Numerical Analysis of Cable Networks
In this section we consider the numerical analysis of cable networks within the framework of the geometrically nonlinear theory by using the modern algorithm for convex optimization.
We begin by recalling the results established in Chapter 4. Consider a cable network placed in the physical three-dimensional space. We denote by m and d the number of members and the number of the degrees of freedom of displacements, respectively. It has been shown that the minimization problem
of the total potential energy can be formulated as (see (4.41))
(PE) : min ϕ,c
wˆicab(ci)− ∑ j∈ΓN
p j (ϕj − xj)
s. t. ci = ‖Biϕ‖ − li, i = 1, . . . ,m, ϕj = ϕj , j ∈ ΓD.