A composite aircraft electrical architecture network modeling and analysis method

Abstract

A composite aircraft electrical structure network modeling and analysis method. It includes constructing a composite aircraft electrical structure network structure model; giving each component geometric dimensions and material parameters; deriving the differential equation of the three-dimensional electromagnetic field frequency domain, and setting the ideal boundary condition; constructing a three-dimensional finite element unit; obtaining the electric field and magnetic field intensity; constraining the electric field and magnetic field intensity; obtaining the weighted integral equation matrix of the difference value; compressing the large sparse matrix in the weighted integral equation matrix for sparse row processing and stable double conjugate gradient processing; completing the accurate discrete division of the three-dimensional finite element unit, and obtaining the electrical performance parameters of the model under the electromagnetic field and the like steps. The present application greatly reduces the calculation space and improves the calculation speed, and can realize more accurate construction of the composite aircraft electrical structure network model, and more accurately reflect the electrical performance of the aircraft electrical system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of three-dimensional modeling and electromagnetic simulation analysis, and particularly relates to a composite aircraft electrical structure network modeling and analysis method. BACKGROUND

[0002] With the development of aerospace technology, the proportion of composite materials in modern civil aircraft is gradually increasing. Modern civil aircraft has developed from all-metal frame aircraft such as A320 and B737 to today's composite aircraft such as A350 and B787. Among them, the use of composite materials in Boeing's B787 aircraft accounts for 50% of the overall fuselage structure, and the proportion of composite materials in Airbus's A350 aircraft is as high as 52%. This is because composite materials have the advantages of low mass density, high strength, high heat resistance, corrosion resistance, fatigue resistance, vibration reduction, etc. Not only can the overall weight of the aircraft be reduced to achieve the purpose of improving the flight range and reducing the flight cost of the aircraft, but also the sustainable and safe flight of the civil aircraft is strengthened. However, the high impedance of composite materials will affect the overall conductive path of the aircraft, and it is difficult to complete the tasks of lightning protection, static electricity and fault current conduction.

[0003] Compared with all-metal aircraft, the structure, component lapping and cable setting of composite aircraft face new problems, and the structure design is more complex. The construction or not of the details of the floor cross beams, the lapping of the components, the connection of the stringers and the frames, and the edge strip connection of the electrical structure network relates to the accuracy of the overall electrical performance of the electrical structure network. At the same time, the construction of more structures means that more computing capacity and computing space are needed, so it is necessary to optimize the construction of the complex composite aircraft electrical structure network model, and provide an important theoretical basis for the normal work and later maintenance of the aircraft electrical system.

[0004] The mainstream methods for three-dimensional electromagnetic field numerical calculation at present include partial element equivalent circuit (PEEC), finite difference method (FDM), method of moments (MoM) and finite element method (FEM). The partial element equivalent circuit method is based on the electric field integral equation and Kirchhoff's law, converts the electromagnetic integral equation into partial independent elements such as resistance, inductance and capacitance, converts the electromagnetic problem into a circuit problem, and obtains the numerical value of the electrical performance by solving the Maxwell equation of the discrete three-dimensional grid. This method has high accuracy when facing small or not high complex models, but the calculation space required is very large when facing large or complex models. Affected by the green function, the method of moments also has the limitations of large amount of calculation and slow simulation speed when dealing with complex electromagnetic field models. The finite difference method is to approximate by direct difference, convert the electromagnetic field differential equation into algebraic equation system for solving, and the effect of processing the boundary shape of the complex aircraft structure is poor, which may cause large error to the result of the overall model. Therefore, a method capable of calculating complex aircraft structures and having acceptable calculation amount and calculation precision is needed.

[0005] The finite element method is a method based on Maxwell's differential equation and solving its boundary value. According to the setting of the size of the finite element unit, the method divides the electromagnetic field model of the determined domain into a finite number of sub-regions, and then reduces the error function to the minimum value by the weighted residual method and generates a stable value. In this process, a large matrix is solved, the matrix storage space is reduced by compressing the sparse row, and the processed matrix is iteratively solved by the stable double conjugate gradient method, so as to obtain the calculation result and take into account the advantages of reducing the calculation space and improving the calculation speed. The improved finite element method has obvious advantages in constructing complex aircraft structures. SUMMARY

[0006] In order to solve the above problems, the purpose of the present application is to provide a composite aircraft electrical structure network modeling and analysis method, which can construct a large and complex composite aircraft electrical structure network model, ensure the model precision, reduce the calculation space and improve the calculation speed, and provide an important guarantee for the model accuracy and result accuracy.

