Consider regular and irregular 3node onedimensional elements in figure 7.3. Both elements are mapped into the same reference element. When three different displacement conditions are imposed:

a. zero strain: \(u(x)=\) constant, \(\mathrm{d} u / \mathrm{d} x=0\)

b. constant strain: \(u(x)=x, \mathrm{~d} u / \mathrm{d} x=1\)

c. linear strain: \(u(x)=x^{2}, \mathrm{~d} u / \mathrm{d} x=2 x\)

Plot the mapping relation \(x(s)\), Jacobian \(d x / d s\), displacement gradient \(\mathrm{d} u / \mathrm{d} s\) in the

reference element, and strain \(\mathrm{d} u / \mathrm{d} x\) for each condition and check whether the interpolation yields accurate results or not.