Stochastic Analysis of a Nonlinear Energy Harvester Model

Floating oscillating-bodies are a kind of wave energy converter developed for harvesting the great amount of energy related to water waves (see Falcão [1] for a review). Although the assumptions of small-wave and linear behavior of oscillating system are reasonable for most of the time during which a floating point harvester is in operation, nonlinear effects may be significant in extreme sea states situations. In this paper a nonlinear dynamic analysis of a point harvester wave energy converter is conducted. The model involves a tightly moored single-body floating device; it captures motion in the horizontal and vertical directions. The stiffness and damping forces, being functions of the displacement and velocity components, make the system nonlinear and coupled. For the input forces, the erratic nature of the waves is modeled by a stochastic process. Specifically, wind-generated waves are modeled by means of the JONSWAP spectrum. The method of statistical linearization [2] is used to determine iteratively the effective linear stiffness and damping matrices and response statistics of the system and to proceed to conducting a dynamic analysis of the harvester model. The reliability of the linearization based approach is demonstrated by comparison with time domain integration, Monte Carlo simulation, data. This approach offers the appealing feature of conducting efficiently a variety of parameter studies which can expedite preliminary evaluations, inter alia, of competing design scenarios for the energy converter in a stochastic environmental setting.

State-of-the-Art Techniques for Seismic Soil-Structure Interaction Analysis of Steel Gravity Structures

The design of steel jacket fixed offshore structures in zones of moderate seismicity is typically governed by Metocean loads. In contrast the steel gravity structure (SGS) presented in this paper, is a heavy and stiff structure. The large mass results in foundation forces from seismic events that may exceed those created by extreme cyclonic storm events. When computing the earthquake response of such structures it is essential to account for soil-structure interaction (SSI) effects. Seismic SSI analysis of the SGS platform was performed using state-of-the-art SSI software, which analyzed a detailed three-dimensional model of the SGS supported on layered soil system. The results of this analysis were then compared with those using industry standard impedance methods whereby the layered soil is replaced by equivalent foundation springs (K) and damping (C). Differences in calculated results resulting from the different ways by which K and C are implemented in different software are presented. The base shear, overturning moment, critical member forces and maximum accelerations were compared for each of the analysis methods. SSI resulted in significant reduction in seismic demands. While it was possible to get reasonable alignment using the different standard industry analysis methods, this was only possible after calibrating the KC foundation model with software that rigorously implements SSI effects. Lessons learned and recommendations for the various methods of analysis are summarized in the paper.

Long-Term Fatigue Analysis of Deepwater Risers in the Time Domain

A floating production system is exposed to many different environmental conditions over its service life. Consequently, the long-term fatigue analysis of deepwater risers is computationally demanding due to the need to evaluate the fatigue damage from a multitude of sea states. Because of the nonlinearities in the system, the dynamic analysis is often performed in the time domain. This further compounds the computational difficulty owing to the time consuming nature of time domain analysis, as well as the need to simulate a sufficient duration for each sea state to minimize sampling variability. This paper presents a new and efficient simulation technique for long-term fatigue analysis. The results based on this new technique are compared against those obtained from the direct simulation of numerous sea states.

Fatigue Reliability Assessment for Brace-Column Details in a Semi-Submersible Hull

Semi-submersible floating platforms used in the offshore deepwater environment have hull structures that are comprised of vertical cylinders (columns) connected by braces, pontoons, etc. Several of the connections between these various members are susceptible to fatigue damage. In fatigue damage assessment or fatigue reliability analysis, a global structural response analysis is typically carried out using a finite element model where internal forces or stresses in the various members are evaluated for specified sea states of interest at the site. Of specific interest in this study is the fatigue reliability analysis of brace-column connection details in a semi-submersible hull unit for selected Brazilian environmental conditions. Stress concentration factors for the selected critical hot spots are applied to the nominal component stresses due to axial forces and biaxial bending. The hot-spot stress response spectra are used with various spectral methods — referred to as Rayleigh, Modified Rayleigh (with bandwidth correction), and Dirlik — to estimate fatigue damage using Miner’s rule. Uncertainty estimates in fatigue damage rates and life based on the various methodologies are discussed and critical sea states are identified, highlighting dynamic and quasi-static influences on the predicted fatigue.

Improving the Early Steel Design Process by Integrating Strength Calculation and Rule Checking Capabilities in a Ship Design Tool

A well-founded determination of steel structure scantlings is essential during the early design process of a ship or an ocean structure. In the first 4 up to 6 weeks of a new building project, the major part of the final building costs has to be fixed. Amongst others a proper steel weight estimation is crucial. The weight depends on the structural dimensions which are determined mostly by experience and rarely by direct calculations. Therefore, a simple direct strength calculation tool has been integrated in a ship design software. The tool uses structural and general ship design information. Besides the structural constraints, posed by the project design, the steel designer has to fulfill also the structural constraints posed by the classification societies. Normally they are checked with software solutions provided by the societies. However these software tools are not well adapted to the early design process as various design parameters change frequently. For this purpose a link has been created between a rule scantling tool on one side and a design software on the other. The link allows an automated exchange of steel scantlings and project information. By this the modeling and design work as well as the structure scantling and steel weight determination is performed in the design software tool, while the rule scantling tool is only used for a quick assessment of class conformity. With the help of the mentioned methods, the structure can be pre-dimensioned directly based on the early design model in accordance with the classification rules. Furthermore the steel dimensions can not only be optimized with regard to local and global loads, but also with regard to design boundary conditions. In consequence the early steel design process is improved by a more accurate steel scantlings determination and results in a better optimized steel structure as well as severely reduced time spent on the steel iterations.