[0007] In order to achieve the above purpose, the composite aircraft electrical structure network modeling and analysis method provided by the present application includes the following steps in sequence:

[0008] A, taking the typical components of the electrical structure network structure as the basic constituent elements, taking the metal rail as the structural member of the longitudinal and transverse direction of the main conductive structure of the floor framework of the passenger cabin and cargo cabin, taking titanium alloy as the structural member of the connecting part of the passenger cabin and cargo cabin, taking the metal aluminum strip and titanium alloy strip as the auxiliary conductive structure installed between the inside of the fuselage skin and each structural member, and constructing a composite aircraft electrical structure network structure model;

[0009] B, giving each component of the composite aircraft electrical structure network structure model constructed in step A geometric dimensions and material parameters;

[0010] C, using the material parameters obtained in step B, simplifying and solving the Maxwell equations, deriving the differential equation of the three-dimensional electromagnetic field frequency domain of the composite aircraft electrical structure network structure model constructed in step A, and setting ideal boundary conditions for determining the variation law of the solved variables or their derivatives on the boundary of the composite aircraft electrical structure network structure model;

[0011] D, constructing a vector basis function of a three-dimensional finite element unit, and then constructing a three-dimensional finite element unit based on the vector basis function of the three-dimensional finite element unit;

[0012] E, using the three-dimensional finite element unit obtained in step D to discretely divide the composite aircraft electrical structure network structure model in step B which has been given geometric dimensions and material parameters into n three-dimensional finite element units, and obtaining the electric field intensity and magnetic field intensity represented by the divided three-dimensional finite element units;

[0013] F, setting the three-dimensional electromagnetic field frequency domain differential equation and ideal boundary condition obtained in step C as the excitation function of the electric field and magnetic field, and then making the electric field intensity or magnetic field intensity obtained in step E respectively equal to the corresponding excitation function of the electric field and magnetic field, thereby constraining the electric field intensity and magnetic field intensity;

[0014] G, using the Galerkin method to calculate the residual of the coefficients of the electric field intensity expression and the coefficients of the magnetic field intensity expression in step E, subtracting the excitation function from the electric field or magnetic field differential equation in step F to form a difference value, and integrating the difference value to obtain a weighted integral equation matrix of the difference value;

[0015] H, compressing and sparsely processing the large sparse matrix in the weighted integral equation matrix obtained in step G, and then using the stable double-conjugate gradient method for preprocessing;

[0016] I, The large sparse matrix is compressed and sparse row processed, and the weighted integral equation matrix obtained in step G is solved after being preprocessed by the stable double conjugate gradient method, so that the coefficients of the electric field intensity expression and the magnetic field intensity expression in step E can be quickly and accurately obtained. The unique solution is obtained, thereby completing the accurate and precise discretization of the three-dimensional finite element unit of the composite aircraft electrical structure network structure model, and obtaining the electrical performance parameters of the model under the electromagnetic field, including the impedance, potential distribution and current density of the electrical structure network under different AC and DC power supplies.

[0017] In step C, the material parameters obtained in step B are used to simplify and solve the Maxwell equations, and the method for setting the ideal boundary conditions of the differential equation of the three-dimensional electromagnetic field frequency domain of the composite aircraft electrical structure network structure model constructed in step A is:

[0018] 1) The Maxwell equations are complex form Maxwell equations in the frequency domain, and the expression is:

[0019]

[0020] 2) According to the above Maxwell equation, by substituting into formula , and simplifying to obtain the differential equation of the three-dimensional electromagnetic field frequency domain:

[0021]

[0022] The boundary condition of the ideal electrical conductor is:

[0023]

[0024] The boundary condition of the ideal magnetic conductor is:

[0025]

[0026] The boundary condition of the impedance is:

[0027]

[0028] Wherein, is the Hamiltonian operator, is the electric field intensity, is the magnetic field intensity, ω is the angular frequency, μ0 is the vacuum magnetic permeability, μ r is the relative magnetic permeability, ε0 is the vacuum dielectric constant, ε r is the relative dielectric constant, is the source current, Γ is the boundary of the three-dimensional electromagnetic field, is the outer normal vector on the boundary, γ e is the impedance factor, i is the imaginary symbol, is the magnetic induction intensity.

[0029] In step D, the method for constructing the vector base function of the three-dimensional finite element unit and then constructing the three-dimensional finite element unit based on the vector base function of the three-dimensional finite element unit is:

[0030] The vector base function equation of the three-dimensional finite element unit is:

[0031]

[0032] wherein V e is the tetrahedron volume, the coefficient is related to the coordinates of the tetrahedron, wherein i = 1, 2, 3, 4;

[0033] Let the above vector base function equation of the three-dimensional finite element unit be and the function is substituted into the coefficient in the vector base function. In the calculation process:

[0034]

[0035] Based on the vector base function of the three-dimensional finite element unit, the Whitmney-I type three-dimensional finite element unit is constructed by using the following constraint condition, and the expression is:

[0036]

[0037] wherein i and j are respectively two end points of the edges of the tetrahedron.

