# Calculate the stress in 2 elements

1. May 8, 2012

### quetzal

1. The problem statement, all variables and given/known data

Let assume that we have two rectangular prism elements of similar dimensions:
e.g. 1.) x0=100.1, y0=100.2, z0=90.4
2.) x0=100.2, y0=100.4, z0=90.0
How can I calculate the stress tensor of each of the two elements if I assembly them by merging their z-y faces together? I'd wanna use the Poisson's ratio(v=0.25)and linear elastic material (E=70GPa).

2. Relevant equations

V=x0(1+ε)*y0(1-vε)*z0(1-vε)
σ=εE

3. The attempt at a solution

The solution is easy If the material is absolutely compressible(v=0). I derived a general formula for the new y dimension(same for both elements) from the condition of mechanical equilibrium ƩFi(in y-direction)=0:
y=Ʃ(xi*zi)/Ʃ((xi*zi)/yi)
But I can't find any equation of mechanical equilibrium for my case. If you know at least how to calculate the principal stresses neglecting the shear elements of the matrices, that would be a great help too. FEM type of solution is welcomed too.

Last edited: May 8, 2012