Fundamental Solutions Of Some Typical Elastic Counter-conformal Contact Problems And The Related Numerical Methods

During the process of mechanical design and manufacturing, one has to consider the contact conditions between the mechanical parts. In the fields of aerospace and national defense technology, the plastic deformation is prohibited in the mechanical parts because of the high-intensity, high-precision design requirements. Otherwise, it will seriously affect the normal operation and mechanical performance, and may even lead to the development of cracks. Therefore, several typical contact models of half-space problems and their corresponding numerical algorithms are studies in this work. The main contents of this thesis consist of the following four parts.In the first part, Green's function related algorithms of the elastic half-space are studied. We first review the governing equations and their numerical discretization, and then present an iterative algorithm based on the conjugate gradient method to determine the contact area and the contact pressure. Finally, we comprehensively list elementary solutions for the elastic half-space contact analyses, while the Flamant-type solution is taken as an example to introduce the discrete Fast Fourier transform algorithm.In the second part, we study the discrete Fast Fourier transform algorithm of the three-dimensional layered(coating) materials. Firstly, the frequency response functions for calculating the displacements and stresses are determined in the frequency domain by using the Papkovich-Neuber potentials. Then we use conversion algorithm to obtain the discrete influence coefficients from a known frequency response function. Finally, we present the analytic solutions of the stress field produced by a sliding Hertzian contact. Three contour plots which are respectively produced through the Green's algorithm, the discrete Fast Fourier transform algorithm as well as the analytic solutions are compared to verify the current study.In the third part, we use the Hankle transformation and the theory of elasticity to derive basic formulas when the surface of a two-layered elastic model is under unit axisymmetric pressure, and propose a new method of meshing with annular grids. The mW transform extrapolation is used to obtain the numerical solution of the elastic field. For the two different loading methods, i.e., indentation depth based and contact loading based, we present the corresponding iterative algorithms with flow charts supplied for the reader's convenience.In the final part, two particular cases were selected to verify the axis-symmetric indentation solution. The influences of the coating thickness and stiffness on the distribution of contact pressure, indentation depth and other critical parameters are further examined. Finally, we present some concluding remarks, which may be of practical use to many mechanical designs and manufacturing processes.