Elastic Analysis of Submarine Pipelines

A submarine pipeline is idealized as a linearly elastic continuous beam subjected to vertical loads, and supported on a discretized frictionless seafloor profile. The structural analysis of this beam is considered as a unilateral contact problem. This paper presents two analytic solutions for the analysis problem under the small displacement assumption, by using the flexibility and stiffness approaches, respectively. These two approaches lead to alternative formulations of the problem as a linear complementarity problem, which is equivalent to a pair of dual quadratic programming problems. A numerical example shows that the flexibility and stiffness formulations yield the same results. In general, the stiffness formulation requires less effort in the data preparation, while the flexibility formulation is computationally more efficient. These two formulations can also be used for the analysis of unilaterally supported continuous beams subjected to various types of vertical loads. The effect of material nonlinearity can be included in the present formulations without difficulty.