Статті в журналах: "Wave bending moments"

1

Ambur, Damodar R., Davresh Hasanyan, Liviu Librescu, and Zhanming Qin. "Diffraction of harmonic flexural waves in a cracked elastic plate carrying electrical current." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2063 (September 14, 2005): 3543–60. http://dx.doi.org/10.1098/rspa.2005.1512.

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The scattering effect of harmonic flexural waves at a through crack in an elastic plate carrying electrical current is investigated. In this context, the Kirchhoffean bending plate theory is extended as to include magnetoelastic interactions. An incident wave giving rise to bending moments symmetric about the longitudinal x -axis of the crack is applied. Fourier transform technique reduces the problem to dual integral equations, which are then cast to a system of two singular integral equations. Efficient numerical computation is implemented to get the bending moment intensity factor for arbitrary frequency of the incident wave and of arbitrary electrical current intensity. The asymptotic behaviour of the bending moment intensity factor is analysed and parametric studies are conducted.

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2

Woodward, John B., Michael G. Parsons, and Armin W. Troesch. "Ship Operational and Safety Aspects of Ballast Water Exchange at Sea." Marine Technology and SNAME News 31, no. 04 (October 1, 1994): 315–26. http://dx.doi.org/10.5957/mt1.1994.31.4.315.

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A dry bulk carrier, a tanker, and a containership—taken as typical of ships trading to U.S. ports—are analyzed for possible hazards caused by emptying and refilling ballast tanks at sea. Using hydrostatic data furnished by the shipowners, hull bending moments and stabilities are investigated to find the tank-emptying operations that produce the greatest changes in those parameters. As should be expected, bending moment changes do not exceed allowable stillwater values. Changes in GM are insignificant. The worst hydrostatic cases serve as a guide to conditions that should be analyzed in rough water. The University of Michigan SHIPMO program shows that in waves of 10-ft significant height wave-induced bending moments and shears are far below the design values published by the American Bureau of Shipping. On the other hand, in waves of 20-ft significant height, the maximum wave heights that occur occasionally can cause moments or shears that exceed design values. For the 20-ft case, both linear and nonlinear versions of SHIPMO are used.

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3

Petranović, Tamara, Antonio Mikulić, Marko Katalinić, Maro Ćorak, and Joško Parunov. "Method for Prediction of Extreme Wave Loads Based on Ship Operability Analysis Using Hindcast Wave Database." Journal of Marine Science and Engineering 9, no. 9 (September 14, 2021): 1002. http://dx.doi.org/10.3390/jmse9091002.

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The method for the prediction of extreme vertical wave bending moments on a passenger ship based on the hindcast database along the shipping route is presented. Operability analysis is performed to identify sea states when the ship is not able to normally operate and which are likely to be avoided. Closed-form expressions are used for the calculation of transfer functions of ship motions and loads. Multiple operability criteria are used and compared to the corresponding limiting values. The most probable extreme wave bending moments for the short-term sea states at discrete locations along the shipping route are calculated, and annual maximum extreme values are determined. Gumbel probability distribution is then fitted to the annual extreme values, and wave bending moments corresponding to a return period of 20 years are determined for discrete locations. The system reliability approach is used to calculate combined extreme vertical wave bending moment along the shipping route. The method is employed on the example of a passenger ship sailing across the Adriatic Sea (Split, Croatia, to Ancona, Italy). The contribution of the study is the method for the extreme values of wave loads using the hindcast wave database and accounting for ship operational restrictions.

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4

Corak, Maro, Joško Parunov, and C. Guedes Soares. "Probabilistic Load Combination Factors of Wave and Whipping Bending Moments." Journal of Ship Research 59, no. 01 (March 1, 2015): 11–30. http://dx.doi.org/10.5957/jsr.2015.59.1.11.

