依据各向异性分形理论的固定结合面椭圆弹塑性法向接触刚度建模及仿真分析

依据各向异性分形几何理论，将结合面微凸体拓展为椭球体，结合微凸体接触点面积大小分布函数以及概率论相关理论获得关于椭圆形接触点接触面积以及离心率的二维联合分布密度函数，应用椭球体的赫兹接触理论，进而建立了依据各向异性分形理论的结合面椭圆弹塑性法向接触刚度模型，并采用MATLAB软件对影响结合面法向刚度的相关因素进行了数值仿真及结果分析。结果表明：结合面椭圆形接触点离心率分布情形对结合面总刚度具有明显影响，结合面总刚度随形状参数 的增大而增大，却随着形状参数 的增大而减小；结合面法向刚度随法向载荷的增大而增大；在同一载荷作用下，结合面法向接触刚度随塑性指数增大而增大，随分形粗糙度的增大而减小，但是随分形维数的增大而先增后减。该模型对模型优化进而提高计算精度提供了一定的理论依据。

Modeling and Simulation Analysis of Elliptic-Plastic Normal Contact Stiffness of Joint Surface Based on Anisotropic Fractal Theory

Establishing a more realistic contact model of joint surfaces is one of the key way to explore the variation law of stiffness characteristics. Firstly, according to the anisotropic fractal geometry theory, this paper equates the micro-convex body on the joint surface to an ellipsoid; Secondly, the two-dimensional joint distribution density function of the micro-contact area and eccentricity of the elliptical contact point was obtained by combining the micro-contact area distribution function and the related theory of probability theory; Finally, based on the Hertz theory, the elliptic elastoplastic normal contact stiffness model of the joint surface was established, and the related factors affecting the normal stiffness of the joint surface were numerically simulated and analyzed using MATLAB software. The results show that the eccentricity distribution of the elliptical micro-contact points on the joint surface has a significant effect on the total rigidity of the joint surface. The total stiffness of the joint surface increases with the increase of the shape parameter , but decreases with the increase of the shape parameter ; The normal stiffness of the joint surface increases with the increase of the normal load. When the load is constant, the normal contact stiffness of the joint surface increases with the increase of the plastic index and decreases with the increase of the fractal roughness, but increases first and then decreases with the increase of the fractal dimension. This model provides a certain theoretical basis for model optimization to improve calculation accuracy.