Direct Variational and Weighted Residual Methods: Classical Trial Function Methods - Mechanics of Structures: Variational and Computational Methods - page 461

N u

From w = w , the approximate deflection would be

p 0 L 4

2 3 4 2 3 4 5

w =

EI [0

. 0125 ( 3 ξ − 5 ξ + 2 ξ ) − 0 . 00417 (ξ + ξ − 4 ξ + 2 ξ ) ]

L 4
120 EI [4

2 3 4 5 ]

= p 0 ξ − 8 ξ + 5 ξ − ξ (9)

w

to be established
which satisfies all boundary conditions as is required by the Galerkin procedure. If fifth
degree Hermitian polynomials (Fig. 7.4) are used, the approximate deflection could be

Use of Hermitian polynomials would also permit an approximate

FIGURE 7.4
Fifth degree Hermitian polynomials, ξ = x / L .