionality reduction, high calculation accuracy, and no connectivity requirements for grid nodes, making it widely used in solving practical problems, such as elasticity problems, cracks and crack propagation, and transient heat transfer problems.

[0005] In the application of BEM in transient elastic dynamic response, the more commonly used methods are time domain method, frequency domain method and double reciprocity method. However, the introduction of additional transformations and numerical integration will reduce the computational efficiency and accuracy of the frequency domain method and the double reciprocity method.

[0006] Domain integration is the process of integrating a multivariable function in a given area. The calculation of domain integration usually requires appropriate segmentation of the integration area, then integrating each segmented area, and finally adding up the integration results to get the final domain integration result. For complex areas and functions, numerical methods or computer-aided methods are required for approximate calculations. The processing of domain integration generally requires dividing the grid within the domain to discretize the region. Although the number of unknowns does not increase, the advantage of the boundary element method that does not require internal grid division is lost, and the amount of calculation is large. Usually, the entire solution domain needs to be discretized into many small areas for numerical calculation.

[0007] The entire solution domain is discretized using the domain integration method, and the boundary element method is used to perform integral calculations on the boundary. In this way, the domain integration can more accurately describe the behavior of the entire solution domain, and the boundary element method can more conveniently deal with the influence of boundary conditions. It can fully utilize the advantages of domain integration and boundary element method, reduce the amount of calculation, and more effectively simulate complex boundary value problems. Summary of the invention

[0008] The technical problem to be solved by the present invention is to provide a simulation solution method for elastic dynamic problems of engineering structures, which is used for simulating and solving elastic dynamic problems of engineering structures.

[0009] The technical solution adopted by the present invention to solve the above technical problems is: a simulation method for solving elastic dynamic problems of engineering structures, comprising the following steps:

[0010] S1: Collect data including displacement, velocity and acceleration of the engineering structure to be evaluated;

[0011] S2: Establish the model to be solved, input the model including information of material parameters, meshing fraction, mesh type and boundary conditions, and output model data information;

[0012] S3: Establish the governing equations of the elastic dynamics problem in the defined bounded domain based on the relationship between stress, strain and displacement;

[0013] S4: Establish boundary integral equations and solve the integral in the computational domain;

[0014] S5: Based on the divergence theorem, the domain integral is transformed into a boundary integral containing a one-dimensional line integral; the boundary is discretized into elements and the background cells are used to obtain the LIM, and the IIMLS is applied to the estimated node values ​​to obtain the shape function;

[0015] S6: The finite element discretization format is established through the discretization formula, and the Newmark scheme is used to obtain the time response simulation to solve the elastic dynamic problem of the engineering structure.

[0016] According to the above scheme, in step S3, the specific steps are:

[0017] set up is a boundary is a bounded domain, x{x1,x2} is a point on Ω, σ ij (x) is the stress tensor, i,j = 1,2; let u i (x) is the displacement, b i (x) is the body force, c is the damping coefficient, ρ is the density of the material, and the dot represents the derivative with respect to time; the governing equation of the elastic dynamics problem is:

[0018]

[0019] Furthermore, in step S3, μ=E / (1+v) / 2 is the shear modulus, λ=2vμ / (1-2v) is the Lame constant, E is the elastic modulus, v is the Poisson's ratio, ε kl are the components of the strain tensor, C ijkl is the elastic tensor component, δ ij , δ kl , δ ik , δ jl , δ il , δ jk is the Kronecker function; i, j, k, l are subscript values, which are 1, 2 in two-dimensional problems and 1, 2, 3 in three-dimensional problems; then the stress σ ij The relationship among (x), strain ε(x) and displacement u(x) is:

[0020] σ ij (x) = C ijkl ε kl (x) (43),

[0021]

[0022] C ijkl =λδ ij δ kl +μ(δ ik δ jl +δ il δ jk ) (45).

