High-precision Cossseerat model and method based on coarsened shell

Abstract

The invention discloses a high-precision Cosseerat model and method based on a coarsened shell. The high-precision Cosseerat model and method are used for solving the problem that an existing Cosseerat model is difficult to carry out high-simulation-precision elastic simulation on a heterogeneous material mixed cable. According to the model, a Cosseerat theory is adopted to carry out modeling on a slender cable, a Kirchhoff-Love shell theory is adopted to carry out modeling on cross section energy of the cable, and a material perception shape function is constructed to carry out numerical coarsening so as to reduce the degree of freedom; meanwhile, a multi-constraint condition module is introduced, and multiple constraint types such as fixed constraint, hinge constraint and sliding constraint are supported. The model combines the advantages of a Cosserat model and a Kirchhoff-Love shell theory, the calculation efficiency is improved through numerical coarsening, complex working conditions are accurately simulated through multiple constraint conditions, the simulation efficiency is improved with less freedom compared with a direct finite element method (FEM), the simulation precision is improved through a material perception energy function and the multiple constraint conditions compared with a traditional Cosserat model, and the simulation efficiency is improved. Local and global deformation of the hybrid cable under complex constraints can be calculated more accurately, and the method has important application value in the field of high-precision simulation of heterogeneous material hybrid cables.

Description

Technical Field

[0001] This invention relates to the field of cable elasticity simulation technology, specifically to a high-precision Cosserat model and method based on a roughened shell. Background Technology

[0002] In industrial applications, accurate simulation of the elastic behavior of slender, elastic objects such as cables is crucial for product design and performance optimization. The Cosserat model and its variants, due to their efficiency and accuracy, have become the mainstream method for studying the elastic behavior of cables. This model treats the cable as a continuum with an internal structure, introducing additional degrees of freedom to describe shear and torsional deformation, thus effectively simulating the mechanical behavior of cables under large deformations.

[0003] However, the Cosserat model has limitations. It assumes a homogeneous internal structure for cables, but in real-world applications, many cables are made from a mixture of heterogeneous materials to meet different performance requirements. For example, cables in the aerospace field need to combine high strength, lightweight, and good electromagnetic shielding performance, and may be composed of high-strength alloy wires combined with insulating shielding materials. Flexible cables in electronic devices need to be flexible and durable, and may contain various polymer materials with different elastic moduli. Because the Cosserat model cannot account for material differences, it is difficult to achieve high simulation accuracy when simulating hybrid cables, and it cannot accurately reflect their local and global deformation characteristics, thus limiting its application in practical engineering.

[0004] Furthermore, while the traditional direct finite element method (FEM) can accurately model complex structures, it requires a large number of degrees of freedom (DOF) to describe structural deformation when simulating slender objects such as cables. This results in low computational efficiency and high costs, making it difficult to meet the rapid simulation needs of practical engineering. At the same time, in actual working conditions, cables are often under multiple constraints, such as being fixed at one end, hinged in the middle, or sliding along a specific track. Existing models do not adequately consider the elasticity simulation of cables under multiple constraints, leading to significant deviations between simulation results and actual working conditions, and thus failing to provide a reliable basis for engineering design. Summary of the Invention

[0005] The purpose of this invention is to provide a high-precision Cosserat model and method based on a roughened shell, which solves the problem that existing Cosserat models are difficult to perform high-precision elastic simulation of heterogeneous material hybrid cables. At the same time, it overcomes the disadvantage of low computational efficiency of the direct finite element method. By introducing a multi-constraint processing module, it accurately simulates the elastic behavior of cables under complex constraint conditions, and achieves a high level of simulation accuracy for heterogeneous material hybrid cables while ensuring computational efficiency.

