Elastic and elasto-plastic analysis of submarine pipelines as unilateral contact problems

Abstract

A submarine pipeline is conceived as a slender beam, subjected to vertical loads and undergoing “small” deflections, contrasted without friction by a supporting rigid profile. The relevant contact (unilateral constraint) problem is formulated in approximate, algebraic terms on the basis of discrete models, allowing for the presence of a significant given tension force. The flexural behaviour is first assumed as linearly elastic and the analysis is formulated as a linear complementarity problem (LCP) (or to a variational inequality). Subsequently, nonlinear, elasto-plastic flexural behaviour is considered. This is described by a piecewise linear moment-curvature relation, and the analysis is shown to lead to the same kinds of mathematical problems as in the elastic case. In both cases a pair of dual extremum principles is pointed out, leading to a pair of equivalent dual quadratic programming problems (QPP). Among available algorithms for the numerical solution, systematic overrelaxation is found to be convenient and efficient for problems arising in engineering situations. Computational experience of practical relevance is discussed.