Cylinder on a Plane Since we aren’t familiar with contact, we’re going to try a problem for which we know the answer. We will consider an infinitely long steel cylinder pressing into a semi‐infinite steel plate. The cylinder has a radius of 0.1m. Steel has E=2x1011 Pa, =0.3, and y=2.5x108 Pa. The force F exerted on the cylinder is 109 N for each meter of length. Use the excerpt from Shigley and Mischke (posted on the website) as a reference and complete (a) and (b) below. (a) Take a 0.1m‐long slice of the infinitely long system. Calculate the maximum pressure in the region between the cylinder and the plate. (How does this compare to the yield strength?) (b) Calculate the width of the contact region between the cylinder and the plate. (What fraction of the diameter is in contact?) If we model the geometry in the plane rather than 3D, it will run much quicker. Which elements would probably be the best choice? Plates/shells Plane Stress Plane Strain Axisymmetric The steel plate is semi‐infinite. How big should we make it? What other simplifications can we make to the geometry to reduce the time it will take to run the model? If we are working in the x‐y plane, which stresses should be continuous across the contact region? (Assume that x points to the right and y is positive upwards.) Select and explain. xx yy xy vonMises (equivalent) (First Principle Stress) 1 (Second Principle Stress) 2 (Third Principle Stress) 3