Abstract
Abstract The purpose of this paper is to provide numerical solutions to the following problems in nonlinear structural mechanics. A slender beam with nonlinear, elastoplastic flexural characteristics is unilaterally supported in the plane by a frictionless, rigid profile. The first problem is to determine the equilibrium configuration under given vertical loads and end traction; the second, seemingly new problem is to determine the changes of the unilaterally supporting profile which reduce the curvatures of the beam below assigned values with the least total cost. Both problems arise in offshore engineering when a pipeline has to be laid on a rough seabottom, but analogous problems are found in other contexts. Approximate solution procedures are developed in view of practical applications in this context by a unified approach resting on suitable discretization (cubic splines, lumped compliance models), complementarity theory and mathematical programming. The former problem (analysis) is dealt with in the range of large displacements; geometric linearity is assumed for the latter optimization problem.
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