ABSTRACT
Eq. (12.128) for element (i - I) gives:
( Q(i-Il M) ( Q(i-Il M) P(i-llM-yo 1 I - +y. 1+ - = 0/- 3 / 6 2
Yi-I I + 6 Yi I 3 2 - 0
Applying Eq. (12.128) for element (i) gives:
( Q(il /h2) (Q(i1 M) P(i1/h2-Yi I - 3 +Yi+1 I + --6-- --2-= 0
( Q(il/h2) (Q(il M) p(i1 MYi I + 6 - Yi+ I I - 3 - --2-= 0
(l2.130a)
(12.130b)
(12.133)
(12.132)
Adding Eqs. (12. I29b) and (12.130a) yields the nodal equation for node i. Thus,
(12.131)
Equation (12.131) is identical to Eq. (12.98), which was obtained by the RayleighRitz nodal approach. Applying the assembly step to Eq. (12.127), which is valid for /hi_1 =I-/hi' yields Eq. (12.97). These results demonstrate that the nodal approach and the element approach yield identical results, and that the Rayleigh-Ritz approach and the Galerkin weighted residual approach yield the same results when the weighting factors W;(x) are the shape functions of the interpolating polynominals.
