This paper describes the development of alternative time domain numerical simulation methods for predicting large amplitude motions of ships and floating structures in response to incoming waves in the frame of potential theory. The developed alternative set of time domain methods simulate the hydrodynamic forces acting on ships advancing in waves with constant speed. For motions’ simulation, the diffraction forces and radiation forces are calculated up to the mean wetted surface, while the Froude-Krylov forces and hydrostatic restoring forces are calculated up to the undisturbed incident wave surface in case of large incident wave amplitude. This enables the study of the above waterline hull form effect. Characteristic case studies on simulating the hydrodynamic forces and motions of standard type of ships have been conducted for validation purpose. Good agreement with other numerical codes and experimental data has been observed. Furthermore, the added resistance of ships in waves can be calculated by the presented methods. This capability supports the increased demand of this type of tools for the proper selection of engine/propulsion systems accounting for ship’s performance in realistic sea conditions, or when optimizing ship’s sailing route for minimum fuel consumption and toxic gas emissions.

Pipes for deep-water applications possess a diameter-to-thickness ratio in a region where failure is dominated by both instability and plastic collapse. This implies that prior to failure the compressive yield strength of the material must be exceeded, followed by ovalisation and further local yielding. This paper presents an investigation into the mechanics of this specific problem and develops an analytical approach that accounts for the effects of geometrical and material data on the collapse pressure of inhomogeneous rings under external hydrostatic pressure. The analytical expressions have been correlated to numerical and experimental test data, proving their accuracy.

Cylindrical structures are commonly used in offshore engineering, for example, a tension-leg platform (TLP). Prediction of hydrodynamic loadings on those cylindrical structures is one of important issues in design of those marine structures. This study aims to provide a numerical model to simulate fluid-structure interaction around the cylindrical structures and to estimate those loadings using the direct-forcing immersed boundary method. Oscillatory flows are considered to simulate the flow caused by progressive waves in shallow water. Virtual forces due to the existence of those cylindrical structures are distributed in the fluid domain in the established immersed boundary model. As a results, influence of the marine structure on the fluid flow is included in the model. Furthermore, hydrodynamic loadings exerted on the marine structure are determined by the integral of virtual forces according to Newton’s third law. A square array of four cylinders is considered as the marine structure in this study. Time histories of inline and lift coefficients are provided in the numerical study. The proposed approach can be useful for scientists and engineers who would like to understand the interaction of the oscillatory flow with the cylinder array or to estimate hydrodynamic loading on the array of cylinders.

Several hypothetical cases of oil spills from tankers in the Kvarner and Rijeka Bay were analyzed using three-dimensional circulation models coupled with oil spill model. Two circulation models—local one covering the area of Kvarner Bay, Rijeka Bay, and Vinodol channel along with the basin-wide one covering the whole Adriatic Sea—are connected through the one-way nesting procedure by imposing the results from the Adriatic model to the open boundaries of the local one. Oil spill model relays on the current fields obtained by the local circulation model during all our simulations. Spreading of the oil pollution from three hypothetical positions of tanker accidents in the local model domain was simulated for the periods of 10 “winter-season” and “summer-season” days. The oil spill model results show that the hypothetical tanker accidents in the center of the Rijeka Bay are the most dangerous for the studied area in both seasons. Summer-season case shows significantly worse situation from the ecological point of view, oil spills spread on the larger area simply because stratification and mixing present during the winter period reduce oil slick effect.

This paper employs the numerical assembly method (NAM) to determine the exact frequency-response amplitudes of an offshore structure such as piles or towers having the form of a hollow column filled with multiple fluids, immersed in water, carrying an eccentric tip mass supported by a translational spring and/or a rotational spring, and subjected to a harmonic force. The hollow column is modeled as a Bernoulli-Euler cantilever beam fixed at the bottom. For the case of zero harmonic force, the simultaneous equations of the vibration system reduce to an eigenvalue problem so that the natural frequencies and mode shapes of the beam can also be obtained. The effect of height of filled fluids on the characteristics of free vibration is also presented.

A deep-sea manganese nodules test miner has not only coupled relationship between system components but also various design requirements of each system to meet the specified multitasks. To accomplish the multiobjectives of complex systems, multidisciplinary design optimization (MDO) is performed. Metamodels such as the kriging model and the response surface model are employed to reduce computational costs for MDO and to integrate component systems in a design framework. After verifying the accuracy of each metamodel, metamodel-based MDO for a deep-ocean test miner is formulated and performed. Finally, results and advantages of the proposed design methodology are discussed.

