Compliant Offshore Structures Research Articles

Functionally graded material and its application to marine structures

Marine structures are exposed to harsh weather conditions, demanding special pre-requisites in design and functional perspectives. Under dynamic loads of larger magnitude, the material-centric design procedure alone is not feasible to ensure the safe disbursement of loads. The compliant offshore structures resist loads primarily by their geometric novelty, and hence their design is form-dominant and no more strength (material) dominant. Large displacements in the rigid body modes in the horizontal plane under lateral loads require their construction material to possess enough ductility to absorb this energy. Steel is one of the most competitive materials for marine structures as it offers good ductility, but corrosion in the marine environment is a major concern. It undergoes strength and functional degradations and therefore requires serious investigation. In the present study, functionally graded material (FGM) is proposed to substitute for steel in marine applications. The method of fabricating FGM and assessing its mechanical and durability properties are discussed. Results show that FGM possesses strength and durability properties at par with the conventionally used X52 steel for marine risers. The presented study will be a major initiative towards future research in exploring competent materials which will be strong and sustainable in the marine environment.

Aerodynamic and hydrodynamic force simulation for the dynamics of double-pendulum articulated offshore tower

Articulated towers are one of the class of compliant offshore structures that freely oscillates with wind and waves, as they are designed to have low natural frequency than ocean waves. The present study deals with the dynamic response of a double-pendulum articulated tower under hydrodynamic and aerodynamic loads. The wind field is simulated by two approaches, namely, single-point and multiple-point. Nonlinearities such as instantaneous tower orientation, variable added mass, fluctuating buoyancy, and geometrical nonlinearities are duly considered in the analysis. Hamilton's principle is used to derive the nonlinear equations of motion (EOM). The EOM is solved in the time domain by using the Wilson-Θ method. The maximum, minimum, mean, and standard deviation and salient power spectral density functions (PSDF) of deck displacement, bending moment, and central hinge shear are drawn for high and moderate sea states. The outcome of the analyses shows that tower response under multiple-point wind-field simulation results in lower responses when compared to that of single-point simulation.

Control variates for efficient long-term extreme analysis of mooring lines

Predicting the long-term extreme response is a major challenge for compliant offshore structures such as mooring lines. The structure is exposed to long-term uncertainties from varying environmental conditions and short-term uncertainties from random waves. The “all sea states approach” is rigorous but computationally prohibitive, since each sea state necessitates time domain simulations to capture the nonlinearities and non-Gaussian characteristics of the dynamic system. This paper presents a new approach for accurate long-term extreme analysis of mooring lines. The short-term conditional failure probability is estimated based on extrapolation of crossing rates. Monte Carlo simulation (MCS) is used to perform the integration over the long-term variables, which include the significant wave height, average period, and the speed/direction of wind and current. The classical control variates technique is invoked to reduce the variance of the MCS estimator. The difficulty of obtaining a good control function for complex problems is resolved through a new auto-control variates scheme, wherein the control is formulated as a surrogate model constructed from existing MCS scatter. Since variance reduction is effected by post-processing, multiple stress locations can be evaluated from the same dynamic simulations. The proposed method is implemented on a turret-moored vessel, and the predicted failure probability is compared against subset simulation, in which all the short- and long-term uncertainties are incorporated as random variables and no arbitrary assumptions are made. The proposed method is found to be in excellent agreement with subset simulation, and the variance reduction is considerable, resulting in a speedup of roughly an order of magnitude or more.

Near Fault Effect on the Response of Single Hinged Compliant Offshore Tower

The response of compliant offshore structure under simultaneous action of random waves and earthquake loading has been analyzed. Since earthquake forces play a significant role in affecting the response of these offshore structures, comparative studies have been carried out considering near fault and far fault seismic excitations in the presence of moderate random sea waves. The offshore tower is modeled as an inverted pendulum with a cylindrical shaft connected by an articulated joint at the base. Seismic forces are evaluated by dividing the tower shaft into finite elements with masses lumped at the nodes. The nonlinearities associated with the system owing to variable submergence, drag force, variable buoyancy along with the geometry are considered in the analysis. The nonlinear dynamic equation of motion is formulated considering Lagrangian approach, which is solved in time domain by the Newmark-beta integration scheme. The sea state conditions, more precisely the water particle kinematics are evaluated using Airy’s wave theory along with the stretching modifications, as suggested by Chakrabarti. To minimize the dynamic responses, emphasis has to be given to the variations in height and position of the buoyancy chamber in extreme wave condition. The results are expressed in the form of time histories of deck displacement, hinge rotation, hinge shear and the bending moment. Parameters like maximum, minimum, mean and standard deviation are also determined by statistical analysis of response time histories of the dynamic responses at articulated joint.