[0038] The constraint condition is:

[0039]

[0040] In step E, the electric field intensity and the magnetic field intensity are:

[0041]

[0042]

[0043] wherein e ij is the electric field intensity , h ij is the magnetic field intensity .

[0044] In step F, the method of setting the three-dimensional electromagnetic field frequency domain differential equations and ideal boundary conditions obtained in step C as excitation functions of the electric and magnetic fields, and then making the electric field strength or magnetic field strength obtained in step E equal to the corresponding electric and magnetic field excitation functions, thereby constraining the electric field strength and magnetic field strength, is as follows:

[0045] First, the electric field strength in step E... With magnetic field strength Decomposed into the following equations:

[0046]

[0047] Where A is the electric field strength or magnetic field strength The equation, {c}, {v} are the expanded column vectors, v i electric field strength or magnetic field strength The expansion function, c i electric field strength or magnetic field strength The expansion coefficients;

[0048] The three-dimensional electromagnetic field frequency domain differential equations and ideal boundary conditions obtained in step C are set as excitation functions for the electric and magnetic fields, and then the above electric field strength is set... or magnetic field strength Equation A is equal to the corresponding excitation functions of the electric and magnetic fields, respectively, that is:

[0049] ξA=f

[0050] Where ξ is the differential operator and f is the activation function.

[0051] In step G, the residuals of the coefficients of the electric field intensity expression and the magnetic field intensity expression in step E are calculated using the Galerkin method. The electric field or magnetic field differential equation in step F is subtracted from the excitation function to form a difference. The difference is then integrated to obtain the weighted integral equation matrix of the difference.

[0052] The coefficients e in the expression for the electric field intensity E in step E are determined using the Galerkin method. ij With magnetic field strength The coefficient h in the expression ij Calculate the residual, and subtract the excitation function f from the differential equation of the electric or magnetic field in step F to form the difference r:

[0053] r=ξA-f

[0054] In the three-dimensional electromagnetic field frequency domain, when the difference r approaches 0, it represents the electric field strength under the actual model. or magnetic field intensity Equation A will be closer to the excitation function f under ideal conditions, so the weighted integral of the difference value r is obtained by integrating the difference value r:

[0055]

[0056] where M i e is the weighted function of the electric or magnetic field differential equation ξA, C is the three-dimensional electromagnetic field frequency domain, and n is the number of three-dimensional finite element units;

[0057] In order to obtain accurate results, the expansion function v i representing the electric or magnetic field intensity equation A is the same as the weighted function M i e of the electric or magnetic field differential equation ξA above, and the weighted integral equation of the difference value r shown in the above formula is simplified as:

[0058]

[0059] Let:

[0060] S ij =∫∫∫ C v i ξ{v} T {c}dC i=1,2,3,...,n

[0061] b ij =∫∫∫ C v i fdC i=1,2,3,...,n

[0062] The weighted integral equation of the difference value r above is represented by a matrix as:

[0063]

[0064] In step H, the large sparse matrix in the weighted integral equation matrix obtained in step G is compressed and processed by sparse row, and then the method of using stable double conjugate gradient method for preprocessing is:

[0065] Let K represent the leftmost matrix in the weighted integral equation matrix obtained in step G is a large sparse matrix K, and the large sparse matrix K is compressed and processed by sparse row, wherein:

[0066]

[0067] K data =(a1 a2 a3 a4 a5 a6 …)

[0068] K indices = (0 2 2 1 2 3...)

[0069] K indptr = (0 2 3 3 5 6...)

[0070] where K data is the submatrix of nonzero elements listed by row, K indices is the submatrix of nonzero elements listed by column, and K indptr is the submatrix of elements in K data corresponding to the first nonzero element in each row.

[0071] The large sparse matrix K after compression and sparse row processing is preprocessed using the stable double conjugate gradient method:

[0072] The weighted integral equation matrix is changed to the following form:

[0073]

[0074] where, is the error value of the weighted integral equation matrix expression on both sides, b is (b 11 …b m1 ) T , x0 is (c 11 …c m1 ) T , and T is the transpose of the matrix.

