Unformatted text preview: Weighted Residual Methods 3 cable. In the latter case, for example, u(x) represents the lateral de ection at position
x of a cable having (scaled) unit length that is subjected to a tensile force p, loaded by
a transverse force per unit length f (x), and supported by a series of springs with elastic
modulus q (Figure 1.2.1). The situation resembles the cable of a suspension bridge. The
tensile force p is independent of x for the assumed small deformations of this model, but
the applied loading and spring moduli could vary with position.
q(x) p x u(x) f(x) Figure 1.2.1: De ection u of a cable under tension p, loaded by a force f per unit length,
and supported by springs having elastic modulus q.
Mathematically, we will assume that p(x) is positive and continuously di erentiable
for x 2 0 1], q(x) is non-negative and continuous on 0 1], and f (x) is continuous on
Even problems of this simplicity cannot generally be solved in terms of known functions thus, the rst topic on our agenda will be the development of a means of calculating
approximate solutions of (1.2.1). With n...
View Full Document