Incremental Response of 3-D Cable Networks

A finite element analog to the nonlinear response of single cables to dynamic loadings has been introduced previously. The intent of this note is to extend the applicability of the finite element model previously presented to networks of intersecting cables in three dimensions. Toward that end, the nonlinear Hamilton's principle in three dimensions for the incremental deformation of a cable element (including corrections to that used previously) is used to generate the linearized matrix analog for the incremental deployment, both static and dynamic, of the cable net. The solution processes for both the forced nonlinear dynamic response and the static nonlinear response of networks are given. In addition, a method for determining the natural frequencies and modes of free vibration of networks about arbitrary equilibrium positions is developed. Examples in three dimensions are used to verify and illustrate those solution methods.