This paper presents a 3-dimensional finite element formulation for predicting the behaviour of complex umbilical cross-sections exposed to loading from tension, torque, internal and external pressure including bending. Helically wound armours and tubes are treated as thin and slender beams formulated within the framework of small strains but large displacements, applying the principle of virtual displacements to obtain finite element equations. Interaction between structural elements is handled by 2- and 3-noded contact elements based on a penalty parameter formulation. The model takes into account a number of features, such as material nonlinearity, gap and friction between individual bodies, and contact with external structures and with a full 3-dimensional description. Numerical studies are presented to validate the model against another model as well as test data.

Generalized solutions of the shallow water equations are obtained. One studies the particular case of a generalized soliton function passing by a variable bottom. We consider a case of discontinuity in bottom depth. We assume that the surface elevation is given by a step soliton which is defined using generalized solutions (Colombeau 1993). Finally, a system of functional equations is obtained where the amplitudes and celerity of wave are the unknown parameters. Numerical results are presented showing that the generalized solution produces good results having physical sense.

This paper focuses on a theoretical approach to access the fatigue life of flexible pipes. This methodology employs functions that convert forces and moments obtained in time-domain global analyses into stresses in their tensile armors. The stresses are then processed by well-known cycle counting methods, and S-N curves are used to evaluate the fatigue damage at several points in the pipe’s cross-section. Finally, Palmgren-Miner linear damage hypothesis is assumed in order to calculate the accumulated fatigue damage. A study on the fatigue life of a flexible pipe employing this methodology is presented. The main points addressed in the study are the influence of friction between layers, the effect of the annulus conditions, the importance of evaluating the fatigue life in various points of the pipe’s cross-section, and the effect of mean stresses. The results obtained suggest that the friction between layers and the annulus conditions strongly influences the fatigue life of flexible pipes. Moreover, mean stress effects are also significant, and at least half of the wires in each analyzed section of the pipe must be considered in a typical fatigue analysis.

Based on the measured data and characteristics of sea ice temperature distribution in space and time, this study is intended to consider a parabolic partial differential equation of the thermodynamic field of sea ice (coupled by snow, ice, and sea water layers) with a time-dependent domain and its parameter identification problem. An optimal model with state constraints is presented with the thicknesses of snow and sea ice as parametric variables and the deviation between the calculated and measured sea ice temperatures as the performance criterion. The unique existence of the weak solution of the thermodynamic system is proved. The properties of the identification problem and the existence of the optimal parameter are discussed, and the one-order necessary condition is derived. Finally, based on the nonoverlapping domain decomposition method and semi-implicit difference scheme, an optimization algorithm is proposed for the numerical simulation. Results show that the simulated temperature of sea ice fit well with the measured data, and the better fit is corresponding to the deeper sea ice.

A two-phase fluid flow model solving Navier-Stokes equations was employed in this paper to investigate liquid sloshing phenomena in cubic tank with horizontal baffle, perforated vertical baffle, and their combinatorial configurations under the harmonic motion excitation. Laboratory experiment of liquid sloshing in cubic tank with perforated vertical baffle was carried out to validate the present numerical model. Fairly good agreements were obtained from the comparisons between the present numerical results and the present experimental data, available numerical data. Liquid sloshing in cubic tank with multiple baffles was investigated numerically in detail under different external excitation frequencies. Power spectrum of the time series of free surface elevation was presented with the aid of fast Fourier transform technique. The dynamic impact pressures acting on the normal and parallel sidewalls were discussed in detail.

The Galerkin method is applied to analyze the elastic large deflection behavior of metal plates subject to a combination of in-plane loads such as biaxial loads, edge shear and biaxial inplane bending moments, and uniformly or nonuniformly distributed lateral pressure loads. The motive of the present study was initiated by the fact that metal plates of ships and ship-shaped offshore structures at sea are often subjected to non-uniformly distributed lateral pressure loads arising from cargo or water pressure, together with inplane axial loads or inplane bending moments, but the current practice of the maritime industry usually applies some simplified design methods assuming that the non-uniform pressure distribution in the plates can be replaced by an equivalence of uniform pressure distribution. Applied examples are presented, demonstrating that the current plate design methods of the maritime industry may be inappropriate when the non-uniformity of lateral pressure loads becomes more significant.

