Application of dynamic optimisation to stabilise bending moments and top tension forces in risers

Abstract

The study discusses the problem of determining vertical displacements of a riser's ends, which, despite its horizontal displacements induced by waves, mitigate stresses. A spatial model of riser dynamics is presented that considers the geometric nonlinearity due to large deflections. The Rigid Finite Element Method was used for riser discretisation. Analyses are reported that enabled riser's vibration frequency determination according to the positions of its upper and lower ends. Then a dynamic optimisation task was formulated and solved. It consists of the selection of riser's vertical displacements that provide bending moments' stabilisation at its selected points, tension forces, despite the defined horizontal movements of the riser's upper end induced by waves. The calculations were performed for variable amplitudes of riser end's horizontal movements.

Effectiveness of the segment method in absolute and joint coordinates when modelling risers

“…In summary, the validation process has proved that the results obtained during the analysis of both free and forced vibrations are compatible with experimental measurements and the calculation results presented in [66] and [67]. Formulation of the segment method in joint coordinates has been used, and in order to calculate frequencies of free vibrations a procedure presented in [60] has been applied. Calculations were carried out on a mid-level PC with a 3.6 GHz processor, and the programs were written in Delphi.…”

“…The procedure for calculation of moments (vectors M i ) acting on segments i − 1 and i is different from the approaches used in previous papers [52][53][54] and [58][59][60].…”

“…Modification of the RFEM formulated in absolute coordinates, which takes into account, apart from bending and torsional flexibilities (like SM), also longitudinal flexibility, is applied to analysis of forced vibrations of risers in [56][57][58][59][60]. Paper [61] presents applications of the method to dynamic analysis of risers and a rotating flexible beam.…”

Application of the finite segment method to stabilisation of the force in a riser connection with a wellhead

“…For modelling such structures as risers, the finite element method is used most often [2], which is reflected in many software packages like ANSYS, Abaqus or Riflex. However, many other methods are also used: finite difference method [3], lumped-mass method [4][5][6], finite segment method [7][8][9][10], or the similar rigid finite element method [11][12][13][14][15][16]. Most of the methods mentioned use Morison equations in order to describe the influence of the sea.…”

“…Its main idea lies in dividing a slender link into rigid elements connected by spherical joints treated as massless spring-damping elements in order to reflect torsional and bending flexibilities, and sometimes also longitudinal flexibility of the discretised links [18]. A similar approach derived from the rigid finite element method [19,20] is used by Drąg [15,16].…”