High-precision mechanical simulation method and system for heterogeneous cable

Abstract

The invention belongs to the technical field of computer aided design, and discloses a high-precision mechanical simulation method and system for a heterogeneous cable, and the method comprises the steps: firstly dispersing the cable into limited sections based on a Cosseerat model, carrying out the fine mesh generation of each section, and constructing a high-resolution network model; then, regarding each section as a thin shell structure, and deducing a shape function of the thin shell structure by utilizing a shell theory; secondly, coarse nodes are introduced to form a coarsened shell model, a displacement vector at the section is constructed through the coarse nodes, and a shape function of the coarsened shell model is reconstructed; and in each section plane, taking coarse node displacement as a degree of freedom, and calculating potential energy of each section of the cable by using a shape function of the coarsening shell model. And the total potential energy is minimized through global optimization, so that the optimal displacement of the thick node of each section is determined, and the accurate simulation of the overall form and deformation of the cable is realized. According to the invention, high simulation precision is maintained, and the behavior of the heterogeneous cable under a complex environment condition can be accurately captured.

Description

Technical Field

[0001] The invention application belongs to the field of computer-aided design technology in aviation intelligent manufacturing, and specifically relates to a high-precision mechanical simulation method and system for heterogeneous cables. It creatively proposes and implements a coarsened shell model based on Cosserat theory, aiming to efficiently solve the problem of accurate simulation of heterogeneous cables in engineering. Background Art

[0002] When discussing the modeling and simulation technology of elastic and slender objects such as cables, because the length of the cable is much greater than the radius, traditional methods are difficult to accurately simulate its complex behaviors, such as bending and torsion. More advanced and sophisticated simulation technology is needed to more accurately describe its material properties and dynamic behavior.

[0003] With the deepening of academic research, a variety of methods have emerged in the field of modeling and simulation of slender objects, including but not limited to the spring mass model, Cosserat elastic rod, energy curve method, etc. These methods are based on different theoretical frameworks and assumptions, so their scope of application and performance show significant differences. Specifically, the energy curve method is an analysis method focusing on static characteristics, and its core is to simulate the bending and tensile deformation of static cables. However, this method is difficult to fully capture the dynamic response of cables in dynamic environments or complex interactions. The spring mass model focuses on dynamic simulation, but because it is based on a simplified physical model, it often cannot accurately reflect the real physical state of the object during complex deformation, thus limiting the application of this method in high-precision scenarios. The Cosserat model improves the original elastic rod model so that it can reflect the bending, torsion, shear and tensile deformation of slender objects and accurately simulate their posture in three-dimensional space. Most existing studies on elastic slender rods use the Cosserat model.

[0004] The model based on Cosserat theory simplifies the elastic rod in three-dimensional space into a continuous one-dimensional curve, and the standard orthogonal frame accompanying its motion provides directional information to define stretching, shearing, bending and torsion, thereby constructing the deformation energy equation. After solving this equation, the mechanical behavior of the elastic rod can be simulated, which is suitable for hair, ropes and single cables with uniform material distribution. However, when faced with slender elastic bodies with complex material distribution, Cosserat theory is difficult to perform high-precision simulation tasks due to its limitations.

[0005] In view of the limitations of Cosserat theory in the simulation of elastic bodies with complex material distribution, scholars have proposed to expand the application scope of Cosserat model by customizing the material matrix into a non-diagonal form to reflect the physical properties of anisotropic materials. However, it is still challenging to accurately obtain the material matrix that reflects the material distribution characteristics. Another solution is a hybrid model proposed to simulate hollow tubes with deformable cross-sections. This model binds the elastic surface network to the Cosserat rod, and uses the surface network to characterize the shape of the hollow tube. The Cosserat rod is responsible for simulating global mechanical properties, such as bending, torsion, shear and stretching. This method achieves high-fidelity simulation of elastic hollow tubes of inhomogeneous materials by coordinating the surface elastic energy and the shape of the reference rod to deform realistically and effectively.

