2 weighted residual methods 3 cable in the latter

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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. p 11 00 11 00 11 00 11 00 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 0 1]. 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...
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