[0023] Furthermore, in step S3, the Kronecker function δ ij The definition is

[0024]

[0025] Assume Γ u is the Dirichlet frontier with displacement u i use Instead, Γ t is the Neumann boundary, the traction force t i use Instead, and Γ=Γ u ∪Γ t ; The boundary conditions are:

[0026]

[0027] and are the initial displacement and initial velocity at the initial time t0 respectively; the initial conditions are:

[0028]

[0029] Furthermore, in step S4, the specific steps are:

[0030] Let U(x,y) and T(x,y) be the Kelvin fundamental solution; c(x) is the 2×2 coefficient matrix relative to the position of point x, and c is 0 in the absence of body force; the integral equation is:

[0031]

[0032] Furthermore, in step S4, let r = r(x, y) be the distance between points x and y, r ,i To find the derivative in the i direction, r ,k is the derivative in the k direction, n is the unit external normal vector at the boundary point, n i is the component of n in the i direction, n k is the component of n in the k direction, δ ki is the Kronecker function; then the component U of the basic solution of the plane problem ki and T ki They are:

[0033]

[0034] For plane stress problems, use the following and Substitute v and E in equations (11) and (12) respectively:

[0035]

[0036] In formula (10), the computational domain integral is:

[0037]

[0038] Furthermore, in step S5, the specific steps are:

[0039] Let Ω be is a bounded domain with a Bekenstein boundary, and f(y) is a function defined on a compact domain. Let g(y) be the function of f(y) on any The continuation of region B, where g(y) is bounded, is is continuous everywhere in; the function a=a(y2) is finite, let point s{s,y2} be in B, n1 be part of the unit external normal n in the direction of Γy1 axis; for At any point in , there is:

[0040]

[0041] Let χ(y) be any bounded function, and is almost continuous everywhere in B; f(y) is a function with a weak singular kernel, and equation (15) also holds; without loss of generality, the specified function f(y) is extended to B:

[0042]

[0043] a(y2) is arbitrary and corresponds only to y2, then let a(y2) be a constant value; point y 0 {a,y2} is inside or outside the region Ω, or on the boundary of Γ; set χ(y) = f(y) or set the range of f(y) to

[0044] Let M be the total number of integral sub-lines, L i is the ith sub-circuit, and w i is the unit external normal and subline L in the y1 direction i The weight is obtained by the integration points corresponding to each boundary element; discretizing the boundary into elements and using the background cells, the LIM is obtained as:

[0045]

[0046] Applying equation (18), the domain integral in equation (14) is calculated by LIM as:

[0047]

[0048] Furthermore, in step S5, Φ j (y) is the shape function obtained by IIMLS, is the node value of the jth node, N = N b +N c is the total number of nodes in the domain, where N b is the number of boundary nodes, N cis the number of nodes in the domain; IIMLS is applied to estimate the node value for:

[0049]

[0050] Each point has a local influence domain when there are at least j nodes in the local influence domain, and Φ j (y)≠0;

[0051] If there are not enough nodes in the local domain, Set to 0;

[0052] Rewrite equation (19) as:

[0053]

[0054] in

[0055]

[0056] Furthermore, in step S6, the specific steps are:

[0057] set up and YesN b Node values ​​at boundary nodes:

[0058]

[0059] Let x k is a boundary node, k is from 1 to N b , l is 1 to N; let is a 2N b ×2N matrix, defined as:

[0060]

[0061] Let matrix and is the coefficient matrix obtained by the boundary element integration on the traditional BEM; the discretization formula (10) using the boundary element method on the traditional BEM is obtained:

[0062]

[0063] set up and is a 2N obtained by integrating over the boundary element c ×2N b The source point is the internal node; is the displacement of the interior point:

[0064]

[0065] is a 2N defined by equation (27) c ×2N matrix, the difference is that x k is the integration node;

[0066] For the nodes in Ω, applying the integral formula (10) yields:

[0067]

[0068] Assume I is the unit matrix, then from equations (24) and (28) we have:

[0069]

[0070] Assume H and M are 2N×2N matrices, G is a 2N×2N b , u is the displacement of boundary nodes and internal nodes, and equation (30) is simplified as:

[0071]

[0072] The Newmark scheme is used to obtain the time response of equation (31). Let Δt be the time step, and for each time step, the following equation is obtained:

[0073]

[0074] Furthermore, in step S6, the basic assumption of Newmarkscheme is

[0075]