[0006] For the high-precision mechanical simulation of heterogeneous cables that the present invention focuses on, it is difficult to construct an accurate material matrix for a specific cable due to its diverse material distribution and numerous models. At the same time, the existing hybrid model is also insufficient when dealing with cables with complex material distribution. In summary, the traditional Cosserat model theory has obvious limitations in simulating cables with complex material distribution. Therefore, it is necessary to invent a high-precision simulation method that is suitable for complex heterogeneous cables. Summary of the invention

[0007] The present invention application proposes a high-precision mechanical simulation method and system for heterogeneous cables, and invents a coarsened shell model based on Cosserat theory. By combining the Kirchhoff-Love shell theory with the Cosserat theory, a material-aware elastic energy function is established at the cable cross section to describe the overall elastic behavior, and a numerical coarsening method is used to reduce the degrees of freedom in the shell simulation, thereby achieving high-precision mechanical simulation of heterogeneous cables.

[0008] In order to achieve the above invention objectives, the technical solutions adopted in this application are as follows:

[0009] A high-precision mechanical simulation method for heterogeneous cables comprises the following steps:

[0010] The cable is discretized into finite cross sections based on the Cosserat model;

[0011] Finely meshing each of the cross sections to construct a high-resolution network model;

[0012] Consider each of the cross sections as a thin shell structure and derive its shape function using shell theory;

[0013] Introducing coarse nodes at the cross section to form a coarsened shell model, constructing a displacement vector at the cross section through the coarsened nodes, and reconstructing a shape function of the coarsened shell model;

[0014] In each of the cross-sectional planes, the displacement of the coarse node is used as the degree of freedom, and the shape function of the coarsened shell model is used to calculate the potential energy of each cross section of the cable. The total potential energy is minimized through global optimization to determine the optimal displacement of the coarse node of each cross section, thereby achieving accurate simulation of the overall shape and deformation of the cable.

[0015] As a further solution of the present invention: the fine grid division strategy is as follows: for each discrete cross-section of the cable, first use a square network with a side length equal to the cable diameter to surround the outside, and then implement discretization processing of standard quadrilateral network units in the square area to construct a refined network structure.

[0016] As a further solution of the present invention: the method for setting the coarse node is specifically as follows:

[0017] In each discrete section of the cable, the coarse nodes are divided into two categories according to their position differences;

[0018] The first type of coarse nodes directly selects the center points of each core inside the cable, and its number is equal to the total number of cores;

[0019] The second type of coarse nodes are located at the four corner points and the midpoints of the four sides of the square grid surrounding the discrete section, totaling 8 nodes.

[0020] As a further solution of the present invention: quadratic B-spline is used as basis function in the fine grid.

[0021] As a further solution of the present invention: the shape function of the coarsened shell model is constructed by: constructing the cross section P from the coarse nodes α The displacement vector Q at α , reconstruct the shape function N of the coarse shell model based on the coarse nodes α (x):

[0022] N α (x) = N h (x)Φ α ;

[0023] Among them, Φ α is the coarsened node displacement Q α Displacement q to fine mesh node α The mapping matrix, N h (x) is the shape function obtained using shell theory.

[0024] As a further solution of the present invention: the mapping matrix Φ α The construction method is: construct the displacement Q from the coarsening node α Displacement to boundary node q b The MLS interpolation matrix Ψ α and boundary node displacement qb Displacement q to fine mesh node α The shell transformation matrix M α ; Hence, we have: Φ α =M α Ψ α .

