In Section 2 2 , before employing any small deformation assumptions, the two dimensional extensional strain component e x was expressed as We now wish to investigate the nature of small deformation theory by exploring this non linear relation for the special case with linear displacement field dist...

For the case u Ax v Bx du Ex 12 8 ...

In Section 2.2 , before employing any small deformation assumptions, the two-dimensional extensional strain component e x

Question:

In Section 2.2 , before employing any small deformation assumptions, the two-dimensional extensional strain component e_x was expressed as:

ex A'B' - AB AB 1+2=+ x 2 + x 2 - 1

We now wish to investigate the nature of small deformation theory by exploring this non-linear relation for the special case with linear displacement field distributions u= Ax; v = Bx (A and B constants). Clearly this case gives constant displacement gradients Numerically evaluate this strain component and make plots of e_x /A versus A for0.001 ≤A≤0.01 with particular values of B = 0.01 ; 0.02 ; 0.03 . Realizing that under small deformation assumptions, e_x/A = 1, comment on the behavior shown in these plots.