The Smith’s method is stipulated by the International Association of Classification Societies in the Common Structure Rules as a standard method for estimating ultimate/residual strength of hull girder in both intact and damaged conditions. However, for the latter case where the effective hull cross-section is asymmetric and the neutral axis of damaged cross-section not only translates but also rotates, the additional force vector equilibrium also needs to be applied so as to determine the neutral axis plane. The commonly adopted iterative methods for the two-force-equilibrium problem do not always converge for the desired accuracy. This paper proposes a Particle Swarm Optimization based iteration method to trace the motion of the neutral axis plane of asymmetric cross sections. The translation and rotation of the neutral axis are taken as the two dimensions of particles in the model, and the force equilibrium error and the force vector equilibrium error are the objective functions. The neutral axis is determined by performing a random search within the entire range of possible position of neutral axis. The proposed method has been implemented and validated for the case of the DOW’s 1/3 frigate model, the analysis of efficiency and accuracy shows that the method performs in general better than traditional ones.

Excitation of steep unidirectional broad-banded wave trains is studied numerically and experimentally. Iterative method is developed to adjust the driving signal of a paddle-type wavemaker to generate wave train with a prescribed free waves’ spectrum. Analytical post-processing procedure based on the Zakharov equation is applied to separate complex amplitude spectrum of the surface elevation into free and bound components, as required for the proposed method of the adjustment of the wavemaker driving signal. Numerical wave tank in the simulations was based on application of the Boundary Element Method. The results of numerical simulations were supported by measurements in a wave tank. The measured and the designed shapes of the surface elevation variation with time, as well as of the corresponding amplitude spectra were found to be in a good agreement.

The stress of a steel catenary riser (SCR) at touch-down zone (TDZ) is substantially affected by its interaction with the seabed. Based on the slender rod theory, the paper adopts a realistic nonlinear load-deflection (P-y) curve to simulate soil deformation and resistance force. This seabed model can better reflect the change of soil stiffness along the vertical direction. According to the P-y curve, the equivalent stiffness at different points are obtained by an iterative method. In order to add the soil resistance force to the equation of motion, the seabed force is multiplied by the shape function a(s) and integrated from 0 to L of an element length. This paper use Gauss integral method to get the seabed force. In fact, the element may be not entirely in contact with the seabed. Therefore, the first step is to get the contact point between element and soil, and then to determine the real integral range. Meanwhile, existing riser-soil models mostly take the support of the seabed as a horizontal plane. However, many SCRs are unavoidable to be laid on the irregular seabed. It makes the strength characteristics of riser flow-line more complicated. This paper has studied the effect of irregular seabed on riser stress. The results indicate that there is a stress peak value at the irregular seabed. This value is almost equal to the value at TDP.

The local approach to modelling ductile tearing is a useful technique to give insight into fracture mechanics. However, applications of the local approach have been stymied by the high cost of finding the parameters that characterize it because of the number of specimens and expensive post-processing that the testing requires. In this paper, a novel iterative method to extract a failure locus from one Crack Tip Opening Displacement (CTOD) specimen is presented. Material points fail under various different stress states in a CTOD specimen, so many different points on the failure locus can be found through thoughtful post-processing in FEA. A phenomological ductile failure locus is fitted through the stress triaxiality, Lode angle, and plastic strains that cause failure at material points in the CTOD test. Simulating a CTOD test with a different aspect ratio has shown that the failure locus found by this method can be predictive, giving both accurate force versus Crack Mouth Opening Displacement (CMOD) curves and realistic fracture surfaces featuring separate tunnelling and shear lips.