[0075] Then, the error value is brought into the following iterative equation:

[0076]

[0077] β = (j i / j i-1 )(α / ω i-1 )i = 1, 2, 3,..., n

[0078] p i = r i-1 + β (p i-1 - ω i-1 k i-1 ) i = 1, 2, 3,..., n

[0079] k i = Kp i i = 0, 1, 2, 3,..., n

[0080]

[0081] s = r i-1 - αk ii = 1, 2, 3,..., n

[0082] t = Ks

[0083] ω i = (t · s) / (t · t) i = 1, 2, 3,..., n

[0084] When reaching the set error value The following iterative calculation is performed:

[0085] x i = x i-1 + αp i + ω i s i = 1, 2, 3,..., n

[0086] r i = s - ω i t i = 1, 2, 3,..., n

[0087] Wherein, j0 = α = ω0 = 1, v0 = p0 = 0, and i herein represents the number n of three-dimensional finite element units from 1 to step E.

[0088] Compared with the prior art, the composite aircraft electrical structure network modeling and analysis method provided by the application has the following effects: compared with using other electromagnetic field calculation methods and using the finite element method to construct a complex aircraft structure, the method can process a large sparse matrix generated in the calculation process by jointly processing the compressed sparse row and the stable double-conjugate gradient method, the memory consumption after processing is reduced by 32.625%-93.03% compared with Bi-CGSTAB processing alone, the processing speed is improved by 76.81% compared with the traditional finite element method processing, the calculation space is greatly reduced and the calculation speed is improved, and the composite aircraft electrical structure network model can be more accurately constructed, and the electrical performance of the aircraft electrical system can be more accurately reflected. BRIEF DESCRIPTION OF DRAWINGS

[0089] Figure 1 The composite aircraft electrical structure network modeling and analysis method flowchart provided by the application;

[0090] Figure 2 The composite aircraft electrical structure network simulation model;

[0091] Figure 3 The Whitmney-I type three-dimensional finite element unit diagram;

[0092] Figure 4 The composite aircraft electrical structure network model finite element unit division diagram;

[0093] Figure 5Add the excited electrical performance chart to the electrical result network model. DETAILED DESCRIPTION

[0094] In order to more clearly illustrate the embodiments of the present application, the present application is further described below in conjunction with the accompanying drawings and examples. The present application is based on the improved composite aircraft electrical structure network modeling and analysis method of finite element method (FEM), and the accompanying drawings are only used for the purpose of showing the preferred embodiments, and are not considered as limiting the present application. Based on the examples in the present application, all other examples obtained by the ordinary skilled in the art without making creative efforts are within the scope of protection of the present application.

[0095] As shown in Figure 1 , the composite aircraft electrical structure network modeling and analysis method provided by the present application comprises the following steps in sequence:

[0096] A. Taking the typical components of the electrical structure network structure as the basic constituent elements, taking the metal guide rail as the structural member of the longitudinal and transverse direction of the main conductive structure of the cabin and cargo cabin floor framework, taking the titanium alloy as the structural member of the connecting part of the cabin and cargo cabin, taking the metal aluminum strip and titanium alloy strip as the auxiliary conductive structure installed between the inner side of the fuselage skin and each structural member, and constructing the composite aircraft electrical structure network structure model;

[0097] This embodiment is based on the A350 fuselage data, and an equal proportion simulation model is established according to the characteristics of the composite aircraft electrical structure network, as shown in Figure 2 . The main conductive structure includes U-shaped metal longitudinal beam, I-shaped metal transverse beam guide rail and U-shaped metal support, and the auxiliary conductive structure is cable and metal strip.

[0098] B. Giving each component of the composite aircraft electrical structure network structure model constructed in step A geometric dimensions and material parameters;

[0099] The geometric dimensions and material parameters of each component are shown in Table 1.

[0100] Table 1, geometric dimensions and material parameters of each component in the composite aircraft electrical structure network structure model

[0101]

[0102] C. Using the material parameters obtained in step B, simplifying and solving the Maxwell equation set, deriving the differential equation of the three-dimensional electromagnetic field frequency domain of the composite aircraft electrical structure network structure model constructed in step A, and setting ideal boundary conditions for determining the variation law of the solved variables or their derivatives on the boundary of the composite aircraft electrical structure network structure model;

[0103] For the problem that the AC voltage of the electric power system of the more electric aircraft is increased from the traditional constant frequency 115V / 400Hz to variable frequency 230V / 360-800Hz, and the DC voltage is increased from 28V to ±270V, the composite aircraft electrical structure network structure model needs to consider the changes of the three-dimensional electromagnetic field under different AC / DC power supplies and different frequencies. Therefore, the electromagnetic field range in which the composite aircraft electrical structure network structure model is located needs to be determined, and then the three-dimensional finite element unit division is performed on the overall electrical structure network model. The method is as follows:

[0104] 1) The Maxwell equations are complex number form Maxwell equations in the frequency domain, and the expression is:

[0105]

