Question: we derived the shape functions for a one dimensional, two node element, N1 and N2. Suppose we now have another type of one dimensional element

we derived the shape functions for a one dimensional, two node element, N1 and N2. Suppose we now have another type of one dimensional element of length L but with three nodes with each located at the left side (x = 0), middle (x = L/2), and the right side (x = L), respectively. Starting with an appropriate polynomial, derive the three shape functions N1, N2, and N3. Also use MATLAB to plot these three functions and discuss their properties. When you make the plots, you can assume L =1 and also put all three plots in one figure.

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