Oil and gas offshore pipelines are one of the main components of a subsea system. A major accident can have a great economic impact due to loss of revenue and the expenses involving actions to mitigate damages to the environment. Therefore, investment in accident prevention through a carefully designed inspection and maintenance plan is necessary. In this scenario, many companies have changed their procedures to ensure the structural integrity of their pipelines — from a model that incorporates empirical safety factors and periodic inspections to another, based on methods that consider concepts of structural reliability to establish risk based inspections. The collapse pressure of pipelines containing corrosion defects is usually predicted by deterministic methods, either numerically or through empirical formulations. The severity of each individual corrosion defect can be determined by comparing the differential pressure during operation with the estimated collapse pressure. However, loads and resistance parameters have uncertainties which define the basic reliability problem. These uncertainties are related to the geometric and material parameters of the pipe and the operational conditions. In recent years, many studies have been developed using reliability concepts in order to predict the probability of failure of a corroded pipeline at any given time. The main problem in assuring the integrity and safe operation of pipelines lies in obtaining the necessary accurate prediction of their future condition. A simple deterministic procedure for estimating the collapse pressure of pipes with narrow and long defects has been recently proposed by Netto (2010). This formulation was based on a combined small-scale experimental program and nonlinear numerical analyses accounting for different materials and defect geometries. Probabilistic failure analyses of pipelines considering different failure mechanisms have been performed by different authors over the last decade. Limit state functions similar to the mentioned above, coupled with reliability algorithms such as the first-order second-moment (FOSM) iterative method, the Monte Carlo integration method, and the first-order and second-order reliability methods (FORM/SORM) are generally used. The analyses take into account the natural spread of material properties, geometric and operational parameters, and the uncertainties associated with the sizing of eventual corrosion defects. In this paper, Netto’s deterministic formulation and the crude Monte Carlo method were used to obtain the reliability of corroded pipelines under external hydrostatic pressure. This approach provides a method to predict the probability of collapse of a corroded pipeline along its operational life. It applies concepts of structural reliability to evaluate the detrimental effect of corrosion damages, giving the basis to develop a risk based maintenance strategy.

As an effective solution for deepwater oil/gas export, steel lazy wave riser (SLWR) could effectively accommodate large platform offsets, decouple platform motions from the touchdown point and reduce top tension in deepwater marine environment. Since the SLWR dynamic response is very essential for design phase and fatigue analysis, it has already drawn extensive research attention. This paper puts forward a developed mathematical model on the basis of the rod theory and finite element method to predict the static/dynamic response of deepwater lazy wave riser. Newmark- β method combined with Newton–Raphson iterative method is employed for time domain integration of the riser dynamics. Besides, the effects of hydrodynamic loading and internal flow are considered in the mathematical model. The verification of the propose model can be well demonstrated by comparing with OrcaFlex simulation. Finally, parametric analyses about the buoyancy segment are conducted to study the SLWR dynamic response in the critical zones, like the hang-off point and touchdown zone (TDZ).

Numerically simulating the six-degrees-of-freedom response motions of a ship executing an unsteady maneuver in a two-dimensional wave environment is one of the most challenging tasks in seakeeping. Mathematical difficulties may occur for several reasons. For example, the rapid change in encounter frequencies may cause a numerical dynamics imbalance. Furthermore, in order to predict the ship’s track (ship heading) accurately, the rudder forces and two-dimensional drift forces must be predicted accurately; otherwise, erroneously predicted headings can ultimately lead to obtaining entirely different ship motions. To overcome these problems, we added a well-behaved, pre-conditional iterative method into the hybrid flow-based, fully-nonlinear ship motion model, DiSSEL (Digital, Self-consistent Ship Experimental Laboratory), in a two-dimensional wave environment. DiSSEL includes two components: a ship-wave interactions model (Lin et al., 2005[1], Lin and Kuang, 2006[2]), and a solid body motions interactions model (Lin and Kuang 2010[3]). The rudder and appendage forces (Lin et al, 2010[4]) are included in the solid body motions component. This refined model is able to overcome the mathematical dynamics imbalance when the encounter frequency rapidly changes as well as accurately calculate the forces on the hull and rudders. Finally the simulations of ship response motions at various relative headings and at various forward speeds in a two-dimensional seaway will be benchmarked against experimental model data for the test cases.