Implementing New Nonlinear Term in Third Generation Wave Models

The non-linear interaction term is one of the three key source functions in every third-generation spectral wave model. An update of physics of this term is discussed. The standard statistical/phase-averaged description of the nonlinear transfer of energy in the wave spectrum (wave-turbulence) is based on Hasselmann’s kinetic equation [1]. In the derivation of the kinetic equation (KE) it is assumed that the evolution takes place on the slow O(ε−4) time scale, where ε is the wave steepness. This excludes the effects of near-resonant quartet interactions that may lead to spectral evolution on the ‘fast’ O(ε−2) time scale. Generalizations of the KE (GKE) that enable description of spectral evolution on the O(ε−2) time scale [2–4] are discussed. The GKE, first solved numerically in [4], is implemented as a source term in the third generation wave model WAVEWATCH-III. The new source term (GKE) is tested and compared to the other nonlinear-interaction source terms in WAVEWATCH-III; the full KE (WRT method) and the approximate DIA method. It is shown that the GKE gives similar results to the KE in the case of a relatively broad banded and directional spread spectrum, while it shows somewhat larger difference in the case of a more narrow banded spectrum with narrower directional distribution. We suggest that the GKE may be a suitable replacement to the KE in situations where ‘fast’ spectral evolution takes place.

Collapse Analysis of Offshore Platforms Using Constrained New Waves

Traditionally regular deterministic wave theories are employed to estimate wave loads on offshore platforms but they cannot capture random nature of the sea states. Randomly generated sea surfaces will lead to most accurate results for structural responses due to waves but they are usually based on long duration simulations and hence need excessive computational efforts. Constrained NewWaves (CNWs), with significantly shorter computational time, have recently been used successfully for estimating of structural response of offshore platforms due to waves. For extreme waves, as long as there is no indication of major structural nonlinearity in the system, they have shown reasonably accurate results as an alternative for long duration randomly generated sea surfaces. This paper is concerned with using CNWs in collapse analysis of offshore platforms under extreme waves where large geometrical and material nonlinearities are expected. It shows how the plastic level of the response, total duration of the loading, the loading pattern and dynamic characteristics of the platform can influence the extreme response and collapse rates of the offshore platforms.

Prediction of Corrosion Condition Considering Effect of Maintenance

Corrosion prediction model which takes an effect of maintenance and repair into account is developed based on the full probability corrosion model. Over-all coating repair, touch-up coating repair and renewing repair of worn member are considered. Change in the corrosion condition due to the maintenance and repair work is modeled and possibility of such change is evaluated. Based on the developed model, the effects of these maintenance and repair methods to the corrosion condition are numerically examined and discussed. In these numerical examinations, a conventional paint coating and a coating which meets the PSPC (IMO’s Performance Standard for Protective Coatings) specification are examined. Change in corrosion wastage condition due to the maintenance and repair works is evaluated and compared. And the probability that the corrosion wastage exceeds the permissible level is also evaluated.

Low Frequency Vibration Control of the Offshore Fixed Platforms by Using Tuned Liquid Column Damper

The offshore fixed platforms are confronted with greater wind and wave forces as their installation site moves toward the deep sea, so it is definitely necessary to reduce the low frequency vibration of structures for the safety and comfort of crews. The dynamic dampers are generally used to reduce vibration of structures. Especially, the tuned liquid column damper (TLCD) has been applied to reduce the low frequency vibration of onshore tall buildings. In this paper, the design procedure of TLCD is proposed to control the low frequency vibration of fixed platforms through the simulation and experiment with a small-scale model. The vibration control target is the surge motion of fixed platforms and the major design variables of TLCD are mass and damping ratios. The optimized design variables of TLCD are determined from the calculation of the amplification factor. In the experiment, the effects of mass and damping ratios are considered by changing the breadth of column, the opening ratio and number of the orifices. The results of experiment are found to well agree with the simulation. The 83% of structure vibration level can be reduced by applying the optimized TLCD.

Shakedown Analysis of Ocean Engineering Structures Subjected to Repeated Dynamic Loads

Ocean engineering structures are frequently subjected to repeated dynamic loads caused by slamming of wave, impact of ice, dropped objects, collisions of store ship and grounding. Shakedown analysis is an extension of plastic limit analysis. Meanwhile, the dynamic strength analysis and shakedown analysis of offshore platform structure have an important place in ensuring the safety and reliability of ocean engineering structures under repeated dynamic loads. Therefore the shakedown analysis theory was introduced to the ultimate strength analysis of brace strut of semisubmersible drilling platform considering cyclic wave load. Based on the kinematic shakedown theorem, a theoretical method of shakedown analysis for typical ocean engineering structures under repeated dynamic loads was presented and compared with existing results to verify the reasonableness. According to the method of finite elastic-plastic theory, the strength of brace strut was analyzed through the overall model of semisubmersible drilling platform. Then based on the boundary conditions getting from the overall three-dimensional model, locally refined model of brace strut was obtained. By applying the theoretical method to shakedown analysis of brace strut under repeated dynamic loads, influence of shell thickness, stiffener thickness and stiffener spacing on shakedown limit were studied. The results show that the theoretical calculation method is consistent with the existing results. The limit load increases with the increase of shell thickness and stiffener thickness, while decreases with the increase of stiffener spacing.