[0025] As a further solution of the present invention: the MLS interpolation matrix Ψ α The construction method is as follows: For the boundary node x0 in the fine grid, the fitting equation at this point is obtained according to the least squares method:

[0026]

[0027] Among them, c is the coefficient vector function, b(x0) is the basis function, and m is the number of basis vectors;

[0028] Based on the moving least squares method, the coefficient c is adjusted to minimize the weighted sum of squares of the difference between the value of the sampling point near the node and the value of the fitting function at the sampling point. The optimization model is established and its minimum value is obtained to obtain the coefficient vector function b(x0) at the node x0. The model is derived and Ψ is introduced p (x), we can get the displacement value q at the boundary node x0 b (x0):

[0029]

[0030] Among them, Q p is the displacement Q at the coarse node α The individual component values ​​of ;

[0031] Written in matrix form, it is expressed as:

[0032]

[0033] This gives the displacement Q from the coarsened node. α Displacement to boundary node q b The MLS interpolation matrix Ψ α :

[0034] Ψ α =[Ψ(x0), x0∈boundary node].

[0035] As a further solution of the present invention: the shell transformation matrix M α The construction method is as follows:

[0036] Each cross-section plane is considered as a thin shell and the shell transformation matrix is ​​constructed using the Kirchhoff-Love shell theory. In a fine mesh with n nodes, q i, i = 1, 2, ..., n is the discretized node displacement, N i (x) is C in the equation 1 Continuous B-spline shape function, according to the classical Galerkin method, the shell displacement is given by the basis function N i The linear combination of (x) is expressed as:

[0037]

[0038] Use B-spline shape function N i (x), calculate the covariant basis vector a α Relative to the displacement u r The first derivative of , the first derivative and the second derivative of the virtual work are taken to obtain the residual vector R h and the tangent stiffness matrix K h , thus, the displacement q α It can be obtained by solving the following linear system:

[0039] K h q α =-R h ;

[0040] By changing the displacement q of the fine node α Classified as boundary fine node displacement q b and the internal fine nodal displacement q i , rearrange the above equation to:

[0041]

[0042] where k b , k bi , k ib , k i and R b , R i K h and R h The relevant submatrices / subvectors in R i =0, we get the following equation:

[0043]

[0044] Where I is the identity matrix, M α is the desired shell transformation matrix.

[0045] A high-precision mechanical simulation system for heterogeneous cables, comprising:

[0046] one or more processors;

[0047] A memory for storing one or more programs;

[0048] When the one or more programs are executed by the one or more processors, the one or more processors implement the steps of the high-precision mechanical simulation method.

[0049] Compared with the prior art, the beneficial effects of this application are:

[0050] 1. In order to achieve high-precision simulation of hybrid cables with inhomogeneous materials, this paper innovatively proposes a coarsened shell model based on Cosserat theory. The model constructs a material-sensitive cable cross-sectional elastic energy function to accurately characterize the elastic behavior of the cable. The model combines the advantages of Cosserat theory in slender structure simulation and the strengths of Kirchhoff-Love shell theory in deformation analysis, and uses numerical coarsening technology to optimize computational efficiency.

[0051] 2. The present invention can not only effectively handle the anisotropy of materials, but also is significantly superior to the traditional Cosserat model in terms of calculation speed and accuracy, showing great potential in high-precision simulation of complex material mixed slender cables.

[0052] The present application is further described below in conjunction with the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0054] In the attached picture:

[0055] Figure 1 It is a typical cable structure, which is discretized with a certain accuracy;

[0056] Figure 2 It is a definition of nodes in the roughened shell model of the present invention;

[0057] Figure 3 Implementation details for the moving least squares method;

[0058] Figure 4 Schematic diagram of the wiring harness model used in the experiment;

[0059] Figure 5 An overall comparison of the simulation results of the method proposed in the present invention and other methods;

[0060] Figure 6 Comparison of stress distribution between the simulation results of the method proposed in this invention and other methods. DETAILED DESCRIPTION