[0076] Assuming γ and β are calculation parameters, we can obtain from equations (33) and (34) at time t+Δt: and for:

[0077]

[0078] Substituting equation (36) into (32), we obtain:

[0079]

[0080] in

[0081]

[0082] The beneficial effects of the present invention are:

[0083] 1. A simulation method for solving the elastic dynamic problem of an engineering structure of the present invention, by writing the corresponding elastic mechanics problem control equation in a defined bounded domain, specifically solving the computational domain integral, by the line integral method of the domain integral, without loss of generality, discretizing the boundary into elements and using background cells to obtain LIM, and applying IIMLS to the estimated node value, obtaining the shape function by IIMLS, through the discretization formula, using the boundary element method on the traditional BEM discretization integral formula, using the Newmark scheme to obtain the time response, realizing the function of simulating and solving the elastic dynamic problem of the engineering structure.

[0084] 2. The method of approximating the integral point outside the domain adopted by the present invention has the advantage of not needing to judge the position of the integral point on the integral line.

[0085] 3. The IIMLS used in the present invention for estimating node values ​​is a local approximation method and is a better choice in large-scale calculations.

[0086] 4. The present invention is applied to analyze and optimize the dynamic response and deformation of engineering structures. The solution has extremely high accuracy and effectiveness, and can analyze the structural dynamics problems in actual engineering projects, and constantly control the dynamic response and deformation of engineering structures to ensure the safety and reliability of engineering structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 1 is a diagram showing the appearance of a device according to an embodiment of the present invention.

[0088] Figure 2 4 is a flow chart of an elastic dynamics simulation solver according to an embodiment of the present invention.

[0089] Figure 3 Schematic diagram of the model and boundary conditions of an embodiment of the present invention.

[0090] Figure 4 It is a comparison chart between the analytical value calculated by the boundary element method of an embodiment of the present invention and the numerical solution of the simulator. DETAILED DESCRIPTION

[0091] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0092] See also Figure 2 , an embodiment of the present invention comprises the following steps:

[0093] Step 1: Use displacement detectors, velocity detectors, and acceleration detectors to detect the displacement, velocity, and acceleration of the engineering structure to be evaluated.

[0094] Step 2: Use modeling software to establish the model to be solved, input the model's material parameters, meshing fraction, mesh type, boundary conditions and other information, and then output the model data information file.

[0095] Step 3: Establish the governing equations for the elastic dynamic problem

[0096] Assumptions is a boundary For a bounded domain, the governing equation for elastic dynamics can be written as:

[0097]

[0098] where x{x1,x2} is a point on Ω, σ ij (x) is the stress tensor, where i,j = 1,2. i (x) is the displacement, b i (x) is the body force, c is the damping coefficient, ρ is the density of the material, and the dot represents the derivative with respect to time.

[0099] Stress σ ij The relationship between (x), strain ε(x), and displacement u(x) is:

[0100] σ ij (x) = C ijkl ε kl (x) (84)

[0101]

[0102] and

[0103] C ijkl =λδ ij δ kl +μ(δ ik δ jl +δ il δ jk ) (86)

[0104] Where μ = E / (1+v) / 2 is the shear modulus, λ = 2vμ / (1-2v) is the Lame constant, E is the elastic modulus, v is the Poisson's ratio, ε kl are the components of the strain tensor, C ijkl is the elastic tensor component. ij is the Kronecker function, defined as

[0105]

[0106] i, j, k, and l are the subscript values ​​of the Kronecker function, which are 1 and 2 in two-dimensional problems and 1, 2, and 3 in three-dimensional problems.

[0107] This problem can be solved using boundary conditions:

[0108]

[0109] and initial conditions

[0110]

[0111] where Γ u is the Dirichlet frontier with displacement u i use Instead, Γ t is the Neumann boundary, the traction force t i use Instead, and Γ=Γ u ∪Γ t . and are the initial displacement and initial velocity at the initial time t0 respectively.

