HOMEWORK 4_W13(1)

# HOMEWORK 4_W13(1) - DREXEL UNIVERSITY Department of...

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DREXEL UNIVERSITY Department of Mechanical Engineering & Mechanics Applied Engineering Analytical & Numerical Methods II MEM 592 - Winter 2013 HOMEWORK #4: Due Thursday, February 14 @ 6 30 pm 1. [100 points] Consider a horizontal beam which is supported at its ends. Let ݕሺݔሻ denote the vertical displacement of the beam ݔ length units away from the left side. If ݕԢሺݔሻ is small and a uniformly transverse load ݓ is applied on the beam then it can be shown that ݕሺݔሻ is modeled by the differential equation: ݕԢԢሺݔሻ ൌ ாூ ݕ ൅ ௪௫ሺ௫ି௅ሻ ଶாூ , 0 ൑ ݔ ൑ ܮ (1) where ܧ is the modulus of elasticity, ܫ is the moment of inertia and ܮ is the length of the beam. i) Formulate the structure of the Shooting Method for this BVP using the Newton-Raphson approach to update ݒ (present all the equations you will need to implement this method). ii) Use the RK4 subroutine that you developed in previous homeworks and the Shooting Method structure in
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• Spring '14
• Numerical Analysis, BVP, Applied Engineering Analytical & Numerical Methods II, shooting method

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