 #1
 22
 2
 Homework Statement:

1D mechanical bar. Two different materials that clamped at x = 0. both are isotropic and perfectly bonded together. Young's modulus E1 = 10GPa and E2 = 50GPa. displacement of 2um at x = 2mm
Find the stresses, strains and displacements in each of the bars.
Plot the energy per unit volume in material 1 as a function of the Young's modulus in material 1, for five cases. E = 1, ,5, 10, 25 and 50
 Relevant Equations:

Epsilon (stress) = sigma (strain) / E (young's modulus)
du (displacement)/ dx = * E = strain
I have a TA that is ignoring me, so I have to resort to this online forum. Also, a very unhelpful example from lecture (just 1).
I have some other equations, but I dont really know how they all tie together.
I find epsilon = 10um/1mm (both materials are 1 mm in length) = 1E2mm/mm
sigma 2 = E1*epsilon = 50E7Pa
sigma 1 = E2*epsilon = 10E7Pa
As far as the second part, I thought I did something reasonable, but after rereading it, I realized I missed a crucial part of the problem.
I can provide anything else that you may want to help me understand this homework (in context) since I don't have anyone to explain it to me. Other than the lectures which are very unhelpful.
I have some other equations, but I dont really know how they all tie together.
I find epsilon = 10um/1mm (both materials are 1 mm in length) = 1E2mm/mm
sigma 2 = E1*epsilon = 50E7Pa
sigma 1 = E2*epsilon = 10E7Pa
As far as the second part, I thought I did something reasonable, but after rereading it, I realized I missed a crucial part of the problem.
I can provide anything else that you may want to help me understand this homework (in context) since I don't have anyone to explain it to me. Other than the lectures which are very unhelpful.