[0112] Step 4: Establish the boundary integral equation

[0113] In the absence of physical strength, set c to 0, and the integral equation can be obtained as:

[0114]

[0115] where c(x) is a 2×2 coefficient matrix relative to the position of point x, U(x,y) and T(x,y) are the Kelvin fundamental solutions, and the components of the fundamental solution for plane problems are U ki and T ki They are:

[0116]

[0117]

[0118] Where r = r(x, y) is the distance between points x and y, r ,i To find the derivative in the i direction, r ,k is the derivative in the k direction, n is the unit external normal vector at the boundary point, n i is the component of n in the i direction, n k is the component of n in the k direction, δ ki is the Kronecker function. For plane stress problems, this can be expressed as follows and to replace v and E in equations (93) and (94).

[0119]

[0120] In formula (92), the domain integral needs to be calculated as

[0121]

[0122] Step 5: Convert domain integrals to boundary integrals

[0123] At present, there are three main methods for processing and calculating domain integrals in the boundary element method: 1) using the Gaussian integral method or the Monte Carlo method to directly calculate the domain integral; 2) for relatively simple loads, the domain integral can be eliminated by the special solution method; 3) for the Green formula, the domain integral is converted into a boundary integral. In method 3, the domain integral is converted into a boundary integral, and the integral dimension is reduced by one dimension, which can greatly save the calculation time.

[0124] The straight line integral method is based on the divergence theorem. It transforms the domain integral into a boundary integral containing a one-dimensional straight line integral. By discretizing the boundary into units, it finally obtains a method for calculating the domain integral containing only a one-dimensional straight line integral.

[0125] The LIM is obtained by discretizing the boundary into elements and using the background cells.

[0126] Assume Ω is is a bounded domain with a Bekenstein boundary, and f(y) is a function defined on a compact domain. Let g(y) be the function of f(y) on any The continuation of region B, where g(y) is bounded, is is continuous everywhere in . Then for At any point in

[0127]

[0128] and

[0129]

[0130] where the function a = a(y2) is finite, the point s{s,y2} is in B, and n1 is part of the unit external normal n in the direction of the Γy1 axis. Without loss of generality, the specified function f(y) can be extended to B

[0131]

[0132] where χ(y) can be any bounded function and is almost continuous everywhere in . f(y) can be a function with a weakly singular kernel, and equation (97) also holds.

[0133] Since a(y2) is arbitrary and corresponds only to y2, we can set a(y2) to a constant value. 0{a,y2} can be inside or outside the region Ω, or on the boundary of Γ. Most importantly, the function χ(y) has little effect on the integral result, so it is convenient to simply set χ(y) = f(y) or set the range of f(y) to

[0134] Finally, discretizing the boundary into elements and using the background cells, we can get the LIM as

[0135]

[0136] Where M is the number of total integral sub-lines, L i is the ith sub-circuit, and w i is the unit external normal and subline L in the y1 direction i The weight is obtained by the integration point corresponding to each boundary element.

[0137] Applying equation (100), the domain integral in equation (96) can be calculated by LIM as

[0138]

[0139] In formula (101), Since the integral cannot be calculated directly, IIMLS is applied to estimate the node value. As shown below

[0140]

[0141] where Φ j (y) is the shape function obtained by IIMLS, is the node value of the jth node, N = N b +N c is the total number of nodes in the domain, where N b is the number of boundary nodes, N c is the number of nodes in the domain.

[0142] In the actual calculation of formula (102), each point has a local influence domain only when the jth node is within the local influence domain, and Φ j (y)≠0. This can be performed simply and directly if the integration point y on the integration line is on the domain. However, in LIM, the integration point y may be outside the domain Ω. For this case, we still apply Eq. (102) to approximate the unknown function, because the value of the integration kernel outside the integration domain has little effect on the final domain integral. In Eq. (102), Φ can only be obtained if there are enough nodes in the local influence domain. j (y), therefore, if there are not enough nodes in the local domain, Simply set it to 0.

[0143] The above method of approximating the integration point outside the domain may reduce the accuracy, however, its advantage is that it does not need to judge the position of the integration point on the integral line. In addition, IIMLS is a local approximation method and is a good choice in large-scale calculations.

