IMPROVEMENTS TO THE CONVECTED CO-ORDINATES METHOD FOR PREDICTING LARGE DEFLECTION EXTREME RISER RESPONSE

摘要

The geometric nonlinearity associated with large motions of compliant riser structures is catered for by defining an orthogonal triad of axes, known as the convected co-ordinate axes, for each beam element. This triad rigidly translates and rotates in three-dimensional space so as to closely follow the motions of the deforming element. The method enables equilibrium equations to be written by expressing the total nodal solution vector as the sum of rigid body and deformation terms. This paper presents and develops newly defined measures of beam deformation that provide a precise measure of beam rotational deformation relative to the convected axes. The use of these new terms no longer depends on the assumption that the deformation rotations behave as true vectors. A mathematical expression that accurately predicts the nonlinear coupling between torque and bending that occurs along the converted axes is also developed. This upgraded definition of rotational deformation also increases the robustness of the analysis technique, enabling larger time-steps during a dynamic simulation and with rapid convergence being achieved at each solution step.