A high performance simulation method for heat conduction and thermal stress of non-uniform half-space embankment

Abstract

A high-performance simulation method for heat conduction and thermal stress of embankment in non-homogeneous half-space. Based on the principle of geometric similarity transformation, the method constructs a scaling boundary modeling strategy, introduces a scaling line coordinate system, realizes the spatial mapping of Cartesian coordinates to scaling coordinates, and uses the Jacobian matrix to complete the coordinate transformation of differential operators, thereby accurately representing the non-uniform characteristics of the medium material. The Galerkin method is used to establish the control equation, and the semi-analytical solution technique is used to obtain the temperature field distribution; then the fourth-order Runge-Kutta algorithm is used for reverse iteration to further calculate the thermal stress field caused by the temperature field. The invention can effectively solve the problems of high calculation cost, complex boundary modeling and poor interface continuity of existing numerical methods in non-homogeneous media. It has high computational efficiency, excellent numerical stability and high precision characteristics, and is suitable for thermal-mechanical coupling analysis of complex engineering structures such as multi-layer foundation, embankment-water-foundation coupling system, etc.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of heat conduction and thermal stress analysis, and particularly relates to a high-performance simulation method for heat conduction and thermal stress of a non-uniform half-space embankment. BACKGROUND

[0002] In embankment engineering, heat conduction and thermal stress problems have an important influence on the safety and stability of the structure. Due to the effects of sunshine, air temperature changes and water temperature differences, a significant temperature gradient will be generated inside the embankment, thereby causing uneven thermal stress distribution. Excessive thermal stress can cause embankment cracking, leakage or structural deformation, thereby affecting the flood control safety and long-term service performance of the embankment. Therefore, carrying out high-precision and high-efficiency thermal-mechanical coupling analysis for a non-homogeneous half-space embankment has important theoretical significance and engineering application value for ensuring the safety and durability of the embankment engineering.

[0003] At present, the commonly used numerical methods such as the finite element method (FEM) and the boundary element method (BEM) have obvious limitations in dealing with semi-infinite domains or non-uniform media: the finite element method needs to divide the whole domain into grids, and the calculation scale is large; the boundary element method reduces the discrete quantity, but the precision is insufficient in complex layered interfaces or non-uniform materials. The analytical method has high precision, but it is only suitable for simple geometry and uniform medium, and it is difficult to deal with actual complex engineering. The traditional scaled boundary finite element method (SBFEM) in multi-domain and layered heterogeneous systems has inconsistent local coordinate systems, and the interface continuity is difficult to guarantee, thereby limiting the calculation precision and stability.

[0004] Therefore, the present application provides a high-performance simulation method for heat conduction and thermal stress of a non-uniform half-space embankment. The method introduces a scaled boundary modeling strategy based on geometric similarity transformation, realizes the interlayer continuity and boundary consistency through coordinate mapping; combined with time domain integration and high-order matrix recursive algorithm, the degrees of freedom and calculation amount can be significantly reduced while maintaining the calculation stability. The method can accurately simulate the temperature field and stress field distribution in complex foundation, rock mass and structure, and provides an efficient and reliable numerical analysis method for half-space thermal-mechanical coupling problems. SUMMARY

[0005] The main purpose of the present application is to provide a high-performance simulation method for heat conduction and thermal stress of a non-uniform half-space embankment, to solve the technical problems of high calculation cost, insufficient processing capacity of heterogeneous media and complex boundary condition modeling in the prior art.

[0006] To achieve the above purpose, the present application provides a high-performance simulation method for heat conduction and thermal stress of a non-uniform half-space embankment, which comprises the following steps:

[0007] S1. Construct a coordinate system based on similar lines to describe the geometry of the non-uniform half-space embankment. By introducing similar lines parallel to the boundary lines, establish a spatial mapping relationship from the Cartesian coordinate system to the proportional boundary SBFEM coordinate system, forming radial coordinates in the SBFEM coordinate system. ξ and circumferential coordinates η, and radial coordinates ξ Achieve a normalized transition from similar lines to boundary lines, circumferential coordinates η Discretize along the boundary line to obtain the coordinates of any point in the problem domain in the SBFEM coordinate system.

[0008] S2. After establishing a coordinate system based on similar lines, the coordinate transformation of the differential operator is realized through the Jacobian matrix, and the spatial partial derivatives in the Cartesian coordinate system are accurately mapped to the SBFEM coordinate system. Based on the relationship between the Cartesian coordinate system and the SBFEM coordinate system, the differential operator expression required for the heat conduction control equation is derived, and the sub-coefficient matrix in the SBFEM coordinate system is formed accordingly.