[0061] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0062] The main process of the present invention is as follows: first, the cable is discretized into finite cross-sections based on the Cosserat model, then the potential energy of each cross-section is calculated using the shell theory, and finally a custom shape function is constructed by a coarsening method to improve the calculation efficiency. The scheme proposes a coarsening shell model based on the Cosserat theory for heterogeneous cable simulation. The coarsening shell model fully utilizes the advantages of the Cosserat theory when simulating slender cables, and cleverly integrates the essence of the Kirchhoff-Love shell theory when simulating the deformation of the cable section. The numerical coarsening method is used to reduce the degree of freedom in the shell simulation. The coarsening shell model describes the elastic behavior of the cable by establishing a cable cross-section energy function with material-sensitive characteristics, and simulates the elastic behavior of the cross-section on a regular rough background grid by constructing a set of new material-aware shape / basis functions, which well captures the material anisotropy of the cross-section. Compared with the direct finite element analysis method, the coarsening shell model has fewer degrees of freedom, thereby improving the simulation efficiency. Compared with the Cosserat model, the coarsening shell model has a stronger ability to perceive materials, thereby improving the accuracy of the simulation.

[0063] The cross-sectional energy function is a new type of material-sensitive shape function constructed on the cross section of the Cosserat model based on the Kirchhoff-Love shell theory by extending the bridge node method for three-dimensional solid linear elastic simulation. The material-sensitive shape function has important geometric properties such as unit division and Lagrangian properties, and can be simulated reliably. The material-sensitive shape function uses a shape function reconstruction method based on the moving least squares method (MLS) to reduce the scale of the model and speed up the simulation by optimizing the number of nodes of the reconstructed shape function.

[0064] The theoretical composition of the method of the present invention will be briefly introduced below.

[0065] Figure 1 For a typical cable structure, it is divided into N-1 sections with a certain accuracy, so as to obtain N cable cross sections P α (α=1,2,…,N). Next, fine mesh division is performed on each cross section of the cable to obtain fine mesh units. Where m is the number of fine grid units. αAs a thin shell, the Kirchhoff-Love shell theory can be used to obtain the shape function of the cross section and further obtain the potential energy equation of the cross section. The fine grid division is specifically as follows: at each discrete cross section of the cable, a square grid with a side length equal to the cable diameter is used to surround the discrete cross section, and then a standard quadrilateral grid unit is used inside the discrete grid to discretize the square grid area. The quadrilateral grid is the fine grid used in the present invention. The size of the fine grid can be adjusted accordingly according to the complexity of the material distribution at the cable cross section. Figure 2 The fine grid division and the boundary fine nodes and internal fine nodes are reflected in it.

[0066] Since the shape function is the basic function of shell simulation, its linear combination is used to describe the deformation of the cross-sectional plane. 1 Continuous shape function. Therefore, on a fine grid The quadratic B-spline is used as the basis function. The basis function is defined as:

[0067]

[0068] Where φ is the univariate quadratic B-spline basis function, h is the fine cell size, and N i (x) is defined on the surrounding 4×4=16 fine units. For any point x in , its x-, y-, and z-displacement components u(x), v(x), and w(x) are interpolated using the surrounding 16 non-zero quadratic B-spline basis functions:

[0069] u(x)=N 1 (x)u1+N 2 (x)u2+…+N 16 (x)u 16 ,

[0070] v(x)=N 1 (x)v1+N 2 (x)v2+…+N 16 (x)v 16 ,

[0071] w(x)=N 1 (x)w1+N 2 (x)w2+…+N 16 (x)w 16 ,

[0072] Among them, u i , v i and w i is the displacement component of the 16 surrounding fine nodes. Further, the displacement component u(x)=(u(x),v(x),w(x)) at any point x can be obtained.T :

[0073]

[0074] Among them, N θ (x) is the shape function of each element in the fine grid, q θ is the displacement vector of each element in the fine grid.

[0075] Each fine grid The shape function N in θ (x) Combine to get the overall fine grid The shape function matrix N h (x):

[0076]

[0077] According to shell theory, using the shape function N h (x) can calculate the cable cross section P α The potential energy equation at the position is used to further simulate the posture of the cable.

