New Solutions in Contact Mechanics

1 - Summary 2 - Symbols and notation 3 - Introduction 4 - Summary of the basic equations Basic equations of linear elasticity; Concentrated forces on a half-plane; Papkovich-Neuber solution; Concentrated normal force on a half-space; Concentrated tangential force on a half-space; Arbitrary load distribution on the surface; Hertz's formula for the stress in cylinders; The reduced elastic friction model; Example: Interior stress field for plane contact; Contact of equal layers 5 - Solutions for plane contact Introduction; Symmetric normal contact; Asymmetric and general normal contact; Oblique contact of symmetric profiles; Uncoupled plane contact with end singularities; Dissimilar half-planes under full sliding; Flat punch with square edge and rounding; Superposition of punches; Multiple contact areas; Table of solutions 6 - Solutions for axi-symmetric profiles Normal contact; Torsional loading; Tangential shift; General equations for the coupled problem; Table of solutions 7 - General contact and comparison with FEM and BEM programs Hertzian normal contact; General load histories for Hertzian contact; Examples for Hertzian contact; Comparison with Ansys; Comparison with Beasy 8 - Computation of contact problems Discretization of half-planes; Uncoupled half-planes; Discrete equations for half-spaces; Contact algorithms for normal contact; Algorithms for frictional contact 9 - Gauss-Seidel method for frictional contact problems Introduction; Contact conditions and sign conventions; Vector formulation of the load displacement equations; The Gauss-Seidel method; Linearization of the friction law; Contact algorithms; Convergence of the Gauss-Seidel method; Convergence of the block iteration method 10 - Numerical results for incremental load-histories Introduction; Spheres; Elliptical contact areas; Dissimilar materials; Torsion with shift; Flat punch; Examples for dissimilar material 11 - Basic equations and solutions for impact The principal axes of inertia and the principal curvatures; The equations of motion; Normal solution; Tangential solution for the compression phase; Restitution phase; Velocity ratio; 12 - Tangential and torsional impact of spheres Tangential contact of spheres; The equations of motion; Impact algorithm and comparison with Maw et al.; Torsion of elastic spheres; Impact with torsion; Algorithm for torsional impact; Comparison with Horak's result 13 - Numerical results for impact Verification of the Cattaneo-Mindlin theory; Impact with dissimilar materials; Torsion; Ellipsoid bodies 14 - Applications Ultrasonic motors; Granular material; Oblique impact of eccentric bodies; Self locking of brakes