[0006] The technical solution adopted in this invention is as follows:

[0007] This invention provides a high-precision elastic simulation model for heterogeneous material hybrid cables under multiple constraints, comprising:

[0008] 1. Cosserat Theory-Based Cable Modeling Module: This module utilizes Cosserat theory to model slender cables, treating them as a series of tiny units with mass, moment of inertia, and elastic properties. By establishing the overall dynamic equations of the cable, it describes the overall geometric and mechanical properties of the slender cable, fully leveraging the advantages of the Cosserat model in representing slender cables holistically, and effectively simulating the overall mechanical behavior of cables under large deformation conditions.

[0009] 2. Cross-sectional energy modeling module based on Kirchhoff-Love shell theory: This module treats the cable cross-section as a thin-shell structure and models its energy based on Kirchhoff-Love shell theory. Considering bending, tension, and shear deformation, it establishes an energy function for the cable cross-section, accurately simulating the deformation of the cable cross-section under different loads, thus overcoming the limitations of the Cosserat model in effectively describing cross-sectional deformation.

[0010] 3. Material-Aware Shape Function Construction and Numerical Coarsening Module: Based on the distribution and characteristics of different materials in the heterogeneous hybrid cable, a new set of material-aware shape functions is constructed. According to the mechanical property parameters (such as elastic modulus, Poisson's ratio, etc.) of different materials in the cable, shape functions that reflect the material differences are designed. These material-aware shape functions are used to interpolate and approximate the deformation of the cross-section, numerically coarsening the high-degree-of-freedom shell simulation, reducing the degrees of freedom (DOF) in the shell simulation, and effectively reducing computational complexity and improving computational efficiency while ensuring simulation accuracy.

[0011] 4. Multi-Constraint Processing Module: This module defines and processes various constraints on the cable during simulation. Supported constraint types include fixed constraints, hinged constraints, and sliding constraints. Fixed constraints restrict all displacement and rotational degrees of freedom at a specific endpoint of the cable; hinged constraints restrict displacement degrees of freedom at a specific endpoint while retaining rotational degrees of freedom; and sliding constraints restrict displacement degrees of freedom at a specific endpoint while retaining displacement and rotational degrees of freedom in other directions. This module transforms user-defined constraints into corresponding boundary conditions and integrates them into the overall simulation model, ensuring that the simulation results conform to actual working conditions.

[0012] Accordingly, the present invention also provides a high-precision elastic simulation method for heterogeneous material hybrid cables under multiple constraints, which, using the above model, includes the following steps:

[0013] S1. Overall cable modeling: The cable modeling module based on Cosserat theory is used to model slender cables. By analyzing and setting the cable's geometric parameters (such as length, diameter, etc.) and mechanical parameters (such as density, elastic modulus, etc.), the overall geometric and mechanical parameters of the cable are obtained, and the overall dynamic equation of the cable is established.

[0014] S2. Cross-sectional Energy Modeling: The cross-sectional energy of the cable is modeled using the cross-sectional energy modeling module based on Kirchhoff-Love shell theory. Based on the shape and material distribution of the cable cross-section, a cross-sectional energy function considering bending, tension, and shear deformation is established according to Kirchhoff-Love shell theory to accurately describe the deformation characteristics of the cross-section.

[0015] S3. Numerical Coarsening: A material-aware shape function construction and numerical coarsening module is used to construct material-aware shape functions based on the characteristics of heterogeneous materials in the cable. These shape functions are used to interpolate and approximate the deformation of the cross-section, achieving numerical coarsening of the shell simulation, reducing the degrees of freedom in the shell simulation, and lowering computational complexity.

[0016] S4. Constraint Definition and Conversion: The multi-constraint processing module defines cable constraints based on actual operating conditions. For example, in aerospace cable installation scenarios, one end of the cable can be defined as a fixed constraint, while the middle section connecting to the equipment can be defined as a hinged constraint. This module converts the defined constraints into corresponding boundary conditions, providing accurate constraint information for subsequent simulation calculations.

[0017] S5. Coupled Solution of Results: The results of the above four modules are coupled together, and the overall dynamic equation of the cable, the energy function of the cross section and the boundary conditions after the transformation of multiple constraints are combined. The degree of freedom after numerical coarsening is also considered. The elastic simulation results of the heterogeneous material hybrid cable under multiple constraints are obtained by numerical solution methods (such as finite element method, finite difference method, etc.). These results include the mechanical performance parameters of the cable under complex constraints, such as local and global deformation and stress distribution.