[0106] 2) According to the above Maxwell equation, by substituting into formula and simplifying, the differential equation of the three-dimensional electromagnetic field in the frequency domain is obtained:

[0107]

[0108] The boundary condition of the ideal electric conductor is:

[0109]

[0110] The boundary condition of the ideal magnetic conductor is:

[0111]

[0112] The boundary condition of the impedance is:

[0113]

[0114] Wherein, is the Hamiltonian operator, is the electric field intensity, is the magnetic field intensity, ω is the angular frequency, μ0 is the vacuum permeability, μ r is the relative permeability, ε0 is the vacuum permittivity, ε r is the relative permittivity, is the source current, Γ is the boundary of the three-dimensional electromagnetic field, is the outer normal vector on the boundary, γ e is the impedance factor, i is the imaginary part symbol, is the magnetic induction intensity.

[0115] D. Construct the vector basis function of the three-dimensional finite element unit, and then construct the three-dimensional finite element unit based on the vector basis function of the three-dimensional finite element unit;

[0116] The vector base function equation of the three-dimensional finite element unit is:

[0117]

[0118] Wherein, V e is the tetrahedron volume, coefficient is related to the coordinates of the tetrahedron, wherein i = 1, 2, 3, 4;

[0119] Let the vector base function equation of the three-dimensional finite element unit above be and substitute the function into the coefficient of the vector base function.In the calculation process:

[0120]

[0121] Based on the vector base function of the three-dimensional finite element unit, an accurate Whitmney-I type three-dimensional finite element unit is constructed by using the following constraint conditions, as shown in the following formula: Figure 3

[0122]

[0123] Wherein, i and j are respectively two end points of the edges of the tetrahedron;

[0124] The constraint condition is:

[0125]

[0126] E. Discretely divide the composite aircraft electrical structure network structure model with geometric size and material parameters assigned in step B into n three-dimensional finite element units by using the three-dimensional finite element unit obtained in step D, to obtain the electric field intensity and magnetic field intensity represented by the divided three-dimensional finite element units:

[0127]

[0128] Wherein, e ij is the electric field intensity coefficient of the expression, h ij is the magnetic field intensity coefficient of the expression.

[0129] F. Set the three-dimensional electromagnetic field frequency domain differential equation and ideal boundary condition obtained in step C as the excitation functions of the electric field and the magnetic field, and then make the electric field intensity or the magnetic field intensity obtained in step E respectively equal to the corresponding electric field and magnetic field excitation functions, so as to constrain the electric field intensity and the magnetic field intensity.

[0130] ​Since this process generates a large number of non-unique solutions, the electric field strength in step E is first... With magnetic field strength Decomposed into the following equations:

[0131]

[0132] Where A is the electric field strength or magnetic field strength The equation, {c}, {v} are the expanded column vectors, v i electric field strength or magnetic field strength The expansion function, c i electric field strength or magnetic field strength The expansion coefficients;

[0133] The three-dimensional electromagnetic field frequency domain differential equations and ideal boundary conditions obtained in step C are set as excitation functions for the electric and magnetic fields, and then the above electric field strength is set... or magnetic field strength Equation A is equal to the corresponding excitation functions of the electric and magnetic fields, respectively, that is:

[0134] ξA=f

[0135] Where ξ is the differential operator and f is the activation function.

[0136] G. Calculate the residuals of the coefficients of the electric field intensity expression and the magnetic field intensity expression in step E using the Galerkin method. Subtract the excitation function from the electric field or magnetic field differential equation in step F to form a difference. Integrate the difference to obtain the weighted integral equation matrix of the difference.

[0137] Due to the electric field strength in step F or magnetic field strength Equation A is the expression for the electric or magnetic field strength under the actual model, while the excitation function f is the equation under ideal conditions, thus leading to the electric field strength in step E. The coefficient e in the expression ij With magnetic field strength The coefficient h in the expression ij There are residuals that make the electric field strength or magnetic field strength Equation A and the excitation function f cannot be completely equal, i.e., there is an error. Therefore, the coefficient e in the expression for the electric field intensity E in step E is adjusted using the Galerkin method. ij With magnetic field strength The coefficient h in the expression ijThe difference value r is calculated by subtracting the excitation function f from the electric field or magnetic field differential equation ξA in step F:

[0138] r = ξA - f

[0139] When the difference value r tends to 0 in the three-dimensional electromagnetic field frequency domain, the equation A of the electric field intensity or the magnetic field intensity under the actual model will be closer to the excitation function f under the ideal condition. Therefore, the weighted integral of the difference value r is obtained:

[0140]

[0141] where M i e is the weighted function of the electric field or magnetic field differential equation ξA, C is the three-dimensional electromagnetic field frequency domain, and n is the number of three-dimensional finite element units.