[0009] S3. Based on Laplace's law, obtain the two-dimensional steady-state heat conduction control equations and boundary conditions, and plot the temperature field along the circumferential coordinate system. η Discretized using one-dimensional higher-order spectral unit shape functions, along radial coordinates ξ To maintain continuity, the Galerkin method is used to handle the heat conduction control equations and boundary conditions, and the surface integral is transformed into a boundary integral. Through integration by parts and Green's theorem, the radial coordinates in the SBFEM coordinate system are derived step by step. ξ The second-order linear nonhomogeneous ordinary differential equation is derived, and the governing equation of the steady-state heat conduction matrix in the SBFEM coordinate system is derived by using the principle of virtual work based on the relationship between temperature and heat flux.

[0010] S4. Based on the relationship between the far-field coefficient matrix and the problem domain coefficient matrix, the following is derived: The governing equations for heat conduction approaching infinity are derived by solving the eigenvalue problem of the Hamiltonian matrix at infinity. This infinity-based heat conduction matrix is ​​then used as an initial value, and a fourth-order Runge-Kutta algorithm is applied. By selecting a step size and gradient, the algorithm iteratively updates the heat conduction matrix from the far field towards the boundary line until convergence. ξ The boundary value is equal to 1, and the temperature field of the entire problem domain is further obtained.

[0011] S5, based on the calculated temperature field, the thermal strain is calculated, and the constitutive relation is established based on the Hook's law, the corresponding relationship between the thermal strain and the thermal stress in the SBFEM coordinate system is obtained, the internal force virtual work expression caused by temperature is constructed, the non-homogeneous control equation with displacement as the unknown quantity is derived by applying the virtual work principle, and the first-order linear differential equation is obtained by Shur decomposition, the homogeneous solution and the particular solution of the first-order linear differential equation are solved, and the displacement field general solution of the equation is obtained by superimposing the two, so that the corresponding thermal stress field distribution is obtained.

[0012] The beneficial effects of the present application are:

[0013] (1) The present application effectively avoids the geometric discretization problem of traditional methods when dealing with heterogeneous media by introducing scaling line coordinate transformation, significantly improving the calculation efficiency and local accuracy;

[0014] (2) The present application combines Galerkin method with Runge-Kutta algorithm to realize semi-analytical solution of heat conduction and thermal stress problem, which has numerical stability and high precision;

[0015] (3) The present application is suitable for various complex embankment engineering scenes, such as layered foundation embankment system, dam-river-ground coupling system, etc., and has good universality and engineering applicability. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 It is a high-performance simulation method flowchart for uneven half-space embankment heat conduction and thermal stress.

[0017] Figure 2 It is Figure 1 The schematic diagram shown in (a) is the space mapping between the Cartesian coordinate system and the SBFEM coordinate system; (b) is the sub-element transformation between the Cartesian coordinate system and the SBFEM coordinate system.

[0018] Figure 3 It is a calculation model and element discretization schematic diagram of the first embodiment: (a) calculation model schematic diagram; (b) element discretization schematic diagram.

[0019] Figure 4 It is a temperature value comparison diagram of the first embodiment calculated by the present application and other methods: (a) y =1, temperature value comparison under different x coordinates; (b) x =0, temperature value comparison under different y coordinates.

[0020] Figure 5 It is a calculation model and element discretization schematic diagram of the second embodiment dam-reservoir-foundation system: (a) calculation model schematic diagram; (b) element discretization schematic diagram. DETAILED DESCRIPTION

[0021] It should be understood that the specific embodiments described herein are merely exemplary and do not limit the present application. The purpose of the present application, functional features and advantages will be further illustrated with reference to the accompanying drawings.

[0022] As shown in the accompanying drawings, Figure 1 The flowchart of the high-performance simulation method for uneven half-space embankment heat conduction and thermal stress of the present application is shown in the figure; Figure 2 The flowchart of the high-performance simulation method for uneven half-space embankment heat conduction and thermal stress of the present application is shown in the figure; Figure 1 The schematic diagram is shown in the figure; Figure 3 The schematic diagram of the calculation model and unit discretization of the first embodiment is shown in the figure; Figure 4 The comparison chart of the temperature values calculated by the method of the present application and other methods for the first embodiment is shown in the figure; Figure 5 The schematic diagram of the calculation model and unit discretization of the second embodiment is shown in the figure.