[0018] Beneficial effects

[0019] (1) It can significantly improve the simulation accuracy. The CSC model of this invention combines the advantages of Cosserat theory and Kirchhoff-Love shell theory. It considers the characteristics of heterogeneous materials through the material-aware shape function and introduces a multi-constraint processing module. Compared with the traditional Cosserat model, it can more accurately calculate the local and global deformation of hybrid cables under complex constraints, effectively improve the accuracy of elastic simulation of heterogeneous hybrid cables, and better fit the actual working conditions.

[0020] (2) It can significantly improve computational efficiency. By constructing a material-aware shape function for numerical coarsening, the degrees of freedom in shell simulation are reduced. Compared with the direct finite element method (FEM), this model can use fewer DOFs to achieve elastic simulation of cables. While ensuring simulation accuracy, it significantly improves simulation efficiency, reduces computational costs, and meets the needs of rapid simulation in practical engineering.

[0021] (3) It has wide applicability. The model and method of this invention are applicable to the elastic simulation of various types of heterogeneous material hybrid cables under various constraint conditions. It can provide accurate theoretical basis and effective technical support for the design, optimization and performance evaluation of cables under complex working conditions, and has broad application prospects in aerospace, mechanical manufacturing, electronics and electrical appliances and other fields. Attached Figure Description

[0022] Figure 1 This is a module diagram for high-precision elastic simulation and modeling of heterogeneous material hybrid cables under multiple constraints. Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0024] Example 1

[0025] Elastic simulation was performed on a heterogeneous hybrid cable composed of high-strength alloy wire and insulating shielding material. One end of the cable is fixed to the aircraft structure, and the middle part is connected to other equipment through a hinge.

[0026] (1) The cable is modeled as a whole using the cable modeling module based on Cosserat theory. Based on the actual length, diameter and other geometric parameters of the cable, as well as the density, elastic modulus and other mechanical parameters of the alloy wire and the insulation shielding material, the overall dynamic equation of the cable is established to describe the overall geometric and mechanical properties of the cable.

[0027] (2) The cross-section of the cable is modeled using the cross-sectional energy modeling module based on the Kirchhoff-Love shell theory. The cross-section of the cable is regarded as a thin shell structure. Based on the distribution of alloy wires and insulating shielding materials, a cross-sectional energy function considering bending, tension and shear deformation is established according to the Kirchhoff-Love shell theory.

[0028] (3) Using the material-aware shape function construction and numerical coarsening module, material-aware shape functions are constructed based on the differences in mechanical properties between alloy wire and insulating shielding material. These shape functions are used to interpolate and approximate the deformation of the cross section, thereby achieving numerical coarsening of the shell simulation and reducing the degrees of freedom in the shell simulation.

[0029] (4) Through the multi-constraint processing module, one end of the cable is defined as a fixed constraint, which restricts all displacement and rotational degrees of freedom of the end point; the middle part connected to the equipment is defined as a hinge constraint, which restricts displacement degrees of freedom, retains rotational degrees of freedom, and converts the constraint conditions into corresponding boundary conditions.

[0030] (5) The results of the above modules are coupled, and the coupled equations are solved using the finite element method to obtain the elastic simulation results of the heterogeneous hybrid cable under aerospace conditions, including the local and global deformation and stress distribution of the cable under fixed and hinged constraints. By comparing and verifying with the actual test results, it is shown that the model and method of the present invention can effectively improve the accuracy and efficiency of the elastic simulation of the heterogeneous hybrid cable under complex constraint conditions.

[0031] Example 2

[0032] Elastic simulation was performed on a flexible heterogeneous hybrid cable composed of multiple polymer materials. One end of the cable is fixed to a circuit board, and the other end can slide along a slide rail.

