Practical Airgap Prediction for Offshore Structures

2004 ◽  
Vol 126 (2) ◽  
pp. 147-155 ◽  
Author(s):  
Bert Sweetman
Keyword(s):  
Model Test ◽  
Offshore Structures ◽  
Value Theory ◽  
Second Order ◽  
New Method ◽  
Statistical Regression ◽  
Post Processing ◽  
Offshore Structure ◽  
First Order ◽  
Order Diffraction

Two new methods are proposed to predict airgap demand. Airgap demand is the maximum expected increase in the water surface elevation caused incident waves interacting with an offshore structure. The first new method enables inclusion of some second-order effects, though it is based on only first-order diffraction results. The method is simple enough to be practical for use as a hand-calculation in the early stages of design. Two existing methods of predicting airgap demand based on first-order diffraction are also briefly presented and results from the three methods are compared with model test results. All three methods yield results superior to those based on conventional post-processing of first-order diffraction results, and comparable to optimal post-processing of second-order diffraction results. A second new method is also presented; it combines extreme value theory with statistical regression to predict extreme airgap events using model test data. Estimates of extreme airgap events based on this method are found to be more reliable than estimates based on extreme observations from a single model test. This second new method is suitable for use in the final stages of design.

scholarly journals Algorithms for Solving Nonhomogeneous Generalized Sylvester Matrix Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Ehab A. El-Sayed ◽  
Eid E. El Behady
Keyword(s):  
Explicit Solution ◽  
Second Order ◽  
New Method ◽  
Matrix Equations ◽  
Numerical Examples ◽  
First Order ◽  
Hessenberg Form ◽  
Sylvester Matrix ◽  
The Matrix ◽  
Sylvester Matrix Equations

This paper considers a new method to solve the first-order and second-order nonhomogeneous generalized Sylvester matrix equations AV+BW= EVF+R and MVF2+DV F+KV=BW+R, respectively, where A,E,M,D,K,B, and F are the arbitrary real known matrices and V and W are the matrices to be determined. An explicit solution for these equations is proposed, based on the orthogonal reduction of the matrix F to an upper Hessenberg form H. The technique is very simple and does not require the eigenvalues of matrix F to be known. The proposed method is illustrated by numerical examples.

scholarly journals Localized Conical Edge Modes of Higher Orders in Photonic Liquid Crystals

Crystals ◽  
2019 ◽  
Vol 9 (10) ◽  
pp. 542 ◽  
Author(s):  
Vladimir A. Belyakov ◽  
Sergei V. Semenov
Keyword(s):  
Liquid Crystals ◽  
Maxwell Equations ◽  
Analytic Solution ◽  
Second Order ◽  
Experimental Results ◽  
Analytical Theory ◽  
Exact Analytic Solution ◽  
Localized Modes ◽  
First Order ◽  
Order Diffraction

Most studies of the localized edge (EM) and defect (DM) modes in cholesteric liquid crystals (CLC) are related to the localized modes in a collinear geometry, i.e., for the case of light propagation along the spiral axis. It is due to the fact that all photonic effects in CLC are most pronounced just for a collinear geometry, and also partially due to the fact that a simple exact analytic solution of the Maxwell equations is known for a collinear geometry, whereas for a non-collinear geometry, there is no exact analytic solution of the Maxwell equations and a theoretical description of the experimental data becomes more complicated. It is why in papers related to the localized modes in CLC for a non-collinear geometry and observing phenomena similar to the case of a collinear geometry, their interpretation is not so clear. Recently, an analytical theory of the conical modes (CEM) related to a first order of light diffraction was developed in the framework of the two-wave dynamic diffraction theory approximation ensuring the results accuracy of order of δ, the CLC dielectric anisotropy. The corresponding experimental results are reasonably well described by this theory, however, some numerical problems related to the CEM polarization properties remain. In the present paper, an analytical theory of a second order diffraction CEM is presented with results that are qualitatively similar to the results for a first order diffraction order CEM and have the accuracy of order of δ2, i.e., practically exact. In particular, second order diffraction CEM polarization properties are related to the linear σ and π polarizations. The known experimental results on the CEM are discussed and optimal conditions for the second order diffraction CEM observations are formulated.

