接触力学英文讲义(精品·公开课件).ppt

Contact Mechanics Maria Persson Gulda Kathleen DiSanto Outline What is Contact Mechanics? The two different kind of contacts. Boussinesq and Cerruti Potential Functions The specific case of an Applied Normal Force Hertz Equations- Derivation, Assumptions Rigid Sphere Contacting a Deformable Plate Deformable Sphere Contacting a Rigid Plate What is Contact Mechanics? “[The theory of contact mechanics] is concerned with the stresses and deformation which arise when the surfaces of two solid bodies are brought into contact.” Professor Johnsson Two kinds of contact Conforming contacts The two surfaces fit exactly or closely together without deformation Non-conforming contact The surfaces, or one of the two surfaces, deforms when there is a contact area in between them. Derivation: Boussinesq and Cerruti Potential Functions Here are the potential functions: Each satisfy Laplace’s equation: Special Case: Applied Pressure Only The potential functions are reduced as follows: Displacement equations: By Hooke’s Law, the stresses are: Concentrated Normal Force on an Elastic Half Space The displacements are: The stresses in polar coordinates: Concentrated Force Cont. Now looking only at the surface, z=0 The displacements in polar coordinates become: For a general pressure distribution, the displacement for any surface point in S, by Green’s function method, becomes: Hertz Pressure The Pressure distribution is: Equation for determining surface displacement: The Hertz displacement equation: Hertz Theory of Elastic Contact Assumptions: The radii of curvature of the contacting bodies are large compared with the radius of the circle of contact. The dimensions of each body are large compared to the radius of the circle of contact. The contacting bodies are in frictionless contact. The surfaces in contact are continuous and nonconforming. Examples Focus on two examples: Rigid spherical indenter pushing to deformable flat sur