[0033] Similarly, we first perform overall cable modeling based on Cosserat theory, cross-sectional energy modeling based on Kirchhoff-Love shell theory, and material-aware shape function construction and numerical coarsening. Then, through a multi-constraint processing module, we define one end of the cable fixed to the circuit board as a fixed constraint and the other end as a sliding constraint, restricting its displacement degree of freedom in the direction perpendicular to the slide rail, while retaining the displacement and rotational degrees of freedom in other directions, and converting them into boundary conditions. Finally, we perform coupled solving to obtain the elastic simulation results of the cable under this working condition, verifying the effectiveness and practicality of this invention in the simulation scenario of electronic device cables.

[0034] The specification and drawings of this invention are intended to be illustrative rather than restrictive. Based on this invention, those skilled in the art can make substitutions and modifications to some of the technical features without creative effort, and all such modifications are within the scope of protection of this invention.

Claims

1. A high-precision Cosserat model and method based on a roughened shell, characterized in that, Includes the following steps: S1, a cable modeling module based on Cosserat theory, used to model slender cables; S2, a cross-sectional energy modeling module based on Kirchhoff-Love shell theory, used to model the cross-sectional energy of cables; S3, Material-aware shape function construction and numerical coarsening module, is used to construct a set of material-aware shape functions and perform numerical coarsening through the material-aware shape functions to reduce the degrees of freedom in shell simulation; S4, the multi-constraint processing module, is used to define and process various constraints on cables during the simulation process.

2. The high-precision Cosserat model and method based on a roughened shell according to claim 1, characterized in that, The multi-constraint processing module supports at least one of the following constraint types: fixed constraint, hinge constraint, and sliding constraint. The fixed constraint is used to restrict all displacement and rotational degrees of freedom of a certain end of the cable. The hinge constraint is used to restrict the displacement degree of freedom of a certain end of the cable, while retaining the rotational degree of freedom. The sliding constraint is used to restrict the displacement degree of freedom of a certain end of the cable in a specific direction, while retaining the displacement and rotational degrees of freedom in other directions.

3. The high-precision Cosserat model and method based on a roughened shell according to claim 1, characterized in that, The cable modeling module based on Cosserat theory describes the overall geometric and mechanical properties of slender cables using Cosserat theory. It treats the cable as a series of tiny units with mass, moment of inertia, and elastic properties, and establishes the overall dynamic equation of the cable.

4. The high-precision elastic simulation model for heterogeneous material hybrid cables considering multiple constraints as described in claim 1, characterized in that, The cross-sectional energy modeling module based on Kirchhoff-Love shell theory treats the cross-section of the cable as a thin shell structure. Based on Kirchhoff-Love shell theory, it considers bending, tension and shear deformation to establish the energy function of the cable cross-section.

5. The high-precision Cosserat model and method based on a roughened shell according to claim 1, characterized in that, The material-sensing shape function construction and numerical coarsening module constructs a material-sensing shape function that reflects the material differences based on the distribution and characteristics of different materials in the heterogeneous material hybrid cable. The material-sensing shape function is used to interpolate and approximate the deformation of the cross section, thereby reducing the degrees of freedom in the shell simulation.

6. A high-precision Cosserat model and method based on a roughened shell, characterized in that, The application of the high-precision elastic simulation model of heterogeneous material hybrid cables considering multiple constraints as described in any one of claims 1 to 5 includes the following steps: S1. Use the cable modeling module based on Cosserat theory to model the slender cable and obtain the overall geometric and mechanical parameters of the cable; S2. The cross-sectional energy of the cable is modeled using the cross-sectional energy modeling module based on Kirchhoff-Love shell theory to obtain the energy function of the cable cross-section; S3. Construct material-aware shape functions using the material-aware shape function construction and numerical coarsening module, and perform numerical coarsening to reduce the degrees of freedom in shell simulation; S4. Define the constraints of the cable through the multi-constraint processing module and convert them into corresponding boundary conditions; S5. Couple the results of the above modules to obtain the elastic simulation results of the heterogeneous material hybrid cable considering multiple constraints.

Images