[0144] Now equation (101) can be written as

[0145]

[0146] in

[0147]

[0148] Step 6: Establish the finite element discretization format

[0149] Using the boundary element method discretization formula (92) on the traditional BEM, we can get

[0150]

[0151] The matrix and It is the coefficient matrix obtained by boundary element integration on traditional BEM. and YesN b The node values ​​on the boundary nodes are as follows

[0152]

[0153] is a 2N b ×2N matrix, defined as

[0154]

[0155] where x k is a boundary node, k is from 1 to N b , l is 1 to N.

[0156] Equation (106) cannot be solved because the number of unknowns is greater than the number of equations, and N is required. c For the nodes in Ω, applying the integral formula (92), we can get

[0157]

[0158] in and is a 2N obtained by integrating over the boundary element c ×2N b The source point is the internal node. is the displacement of the internal point

[0159]

[0160] is a 2N defined by equation (109) c ×2N matrix, the difference is that x k is the integration node.

[0161] Then from equations (106) and (110), we can have

[0162]

[0163] Where I is the identity matrix, equation (112) can be simply written as

[0164]

[0165] Where H and M are 2N×2N matrices, and G is a 2N×2N b , and u is the displacement of the boundary nodes and internal nodes.

[0166] The Newmark scheme is used to obtain the time response of equation (113). For each time step, the following equation can be obtained:

[0167]

[0168] Where Δt is the time step.

[0169] The basic assumption of the Newmark scheme is

[0170]

[0171] Where γ and β are calculated parameters. According to equations (115) and (116), we can get and for

[0172]

[0173] Substituting equation (118) into (114), we can obtain

[0174]

[0175] in

[0176]

[0177] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0178] The above embodiments are only used to illustrate the design ideas and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design ideas disclosed by the present invention are within the protection scope of the present invention.

Claims

1. A simulation method for solving elastic dynamic problems of engineering structures, characterized by: The following steps are involved: S1: Collect data including displacement, velocity and acceleration of the engineering structure to be evaluated; S2: Establish the model to be solved, input the model including information of material parameters, meshing fraction, mesh type and boundary conditions, and output model data information; S3: Establish the governing equations of the elastic dynamics problem in the defined bounded domain based on the relationship between stress, strain and displacement; S4: Establish boundary integral equations and solve the integral in the computational domain; S5: Based on the divergence theorem, the domain integral is transformed into a boundary integral containing a one-dimensional line integral; the boundary is discretized into elements and the background cells are used to obtain the LIM, and the IIMLS is applied to the estimated node values ​​to obtain the shape function; S6: The finite element discretization format is established through the discretization formula, and the Newmark scheme is used to obtain the time response simulation to solve the elastic dynamic problem of the engineering structure.

2. A method for simulating and solving elastic dynamic problems of engineering structures according to claim 1, characterized in that: In the step S3, the specific steps are: set up is a boundary is a bounded domain, x{x1,x2} is a point on Ω, σ ij (x) is the stress tensor, i,j = 1,2; let u i (x) is the displacement, b i (x) is the body force, c is the damping coefficient, ρ is the density of the material, and the dot represents the derivative with respect to time; the governing equation of the elastic dynamics problem is:

3. A method for simulating and solving elastic dynamic problems of engineering structures according to claim 2, characterized in that: In step S3, μ = E / (1+v) / 2 is the shear modulus, λ = 2vμ / (1-2v) is the Lame constant, E is the elastic modulus, v is the Poisson's ratio, ε kl is the component of the strain tensor, C ijkl is the elastic tensor component, δ ij , δ kl , δ ik , δ jl , δ il , δ jk is the Kronecker function; i, j, k, l are subscript values, which are 1, 2 in two-dimensional problems and 1, 2, 3 in three-dimensional problems; then the stress σ ij The relationship among (x), strain ε(x) and displacement u(x) is: s ij (x)=C ijkl e kl (x) (2), C ijkl =λδ ij d kl +μ(d ik d jl +d il d jk ) (4).

