# Homework Help: Boundary value problems (Ordinary differential equations) with a beam

1. Sep 11, 2011

### CptJackWest

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

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