[0023] S1, a coordinate system based on similar lines is constructed to describe the geometry of the uneven half-space embankment, a spatial mapping relationship from the Cartesian coordinate system to the proportional boundary SBFEM coordinate system is established by introducing similar lines parallel to the boundary line, forming the radial coordinate ξ and the ring coordinate η, in the SBFEM coordinate system, and the radial coordinate ξ is normalized to realize the transition from the similar line to the boundary line, and the ring coordinate η is discretized along the boundary line to obtain the coordinates of any point in the problem domain in the SBFEM coordinate system.

[0024] S2, after the coordinate system based on similar lines is established, the coordinate transformation of differential operators is realized through the Jacobian matrix to accurately map the spatial partial derivatives in the Cartesian coordinate system to the SBFEM coordinate system, the differential operator expression required by the heat conduction control equation is derived according to the relationship between the Cartesian coordinate system and the SBFEM coordinate system, and the sub-coefficient matrix in the SBFEM coordinate system is formed accordingly.

[0025] S3, based on the Laplace law, the heat conduction control equation and boundary conditions of two-dimensional steady state are obtained, and the temperature field along the ring coordinate η is discretized using one-dimensional high-order spectral element shape functions, and the radial coordinate ξ is kept continuous, the heat conduction control equation and boundary conditions are processed using the Galerkin method, and the area integral is converted into boundary integral, and through step-by-step derivation by partial integration and Green's theorem, the second-order linear non-homogeneous ordinary differential equation about the radial coordinate ξ in the SBFEM coordinate system is obtained, and then according to the relationship between temperature and heat flux, the control equation of the steady-state heat conduction matrix in the SBFEM coordinate system is derived by using the virtual work principle.

[0026] S4. Based on the relationship between the far-field coefficient matrix and the problem domain coefficient matrix, the following is derived: The governing equations for heat conduction approaching infinity are derived by solving the eigenvalue problem of the Hamiltonian matrix at infinity. This infinity-based heat conduction matrix is ​​then used as an initial value, and a fourth-order Runge-Kutta algorithm is applied. By selecting a step size and gradient, the algorithm iteratively updates the heat conduction matrix from the far field towards the boundary line until convergence. ξ The boundary value is equal to 1, and the temperature field of the entire problem domain is further obtained.

[0027] S5. Calculate the thermal strain based on the known temperature field, establish the constitutive relation using Hooke's law, obtain the correspondence between thermal strain and thermal stress in the SBFEM coordinate system, construct the virtual work expression for internal forces caused by temperature, derive the non-homogeneous governing equation with displacement as the unknown quantity using the principle of virtual work, obtain the first-order linear differential equation through Schul decomposition, solve the homogeneous solution and particular solution of the first-order linear differential equation, and superimpose the two to obtain the general solution of the displacement field of the equation, thereby obtaining the corresponding thermal stress field distribution.

[0028] Furthermore, in step S1, a coordinate system based on similar lines is constructed to describe the geometry of the heterogeneous half-space embankment. By introducing similar lines parallel to the boundary lines, a spatial mapping relationship from the Cartesian coordinate system to the SBFEM coordinate system is established.

[0029]

[0030] in, and This represents the coordinates of a point within the problem domain in the SBFEM coordinate system. and This represents the coordinates of a point on a line of similarity in the Cartesian coordinate system. and This represents the coordinates of a point on the boundary line in the Cartesian coordinate system.

[0031] Furthermore, the radial coordinates formed in the SBFEM coordinate system ξ and circumferential coordinates η and radial coordinates ξ Achieve a normalized transition from similar lines to boundary lines, circumferential coordinates η Discretize along the boundary line:

[0032]

[0033] in The shape function of the line element; and These are the node coordinate vectors of similar line nodes within the line element; and A node coordinate vector representing a node of a line element inner boundary line.

[0034] Further, the coordinates of any point in the problem domain in the SBFEM coordinate system are obtained:

[0035] .

[0036] Further, in the step S2, after the coordinate system based on the similar line is established, the coordinate transformation of the differential operator is realized by the Jacobian matrix, so as to accurately map the spatial partial derivative in the Cartesian coordinate system into the SBFEM coordinate system, and the specific process is as follows:

[0037]

[0038] wherein, denotes the Jacobian matrix, and the subscript denotes the radial coordinate and the circumferential coordinate .

