1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Optimisation - Using the lagrange method

  1. Sep 8, 2013 #1
    1. The problem statement, all variables and given/known data
    The problem asks to design a cantilever beam of a minimum weight consisting of 2 steps.

    Given: total length (L), Force (F) at the end of the beam and allowable stress (σ)
    Need to find the diameters D and d, the length of the smaller shoulder of the beam (x).


    2. Relevant equations
    MB = F*x
    MA= F*L

    σB = MB/ZB = (32 * F* x)/ (pi * d^3)
    σA = MA/ZA = (32 * F* L)/ (pi * d^3)

    Where zA = (pi*D^3)/32 zB = (pi*D^3)/32 section modulus


    So this is what I have done so far :

    Solve for D = ((32*F*L)/(4*pi*(σ))^1/3
    Solve for V = (pi*D^2/4)*(L-2*x) +2*(pi*d^2/4)*x = pi*D^2*x/2+ pi*d^2*x/2



    Im not sure how to implement this into the lagrange expression.

    I now that the volume represents the objective function and the the condition of strength at point A represents a constraint.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?