This paper presents the numerical solutions of slamming problems for 3D bodies entering calm water. The highly nonlinear water entry problems are governed by the Navier-Stokes equations and were solved by a Constrained Interpolation Profile (CIP)-based finite difference method on a fixed Cartesian grid. In the computation, the 3D CIP method was employed for the advection calculations and a pressured-based algorithm was applied for non-advection calculations. The solid body and the free surface interfaces were captured by density functions. For the pressure computation, a Poisson-type equation was solved at each time step by the Conjugate Gradient iterative method. Validation studies were carried out for a 3D wedge entering calm water and the entry of a sphere into calm water at both vertical and horizontal velocities. The predicted hydrodynamic forces on the wedge and the sphere were compared with experimental data.

In the deepwater exploitation of oil and gas, the replacement of polyester rope for the wire in chain-wire-chain mooring line is proved to be fairly economic. Previous studies are mainly conducted to hydrodynamic analysis and dynamic response calculation, but there are few studies on the fatigue damage analysis of hybrid mooring line. Take the mooring system of a Spar platform as the research object, and the multi-component mooring lines are usually made up of chain-wire-chain. The representative mooring line has been considered while other conditions are kept unchanged, and top end tension-static offset characteristic curve of the two mooring lines are consistent as much as possible, meanwhile the polyester rope is adopted as the substitute for the wire, then the comparative calculation on fatigue damage of deepwater hybrid mooring line is carried on. The analysis of Spar platform response is carried out in which the wave force is calculated under diffraction theory. After the establishment of two-dimensional nonlinear finite element dynamic model of the hybrid mooring line, the calculation on stiffness of the hybrid mooring line is accomplished through the iterative method based on the empirical formula proposed by Del Vecchio in 1992. The mooring line and seabed interaction is based on the hypothesis of rigid seabed. The fluid drag force and inertia force on the mooring line are calculated according to the Morrison formula. The dynamic analysis is executed through time-domain nonlinear finite element method accounting for the response of the Spar platform which is calculated as above. The stress time histories of the hybrid mooring line in each short-term sea state of South China Sea area are calculated, and then the rain flow counting method is employed to obtain the fatigue load spectrum in each short-term sea state. The Miner linear cumulative law model is used to compare the fatigue damage of the hybrid mooring lines in long-term sea state which consists of tens of short-term sea states. The results show that the using of polyester rope as the substitute for the wire can significantly improve the fatigue resistance.

Articulated tower motions have been characterized by rigid body mode of vibrations falling in the wind excitation frequency range due to its compliant nature. Dynamic response analysis of a multi hinged articulated tower platform to random wind and wave forces are presented in this paper. The wave forces on the submerged elements of the tower are calculated by using Morison’s Equation. The fluctuating wind is modeled with Ochi and Shin wind gust spectrum. The effect of wave age (young, intermediate and fully developed waves) on the wind gust spectrum is incorporated by adopting the wave age dependent Volkov, and wave age independent Charnock sea surface roughness models. The response of the tower is determined by a time domain iterative method. An example of results demonstrates the clear effect of wave age on the nonlinear dynamic response on the system. The mean wind modifies the mean position of the surge response to the positive side, causing an offset. Moreover, for high mean wind speeds the total wind response is much smaller than the wave response, but for low wind speeds the wind appears to be more important.

This contribution presents our recent progress on developing an efficient solution for fully nonlinear wave-structure interaction. The approach is to solve directly the three-dimensional (3D) potential flow problem. The time evolution of the wave field is captured by integrating the free-surface boundary conditions using a fourth-order Runge-Kutta scheme. A coordinate-transformation is employed to obtain a time-constant spatial computational domain which is discretized using arbitrary-order finite difference schemes on a grid with one stretching in each coordinate direction. The resultant linear system of equations is solved by the GMRES iterative method, preconditioned using a multigrid solution to the linearized, lowest-order version of the matrix. The computational effort and required memory use are shown to scale linearly with increasing problem size (total number of grid points). Preliminary examples of nonlinear wave interaction with variable bottom bathymetry and simple bottom mounted structures are given.