[0078] However, if the above-mentioned fine grid is directly used, a high-fidelity solution will be produced, but the large number of degrees of freedom will bring expensive computational costs; on the other hand, the Cosserat model treats the rod as a homogeneous material, resulting in a large loss of simulation accuracy. Therefore, the present invention solves this problem by introducing a coarsened shell model, as described below:

[0079] A series of coarse nodes are introduced at the cross section to form a coarse shell model. The displacement vector at the cross section is constructed by the coarse nodes, and the shape function of the coarse shell model is reconstructed. In each cross-sectional plane, the displacement of the coarse nodes is used as the degree of freedom, and the shape function of the coarse shell model is used to obtain the potential energy of each cross section of the cable, and the displacement of the coarse nodes of each cross section is determined by minimizing the total potential energy.

[0080] The specific method for setting coarse nodes is as follows: corresponding coarse nodes are set in each discrete section of the cable. According to the different positions of the coarse nodes, the setting of coarse nodes is divided into two categories: one is the center points of each core inside the cable as coarse nodes, and the number is the number of cores; the other is the four corner points and the midpoints of the four sides of the square surrounding the discrete section, and the number is 8. Figure 2 The following is a description of the definition of nodes in the roughened shell model of the present invention. Figure 2 (b) shows a series of coarse nodes χ we introduced α , the section P is constructed from the coarse nodes α The displacement vector Q at α The present invention reconstructs the shape function N of the coarsened shell model based on the coarse nodes. α (x):

[0081] N α (x) = N h (x)Φ α ;

[0082] Among them, Φ α is the coarsened node displacement Q α Displacement q to fine mesh node α The mapping matrix, the construction of which is the key to the present invention. The construction of the mapping matrix involves the displacement of Q from the coarsening node α Displacement to boundary node q b The MLS interpolation matrix Ψ α and boundary node displacement q b Displacement q to fine mesh node α The shell transformation matrix M α The specific construction methods of these two matrices will be introduced in detail below.

[0083] The above is the theoretical structure of the present invention. Since the present invention newly introduces a coarsened shell model, a coarsened shell shape function with higher material perception ability can be obtained by using fewer coarse nodes, thereby greatly reducing the amount of calculation while ensuring accuracy.

[0084] The MLS interpolation matrix Ψ in the present invention is specifically introduced below. α construction details. Figure 3 The implementation details of the MLS method are as follows. Based on the displacement of the coarse node, the displacement Q α Displacement to boundary node q b The MLS interpolation matrix Ψ α x0 is a boundary node in the fine grid. According to the least squares method, the fitting equation at this point is:

[0085]

[0086] Wherein, c is the coefficient vector function, b(x0) is the basis function, and m is the number of basis vectors. In the present invention, the basis function takes a three-dimensional second-order form:

[0087] b(x0)=[1,x,y,z,xy,yz,zx,x 2 ,y 2 , z 2 ] T ;

[0088] c=[c1,c2,...c m ] T ;

[0089] In the moving least squares method, the coefficient c needs to be adjusted to minimize the weighted sum of squares of the difference between the value of the sampling point near the node and the value of the fitting function at the sampling point, thereby establishing the optimal model.

[0090]

[0091] Where n is the number of coarse nodes, and x p is the position coordinate of the pth coarse node; Q p is the displacement Q at the coarse node α A single component value; w(x) is a weighted function with a search radius of R, which takes the maximum value at the center of the circle and gradually decays to 0 as the radius increases:

[0092]

[0093] Next, by asking The coefficient vector c at the node x0 is obtained by taking the minimum value of . The following equation is obtained by differentiating the model:

[0094] Where = 0, 1, ... m;

[0095] Right now:

[0096] In order to simplify the formula, variables H(x0) and Ψ are introduced p (x), H(x0) and Ψ p (x) is defined as follows:

[0097]

[0098] Ψ p (x) = b T (x)H -1 (x0)b(x p )w(x p -x0);

[0099] The above formula can be written as follows:

[0100]

[0101] Converted to vector form:

[0102]

[0103] From this, the displacement value q at any boundary node x0 can be obtained b (x0):

[0104]

[0105] Written in matrix form, it can be expressed as:

[0106]

[0107] This gives the displacement Q from the coarsened node. α Displacement to boundary node q b The MLS interpolation matrix Ψ α :

[0108] Ψ α =[Ψ(x0), x0∈boundary node].

