In one-dimensional bar elements, there is only one rigid body motion test ( (x) translation) and one

Question:

In one-dimensional bar elements, there is only one rigid body motion test ( $x$ translation) and one constant strain test ( $\varepsilon_{x x}=$ constant). Consider a patch of two bar elements shown in figure 9.40 with $E=10 \mathrm{GPa}, A=10^{-6} \mathrm{~m}^{2}$. Show that the element passes the two patch tests using the following shape functions for element ( $i$ ):

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