Currently, the linear diffraction-radiation wave theory is still most-widely used by naval architects and ocean engineers to obtain wave loads on floating structures. The hydrodynamic coefficients (added mass and radiation damping coefficients, wave excitation force transfer functions, second-order wave force functions, etc.) depend only on the shape of the underwater portion of the hull, the wave direction and frequency, and the motion modes. They only need to be evaluated once and stored as a database which can be repeatedly used to calculate the wave loads in different environmental conditions. It is therefore very important to ensure a high quality of the database covering the whole range of wave frequency. This paper presents a practical procedure for the evaluation, assessment and improvement of the added mass and radiation damping coefficients. An accurate semi-analytical method is introduced for the evaluation of the retardation functions and time domain added mass. The quality of the added mass and damping is then assessed using Kramer-Kronig relations . Finally, an iterative method is presented for improving (re-constructing) the added mass and radiation damping so that Kramer-Kronig relations are better satisfied.

A nonlinear sloshing problem in LNG tanker is numerically simulated. During excessive sloshing, the sloshing-induced impact load can cause a critical damage on the tank structure. Recently, this problem became one of important issues in FPSO design. A three-dimensional free surface flow in a tank is formulated in the scope of potential flow theory. The exact nonlinear free surface condition is satisfied numerically. A finite-element method based on Hamilton’s principle is employed as a numerical scheme. The problem is treated as an initial-value problem. The computations are made through an iterative method at each time step. The hydrodynamic loading on the pillar in the tank is computed and compared with other results.

The damage identification problem in offshore platforms, specifically in jacket platforms, has been studied since the seventies. In spite of the effort dispended, there is still no spread out methodology that can be applied in this kind of structure, due its specific characteristics (structural complexity, load and operational conditions, etc.). The development of such methods would be extremely useful to preview structural failures, once this kind of structures is almost completely under water. Most of the developed methods for damage identification use modal parameters, by comparisons of different structural time conditions, and the damage may be expressed through the observed discrepancy. This paper presents a methodology to locate damage based on an iterative method. It was developed an optimization software which uses the Goal Programming Technique to choose the best set of variables that minimizes the difference between experimental and numerical Frequency Response Functions (FRFs), which can better represent the structure situation. Some numerical simulations were performed on a scaled fixed oil platform model to verify the efficiency of the method. The results show that such method is efficient when damages are restricted to a set of optimization variables.

Wave impact load occurring in a liquid storage tank during a sloshing motion is numerically simulated. Due to a violent sloshing, an excessive impact load can cause a critical damage to the tank structure. Recently this type of the accidents are reported and the problem becomes an important research topic in LNG (Liquefied Natural Gas) Tanker and FPSO (Floating Production Storage Offloading) design. To predict the sloshing impact load, Morison’s formula could be used for a practical reason. But using the Morison formula may provide directly an inaccurate estimation for the impact load because this formula is based on the linear model in the present nonlinear dominating phenomena. In this study, the wave impact load on the structure is obtained by imposing the exact nonlinear free surface conditions numerically and compared with that predicted by Morison’s formula. As a numerical method, a three-dimensional free surface flow in a tank is formulated in the scope of potential flow theory with the nonlinear free-surface conditions. A finite-element method based on Hamilton’s principle is employed as a numerical scheme. The problem is treated as an initial-value problem. The nonlinear problem is numerically solved through an iterative method at each time step.

We employ a fully nonlinear numerical model to generate and propagate long-crested gravity waves in a tank containing an incompressible invicid homogeneous fluid, initially at rest, with a horizontal free surface of finite extent and of finite depth. A non-orthogonal curvilinear coordinate system is constructed which follows the free surface and is “fitted” to the bottom topography of the tank and therefore tracks the entire fluid domain at all times. A waveform relaxation algorithm provides an efficient iterative method to solve the resulting discrete Laplace equation, and the full nonlinear kinematic and dynamic free surface boundary conditions are employed to propagate the solution. In addition, a monochromatic deterministic theoretical wave-maker, employing a Dirichlet type boundary condition, and a suitably tuned numerical beach are utilized in the numerical model. We first show that the model generates the appropriate dispersion relation for both the deep water and shallow water conditions. Subsequently, we calculate the energy and energy flux for small steepness waves and show that the model produces the expected linear results. We complete the paper by considering steeper waves where the linear results are suspect.