[0109] The shell transformation matrix M in the present invention will be specifically introduced below. α The construction details. Figure 1 As shown in the figure, the cable is discretized according to a certain accuracy to obtain a series of cable cross-sections P α , each section plane P α They are all regarded as a thin shell, and the Kirchhoff-Love shell formula is used to establish the equilibrium equation, and then the shell transformation matrix is ​​constructed based on the equilibrium equation.

[0110] First, the basic theory of Kirchhoff-Love shells is introduced. In Kirchhoff-Love shell theory, the transverse shear strain deformation is neglected and the vector perpendicular to the mid-surface remains normal after deformation. By using curvilinear coordinates (ξ 1 ,ξ 2 ,ξ 3 ), cross-section shell P α It can be expressed as:

[0111] x(ξ 1 ,ξ 2 ,ξ 3 )=r(ξ 1 ,ξ 2 )+ξ 3 a3(ξ 1 ,ξ 2 );

[0112] Among them, r(ξ 1 ,ξ 2 ) represents the mid-surface of the shell, a3 is the unit normal vector to the mid-surface, ξ 3 is the coordinate in the thickness direction (-0.5t≤ξ 3 ≤0.5t, where t is the thickness of the shell). The deformed and undeformed configurations are denoted by x,r and X,R, respectively. From this, the covariant basis vectors of the midsurface and normal vector can be obtained:

[0113]

[0114] Among them, α represents the components of the two bases parallel to the mid-surface. Next, the covariance coefficient a is defined as αβ and the curvature tensor coefficient b αβ for:

[0115] a αβ =a α ·a β , b αβ =a3·a α，β .;

[0116] Based on the above definition, we can get the Green-Lagrange strain E α，β :

[0117] E αβ =ε αβ +ξ3κ αβ ;

[0118] In the formula, ε αβ , κ αβ are membrane strain and bending strain respectively:

[0119]

[0120] κ αβ =b αβ -B αβ ;

[0121] Among them, A αβ and B αβ denote the covariance coefficient and curvature tensor coefficient under the undeformed configuration, respectively, from which the membrane stress n of the linear elastic material can be obtained αβ and bending moment m αβ , whose components are as follows:

[0122]

[0123] Among them, E and v are Young's modulus and Poisson's ratio of the material, and the symbol (-) represents the corresponding physical quantity based on the Cartesian coordinate system. Using the principle of virtual work to define the variational formula of the Kirchhoff-Love shell problem, the potential energy equation of the shell can be obtained:

[0124]

[0125] Where u represents the displacement, δu is the virtual displacement, δε is the virtual membrane strain, δκ is the virtual bending strain, and f is the enforcing body force.

[0126] Next, we use the Kirchhoff-Love shell theory to construct the shell transformation matrix. Figure 2 In the fine quadrilateral mesh with n nodes shown in the figure, q i, i = 1, 2, ..., n is the discretized node displacement, N i (x) is C in the equation 1 Continuous B-spline shape function. According to the classical Galerkin method, the shell displacement can be expressed by the basis function N i The linear combination of (x) is expressed as:

[0127]

[0128] Use B-spline shape function N i (x), we can calculate the covariant basis vector a α Relative to the displacement u r The first derivative of for:

[0129]

[0130] Take the first and second derivatives of the virtual work and get the residual vector R h and the tangent stiffness matrix K h :

[0131]

[0132] Therefore, the displacement q α It can be obtained by solving the following linear system:

[0133] K h q α =-R h .

[0134] By changing the displacement q of the fine node α Classified as boundary fine node displacement q b and the internal fine nodal displacement q i , the above equation can be rearranged as:

[0135]

[0136] Among them, k b , k bi , k ib , k i and R b , R i K h and R h The relevant submatrices / subvectors in . Assume R i =0, we can get the following equation:

[0137]

[0138] Where I is the identity matrix, M αis the desired shell transformation matrix.

