For the analysis of highly flexible structures, the convected coordinates are introduced. The convected material coordinates are not often used in the field of structural analysis because of the mathematical difficulty. However for large rotation-small strain problems, complex tensor transformation rules become simpler.
This paper addresses the static and transient finite element analysis of large displacement-small strain problems in highly flexible structures which exhibit highly geometrical nonlinearities. The method employs convected coordinates for the description of the material constitutive behavior and detailed formulations are given for a Euler-Bernoulli beam element. The main advantages of the convected coordinate description presented here are its simplicity and applicability to highly flexible structures.
The method is applied for the analysis of the risers in the off-shore structures and also for other highly flexible structures.