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Extreme values of wave and whipping bending moments are important in structural design of large containerships. Since the extreme values of these two, partially correlated processes do not occur at the same time instant and even at the same environmental conditions, it is necessary to combine them by using probabilistic load combination methods. The correlation analysis between wave and whipping bending moments is performed and a practical method for calculation of the most probable load combination factor between considered bending moments is presented. Short-term load combination factors are calculated by reconstruction of the signal from the frequency domain solution. Results are validated by comparison with model test data of the 9400-TEU containership for various sea states and speeds and heading angles. Practical regression equations for estimation of the most probable short-term load combination factor are formulated. Regression equations are then used in the computation of the long-term distribution of combined bending moment. The procedure is demonstrated on the example of the two large containerships.

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5

O¨stergaard, C. "Partial Safety Factors for Vertical Bending Loads on Containerships." Journal of Offshore Mechanics and Arctic Engineering 114, no. 2 (May 1, 1992): 129–36. http://dx.doi.org/10.1115/1.2919960.

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International design codes for seagoing steel ships of today are in the process of testing a new safety format with load factors separately multiplied with nominal (code) values of still water and wave loads. This leads to two design values of these loads, the sum of which must not exceed a design value of the strength of the ship structure, which is again a nominal (code) value of strength, this time divided by a strength factor. Such load and strength factors are generally termed partial safety factors. In the paper, vertical still water and wave bending moments of containerships are considered as loads. The partial safety factors are determined on the basis of reliability analysis, i.e., the sum of the design values of the loads will not exceed a design serviceability limit state of the ship’s structure with given probability. To enable reliability analysis, distribution density of the ship’s strength to resist bending moments is based on a stochastic interpretation of nominal (code) values used in the conventional safety format. The probability density of the still water bending moment is obtained from recently published statistical data. The probability density of the wave bending moment is calculated using advanced hydrodynamic and spectral analysis, including long-term statistics of the (North Atlantic) seaway. Reliability and related design values are estimated using the FORM algorithm with due consideration of the different repetition numbers for which the stochastic models of the two bending moments are valid. The results are presented as nonlinear regression formulas and as diagrams that specify partial safety factors related to length and beam of containerships. The nominal values of bending moments to be used with these partial safety factors are given as functions of length, beam, and block coefficient of those ships.

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6

Sulisetyono, Aries, and Teguh Putranto. "Wave Load Analysis of the Corvette Ship in the Sea Water of Indonesia." Applied Mechanics and Materials 862 (January 2017): 291–95. http://dx.doi.org/10.4028/www.scientific.net/amm.862.291.

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Wave load prediction of ship should be considered in the design stage of ship’s construction. The excessive of wave load might cause a structural failure of ship during operational in seaway. The bending moment might be experienced on the ship structure that it contributes to stress concentration on the particular part of construction. This paper describes the prediction of bending moment and shear forces of the warship corvette type considered to the sea condition of Indonesia. The 3D diffraction theory was adopted to analyze ship’s motion responses, bending moments, and shear forces numerically. In this numerical simulation, the variations of speed and heading angle of ship were performed with respect to environmental condition of sea state 4, 5, 6 and 7. The simulation results had shown that the maximum shear force and bending moment was occurred on the area of mid-ship.

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7

Pedersen, P. T., and J. J. Jensen. "Estimation of hull girder vertical bending moments including non-linear and flexibility effects using closed form expressions." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 223, no. 3 (June 12, 2009): 377–90. http://dx.doi.org/10.1243/14750902jeme143.