[0139] The following will introduce the process of applying the roughened shell shape function to cable simulation. α (x) is expressed as:

[0140] N α (x) = N h (x)Φ α =N h (x)M α Ψ α ;

[0141] It can be seen that the shape function proposed in the present invention can utilize the Q α To approximate the high-fidelity displacement q of the fine node α :

[0142] u(x)=N α (x)Q α

[0143] =N h (x)M α Ψ α Q α

[0144] =N h (x)M α q b

[0145] =N h (x)q α .;

[0146] Therefore, the shape function N proposed by the present invention is adopted α (x) provides higher accuracy at lower computational cost. In each section plane, the coarse node displacement Q α as degrees of freedom and using the coarse shell shape function N α (x), the derivative of the covariant basis vector can be similarly calculated to obtain the residual vector R H，α and the stiffness matrix K H，α , and then the potential energy of each cross section of the cable is obtained

[0147]

[0148] Based on this, the displacement Q of the coarse nodes of all cross-sectional planes is α The total potential energy can be minimized by get:

[0149]

[0150] In order to verify the effectiveness of the present invention, the following is a specific test case using the method of the present invention:

[0151] Figure 4 This is a typical heterogeneous harness model in this experiment. The harness is made of four cables. The material differences in the harness are marked in the figure. One end of the harness is fixed and the other end is free. The harness as a whole is subject to gravity.

[0152] Based on this test model, the finite element method, Cosserat method and improved roughened shell model are used to simulate it, and three different simulation results are obtained, such as Figure 5 , 6 As shown, the deformation and stress distribution of three different methods are shown. Taking the simulation results of the finite element method as a benchmark, the simulation results of the method of the present invention and the Cosserat method are compared and analyzed. From the results, it can be seen that the simulation results of the Cosserat method are quite different from the calculation results of the finite element method, with an error index of 1.01, while the calculation results of the method of the present invention are relatively close to the finite element method, with an error index of 0.16. In terms of accuracy, the latter is 6 times higher than the former. This is because the Cosserat method fails to take into account the material anisotropy of the heterogeneous wire bundle, which is quite different from the benchmark finite element results. In addition, the calculation time of Cosserat is 4.3s, while the calculation time of the present invention is 6.7s. This is because the method of the present invention introduces more degrees of freedom when calculating the global displacement, but the overall simulation speed can still meet the needs of practical applications.

[0153] The present application also provides a high-precision mechanical simulation system for heterogeneous cables, the system comprising:

[0154] one or more processors;

[0155] A memory for storing one or more programs;

[0156] When the one or more programs are executed by the one or more processors, the one or more processors implement any of the above-mentioned high-precision mechanical simulation methods for heterogeneous cables.

[0157] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0158] So far, the purpose of the present invention has been achieved.

[0159] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A high-precision mechanical simulation method for heterogeneous cables, characterized in that: The steps include: The cable is discretized into finite cross sections based on the Cosserat model; Finely meshing each of the cross sections to construct a high-resolution network model; Consider each of the cross sections as a thin shell structure and derive its shape function using shell theory; Introducing coarse nodes at the cross section to form a coarsened shell model, constructing a displacement vector at the cross section through the coarsened nodes, and reconstructing a shape function of the coarsened shell model; In each of the cross-sectional planes, the displacement of the coarse node is used as the degree of freedom, and the shape function of the coarsened shell model is used to calculate the potential energy of each cross section of the cable. The total potential energy is minimized through global optimization to determine the optimal displacement of the coarse node of each cross section, thereby achieving accurate simulation of the overall shape and deformation of the cable.

2. The high-precision mechanical simulation method for heterogeneous cables according to claim 1, characterized in that: The fine grid division strategy is as follows: for each discrete cross-section of the cable, a square network with a side length equal to the cable diameter is first used to surround the outside, and then the standard quadrilateral network unit is discretized in the square area to construct a refined network structure.