Results From Model Testing of Ice Protection Piles in Shallow Water

2006 ◽  
Author(s):  
Arne Gu¨rtner ◽  
Joachim Berger
Keyword(s):  
Model Test ◽  
Oil And Gas ◽  
Offshore Structures ◽  
Full Scale ◽  
Offshore Structure ◽  
Oil And Gas Fields ◽  
Ice Loads ◽  
Drifting Ice ◽  
Ice Model Test ◽  
Gas Fields

The development of oil and gas fields in shallow icy waters, for instance in the Northern Caspian Sea, have increased the awareness of protecting offshore structures by means of ice barriers from the impacts of drifting ice. Protection could be provided by Ice Protection Piles (IPPs), installed in close vicinity to the offshore structure to be protected. Piles then take the main loads from the drifting ice by pre-fracturing the advancing ice sheet. Hence, the partly shielded offshore structure could be designed according to significant lower global design ice loads. In this regard, various configurations of pile arrangements have been model tested during the MATRA-OSE research project in the Ice Model Test Basin of the Hamburg Sip Model Basin (HSVA). The main objective was to analyse the behaviour of ice interactions with the protection piles together with the establishment of design ice loads on an individual pile within the pile arrangement. The pile to pile distances within each arrangement were varied from 2 to 8 times the pile diameter for both, vertical and inclined (30° to the horizontal) pile arrangements. Two test runs with 0.1 m and 0.5 m thick ice (full scale values) were conducted respectively. The full scale water depth was 4 m. Based on the model test observations, it was found that the rubble generation increases with decreasing pile to pile distances. Inclined piles were capable to produce more rubble than vertical piles and considerable lower ice loads were measured on inclined arrangements compared to vertical arrangements. As initial rubble has formed in front of the arrangements, the rubble effect accelerated considerable. Subsequent to the build-up of rubble accumulations, no effect of the pile inclination on the exerted ice loads could be observed. If piles are used as ice barriers, the distance between the piles should be less than 4D for inclined piles and 6D for vertical piles to allow sufficient rubble generation. Larger distances only generated significant ice rubble after initial grounding of the ice had occurred.

Research Studies on Modeling Soil Erosion Caused by External Factors Near Offshore Structures

2013 ◽  
Author(s):  
Leonid G. Shchemelinin ◽  
Kirill E. Sazonov ◽  
Valeriy I. Denisov
Keyword(s):  
Soil Erosion ◽  
Model Test ◽  
Offshore Structures ◽  
Bottom Current ◽  
Offshore Structure ◽  
Sandy Bottom ◽  
Towing Tank ◽  
Sea Bed ◽  
Sea Currents ◽  
Research Studies

For development of hydrocarbon deposits located in a shallow part of coastal shelf, offshore structures of gravitational type are widely used. The foundations of such structures are towed to sites where they are flooded and installed directly on sea bed. During operation of offshore structures the sea bed soil around and beneath the structure foundations are exposed to external effects such as sea currents, waves and also propeller streams generated by ships approaching the structures. As a result the soil is washed out from under the structure which may cause reduction of bearing surface area and even lead to loss of stability of the structure on seabed. The model studies on soil erosion process near foundations of gravitational-type offshore platforms have been conducted at Krylov’s shallow water towing tank since 2000. This towing tank was not originally intended for such experiments, and, therefore, special experimental equipment has been developed for this purpose. These include a sandy bottom, current generation arrangements in the model test zone, instrumentation for measuring the bottom profile. Also specific model test procedures and methods for research on soil scour near the test objects have been developed and verified. The paper gives a review of these research studies at the Krylov Centre, describe the test equipment, modeling techniques and test data scaling procedures as well as the experience learned from the experiments. The paper gives some results of research studies of soil erosion near the foundations of offshore structures as a result of influence from sea currents and waves with coincident directions, and also as a result of influence from propeller streams of moored tankers and supply vessels. The paper presents the model test results regarding the efficiency of a mobile system developed for soil erosion protection near the offshore structure intended for exploratory drilling in shallow waters of the Gulf of Ob in the Kara Sea. A review of the recent Krylov’s studies in this field of research is given.

