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Unformatted text preview: 1.033/1.57: H#4: Champagne Method (3D-ElastoPlasticity) Due: Part 1-3 (H#4): December 1, 2003 Part 4 (Q#3): December 5, 2003 MIT 1.033/1.57 Fall 2003 Instructor: Franz-Josef ULM We consider a rigid infinite half-space with an empty hole of diameter 2 a and length L (see figure below). In this hole we want to force a deformable cylinder sample of same length L but of a greater diameter 2 R > 2 a than the bore hole. The cylinder is initially stress free, and it is entirely forced into the hole. During this processus, the cylinder preserves its length. The contact between the cylinder walls and the bore hole walls is frictionless. We want to study the stress fields and the required force F to maintain the cylinder in the bore hole. Throughout this exercise we assume isothermal and quasi-static evolutions, and body forces are disregarded. L L 2 R 2 a e z F 2 R 2 a e r e A A B B Rigid Halfspace Deformable Cylinder Section A Section B Deformable cylinder in a rigid halfspace. Due: Part 1-3 (H#4): December 1, 2003 Part 4 (Q#3): December 5, 2003 page 2 1. Deformation and Strain: We consider a displacement field of the form: = u ( r ) e r + D with u...
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