Derive the Lagrange cubic interpolation functions for a four-node (one-dimensional) element (with equally spaced nodes) using the alternative procedure based on interpolation properties listed in Eqs...

Derive the Lagrange cubic interpolation functions for a four-node (one-dimensional) element (with equally spaced nodes) using the alternative procedure based on interpolation properties listed in Eqs. (3.2.23) and (3.2.24). Use the local coordinate ¯x for simplicity.