[0039] Further, the differential operator expression required by the heat conduction control equation is derived according to the relationship between the Cartesian coordinate system and the SBFEM coordinate system:

[0040]

[0041] wherein, denotes the differential operator of the heat conduction problem; the superscript -1 denotes the inverse of the matrix; , , , denote four components of the inverse of the Jacobian matrix; and denote the sub-coefficient matrices of the heat conduction problem, and the expressions are as follows:

[0042]

[0043]

[0044] wherein, denotes the determinant of the Jacobian matrix.

[0045] Further, in the step S3, the heat conduction control equation and the boundary condition of the two-dimensional steady state are obtained based on the Laplace law, and the expression of the heat conduction control equation is as follows:

[0046]

[0047] wherein, denotes the heat flow vector; the superscript T denotes the matrix transpose.​

[0048] The boundary conditions are expressed as:

[0049]

[0050]

[0051]

[0052] where , and denote the Dirichlet, Neumann and Robin boundary conditions, respectively; and are the given temperature and heat flux density, respectively; k is the thermal conductivity; h is the convective heat transfer coefficient; is the ambient temperature; denotes the partial derivative of temperature along the normal direction; is the temperature value; is the normal vector of the boundary S.

[0053] Further, the temperature field is discretized along the circumferential coordinate η by using one-dimensional high-order spectral element shape functions, while keeping it continuous along the radial coordinate ξ:

[0054]

[0055] where denotes the nodal temperature at any point in the problem domain; denotes the directional temperature vector of the ray connecting the nodal points of the similar line element and the boundary line element; denotes the temperature interpolation shape function matrix of the boundary line and similar line elements.

[0056] Further, the heat conduction governing equation and the boundary conditions are solved by using the Galerkin method:

[0057]

[0058] where, denotes the virtual variation of the nodal temperature in the problem domain; denotes the calculation domain.

[0059] The area integral is converted into a boundary integral to obtain:

[0060]

[0061] where denotes the area integral, and denote the radial and circumferential boundary integrals, respectively.

[0062] Further, the equation is solved by the partial integral:

[0063]

[0064] where represents the thermal conductivity matrix.

[0065] The above equation is expanded and the Green's theorem is applied to obtain:

[0066]

[0067] where is a short form of ; S represents the calculation boundary, ; represents the virtual variation of the radial direction temperature vector connecting the similar line element node and the boundary line element node; subscript represents the second derivative of the radial coordinate . , , is the coefficient matrix of the heat conduction problem domain, and the specific expression is:

[0068]

[0069]

[0070]

[0071] where , represents the coordinate transformation matrix in the heat conduction problem, and has the following relationship with the sub-coefficient matrix:

[0072]

[0073] Simplifying obtains the second-order linear non-homogeneous ordinary differential equation about the radial coordinate ξ in the SBFEM coordinate system:

[0074]

[0075] Further, according to the relationship between temperature and heat flux:

[0076]

[0077] where represents the steady-state heat conduction matrix of the problem domain; and represent the internal node heat flux and the external node heat flux.

[0078] The governing equations for the steady-state heat conduction matrix in the SBFEM coordinate system are derived using the principle of virtual work:

[0079] .

[0080] Furthermore, in step S4, based on the relationship between the far-field coefficient matrix and the problem domain coefficient matrix:

[0081]

[0082] in , , This is the far-field coefficient matrix for the heat conduction problem.

[0083] Furthermore, the derivation yields... The governing equation for heat conduction as it approaches infinity:

[0084]

[0085] in The heat conduction matrix is ​​located at infinity.

[0086] Furthermore, by solving the eigenvalue problem of the Hamiltonian matrix at infinity:

[0087]

[0088] in This represents the eigenvector matrix of the heat conduction problem. These are characteristic values ​​for the heat conduction problem; This is the Hamiltonian matrix for the heat conduction problem.

[0089] The solution to the above equation is expressed as:

[0090]

[0091] in , The eigenvector submatrix of the heat conduction problem; For the eigenvalue submatrix of the heat conduction problem; Let be the constant vector for the heat conduction problem.

[0092] This yields the heat conduction matrix at infinity:

[0093]

[0094] Furthermore, using the heat conduction matrix at infinity as the initial value, and applying the fourth-order Runge-Kutta algorithm, we iterate backward from the far field towards the boundary line. The specific expression is as follows:

[0095]

[0096] wherein is the steady-state heat conduction iteration matrix, is the steady-state heat conduction matrix iteration initial value, , , is the far field coefficient matrix iteration initial value.