Effect of pontoons on free surface elevation around a TLP platform

Tension leg platform (TLP) is a typical compliant offshore structure for oil/gas resources exploitation. In the design process, the prediction of the free surface elevation is of great importance for the determination of the air gap. So far, the existing researches for predicting the air gap of the TLPs focus on the supporting columns while pay little attention to the horizontal pontoons. For the second order diffraction problem or long incident wave condition, the velocity potential decays slowly with water depth and the effect of pontoons should not be neglected. Herein the effect of pontoons on the diffracted wave field in the vicinity of a TLP platform is investigated in this study. The diffraction of regular waves by a square array of truncated cylinders and a whole TLP structure is studied in detail by using both the linear and the second-order diffraction theory. Numerical calculation is performed for the free surface elevation and wave run up. Numerical results show that the near-trapping phenomenon can occur inside the TLP and leads to significantly increased wave height. To study the effect of pontoons on the free surface elevation comparisons are carried out between the results of these two structures with and without pontoons. It is found that pontoons have an appreciable effect on the diffracted wave field for long incident regular waves and increase the largest response notably when the near-trapping phenomenon occurs at the second-order.

Compound Path Integral Solution of Response Exceedance Probabilities of an Offshore Structure

ABSTRACTIn this technical note, a compound path integral solution (CPIS) method is utilized to calculate the response exceedance probabilities of a nonlinear compliant offshore structure subjected to slow drift wave force excitations. The structure's slow drift response exceedance probabilities have also been calculated by using the original PIS method for comparison purpose. It is found that the efficiency of the CPIS method for predicting the structure's slow drift response exceedance probabilities is higher than that of the original PIS method.

Estimation of wave forces on large compliant platforms

Compliant offshore structures such as spars, tension leg platforms (TLPs) and semi-submersibles have been dramatically improved in recent years due to their capability for deep water operation. Waves are the most important environmental phenomenon affecting these offshore structures. Estimation of wave forces is vital in offshore structure design. For large compliant offshore platforms, Morrison’s equation is not valid anymore and usually diffraction theory is used. In this research, by using the finite difference method, a detailed analysis of the first-order diffraction of monochromatic waves on a large cylinder as a structural element is performed to solve the radiation and diffraction potentials. The results showed that the developed model is a reliable tool to estimate the wave forces and hydrodynamic coefficients on large structure elements when wave diffraction and radiation are considered.

Nonlinear analysis of slow drift extreme responses of a compliant offshore structure

This paper first demonstrates that the accuracy and efficiency of the method of numerical simulation often used is not very high in predicting the slow drift surge extreme responses of a compliant offshore structure. Next, the slow drift surge extreme responses of the structure are analyzed via the path integral solution (PIS) method, and the accuracy and efficiency of the PIS method is found to be higher than those of the numerical simulation method. A compound PIS (CPIS) method is first proposed in this article to further improve the efficiency of the path integral solution method, and the accuracy and efficiency of the CPIS method is validated.

The asymptotic behaviour of second-order stochastic Volterra series models of slow drift response

The paper presents a detailed study of the structure and asymptotic behaviour of a second-order stochastic Volterra series model of the slow drift response of large volume compliant offshore structures subjected to random seas. A long standing challenge has been to develop efficient and accurate methods for calculating the response statistics of compliant offshore structures to random seas. Recent work has revealed that the statistical properties of the response process, which consist of a linear, first-order component and a nonlinear, second-order component, is surprisingly complex. The goal of the research work presented here is to complement efforts to develop numerical procedures to calculate the statistics of the response process.