scholarly journals A Dynamic Ice-structure Interaction Model for Prediction of Ice-induced Vibration

2019 ◽  
Author(s):  
Tianyu Wu ◽  
Wenliang Qiu
Keyword(s):  
Sea Ice ◽  
Model Test ◽  
Interaction Model ◽  
Simulation Method ◽  
Offshore Structures ◽  
Full Scale ◽  
Structural Safety ◽  
Offshore Structure ◽  
The Impact ◽  
Ice Induced Vibration

Sea ice crashing against offshore structures can cause strong ice-induced vibration and have a major impact on offshore structural safety and serviceability. This paper describes a numerical method for the prediction of ice-induced vibration when a vertical offshore structure is subjected to the impact of sea ice. In this approach, negative damping theory and fracture length theory are combined and, along with ice strength-stress rate curve and ice failure length, are coupled to model the internal fluctuating nature of ice load. Considering the elastic deformation of ice and the effect of non-simultaneous crushing failure of local contact between ice and structures, the present ice-induced vibration model is established, and the general features of the interaction process are captured. To verify its efficacy, the presented simulation methodology is subjected to a model test and two full-scale measurements based on referenced studies. Example calculations show good agreement with the results of the model test and full-scale measurements, which directly indicates the validity of the proposed simulation method. In addition, the numerical simulation method can be used in connection with FE programs to perform ice-induced vibration analysis of offshore structures.

Second-Order Diffraction in Short Waves

2005 ◽  
Vol 49 (04) ◽  
pp. 263-273
Author(s):  
J. N. Newman
Keyword(s):  
Short Wavelength ◽  
Second Order ◽  
Asymptotic Approximations ◽  
First Order ◽  
Short Waves ◽  
Order Diffraction ◽  
Incident Waves

Asymptotic approximations are derived for the second-order potential and the result-ing pressure forces acting on fixed vessels in monochromatic or bichromatic incident waves. These approximations are based on the short-wavelength assumption, with respect to the first-order incident waves. Comparisons are made with computations based on the second-order panel code WAMIT, to indicate the domains where the approximate results are useful.

Bivariate Extreme Value Statistics of Offshore Jacket Support Stresses in Bohai Bay

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Zhang Jian ◽  
Oleg Gaidai ◽  
Junliang Gao
Keyword(s):  
Offshore Structures ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Bohai Bay ◽  
Wave Load ◽  
Offshore Structure ◽  
Response Dynamics ◽  
Extreme Response ◽  
Hydrodynamic Wave

This paper presents a generic Monte Carlo-based approach for bivariate extreme response prediction for fixed offshore structures, particularly jacket type. The bivariate analysis of extremes is often poorly understood and generally not adequately considered in most practical measurements/situations; that is why it is important to utilize the recently developed bivariate average conditional exceedance rate (ACER) method. According to the current literature study, there is not yet a direct application of the bivariate ACER method to coupled offshore jacket stresses. This study aims at being first to apply bivariate ACER method to jacket critical stresses, aiming at contributing to safety and reliability studies for a wide class of fixed offshore structures. An operating jacket located in the Bohai bay was taken as an example to demonstrate the proposed methodology. Satellite measured global wave statistics was used to obtain realistic wave scatter diagram in the jacket location area. Second-order wave load effects were taken into account, while simulating jacket structural response. An accurate finite element ANSYS model was used to model jacket response dynamics, subject to nonlinear hydrodynamic wave and sea current loads. Offshore structure design values are often based on univariate statistical analysis, while actually multivariate statistics is more appropriate for modeling the whole structure. This paper studies extreme stresses that are simultaneously measured/simulated at two different jacket locations. Due to less than full correlation between stresses in different critical jacket locations, application of the multivariate (or at least bivariate) extreme value theory is of practical engineering interest.