[0097] Further, the step size and gradient are selected to perform backward iteration from the far field to the boundary line, and the heat conduction matrix is gradually updated until the boundary of ξ = 1 is converged, and the specific iteration steps are as follows:

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] wherein represents the determined radial position; represents the step size; , , , corresponding to the gradient at point , , , . represents the steady-state heat conduction matrix after iteration.

[0104] Further, the temperature field of the entire problem domain can be obtained, and the expression is as follows:

[0105]

[0106] wherein represents the obtained temperature field of the entire problem domain.

[0107] Further, in the step S5, the thermal strain is calculated based on the obtained temperature field, and the specific expression is as follows:

[0108]

[0109] wherein, represents the thermal strain vector; represents the thermal expansion coefficient vector.

[0110] The constitutive relation established in combination with Hooke's law is as follows:

[0111]

[0112] wherein represents thermal stress, represents elastic matrix.

[0113] Further, the correspondence between thermal strain and thermal stress in the SBFEM coordinate system is obtained as follows:

[0114]

[0115] wherein, represents displacement vector; and is the coordinate transformation matrix in the thermal stress problem, and the specific expression is as follows:

[0116]

[0117] wherein, is the displacement interpolation shape function matrix of the boundary line and similar line element; and represents the sub-coefficient matrix of the thermal stress problem, and the expression is as follows:

[0118]

[0119] Further, the virtual work expression of the internal force caused by temperature is constructed:

[0120]

[0121] wherein represents the virtual variation of thermal strain vector; represents the virtual variation of thermal strain vector; and represents the starting value and the ending value of the radial boundary; , , is the coefficient matrix of the thermal stress problem domain:

[0122]

[0123]

[0124]

[0125] The virtual work principle is applied to obtain:

[0126]

[0127] wherein is the non-homogeneous term contributed by the temperature load. Equivalent nodal internal forces contributed by temperature loads.

[0128] Further, the non-homogeneous governing equation in terms of displacement is derived as

[0129]

[0130]

[0131] where, represents nodal external loads.

[0132] Further, the first order linear differential equation is obtained by Schur decomposition:

[0133]

[0134] where is the displacement vector; is the equivalent nodal internal force; is the Hamiltonian matrix of the thermal stress problem.

[0135] Further, the homogeneous solution and the particular solution of the first order linear differential equation are solved, and the specific steps are as follows:

[0136] The following equation is solved:

[0137]

[0138] where , , is the far field coefficient matrix of the thermal stress problem; , , , is the eigenvector sub-matrix of the thermal stress problem; is the eigenvalue sub-matrix of the thermal stress problem.

[0139] The homogeneous solution of the equation should satisfy:

[0140]

[0141] where is the constant vector of the thermal stress problem.

[0142] Substitute the calculated temperature field of the entire problem domain into to obtain the particular solution of the equation:

[0143]

[0144] where, represents the order of approximation taken.

[0145] Further, the homogeneous solution and the particular solution of the first-order linear differential equation are superimposed to obtain the general solution of the displacement field of the equation, which is specifically represented as:

[0146]

[0147] wherein, is the displacement modulus of the temperature contribution, is the internal force modulus of the temperature contribution.

[0148] Further, the corresponding thermal stress field distribution is obtained according to the relationship between the thermal stress and the thermal strain:

[0149]

[0150]

[0151] wherein, is the equivalent node load contributed by the temperature load; is the boundary stiffness matrix, which is specifically represented as:

[0152] .

[0153] Further, in order to verify the correctness of the calculation of the thermal conduction and the thermal stress of the uneven half-space dike in the present application, two benchmark examples are proposed.

[0154] The first embodiment is a semi-infinite domain thermal conduction verification example, and the geometric model and the boundary condition are as shown in (a) of Figure 3 . The entire calculation domain is divided into a near-field region and a far-field region, wherein the near-field region is surrounded by ADCB, and the far-field region extends to infinity outward. At the boundary of y =0, the EF section maintains a unit temperature ， And the rest of AE and BF is set to zero. In addition, the near-field region is modeled by SBFEM and discretized into 34 third-order linear spectral elements, and the far-field is calculated by similar lines and discretized into 22 linear spectral elements (b) of Figure 3 . The parameter settings of the RK-4 method are as follows: the initial radial position , the step size of the reverse iteration , and the calculation through 2000 iterations to the radial coordinate .