3. The high-precision mechanical simulation method for heterogeneous cables according to claim 1, characterized in that: The method for setting the coarse node is specifically as follows: In each discrete section of the cable, the coarse nodes are divided into two categories according to their position differences; The first type of coarse nodes directly selects the center points of each core inside the cable, and its number is equal to the total number of cores; The second type of coarse nodes are located at the four corner points and the midpoints of the four sides of the square grid surrounding the discrete section, totaling 8 nodes.

4. The high-precision mechanical simulation method for heterogeneous cables according to claim 2, characterized in that: In the fine grid, quadratic B-spline is used as basis function.

5. The high-precision mechanical simulation method for heterogeneous cables according to claim 1, characterized in that: The shape function of the coarsened shell model is constructed by: constructing the cross section P from the coarse nodes a The displacement vector Q at a , reconstruct the shape function N of the coarse shell model based on the coarse nodes a (x): N a (x)=N h (x)Φ a 4 Among them, Φ a is the coarsened node displacement Q a Displacement q to fine mesh node a The mapping matrix, N h (x) is the shape function obtained using shell theory.

6. The high-precision mechanical simulation method for heterogeneous cables according to claim 5, characterized in that: The mapping matrix Φ a The construction method is: construct the displacement Q from the coarsening node a Displacement to boundary node q b The MLS interpolation matrix Ψ a and boundary node displacement q b Displacement q to fine mesh node a The shell transformation matrix M a ; Therefore, we have: Φ a =M a Ψ a .

7. The high-precision mechanical simulation method for heterogeneous cables according to claim 6, characterized in that: The MLS interpolation matrix Ψ a The construction method is as follows: For the boundary node x0 in the fine grid, the fitting equation at this point is obtained according to the least squares method: Among them, c is the coefficient vector function, b(x0) is the basis function, and m is the number of basis vectors; Based on the moving least squares method, the coefficient c is adjusted to minimize the weighted sum of squares of the difference between the value of the sampling point near the node and the value of the fitting function at the sampling point. The optimization model is established and its minimum value is obtained to obtain the coefficient vector function b(x0) at the node x0. The model is derived and Ψ is introduced p (x), we can get the displacement value q at the boundary node x0 b (x0): Among them, Q p is the displacement Q at the coarse node a The individual component values ​​of ; Written in matrix form, it is expressed as: This gives the displacement Q from the coarsened node. a Displacement to boundary node q b The MLS interpolation matrix Ψ a : Ψ a =[Ψ(x0), x0∈boundary node].

8. The high-precision mechanical simulation method and system for heterogeneous cables according to claim 6, characterized in that: The shell transformation matrix M a The construction method is as follows: Each cross-section plane is considered as a thin shell and the shell transformation matrix is ​​constructed using the Kirchhoff-Love shell theory. In a fine mesh with n nodes, q i , i = 1, 2, ..., n is the discretized node displacement, N i (x) is C in the equation 1 Continuous B-spline shape function, according to the classical Galerkin method, the shell displacement is given by the basis function N i The linear combination of (x) is expressed as: Use B-spline shape function N i (x), calculate the covariant basis vector a a Relative to the displacement u r The first derivative of , the first derivative and the second derivative of the virtual work are taken to obtain the residual vector R h and the tangent stiffness matrix K h , thus, the displacement q a It can be obtained by solving the following linear system: K h q a =-R h ; By changing the displacement q of the fine node a Classified as boundary fine node displacement q b and the internal fine nodal displacement q i , rearrange the above equation to: where k b , k bi , k ib , k i and R b , R i K h and R h The relevant submatrices / subvectors in R i =0, we get the following equation: Where I is the identity matrix, M a is the desired shell transformation matrix.

9. A high-precision mechanical simulation system for heterogeneous cables, characterized in that: include: one or more processors; A memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the steps of the method according to any one of claims 1 to 8.

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