This paper aims at presenting a general formulation of the hydrodynamic problem of a floating or restrained oscillating water column device. Three types of first-order boundary value problems are investigated in order to calculate the velocity potential of the flow field around the device. The horizontal and vertical exciting wave forces, the rolling moment, the hydrodynamic parameters, the volume flows, and the drift forces are obtained in order to find the loads on the structure. The efficiency rate of the device is calculated in connection with the absorbed power and the capture length of energy absorption. Finally, the resulting wave motion inside and outside the device and the inner air pressure are examined.

A numerical wave flume based on the particle finite element method (PFEM) is applied to simulate wave overtopping for impermeable maritime structures. An assessment of the performance and robustness of the numerical wave flume is carried out for two different cases comparing numerical results with experimental data. In the first case, a well-defined benchmark test of a simple low-crested structure overtopped by regular nonbreaking waves is presented, tested in the lab, and simulated in the numerical wave flume. In the second case, state-of-the-art physical experiments of a trapezoidal structure placed on a sloping beach overtopped by regular breaking waves are simulated in the numerical wave flume. For both cases, main overtopping events are well detected by the numerical wave flume. However, nonlinear processes controlling the tests proposed, such as nonlinear wave generation, energy losses along the wave propagation track, wave reflection, and overtopping events, are reproduced with more accuracy in the first case. Results indicate that a numerical wave flume based on the PFEM can be applied as an efficient tool to supplement physical models, semiempirical formulations, and other numerical techniques to deal with overtopping of maritime structures.

Tsunami wave interaction with coastal regions is responsible for very important human and economic losses. In order to properly design coastal defenses against these natural catastrophes, new numerical models need to be developed that complement existing laboratory measurements and field data. The use of numerical models based on the Navier-Stokes equations appears as a reasonable approach due to their ability to evaluate complex flow patterns around coastal structures without the inherent limitations of the classical depth-averaged models. In the present study, a Navier-Stokes-based model, IH-3VOF, is applied to study the interaction of tsunami waves with porous and impermeable structures. IH-3VOF is able to simulate wave flow within the porous structures by means of the volume-averaged Reynolds-averaged Navier-Stokes (VARANS) equations. The equations solved by the model and their numerical implementation are presented here. A numerical analysis of the interaction of a tsunami wave with both an impermeable and porous vertical breakwater is carried out. The wave-induced three-dimensional wave pattern is analysed from the simulations. The role paid by the porous media is also investigated. Finally, flow around the breakwater is analyzed identifying different flow behaviors in the vicinity of the breakwater and in the far field of the structure.

A time-domain numerical model is established based on the higher-order boundary element method (HOBEM) to simulate wave diffraction problem in a two-layer fluid of finite depth. There are two possible incident wave modes (surface-wave mode and internal-wave mode) exist in the incident wave for a prescribed frequency in a two-layer fluid. For surface-wave mode, the hydrodynamic characters of fluid particles are similar to single-layer fluid. For the internal-wave mode, through the definition of a new function respected to velocity potentials of upper and lower fluid on the interface by using matching condition, a single set of linear equations is set up to compute the time histories of wave forces and wave profiles by using a fourth-order Runge-Kutta method. An artificial damping layer is adopted both on the free surface and interface to avoid the wave reflection. Examinations of the accuracy of this time-domain algorithm are carried out for a truncated cylinder and a rectangular barge, and the results demonstrate the effectiveness of this method.

Sloshing flows in a two-dimensional rigid rectangular tank under specified excitations in the coupled horizontal and vertical modes are simulated by using a higher-order boundary element method (BEM). The liquid sloshing is formulated as an initial-boundary-value problem based on the fully nonlinear potential flow theory. And a semi-mixed Eulerian-Lagrangian technique combined with the 4th-order Runge-Kutta scheme is employed to advance the solutions in the time marching process. A smoothing technique is applied to the free surface at every several time steps to avoid the possible numerical instabilities. Numerical results obtained are compared with the available solutions to validate the developed model. The parametric studies are carried out to show the liquid sloshing effects in terms of the slosh frequencies and excitation amplitudes in horizontal and vertical modes, the second-order resonance frequency, a bottom-mounted vertical rigid baffle, free surface displacement, and hydrodynamic forces acting on the tank.

