Statistical model of strongly anisotropic rough surfaces for finite element contact analysis

The elastic model of anisotropic rough surfaces is considered by approximating the summits by elliptic paraboloids (vertical cross-sections are parabolas and horizontal cross-sections are ellipses). The complete description of anisotropic random surfaces is restricted here to strongly rough surfaces; for such surfaces the summits are represented by highly ecctentric elliptic paraboloids having their semi-major axes oriented in the direction of the grain. The statistical description of random, strongly anisotropic Gaussian surfaces based on the model of Bush et al. [5] is adopted. To calculate the forces and contact area for the single asperity in the elastic range the solution of Hertz is used. For modelling of the discontinuity at the contact surface a quadratic 18-node zero thickness interface element interacting with a transient 21-node hexahedral nite element is used. A beam of rectangular cross-section lying with one of its longitudinal narrow faces against at rigid base is selected to demonstrate applicability of the method proposed.