[0155] The displacement field is calculated along different y coordinate directions at x =1 and along different x coordinate directions at yThe temperature distribution was evaluated in the coordinate directions. The calculated results were compared with the analytical solution and the numerical results obtained using the scaled boundary integral-geometric algebra (SBIGA) method proposed by Pang et al. (2016) and the reproducing kernel particle method-dynamic infinite element method (RKPM-DIEM) proposed by Lin et al. (2023), respectively. Figure 4 The analytical solution expression of this problem is as follows:

[0156]

[0157] As shown in Figure 4 , the results obtained by the present application are highly consistent with the reference method and the analytical solution, demonstrating excellent accuracy. The data points are highly coincident with the analytical curve, indicating that the method can accurately capture the thermal distribution characteristics with minimal deviation. The high degree of agreement between the method and the analytical solution verifies its accuracy and effectiveness. In addition, compared with the 224 linear spectral elements used in the SBIGA method proposed by Pang et al. (2016), the present method only requires 56 linear spectral elements, significantly improving the computational efficiency.

[0158] Further, to verify the applicability of the method in actual complex engineering, we introduce a second embodiment, which is a dam foundation reservoir water interaction system. Similar to the previous model, this model is also divided into a near-field region and a far-field region: the near-field region includes the dam, the upstream water area, and the finite domain foundation; the far-field region is the infinite domain foundation extending infinitely from the AEFB, Figure 5 Figure (b) shows the discrete form of the model. The model geometric parameters are as follows: the dam height L = 80 meters, the upper base width d = 20 meters, and the lower base width W = 60 meters; the upstream water area range AC = 80 meters, and the water level = 70 meters. The temperature changes in January and July are selected for simulation, and the temperature change trends are shown in Figure 5 In addition, the model physical parameters are shown in Table 1.

[0159] Table 1: Calculated values of dam and foundation physical parameters

[0160]

[0161] Table 2 shows the quantitative comparison of temperature, stress, and displacement values between the finite element method and the present application at four monitoring points A, B, C, and D under the conditions of January and July. It is worth noting that the average error of the temperature field is very low and almost negligible. In addition, the displacement prediction shows an error of less than 2%, and the stress calculation deviation remains below 2.5%. These results verify the accuracy of the present application in simulating complex problems under different temperature change conditions.

[0162] Table 2: Comparison of physical values calculated by the present application and the finite element method

[0163] 。

Claims

1. A method for high performance simulation of heat conduction and thermal stresses in non-homogeneous half-space embankments, characterized in that, The method comprises the following steps: S1, Constructing the coordinate system based on the similar line to describe the uneven half-space embankment geometry, by introducing the similar line parallel to the boundary line, the spatial mapping relationship from the Cartesian coordinate system to the proportional boundary SBFEM coordinate system is established, forming the radial coordinate in the SBFEM coordinate system X and ring coordinate Y, and the radial coordinate X Realize the normalized transition from the similar line to the boundary line, the ring coordinate Y Discrete along the boundary line, get the coordinates of any point in the problem domain in the SBFEM coordinate system; S2, after the establishment of the coordinate system based on the similar line, the coordinate transformation of the differential operator is realized by the Jacobian matrix, the spatial partial derivative in the Cartesian coordinate system is accurately mapped into the SBFEM coordinate system, the expression of the differential operator required by the heat conduction control equation is derived according to the relationship between the Cartesian coordinate system and the SBFEM coordinate system, and the sub-coefficient matrix in the SBFEM coordinate system is formed accordingly; S3, based on Laplace law to obtain two-dimensional steady-state heat conduction control equation and boundary conditions, temperature field along the ring coordinate Y Using one-dimensional high-order spectral element shape function discrete, along the radial coordinate X Keep continuous, using Galerkin method to deal with heat conduction control equation and boundary conditions and convert the area integral into boundary integral, through the integral and Green's theorem step by step, get SBFEM coordinate system under the second order linear nonhomogeneous ordinary differential equation about radial coordinate X , and according to the relationship between temperature and heat flux, using the principle of virtual work to derive the SBFEM coordinate system under the steady-state heat conduction matrix control equation; S4, according to the relationship between the far field coefficient matrix and the problem domain coefficient matrix, the heat conduction control equation is derived The heat conduction control equation approaching to infinity is solved by solving the eigenvalue problem of the Hamilton matrix at infinity to obtain the heat conduction matrix at infinity, the heat conduction matrix at infinity is taken as the initial value and the fourth-order Runge-Kutta algorithm is applied, the step length and gradient are selected to perform reverse iteration from the far field to the boundary line, and the heat conduction matrix is updated step by step until the boundary is converged to X =1, and the temperature field of the entire problem domain is further obtained; S5, based on the calculated temperature field, the thermal strain is calculated, the constitutive relation is established combined with the Hook's law, the corresponding relationship between the thermal strain and the thermal stress in the SBFEM coordinate system is obtained, the expression of the internal force virtual work caused by the temperature is constructed, the non-homogeneous control equation with displacement as the unknown quantity is derived by applying the virtual work principle, the first-order linear differential equation is obtained through the Schur decomposition, the homogeneous solution and the particular solution of the first-order linear differential equation are solved, and the displacement field general solution of the equation is obtained by superimposing the two, so that the corresponding thermal stress field distribution is obtained.