Fatigue analysis of structural components such as helix tensile armors and steel tubes is a critical design issue for dynamic umbilicals and flexible pipes. The basis for assessment of fatigue damage of such elements is the long-term stress cycle distribution at critical locations on the helix elements caused by long-term environmental loading on the system. The long-term stress cycle distribution will hence require global dynamic time domain analysis followed by a detailed cross-sectional analysis in a large number of irregular sea states. An overall computational consistent and efficient fatigue analysis scheme is outlined with due regard of the cross-sectional analysis technique required for fatigue stress calculation with particular attention to the helix elements. The global cross-section is exposed to pure bending, tensile, torsion, and pressure loading. The state of the different cross-section elements is based on the global response. Special emphasis is placed on assessment of friction stresses caused by the stick-slip behavior of helix elements in bending that are of special importance for fatigue life assessments. The described cross-sectional analysis techniques are based on an extensive literature survey and are hence considered to represent industry consensus. The performance of the described calculation scheme is illustrated by case studies.

This paper presents a user-friendly rapid prediction tool of damage to struck and striking vessels in a ship collision event. To do this, the so-called upper bound theorem is applied to calculate internal forces and energies of any substructure involved in the ships crushing process. At each increment of indentation, the total crushing force is transmitted to the external dynamics MCOL program, which calculates the global ship motion correction by solving the hydrodynamic force equilibrium equations. As a first step, the paper gives a brief description of the upper bound method originally developed for perpendicular collisions and recently enhanced for oblique ones. Then, the theory developed in MCOL program for large rotational ship movements is detailed. By comparing results obtained with and without MCOL, the importance of hydrodynamic effects is highlighted. Some simulation results are compared with results provided by classical nonlinear finite element calculations. Finally, by using the developed analytical tool, which mixes internal and external dynamics, different crushing scenarios including oblique collisions are investigated and the influence of some collision parameters like longitudinal and vertical impact location, impact angle, and struck ship velocity is studied.

Modulation instability is one of the most ubiquitous types of instabilities in nature. As one of the key characteristics of modulation instability, the most unstable condition attracts lots of attention. The most unstable condition is investigated here with two kinds of initial wave systems via a numerical high-order spectral method (HOS) for surface water wave field. Classically, one carrier wave and a pair of sidebands are implied as the first kind of initial wave system: “seeded” wave system. In the second kind of initial wave system: “un-seeded” wave system, only one carrier wave is implied. Two impressive new results are present. One result shows that the grow rates of lower and upper sideband are different within the “seeded” wave system. It means that, for a given wave steepness, the most unstable lower sideband is not in pair with the most unstable upper sideband. Another result shows the fastest growing sidebands are exactly in pair from “unseeded” wave system. And the most unstable conditions of “unseeded” wave system are more or less the mean value of those derived from the lower sidebands and upper sidebands within the “seeded” wave system.

The present paper is concerned with the design of lock gates submitted to ship impacts. In this paper, a simplified analytical method is presented to evaluate the resistance of such structures under collision. The basic idea is to assume that the resistance is first provided through a local deforming mode, corresponding to a localized crushing of some impacted structural elements. For consecutive larger deformations, the resistance is then mostly provided through a global deforming mode, corresponding to an overall movement of the entire gate. For assessing the resistance in the case of the local deforming mode, the structure is divided into a given number of large structural entities called “superelements.” For each of them, a relation between the resistance of the gate and the penetration of the striking ship is established. However, as some results are already available in the literature, this subject is not treated extensively in this paper. On the contrary, the calculation of the resistance of the gate provided through the global mode is detailed and the strategy to switch from local to global deformation is highlighted. Finally, we propose to validate our developments by making a comparison between results obtained numerically and those predicted by the present analytical approach.

The use of powerful numerical tools based on the finite-element method has been improving the prediction of the holding capacity of fixed anchors employed by the offshore oil industry. One of the main achievements of these tools is the reduction of the uncertainty related to the holding capacity calculation of these anchors. Therefore, it is also possible to reduce the values of the associated design safety factors, which have been calibrated relying on models with higher uncertainty, without impairing the original level of structural safety. This paper presents a study on the calibration of reliability-based safety factors for the design of torpedo anchors considering the statistical model uncertainty evaluated using results from experimental tests and their correspondent finite-element-based numerical predictions. Both working stress design (WSD) and load and resistance factors design (LRFD) design methodologies are investigated. Considering the WSD design methodology, the single safety is considerably lower than the value typically employed in the design of torpedo anchors. Moreover, a LRFD design code format for torpedo anchors is more appropriate since it leads to designs having less-scattered safety levels around the target value.