Finite element formulation (Galerikan method)

Let the solution be

                                (12.17)

where a, b, c, ... are constants to be determined by boundary conditions, N is the shape function, r is the number of nodes in an element, and w is the nodal displacement. On substituting the approximate solution from equation (12.17) into EOM (12.15), the residue can be written as

                                                      (12.18)

where the superscript (e) represents the element.