基于分形接触理论和半解析法的结合部分区域虚拟材料等效建模

In order to accurately characterize the dynamic performance of joint interface, a precise sub-regional virtual material equivalent modeling approach is proposed based on fractal contact theory and semi-analytical method, considering uneven contact pressure of joint interface. Firstly, the contact pressure of a joint interface is equivalent to a polynomial function, and the joint interface was divided into several sub-regions according to pressure distribution, so that the pressure within each sub-region is approximately uniform. Secondly, considering the micro morphology of the rough surface in each sub-region, W-M function is used to solve elastic-plastic deformation of asperities in sub-regions. With the purpose of accurately calculate the contact stiffness of sub-regions, a semi-analytical method is developed, so that the dimensionless contact area of rough surface under elastic-plastic deformation can be solved. Next, based on the fractal contact theory, the contact stiffness of sub-regions is calculated, and the equivalent virtual material parameters of sub-regions are derived. By weighting the nominal contact area of sub-regions, the equivalent virtual material parameters of whole joint interface are obtained. Finally, a modal test platform is built up, and a finite element model containing equivalent virtual material parameters is established. The result is compared with the equivalent virtual material parameters obtained through uniform pressure distribution and regardless of the microscopic morphology of rough surface. The accuracy and reliability of the modeling method proposed in this paper are verified through the analysis of experimental and simulation results.