[0142] To make the result accurate, the expansion function v i of the equation A representing the electric field intensity or the magnetic field intensity is the same as the weighted function M i e of the electric field or magnetic field differential equation ξA, and the weighted integral equation of the difference value r shown in the above formula is simplified as:

[0143] R i e = ∫∫∫ C (v i ξ{v} T {c}-v i f)dC = 0 i = 1, 2, 3,..., n

[0144] Let:

[0145] S ij = ∫∫∫ C v i ξ{v} T {c}dC i = 1, 2, 3,..., n

[0146] b ij = ∫∫∫ C v i fdC i = 1, 2, 3,..., n

[0147] The weighted integral equation of the difference value r is represented by a matrix as:

[0148]

[0149] H. Compressing and sparse row processing the large sparse matrix in the weighted integral equation matrix obtained in step G, and then using stable double conjugate gradient method for preconditioning;

[0150] In the process of constructing complex model, the operation of step G will produce large sparse matrix, thus occupying more calculation memory and having low calculation efficiency. Therefore, let K represent the leftmost matrix in the weighted integral equation matrix obtained in step G for large sparse matrix K, and compressing and sparse row processing the large sparse matrix K, wherein

[0151]

[0152] K data =(a1 a2 a3 a4 a5 a6 …)

[0153] K indices =(0 2 2 1 2 3 …)

[0154] K indptr =(0 2 3 3 5 6 …)

[0155] Wherein, K data is the non-zero element submatrix arranged by row, K indices is the submatrix arranged by the column where the non-zero element is located, K indptr is the submatrix of the element corresponding to the first non-zero element in each row in K data ;

[0156] Using stable double conjugate gradient method to precondition the large sparse matrix K after compressing and sparse row processing:

[0157] Firstly, since the above weighted integral equation matrix is calculated in the case of tending to 0, there is still error on both sides of the equation, so further iterative operation is needed for the weighted integral equation matrix to make the result more appropriate, and the weighted integral equation matrix is changed to the following formula:

[0158]

[0159] Wherein, is the error value of the difference between the expression of the weighted integral equation matrix on both sides, b is (b 11 …b m1 ) T , x0 is (c 11 …c m1 ) T , and T is the transpose of the matrix;

[0160] Then, the error value is brought into the following iterative equation:

[0161]

[0162] β = (j i / j i-1 )(α / ω i-1 ) i = 1, 2, 3,..., n

[0163] p i = r i-1 + β (p i-1 - ω i-1 k i-1 ) i = 1, 2, 3,..., n

[0164] k i = Kp i i = 0, 1, 2, 3,..., n

[0165]

[0166] s = r i-1 - αk i i = 1, 2, 3,..., n

[0167] t = Ks

[0168] ω i = (t • s) / (t • t) i = 1, 2, 3,..., n

[0169] As described above, the weighted integral equation matrix There is a certain error, therefore, need to set the acceptable error value to calculate the results; when reaching the set error value below, the following iterative calculation is performed:

[0170] x i = x i-1 + αp i + ω i s i = 1, 2, 3,..., n

[0171] r i = s - ω i t i = 1, 2, 3,..., n

[0172] Wherein, j0= α = ω0= 1, v0= p0= 0, i here indicates from 1 to the number n of three-dimensional finite element units described in step E.

[0173] I, after the large sparse matrix K is compressed and sparse row processing and the pre-processing of the stable double conjugate gradient method, the weighted integral equation matrix obtained in step G is solved, the electric field intensity The coefficient e of the expressionij with the magnetic field strength coefficient h of the expression ij accurate and unique solution, as Figure 4 shown, thus completing the accurate discrete division of the three-dimensional finite element unit of the composite aircraft electrical structure network structure model, and obtaining the electrical performance parameters of the model under the electromagnetic field, including the impedance of the electrical structure network under different AC and DC power supplies, potential distribution and current density, etc., as Figure 5 shown.

[0174] Thus, the present application realizes the composite aircraft electrical structure network modeling and analysis based on the improved finite element method, which can meet the construction requirements of the detailed model in the calculation of the complex electrical structure network, and the calculation and analysis method has good universal applicability.

[0175] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit them. Those skilled in the art should understand that: the technical personnel in the art can modify or replace the embodiments of the present application, but these modifications or changes are within the scope of protection of the claims.

