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Abstract: The purpose of this paper is to model the detailed effects of interactions that take place between components of un-bonded flexible risers, and to study the three-dimensional motion responses of risers when subjected to axial loads, bending moments, and internal and external pressures. A constitutive law for un-bonded flexible risers is proposed and a procedure for the identification of the related input parameters is developed using a multi-scale approach. A generalized finite element structural model based on the Euler–Bernoulli beam theory is developed in which the constitutive law is embedded. The beam theory is enhanced by the addition of suitable pressure terms to the generalized stresses to account for the internal and external pressures, and it can therefore be efficiently used for large-scale analyses. The developed nonlinear relationship between generalized stresses and strains in the beam is based on the analogy between frictional slipping between different layers of a flexible riser and frictional slipping between micro-planes of a continuum medium in non-associative elasto-plasticity. The merit of the present constitutive law lies in its ability to capture many important aspects of the structural response of risers, including the energy dissipation due to frictional slip between layers and the hysteresis response. [Copyright &y& Elsevier]

Abstract: In this paper a new constitutive model for flexible risers is proposed and a procedure for the identification of the related input parameters is developed using a multi-scale approach. The constitutive model is formulated in the framework of an Euler–Bernoulli beam model, with the addition of suitable pressure terms to the generalized stresses to account for the internal and external pressures, and therefore can be efficiently used for large-scale analyses. The developed non-linear relationship between generalized stresses and strains in the beam is based on the analogy between frictional slipping between different layers of a flexible riser and frictional slipping between micro-planes of a continuum medium in non-associative elasto-plasticity. Hence, a linear elastic relationship is used for the initial response in which no-slip occurs; an onset-slip function is introduced to define the ‘no-slip’ domain, i.e. the set of generalized stresses for which no slip occurs; a non-associative rule with linear kinematic hardening is used to model the full-slip phase. The results of several numerical simulations for a riser of small-length, obtained with a very detailed (small-scale) non-linear finite-element model, are used to identify the parameters of the constitutive law, bridging in this way the small scale of the detailed finite-element simulations with the large scale of the beam model. The effectiveness of the proposed method is validated by the satisfactory agreement between the results of various detailed finite-element simulations for a short riser, subject to internal and external uniform pressure and uniform cyclic bending loading, with those given by the proposed constitutive law. [Copyright &y& Elsevier]

Abstract: In this paper, the first and second order derivatives of natural frequencies and buckling loads with respect to an arbitrary geometrical or physical property of a plate structure are calculated. Based on these eigenderivatives, and by using first and second order Taylor expansions, an approximate method is presented for simultaneous modification of natural frequencies and buckling loads. In the proposed method, the structural modification is considered as an inverse eigenvalue problem and calculated eigenderivatives are used for transforming this inverse problem to solving a system of algebraic equations. By solving this set of equations, the necessary changes in design parameters are calculated, in order to achieve predefined simultaneous shifts in natural frequencies and buckling loads. A plate with two boundary conditions is considered as a case study. The plate is divided into eight regions and the plate thickness in each region is considered as a design parameter. By considering several case studies, the required modification in design variables is calculated for achieving a predefined change in natural frequencies, buckling loads or simultaneous change of both. In each case, the calculated changes in design variables are implemented on the initial structure, and the changes in eigenvalues are computed using FE method. It is shown that the results from presented method compare very well with those obtained from a direct optimization procedure. [Copyright &y& Elsevier]