# Consider the fourth-order equation (4.1) and its weak form (4.4). Suppose that a two-node element is

Consider the fourth-order equation (4.1) and its inefficient form
(4.4). Suppose that a two-node atom is industrious, delay three primary
variables at each node: where θ = dw/dx and K = d^{2}
w/dx^{2 }. Show that the associated interpolation (Hermite) functions
are ardent by

where x is the atom coordinate delay the commencement at node 1. Also appraise the atom barbarism matrix and hardness vector.