4. A method for simulating and solving elastic dynamic problems of engineering structures according to claim 3, characterized in that: In step S3, the Kronecker function δ ij The definition is Assume Γ u is the Dirichlet frontier with displacement u i use Instead, Γ t is the Neumann boundary, the traction force t i use Instead, and Γ=Γ u ∪Γ t ; The boundary conditions are: and are the initial displacement and initial velocity at the initial time t0 respectively; the initial conditions are:

5. The method for simulating and solving elastic dynamic problems of engineering structures according to claim 2, characterized in that: In the step S4, the specific steps are: Let U(x,y) and T(x,y) be the Kelvin fundamental solution; c(x) is the 2×2 coefficient matrix relative to the position of point x, and c is 0 in the absence of body force; the integral equation is:

6. A method for simulating and solving elastic dynamic problems of engineering structures according to claim 5, characterized in that: In step S4, let r = r(x, y) be the distance between points x and y, r ,i To find the derivative in the i direction, r ,k is the derivative in the k direction, n is the unit external normal vector at the boundary point, n i is the component of n in the i direction, n k is the component of n in the k direction, δ ki is the Kronecker function; then the component U of the basic solution of the plane problem ki and T ki They are: For plane stress problems, use the following and Substitute v and E in equations (11) and (12) respectively: In formula (10), the computational domain integral is:

7. A method for simulating and solving elastic dynamic problems of engineering structures according to claim 6, characterized in that: In the step S5, the specific steps are: Let Ω be is a bounded domain with a Bekenstein boundary, and f(y) is a function defined on a compact domain. Let g(y) be the function of f(y) on any The continuation of region B, where g(y) is bounded, is is continuous everywhere in; the function a=a(y2) is finite, let point s{s,y2} be in B, n1 be part of the unit external normal n in the direction of Γy1 axis; for At any point in , there is: Let χ(y) be any bounded function, and is almost continuous everywhere in B; f(y) is a function with a weak singular kernel, and equation (15) also holds; without loss of generality, the specified function f(y) is extended to B: a(y2) is arbitrary and corresponds only to y2, then let a(y2) be a constant value; point y 0 {a,y2} is inside or outside the region Ω, or on the boundary of Γ; set χ(y) = f(y) or set the range of f(y) to Let M be the number of total integral sub-lines, L i is the ith sub-circuit, and w i is the unit external normal and subline L in the y1 direction i The weight is obtained by the integration points corresponding to each boundary element; discretizing the boundary into elements and using the background cells, the LIM is obtained as: Applying equation (18), the domain integral in equation (14) is calculated by LIM as:

8. A method for simulating and solving elastic dynamic problems of engineering structures according to claim 7, characterized in that: In the step S5, Φ j (y) is the shape function obtained by IIMLS, is the node value of the jth node, N = N b +N c is the total number of nodes in the domain, where N b is the number of boundary nodes, N c is the number of nodes in the domain; IIMLS is applied to estimate the node value for: Each point has a local influence domain when there are at least j nodes in the local influence domain, and Φ j (y)≠0; if there are not enough nodes in the local domain, Set to 0; Rewrite equation (19) as: in 9. The method for simulating and solving elastic dynamic problems of engineering structures according to claim 5, characterized in that: In the step S6, the specific steps are: set up and YesN b Node values ​​at boundary nodes: Let x k is a boundary node, k is from 1 to N b , l is 1 to N; let is a 2N b ×2N matrix, defined as: Let matrix and is the coefficient matrix obtained by the boundary element integration on the traditional BEM; the discretization formula (10) using the boundary element method on the traditional BEM is obtained: set up and is a 2N obtained by integrating over the boundary element c ×2N b The source point is the internal node; is the displacement of the interior point: is a 2N defined by equation (27) c ×2N matrix, the difference is that x k is the integration node; For the nodes in Ω, applying the integral formula (10) yields: Assume I is the unit matrix, then from equations (24) and (28) we have: Assume H and M are 2N×2N matrices, G is a 2N×2N b , u is the displacement of boundary nodes and internal nodes, and equation (30) is simplified as: The Newmark scheme is used to obtain the time response of equation (31). Let Δt be the time step, and for each time step, the following equation is obtained:

10. A method for simulating and solving elastic dynamic problems of engineering structures according to claim 9, characterized in that: In step S6, the basic assumption of Newmarkscheme is Assuming γ and β are calculation parameters, we can obtain from equations (33) and (34) at time t+Δt: and for: Substituting equation (36) into (32), we obtain: in

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