ABSTRACT

Since riser includes both catenary and bending & torsion effects, it is a nonlinear system and needs many computations in dynamic analysis. In some cases, the analysis is simplified without bending & torsion effect assuming catenary behavior is dominant. A previous study by Kim and Kim (2019) presented a linearised beam analysis for riser. The method finds static position and pre-tension at t=0 with nonlinear analysis. With those initial configurations, linear beam analysis is done for t>0. The method provides approximate solutions but saves computing time. The previous study applied the method to riser alone. This study extended the method to coupled analysis of floating body, mooring lines and risers and compared three calculation cases such as nonlinear analysis with bending & torsion effect of riser, nonlinear analysis without bending & torsion effect of riser and linearised beam analysis. As a numerical example, a ship with twelve mooring chains and four risers was analyzed in waves. Ship motions, chain tensions, riser tensions and bending & torsion moments or risers were calculated for the three calculation cases to compare their numerical accuracy. Computing times of the three methods were also compared.

INTRODUCTION

In the numerical analysis of mooring line, the catenary behavior is dominant and bending or torsion effects are usually ignored if chain is applied for mooring lines. On the other hand, riser includes behavior of bending and torsion as well as catenary because it is usually a steel pipe type. So, it needs many computations in numerical analysis. A linearised beam approximation (Kim and Kim, 2019) was proposed to save computing time. But, the method was applied to riser only.

The objective of this study is to extend the linear beam method to coupled analysis of floating body, mooring lines and risers. And, the linear analysis was compared with nonlinear analysis. The bending and torsion effect of riser on coupled responses was also investigated by including or ignoring those effect in the analysis. A ship with 12 mooring lines and 4 risers was analyzed as a numerical sample. Higher order boundary element method namely HOBEM (Choi et al, 2000; Hong et al, 2005) and convolution method (Cummins, 1962) were applied for formulating floating body equation. Finite element method namely FEM (Kim et al, 1999; Garrett, 2005; Kim et al, 2010, 2013) was applied to formulation of mooring line and riser equations. The coupled time domain dynamic equations were solved by Hamming method (Hamming, 1959) and generalized Newmark method (Chung and Hulbert, 1993) and three numerical cases were analyzed to compare linear and nonlinear results and to investigate bending and torsion effect of risers. Those cases are as follows.

– Case 1: Nonlinear body-mooring-riser coupled analysis including bending & torsion effect of riser

– Case 2: Nonlinear body-mooring-riser coupled analysis ignoring bending & torsion effect of riser

– Case 3: Linearised body-mooring-riser coupled analysis including bending & torsion effect of riser

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