# HW4 - EN222 Mechanics of Solids Homework 4 The Dreaded...

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EN222: Mechanics of Solids Homework 4: The Dreaded Polar Coordinates! Due Thursday February 3, 2003 Division of Engineering Brown University 1. Derive results corresponding to those developed in class for the Spherical coordinate system for the Cylindrical system. Your answer should include: 1. Formulas that convert from ,, rz q to 123 ,, xxx and back again 2. The position vector in the { i,j,k } basis in terms of ,, q 3. The components of the basis vectors {,,} q eee in the { i,j,k } basis, and corresponding expressions for { i,j,k } vectors in terms of q 4. Basis change matrices that map vector and tensor components between { i,j,k } and q 5. Expressions for the derivatives of the basis vectors q in terms of ,, q 6. A derivation of the gradient operator in cylindrical coordinates 7. The matrix of components of the gradients of a vector field

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2. Fig 1. shows a test designed to measure the response of a polymer to large shear strains. The sample is a hollow cylinder with internal radius 0 a and external radius 1 a . The inside diameter is bonded to a fixed rigid cylinder.
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HW4 - EN222 Mechanics of Solids Homework 4 The Dreaded...

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