A First-Order Second-Moment Approach to Systems Fatigue Reliability of Offshore Structures

1995 ◽  
Vol 117 (2) ◽  
pp. 105-112
Author(s):  
Y. Hu ◽  
B. Chen
Keyword(s):  
Offshore Structures ◽  
Probability Of Failure ◽  
Fatigue Reliability ◽  
Offshore Structure ◽  
Second Moment ◽  
First Order ◽  
Failure Path ◽  
First Order Second Moment ◽  
Moment Approach ◽  
Second Moment Method

A method to evaluate the probability of failure of a failure path leading to fatigue collapse of an offshore structure is presented. The failure path is modeled by a number of failure elements, which represent the fatigue-sensitive joints in the structure, connecting in parallel and failing in sequence. The probability of failure of the parallel system is calculated by using first-order second-moment method. The formulation is further improved by considering the probability of occurrence of a specified sequence in which the failure elements fail. The method can be employed both in searching for important failure paths and in evaluating the probability of failure of the whole structure in systems fatigue reliability analysis of offshore structures.

A Tutorial on Soize’s Method for Stochastic Modeling in Structural Acoustics (Fuzzy Structures Analysis)

1995 ◽  
Author(s):  
Christopher E. Ruckman ◽  
David Feit
Keyword(s):  
Stochastic Modeling ◽  
Order Term ◽  
Stochastic Approach ◽  
Second Order ◽  
Acoustic Modeling ◽  
Complex Structures ◽  
Structural Acoustics ◽  
Post Processing ◽  
Element Analysis ◽  
First Order

Abstract Fuzzy structures analysis (FSA) is a stochastic approach for vibro-acoustic modeling of structures whose details cannot be modeled precisely. Pioneered by C. Soize, FSA provides a new tool that may lead to more realistic models of damping mechanisms in complex structures. This paper summarizes Soize’s method in simplified form, emphasizing the solution and post-processing procedures needed to implement FSA in computer programs. Input data needed for implementing FSA with a numerical method such as finite-element analysis are summarized. Stochastic modeling of fuzzy structures is outlined, with Newmann series expressions truncated explicitly after the second-order term. Selected post-processing formulas are given for first-order and second-order solutions.

Nonlinear Analysis of Visual Evoked Potentials Elicited by Color Stimulation

1997 ◽  
Vol 36 (04/05) ◽  
pp. 315-318 ◽  
Author(s):  
K. Momose ◽  
K. Komiya ◽  
A. Uchiyama
Keyword(s):  
Visual System ◽  
Evoked Potentials ◽  
Visual Evoked Potentials ◽  
Normal Subjects ◽  
Second Order ◽  
First Order ◽  
The Relationship ◽  
Perceived Color ◽  
Second Order Nonlinearity ◽  
Visual Evoked

Abstract:The relationship between chromatically modulated stimuli and visual evoked potentials (VEPs) was considered. VEPs of normal subjects elicited by chromatically modulated stimuli were measured under several color adaptations, and their binary kernels were estimated. Up to the second-order, binary kernels obtained from VEPs were so characteristic that the VEP-chromatic modulation system showed second-order nonlinearity. First-order binary kernels depended on the color of the stimulus and adaptation, whereas second-order kernels showed almost no difference. This result indicates that the waveforms of first-order binary kernels reflect perceived color (hue). This supports the suggestion that kernels of VEPs include color responses, and could be used as a probe with which to examine the color visual system.

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