Reliability of articulated tower joint against random base shear

An Articulated tower is one of the compliant offshore structures connected to the sea-bed through a universal joint which is the most vulnerable location of the tower that sustains the randomly fluctuating shear stresses. The time history response of the bottom hinge shear is obtained and presented in the spectral form. The fatigue and fracture reliability assessment of the tower joint against randomly varying shear stresses have been carried out. Non-linear limit state functions are derived in terms of important random variables using S-N curve and fracture mechanics approaches. Advanced First Order Reliability Method is used for reliability assessment. Sensitivity analysis shows the influence of various variables on the hinge safety. Fatigue life estimation has been made using probabilistic approach.

Comprehensive study on the results of tension leg platform responses in random sea

Compliant offshore structures are used for oil exploitation in deep water. Tension leg platform (TLP) is a suitable type for very deep water. The nonlinear dynamic response of TLP under random sea wave load is necessary for determining the maximum deformations and stresses. Accurate and reliable responses are needed for optimum design and control of the structure. In this paper nonlinear dynamic analysis of TLP is carried out in both time and frequency domains. The time history of random wave is generated based on Pierson-Moskowitz spectrum and acts on the structure in arbitrary direction. The hydrodynamic forces are calculated using the modified Morison equation according to Airy's linear wave theory. The power spectral densities (PSDs) of displacements, velocities and accelerations are calculated from nonlinear responses. The focus of the paper is on the comprehen- sive interpretation of the responses of the structure related to wave excitation and structural characteristics. As an example a case study is investigated and numerical results are discussed.

A random ice force model for narrow conical structures

This paper describes a time-varying random ice force model for narrow conical structures. The model concerns a situation where a uniform ice sheet acts on a narrow cone and fails by bending in a mode where the broken ice pieces are cleared away. The ice force is simplified as a series of impulses with random magnitudes and periods, which are based on a statistical analysis of the load panel data obtained in full scale tests. It was found that normal distributions can be used as approximations to the statistical characteristics of the force amplitudes and periods. This paper addresses the determination of the distribution parameters. The random ice load function that is derived in this paper can be used in the dynamic analysis of compliant offshore structures with narrow ice breaking cones that are subjected to ice actions. Further limitations are discussed in the paper.

Numerical methods for calculating the crossing rate of high and extreme response levels of compliant offshore structures subjected to random waves

The focus of the paper is on methods for calculating the mean upcrossing rate of stationary stochastic processes that can be represented as second order stochastic Volterra series. This is the current state-of-the-art representation of the horizontal motion response of e.g. a tension leg platform in random seas. Until recently, there has been no method available for accurately calculating the mean level upcrossing rate of such response processes. Since the mean upcrossing rate is a key parameter for estimating the large and extreme responses it is clearly of importance to develop methods for its calculation. The paper describes in some detail a numerical method for calculating the mean level upcrossing rate of a stochastic response process of the type considered. Since no approximations are made, the only source of inaccuracy is in the numerical calculation, which can be controlled. In addition to this exact method, two approximate methods are also discussed.

Statistical response predictions for a nonlinearly moored large volume structure in random seas

The challenge to calculate the response statistics of nonlinear, compliant offshore structures subjected to a random seaway is still substantial. In this paper the results are presented of a renewed effort to use the method of numerical path integration for this purpose. In particular, the goal is to calculate the response statistics of a nonlinearly moored large volume floater designed for use in oil production in deep waters. Specific emphasis has been placed on the modelling of nonlinear wave loads in addition to the nonlinear mooring characteristics. The results calculated for the response statistics are compared with the results obtained by Monte Carlo simulation, and the agreement is found to be very good.

Estimating nonlinear coupled frequency-dependent parameters in offshore engineering

The design of deepwater compliant offshore structures requires engineers to address many difficult challenges including defining and modeling the local offshore environment, specifying the associated combined global loading on innovative platform designs, and numerical simulation and model test verification of the platform response characteristics. The focus of this research investigation is the recovery of key parameters from time series measured during an industry type model basin test program using the reverse multiple input/single output technique. In particular, this study confronts critical problems of practical interest and extends the methodology to address the inclusion of nonlinear coupled systems in which the parameters of interest can be frequency-dependent. The analysis is developed around the nonlinear coupled equations of motions for a deepwater mini-TLP design and includes the consideration of nonlinear stiffness, quadratic damping, surge/pitch and sway/roll coupling and the frequency dependency of both the hydrodynamic added-mass and damping coefficients. A series of complementary model test measurements for the complete compliant model and the rigidly restrained hull by itself were used as the basis for the data in the system identification procedures. In addition, behavior of the hydrodynamic added-mass and damping coefficients as a function of frequency was simulated for the mini-TLP using an industry standard radiation–diffraction software package. These results were used in evaluating the accuracy of some of the key problem parameters. The results presented demonstrate the methodology as modified in this study is quite robust and yields predications that are more accurate for the parameters associated with the largest motions of the platform. Practical issues regarding the application of this approach, utilization of both force and moment measurements, and observed strengths and weakness in dealing with data regardless of its source are discussed.