Claims

1. A method for modeling and analyzing electrical structure networks of composite material aircraft, characterized in that: The method for modeling and analyzing the electrical structure network of composite aircraft includes the following steps performed in sequence: A. Using typical components of the electrical structure network structure as basic constituent elements, metal rails as structural components in the longitudinal and transverse directions of the main conductive structure of the cabin and cargo hold floor skeleton, titanium alloys as structural components in the connection between the cabin and cargo hold, and aluminum strips and titanium alloy strips as auxiliary conductive structures installed on the inner side of the fuselage skin and between various structural components, a composite material aircraft electrical structure network structure model is constructed. B. Assign geometric dimensions and material parameters to each component in the composite material aircraft electrical structure network model constructed in step A; C. Using the material parameters obtained in step B, simplify and solve Maxwell's equations to derive the differential equations in the three-dimensional electromagnetic field frequency domain of the composite material aircraft electrical structure network model constructed in step A, and set ideal boundary conditions to determine the variation law of the solved variables or their derivatives on the boundary of the composite material aircraft electrical structure network model. D. Construct the vector basis functions of the three-dimensional finite element element, and then construct the three-dimensional finite element element based on the vector basis functions of the three-dimensional finite element element. E. Using the three-dimensional finite element elements obtained in step D, the composite material aircraft electrical structure network model with assigned geometric dimensions and material parameters in step B is discretized into n three-dimensional finite element elements, and the electric field strength and magnetic field strength represented by the divided three-dimensional finite element elements are obtained. F. Set the differential equations and ideal boundary conditions of the three-dimensional electromagnetic field frequency domain obtained in step C as excitation functions of the electric field and magnetic field, and then make the electric field strength or magnetic field strength obtained in step E equal to the corresponding excitation functions of the electric field and magnetic field, thereby constraining the electric field strength and magnetic field strength. G. Calculate the residuals of the coefficients of the electric field intensity expression and the magnetic field intensity expression in step E using the Galerkin method. Subtract the excitation function from the electric field or magnetic field differential equation in step F to form a difference. Integrate the difference to obtain the weighted integral equation matrix of the difference. H. Compress the sparse rows of the large sparse matrix in the weighted integral equation matrix obtained in step G, and then preprocess it using the stable biconjugate gradient method. I. After the large sparse matrix is ​​preprocessed by sparse row compression and stable double conjugate gradient method, the weighted integral equation matrix obtained in step G is solved. This allows for the rapid and accurate solution of the coefficients of the electric field strength expression and the magnetic field strength expression in step E. This completes the precise discretization of the three-dimensional finite element structure model of the composite material aircraft electrical structure network and obtains the electrical performance parameters of the model under electromagnetic fields, including the impedance, potential distribution and current density of the electrical structure network under different AC and DC power supplies.

2. The method for modeling and analyzing the electrical structure network of composite aircraft according to claim 1, characterized in that: In step C, the method for simplifying and solving Maxwell's equations using the material parameters obtained in step B, deriving the differential equations in the three-dimensional electromagnetic field frequency domain of the composite material aircraft electrical structure network model constructed in step A, and setting ideal boundary conditions is as follows: 1) The Maxwell equations are in complex form in the frequency domain, and their expression is: 2) Based on the Maxwell equations above, by... Substitution In the middle, and simplified, we obtain the differential equation in the frequency domain of the three-dimensional electromagnetic field: The boundary conditions for an ideal electrical conductor are: The boundary conditions for an ideal magnetic conductor are: The boundary conditions for impedance are: in, For Hamiltonian operators, For electric field strength, ω is the magnetic field strength, ω is the angular frequency, μ0 is the free permeability, and μ r ε is the relative permeability, ε0 ​​is the vacuum permittivity, and ε r The relative permittivity, Let Γ be the source current, and Γ be the boundary of the three-dimensional electromagnetic field. Let γ be the external normal vector on the boundary. e Here, i represents the impedance factor, and i is the imaginary part. denoted as magnetic flux density.

3. The method for modeling and analyzing the electrical structure network of composite aircraft according to claim 1, characterized in that: In step D, the method for constructing the vector basis functions of the three-dimensional finite element element, and then constructing the three-dimensional finite element element based on the vector basis functions of the three-dimensional finite element element, is as follows: The vector basis function equations of the three-dimensional finite element are: Among them, V e It is the volume of a tetrahedron, and its coefficient is... It is related to the coordinates of the tetrahedron, where i = 1, 2, 3, 4; Let the vector basis function equations of the above three-dimensional finite element be... for and the function Substitute the coefficients into the vector basis functions During the calculation process: Based on the vector basis functions of the three-dimensional finite element element, and using the following constraints, an accurate Whitmney-I type three-dimensional finite element element is constructed, expressed as follows: Where i and j are the two endpoints of the edges of the tetrahedron; Its constraints are:

4. The method for modeling and analyzing the electrical structure network of composite aircraft according to claim 1, characterized in that: In step E, the electric field strength and magnetic field strength are: Among them, e ij electric field strength The coefficients of the expression, h ij magnetic field strength The coefficients of the expression.

