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MIT2_094S11_hw_6 - 2.094 FINITE ELEMENT ANALYSIS OF SOLIDS...

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2.094 F INITE E LEMENT A NALYSIS OF S OLIDS AND F LUIDS S PRING 2008 Homework 6 Instructor: Prof. K. J. Bathe Assigned: 03/13/2008 Due: 03/20/2008 Problem 1 (20 points): Consider Example 6.3 in the textbook, pages 494, 495. Assume that the equilibrium has been established for 3 2 10 2 t R kL = × where 2 3.70223 10 t L Δ = × . Next, the equilibrium for 3 3 10 2 t t R kL Δ + = × shall be established. Perform the full Newton-Raphson iteration in Eqs. (6.11) and (6.12) to calculate t t L Δ Δ + . Use as the convergence criterion ( ) ( 1 6 ) 1 1.0 10 2 t t t t i R F kL Δ Δ + + = × . Calculate the tangent stiffness matrices using the finite difference scheme given in class; you need to select an
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