Question

w that Oxy Suppose that the infinitesimal element shown below is in equilibrium. Sho 1. origin (0,0,0 4z dx 2. Compute the values of the components of the 2-D Green strain Exx, Evy, and Exy and compare to those for the linearized strain Exx,eyy, and εxy. (a) ur = (X + 0.001Y)-X, ux = (x + 0.00 1y)-x (b) ux(X +0.8Y)-X, xx + 0.8y)-x lly=y-y. Explain why the linearized strain in Problem 2 (b) does not give a good approximation of the Green strain.

Answer 1

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Question 1:

For equilibrium,

$\sum F_{y}=0$

$\sigma _{xy}-\sigma _{yx}=0$

ry

Hence proved.