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Boundary value problems (Ordinary differential equations) with a beam

  1. Sep 11, 2011 #1
    1. The problem statement, all variables and given/known data

    The deflection y of a non-uniform beam of length equal to 1, simply supported at both
    ends and with uniformly distributed load q, is governed by the equation

    (E*I(x)*y'')'' + k*y=q
    y(0)=0, y''(0)=0, y(1)=0, y''(0)=0

    I(x)=A[1-0.5(1-x)2]2, 0<=x<=1

    where E =Young’s modulus of elasticity, I =moment of inertia, k =elastic foundation,
    q =load on the beam, A=area of cross-section of the beam and k = 6EA.
    Use the central difference approximation to solve the above differential equation to
    compute values for y(0.5) using h=1/2 and h=1/4.


    2. Relevant equations

    y'=(yr+1-yr-1)/2h

    y''=(yr-1-2yr+yr+1)/h2

    y'''=(yr+2-2yr+1+2yr-1-yr-2)/2h3

    y''''=(yr-2-4yr-1+6yr-4yr+1+yr+2)/h4

    k=6E*A

    3. The attempt at a solution

    I am not really sure what to do (E*I(x)*y'')''how to expand brackets with the differentiation on the outside. Other than that I am good with this sought of problem
    Thanks Jack
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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