HW6 - EN222 Mechanics of Solids Homework 6 Contact...

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EN222: Mechanics of Solids Homework 6: Contact Mechanics Due Thursday March 23, 2006 Division of Engineering Brown University 1. The figure shows a rigid wedge with profile ( ) f x k x = indenting an isotropic, linear elastic half- space with Young’s modulus E and Poisson ratio ν (a) Write down an integral equation for the contact pressure distribution (b) Solve the integral equation to find an expression for the contact size a in terms of k, material properties, and the applied load P , and find an expression for the contact pressure distribution. The following singular integral (which MAPLE has trouble with) will be helpful a P 1 2 2 2 2 1 ( ) 1 1 1 2 1 log 1 1 (1 ) sign x d x x x ξ ξ ξ ξ + 1 x = < < 2. A sphere with radius R and Young’s modulus E and Poisson ratio ν is pressed into the surface of an elastic half-space with identical elastic properties by an applied force P . Using the procedure outlined in class to model contact between two elastic cylinders, write down an integral equation for
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