f02q2sol

# f02q2sol - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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MIT OpenCourseWare http://ocw.mit.edu 18.085 Computational Science and Engineering I Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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FALL 2002 QUIZ2 SOLUTIONS Problem 1 (40 points) This question is ahoiit a fixed-free hanging har (made of 2 materials) with a point load at z = i: a) (i) At x = i, u and w are continuous. Then 1~, must have a jump (ii) At x = i, r~ is continuoils (as always) while w jumps by 1. We should expect 2 to have a jump unless such jump is "accidentally" 0. b) where the three constants A, B, and C are determined from the boundary condition w (1) = 0; resulting in continuity of w at z = i, resulting in 4BA=0, + and [w]- = 1,resulting in 4C4B=l This system with three equation and three linkowns is easily solved, yielding A = 1;B = i, C = 0. Summarizing: s+D, O<x<l \$s+E,L<z<, 3 F, 3 ,<2<1 where the three constants D, E; and F are detemined from the boundary condition n (0) = 0:
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• Fall '10
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• Boundary value problem, Jump, South Yorkshire, Jump In!, boundary condition, OpenCourseWare, fixed-free hanging har

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f02q2sol - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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