2. A high performance simulation method of heat conduction and thermal stresses in non-homogeneous half-space embankments according to claim 1, characterized in that, In the step S1, the coordinate system based on the similar line is constructed to describe the heterogeneous half-space dike geometry, the spatial mapping relationship from the Cartesian coordinate system to the SBFEM coordinate system is established by introducing the similar line parallel to the boundary line: wherein, and denotes the coordinates of a point in the problem domain in the SBFEM coordinate system; and denotes the coordinates of a point on the similarity line in the Cartesian coordinate system; and denotes the coordinates of a point on the boundary line in the Cartesian coordinate system; radial coordinate formed in the SBFEM coordinate system X and a hoop coordinate Y and the radial coordinate X implements a normalized transition from the similarity line to the boundary line, the hoop coordinate Y is discretized along the boundary line: wherein denotes a shape function of the line element; and are node coordinate vectors of similar line nodes within the line element, respectively; and denotes a node coordinate vector of a boundary line node within the line element. The coordinates of any point in the problem domain in the SBFEM coordinate system are obtained: 。 3. A high performance simulation method of heat conduction and thermal stresses in non-homogeneous half-space embankments according to claim 2, characterized in that, In the step S2, after the establishment of the coordinate system based on the similar line, the coordinate transformation of the differential operator is realized by the Jacobian matrix, the spatial partial derivative in the Cartesian coordinate system is accurately mapped into the SBFEM coordinate system, and the specific process is as follows: in, Represents the Jacobian matrix, with subscripts middle Representing radial coordinates respectively and circumferential coordinates Find the first derivative; According to the relationship between the Cartesian coordinate system and the SBFEM coordinate system, the expression of the differential operator required by the heat conduction control equation is derived: where denotes the differential operator of the heat conduction problem; the superscript -1 denotes the inverse of a matrix; , , , denote the four components of the inverse of the Jacobian matrix; and denote the sub-coefficient matrices of the heat conduction problem, whose expressions are as follows: wherein denotes the determinant of the Jacobian matrix.

