An explicit formulation for restoring stiffness and its performance in ship hydroelasticity

Senjanović, Ivo; Tomić, Marko; Tomašević, Stipe

doi:10.1016/j.oceaneng.2008.06.004

Cited by 34 publications

(10 citation statements)

References 8 publications

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“…Handling of the so-called m-term and restoring force in the nodebased coupling is different from that in mode-based coupling. For example, the fluid restoring force is composed of pressure, normal vector, and mode variations in a generalized coordinate system (Senjanović et al, 2008). Their contributions depend on the wetted hull surface.…”

Section: Beam Theory Approximationmentioning

confidence: 99%

Numerical analysis on springing and whipping using fully-coupled FSI models

Kim

2014

Ocean Engineering

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a b s t r a c tThis paper focuses on ship springing and whipping analysis using a three-dimensional (3-D) Rankine panel method combined with a beam-element-based 1-D structural model and a shell-element-based 3-D structural model. In addition, slamming loads are considered by 2-D generalized Wagner model (GWM). The beam model is a classical idealization of a ship structure, which is based on Timoshenko beam theory for bending and Vlasov beam theory for non-uniform torsion. The 3-D model consists of beam and shell elements, and its motions are approximated by a few of lower modes. Different coupling schemes are applied to couple the 3-D panel method and the different structure models. Whereas the 1-D beam model is coupled in a Cartesian coordinate system, the 3-D finite element (FE) model is coupled in a generalized coordinate system. The difference in coordinate systems leads to different numerical implementations of coupling. Agreement and discrepancy between the coupled models are discussed regarding results for a 60 m barge, a 6500 TEU containership, and an experimental model of a virtual 10,000 TEU containership. The bulkheads in the barge and the 6500 TEU containership are properly considered in beam modeling according to relative stiffness between the bulkheads and hulls. In linear responses to waves, good agreement is obtained between all the models. However, differences between the models are found in nonlinear springing and whipping responses.

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Section: Beam Theory Approximationmentioning

confidence: 99%

Numerical analysis on springing and whipping using fully-coupled FSI models

Kim

2014

Ocean Engineering

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“…It is obvious that the above formulations of the restoring stiffness, which is used in a few of references [1,2,12], result in an asymmetric stiffness matrix. It is shown in [17] that the Newman formulation [8] gives exactly the same coefficients C * p i j , C * n i j and C * h i j in Eq.…”

Section: State-of-the-artmentioning

confidence: 99%

“…(2) are correct and some are not, the known stiffness formulation is called hybrid for short. It is applied in [1,2] and discussed in [12,18,19], and is not recommended for further use.…”

Section: Comparison Of the Existing Restoring Stiffness With The New Onementioning

confidence: 99%

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Formulation of consistent restoring stiffness in ship hydroelastic analysis

2011

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In this article, the role of the restoring stiffness, as one of the basic parameters in ship hydroelastic analysis, is brought out. It is formulated using the variational principle and the method of virtual displacements. It is shown that asymmetry of the restoring stiffness is a physical reality. Moreover, it is confirmed that modal variation, still disputed in the relevant literature, has to be taken into account to satisfy the ship's stability. Consistent stiffness is formulated here by regarding stiffness definition as relation between forces and displacements. Hybrid stiffness known from the literature is wrong since some terms are specified as relation between forces and displacement gradient. Influence of the consistent and symmetrized stiffness matrix, and the hybrid one, on dynamic response is illustrated for a prismatic pontoon and a large container ship. It is found that the latter two matrices do not assure convergence of transfer functions of sectional forces to zero value as the wave frequency approaches zero. The rigid body and elastic responses are compared, and pertinent conclusions are drawn. It is also shown that it is not necessary to use the unified geometric and restoring stiffness for ordinary hydroelastic analysis of ship structures. The consistent formulation of the restoring stiffness matrix will be useful for extending linear potential theory hydrodynamic codes for rigid body analysis to deformable bodies.

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“…Calculating the hydrostatic equilibrium [2][3][4][5][6][7][8][9] is basic and important for analyzing the stability and the strength of floating structures. Also, in 3D hydroelastic analyses [10][11][12][13][14][15][16], a hydrostatic analysis has become a prerequisite to obtain the hydrostatic equilibrium and stress fields required for constructing the complete hydrostatic stiffness [10][11][12]16] whereas it is not essential for 2D hydroelastic analyses [17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear hydrostatic analysis of flexible floating structures

Lee

2016

Applied Ocean Research

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An explicit formulation for restoring stiffness and its performance in ship hydroelasticity

Cited by 34 publications

References 8 publications

Numerical analysis on springing and whipping using fully-coupled FSI models

Numerical analysis on springing and whipping using fully-coupled FSI models

Formulation of consistent restoring stiffness in ship hydroelastic analysis

Nonlinear hydrostatic analysis of flexible floating structures

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