5. The method for modeling and analyzing the electrical structure network of composite aircraft according to claim 1, characterized in that: In step F, the method of setting the three-dimensional electromagnetic field frequency domain differential equations and ideal boundary conditions obtained in step C as excitation functions of the electric and magnetic fields, and then making the electric field strength or magnetic field strength obtained in step E equal to the corresponding electric and magnetic field excitation functions, thereby constraining the electric field strength and magnetic field strength, is as follows: First, the electric field strength in step E... With magnetic field strength Decomposed into the following equations: Where A is the electric field strength or magnetic field strength The equation, {c}, {v} are the expanded column vectors, v i electric field strength or magnetic field strength The expansion function, c i electric field strength or magnetic field strength The expansion coefficients; The three-dimensional electromagnetic field frequency domain differential equations and ideal boundary conditions obtained in step C are set as excitation functions for the electric and magnetic fields, and then the above electric field strength is set... or magnetic field strength Equation A is equal to the corresponding excitation functions of the electric and magnetic fields, respectively, that is: ξA=f Where ξ is the differential operator and f is the activation function.

6. The method for modeling and analyzing the electrical structure network of composite aircraft according to claim 1, characterized in that: In step G, the residuals of the coefficients of the electric field intensity expression and the magnetic field intensity expression in step E are calculated using the Galerkin method. The electric field or magnetic field differential equation in step F is subtracted from the excitation function to form a difference. The difference is then integrated to obtain the weighted integral equation matrix of the difference. The electric field strength in step E was determined using the Galerkin method. The coefficient e in the expression ij With magnetic field strength The coefficient h in the expression ij Calculate the residual, subtract the excitation function f from the differential equation of the electric or magnetic field in step F, and form the difference r: r=ξA-f In the three-dimensional electromagnetic field frequency domain, when the difference r approaches 0, it represents the electric field strength under the actual model. or magnetic field strength Equation A will be closer to the excitation function f under ideal conditions. Therefore, by performing a weighted integral over the difference r, we obtain the weighted integral equation for the difference r: Among them, M i e ξA is the weighting function of the differential equation of electric or magnetic field, C is the frequency domain of the three-dimensional electromagnetic field, and n is the number of three-dimensional finite element elements; To ensure accurate results, the expansion function v of equation A, representing electric or magnetic field strength, should be... i The weighting function M of the above electric or magnetic field differential equation ξA i e Similarly, the weighted integral equation for the difference r shown in the above equation is simplified to: make: S ij =∫∫∫ C v i ξ{v} T {c}dC i=1,2,3,...,n b ij =∫∫∫ C v i fdC i=1,2,3,...,n The weighted integral equation for the difference r is then expressed in matrix form as follows: 。 7. The method for modeling and analyzing the electrical structure network of composite aircraft according to claim 1, characterized in that: In step H, the method of compressing the sparse rows of the large sparse matrix in the weighted integral equation matrix obtained in step G, and then preprocessing it using the stable biconjugate gradient method, is as follows: Let K denote the leftmost matrix of the weighted integral equation matrix obtained in step G. Let K be a large sparse matrix, and then perform sparse row compression on the large sparse matrix K, where: K data (a1 a2 a3 a4 a5 a6 …) K indices ＝(0 2 2 1 2 3 …) K indptr ＝(0 2 3 3 5 6 …) Among them, K data For a non-zero submatrix arranged by rows and columns, K indices K is a submatrix listed according to the columns containing non-zero elements. indptr K corresponds to the first non-zero element in each row. data A submatrix of elements in the matrix; The large sparse matrix K, after compression of sparse rows, is preprocessed using the stable biconjugate gradient method: The weighted integral equation matrix is ​​transformed into the following expression: in, Let b be the error value obtained by subtracting both sides of the matrix expression of the weighted integral equation, where b is (b 11 …b m1 ) T x0 is (c 11 …c m1 ) T T is the transpose of the matrix; Then, the error value Substitute the following iterative equation: β=(j i / j i-1 (a / w) i-1 ) i=1,2,3,...,n p i =r i-1 +β(p i-1 -oh i-1 k i-1 )i=1,2,3,...,n k i =Kp i i=0,1,2,3,...,n s=r i-1 -αk i i=1,2,3,...,n t = Ks ω i =(t·s) / (t·t) i=1,2,3,...,n When the set error value is reached The following iterative calculations are performed: x i =x i-1 +αp i +ω i s i=1,2,3,...,n r i =s-ω i t i=1,2,3,...,n Where j0 = α = ω0 = 1, v0 = p0 = 0, and i represents the number n of the three-dimensional finite element elements from 1 to step E.

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