4. A high performance simulation method of heat conduction and thermal stresses in non-homogeneous half-space embankments according to claim 3, characterized in that, In the step S3, the two-dimensional steady heat conduction control equation and the boundary condition are obtained based on the Laplace law, wherein the expression of the heat conduction control equation is as follows: wherein represents the heat flow vector; the superscript T represents matrix transposition; The boundary condition is expressed as: where , and denote the Dirichlet, Neumann and Robin boundary conditions, respectively; and are the given temperature and heat flux density, respectively; k is the thermal conductivity; h is the convective heat transfer coefficient; is the ambient temperature; denotes the partial derivative of the temperature along the normal direction; is the temperature value; is the normal vector to the boundary S; The temperature field is discretized along the ring coordinate η by using one-dimensional high-order spectral element shape function, and remains continuous along the radial coordinate ξ: wherein a nodal temperature representing a problem domain arbitrary point; a ray direction temperature vector representing a connection of a similar line element node and a boundary line element node; a temperature interpolation shape function matrix of a boundary line and a similar line element; The heat conduction control equation and the boundary condition are obtained by using the Galerkin method: wherein, φ represents a virtual variation of the temperature of the node in the problem domain; φ represents a computational domain; The area integral is converted into the boundary integral to obtain: wherein denotes the integration over the area, and denotes the integration over the radial and the azimuthal boundary, respectively; The equation is processed by partial integration to obtain: wherein represents the thermal conductivity matrix; The above formula is expanded and the Green's theorem is applied to obtain: where is the short hand for ; S represents the calculation of the boundary, ; represents the imaginary variation of the direction temperature vector of the connecting similar line unit node and the boundary line unit node; the subscript represents the second derivative of the radial coordinate ; , , is the coefficient matrix of the heat conduction problem domain, and the specific expression is: wherein , denotes the coordinate transformation matrix in the heat conduction problem, which has the following relationship with the sub-coefficient matrix: Simplifying, we obtain the second order linear nonhomogeneous ordinary differential equation in the SBFEM coordinate system with respect to the radial coordinate X r: According to the relationship between the temperature and the heat flux: wherein represents a steady-state heat conduction matrix of the problem domain; and represents internal node heat flux and external node heat flux; The control equation of the steady heat conduction matrix in the SBFEM coordinate system is derived by using the virtual work principle: 。 5. A high performance simulation method of heat conduction and thermal stresses in non-homogeneous half-space embankments according to claim 4, characterized in that, In the step S4, according to the relationship between the far-field coefficient matrix and the problem domain coefficient matrix: wherein , , is the far-field coefficient matrix for the heat conduction problem; derived Heat conduction control equation as approaching to infinity: wherein is the heat conduction matrix at infinity; The eigenvalue problem of the infinite Hamilton matrix is solved: wherein is the eigenvector matrix of the heat conduction problem; is the eigenvalue of the heat conduction problem; is the Hamiltonian matrix of the heat conduction problem; The solution of the above equation is expressed as: wherein , is an eigenvector submatrix of the heat conduction problem; is an eigenvalue submatrix of the heat conduction problem; is a constant vector of the heat conduction problem; The heat conduction matrix at infinity is obtained: The heat conduction matrix at infinity is taken as the initial value, and the fourth-order Runge-Kutta algorithm is applied to perform reverse iteration from the far field to the boundary line, and the specific expression is as follows: wherein is the steady state heat conduction iteration matrix, is the steady state heat conduction matrix iteration initial value, , , is the far field coefficient matrix iteration initial value; The step length and gradient are selected to perform reverse iteration from the far field to the boundary line, and the heat conduction matrix is updated gradually until the boundary of ξ=1 is converged, and the specific iteration steps are as follows: wherein represents a determined radial position; represents a step size; , , , corresponds to the point , , , . the gradient at the point represents the steady-state heat conduction matrix after iteration; The temperature field of the whole problem domain is obtained, and the expression is as follows: wherein represents the temperature field of the entire problem domain obtained.

6. A high performance simulation method of heat conduction and thermal stresses in non-homogeneous half-space embankments according to claim 5, characterized in that, In the step S5, the thermal strain is calculated based on the calculated temperature field, and the specific expression is as follows: wherein represents a thermal strain vector; represents a thermal expansion coefficient vector; The constitutive relation established combined with the Hook's law is as follows: wherein represents thermal stress, represents elastic matrix; The relationship between thermal strain and thermal stress in the SBFEM coordinate system is obtained as follows: wherein represents a displacement vector; and is a coordinate transformation matrix in the thermal stress problem, and the specific expression is as follows: wherein is the displacement interpolation shape function matrix for the boundary line and the similar line element; and is the sub-coefficient matrix for the thermal stress problem, which is expressed as follows: The virtual work expression of the temperature-induced internal force is constructed as wherein denotes a virtual variation of the thermal strain vector; denotes a virtual variation of the thermal strain vector; and denotes a start value and an end value of the radial boundary; , , is the coefficient matrix of the thermal stress problem domain: The virtual work principle is applied to obtain wherein non-homogeneous term contributing to the temperature load; equivalent nodal internal force contributing to the temperature load; The non-homogeneous governing equation with displacement as the unknown is derived as wherein represents the nodal external load; The first-order linear differential equation is obtained by Schur decomposition as wherein is the displacement vector; is the equivalent internal nodal force; is the Hamiltonian matrix for the thermal stress problem; The homogeneous solution and particular solution of the first-order linear differential equation are solved by the following steps: The following equation is solved as wherein , , is a far field coefficient matrix of the thermal stress problem; , , , is an eigenvector submatrix of the thermal stress problem; is an eigenvalue submatrix of the thermal stress problem; The homogeneous solution of the equation should satisfy wherein is the constant vector for the thermal stress problem; the computed temperature field of the entire problem domain substituting obtaining a particular solution of the equation: wherein denotes the order of approximation; The general solution of the displacement field is obtained by superimposing the homogeneous solution and particular solution of the first-order linear differential equation, which is specifically expressed as wherein displacement modulus contributing to the temperature, internal force modulus contributing to the temperature; The corresponding thermal stress field distribution is obtained according to the relationship between thermal stress and thermal strain. wherein, equivalent nodal loads that contribute to the temperature loads; is the boundary stiffness matrix, which is specifically represented as: 。

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