Numerical solution of dry contact problem based on fast Fourier transform and conjugate gradient method

In order to solve elastic contacts of rough surfaces, the problem is firstly formulated as a linear complementarity energy problem, and then converted into a quadratic programming problem with constrictions. A conjugate gradient method (CGM) is used to solve the pressure distribution, whose correct factor in conjugate gradient direction is specially optimized to improve the convergence. A fast Fourier transform (FFT) based method for calculation of surface deformation is used to speed up the calculation of elastic deformation, which takes much computation time. The algorithm efficiently overcomes the periodical error caused by FFT. Several cases are presented for point contacts including single asperity, wavy surface and real engineering rough surfaces, and also for finite line contact. It can be found that present numerical algorithm is very efficient, and has consistently convergent property for different rough surfaces and contact types; meantime, its accuracy little depends on the mesh density. It appears to be a useful tool for engineers.