Comparison of linear and nonlinear responses of a compliant tower to random wave forces

A vertical member of a compliant offshore structure is modeled as a beam undergoing both bending and extension. The beam has a point mass and is subjected to a point axial load at the free end. The equations of motion for the axial and transverse displacements are nonlinear and coupled. A linear tension model is derived as a special case of the nonlinear coupled model with negligible axial displacement. The responses are obtained numerically for both models. A quarter of the International Ship and Offshore Structures Congress (ISSC) tension leg platform model is used as a numerical example. The free and forced responses obtained using the nonlinear coupled modeled are compared to those of the linear tension model.

A neural network model for the uplift capacity of suction caissons

Abstract Suction caissons are frequently used for the anchorage of large compliant offshore structures. The uplift capacity of the suction caissons is a critical issue in these applications, and reliable methods of predicting the capacity are required in order to produce effective designs. In this paper a back-propagation neural network model is developed to predict the uplift capacity of suction foundations. A database containing the results from a number of model and centrifuge tests is used. The results of this study indicate that the neural network model serves as a reliable and simple predictive tool for the uplift capacity of suction caissons. As more data becomes available, the model itself can be improved to make more accurate capacity prediction for a wider range of load and site conditions. The neural network predictions are also compared with finite element based predictions.

Active control of non-linearly coupled TLP response under wind and wave environments

This paper deals with an active control strategy to check the non-linearly coupled response of a tension leg platform (TLP), a deep water semi-submersible type compliant offshore structure moored by vertical taut cables called tendons or tethers. The effects of potential non-linearities together with coupling of various degrees of freedom are studied. Low-frequency viscous drift force has also been taken into account with first-order wave forces. Simulation techniques have been employed to incorporate the random sea and fluctuating wind characteristics. Corrective control force is generated to alleviate the undesirable motion characteristics. The Riccati equation is used to determine the optimal control force. Response time histories and power spectra are generated for long crested random sea along with drift and wind forces. These responses are compared with the same under control. The present study aims at an efficient method of determination of the control force magnitude to design a control strategy for serviceability and survival of tension leg platforms in hostile ocean environments.

Wind-induced response of a tension leg platform

Dynamic response studies of a tension leg platform (TLP) are carried out in time domain to investigate the influence of non-linearities due to the hydrodynamic drag force, variable cable tension, variable submergence, long excursions and fluctuating wind together with the effect of coupling. The sea state is characterised by Pierson Moskovitz spectrum while the fluctuating wind has been estimated using Emil Simiu's wind spectrum which is meant for the compliant offshore structures. Random wind and waves are modelled by Monte-Carlo simulation. Power spectral density functions (PSDF) are plotted to highlight the wind-induced dynamic responses of the structure.

Dynamic Response of Compliant Offshore Structures—Review

Offshore compliant structures such as guyed platforms, tension leg platforms and articulated towers are economically attractive for deep water conditions because of their reduced structural weight compared to conventional platforms. The foundations of these kinds of structures do not resist lateral environmental loads forces; instead, restoring moments are provided by a large buoyancy force, a set of guylines or a combination of both. These structures have a fundamental frequency well below the ocean wave’s lower frequency-bound. As a result of the relatively large displacements, geometric nonlinearity is an important consideration in the analysis of such a structure. This paper presents a literature review on offshore compliant structures. The review focuses on the static and dynamic response of the structure due to various environmental conditions, such as wind, waves and current. Emphasis is placed on modeling techniques and methods of solution. Many modeling and analysis techniques are common to the aerospace and ocean engineering communities due to the similarities in structural and environmental complexities. For example, aerodynamic loads on offshore platforms are a significant part of any analysis. Also, fluid loading models bear great similarities to mechanistic wind loading models. It is in this vein that a review paper with the focus on offshore structures is included in a journal of aerospace engineering.