hw1-1 - EN222: Mechanics of Solids Homework 1: Basic...

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EN222: Mechanics of Solids Homework 1: Basic Kinematics and Kinetics Due Tuesday February 3, 2002 Division of Engineering Brown University 1. Write down the displacement field associated with a rigid rotation through an angle q about the 3 x axis. Calculate the Lagrange strain tensor E and the infinitesimal strain tensor e for this motion. 2. Find expressions for the three strain invariants defined in class (or the e-notes) in terms of the principal values of the reduced right stretch tensor B . 3. A cylindrical bar with length L and radius a is held at its base and twisted at constant rate f & through an angle f at the top while keeping its length fixed. Take the undeformed configuration as reference. Let (,, ) RZ Θ denote the cylindrical-polar coordinates of a material point in the reference configuration, and let {,, } R Z Θ ee e be cylindrical-polar basis vectors at ) Θ . Let (,, ) rz q denote the coordinates of this point in the deformed configuration, and let } r z q e by cylindrical-polar basis vectors located at (,, ) q . Assume that plane sections
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hw1-1 - EN222: Mechanics of Solids Homework 1: Basic...

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