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A simple but rational procedure for prediction of extreme wave-induced hull girder bending moment in slender mono-hull displacement vessels is presented. The procedure takes into account main ship hull characteristics such as length, breadth, draught, block coefficient, bow flare coefficient, forward speed, and hull flexibility. The wave-induced loads are evaluated for specific operational profiles. Non-linearity in the wave bending moment is modelled using results derived from a second-order strip theory and water entry solutions for wedge-type sections. Hence, bow flare slamming is accounted for through a momentum type of approach. The stochastic properties of this non-linear response are calculated through a monotonic Hermite transformation. In addition, the impulse loading attributable to, for example, bottom slamming or a rapid change in bow flare is included using a modal expansion in the two lowest vertical vibration modes. These whipping vibrations are added to the wave frequency non-linear response, taking into account the rise time of the impulse response as well as the phase lag between the occurrence of the maximum non-linear load and the maximum impulse load. Previous results for the sagging bending moment are validated by comparison with fully non-linear strip theory calculations and supplemented with new closed form results for the hogging bending moment. Focus is on the extreme hull girder hogging bending moment. Owing to the few input parameters, this procedure can be used to estimate the wave-induced bending moments at the conceptual design phase. Another application area is for novel single-hull ship types not presently covered by the rules of the classification societies. As one application example the container ship MSC Napoli is considered. Further validations are needed, however, in order to select proper values of the parameters entering the analytical form of the slamming impulse.

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8

Perišić, Nevena, and Poul Henning Kirkegaard. "Low-Cost Tower Root Fatigue Load Estimation for Structural Health Monitoring of Grouted Connections in Offshore Wind Turbines." Key Engineering Materials 569-570 (July 2013): 676–83. http://dx.doi.org/10.4028/www.scientific.net/kem.569-570.676.

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The sinking of wind turbines (WTs) with monopile foundations is one of the major issues in the offshore wind industry nowadays. Dynamic wind and wave loads act on the WTs causing vibrations of the structure. However, grouted connections in the monopiled WTs are not designed well enough to transfer bending moments from the wind loading. When the load capacity of the grouted connection is reached, stress cracks appear in the grout causing transition piece to slide down. Direct measuring of the fatigue load, called the tower bending moment, causing fatigue failures and sinking of the WTs is expensive and practically unfeasible. This paper suggests a low-cost, model-based algorithm for indirect measuring of the tower bending moments from the WT dynamic response measurements. The bending moment is estimated recursively using well-known Kalman filter theory. The method is validated using WT simulated data, assuming different measurement noise levels.

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9

Mansour, A. E., and J.-P. Wasson. "Charts for Estimating Nonlinear Hogging and Sagging Bending Moments." Journal of Ship Research 39, no. 03 (September 1, 1995): 240–49. http://dx.doi.org/10.5957/jsr.1995.39.3.240.

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Abstract This paper presents charts for preliminary estimates of the nonlinearities associated with wave bending moments acting on a ship moving in a stationary sea. Deviation of the actual hull shape above the waterline from "vertical wall" is characterized by a flare coefficient. The charts show the influence of the flare coefficient, among other parameters, on a nonlinearity parameter which may be used to estimate the difference between wave hogging and sagging moments. Three application examples are given at the end of the paper to illustrate how the charts can be used in conjunction with linear strip theory results in order to estimate slightly nonlinear hogging and sagging moments.

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10

Gui, E. H., and V. A. Squire. "Random vibration of floating ice tongues." Antarctic Science 1, no. 2 (June 1989): 157–63. http://dx.doi.org/10.1017/s0954102089000234.

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A normal mode approach is used to model the behaviour of a linearly-damped, elastic, ice beam floating on a fluid foundation and subjected to a random distributed loading. As an example, two loading regimes are considered to act on the Erebus Glacier Tongue, McMurdo Sound: broad bandwidth (‘white noise’) loading, and an ocean wave-type pressure distribution beneath the tongue. For white noise input, the root mean square (rms) deflexion is found to good accuracy within the first few modes, but the rms bending moment increases with the number of modes included in the summation due to the unlimited frequency content of the forcing. Solutions for the rms deflexion and bending moments quickly converge to their mathematical limit after six modes when the forcing is due to ocean waves. A local maximum in rms bending moment near the end of the beam confirms that waves may be important as a mechanism for iceberg calving.

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11

Soares, C. Guedes. "Effect of Heavy Weather Maneuvering on the Wave-Induced Vertical Bending Moments in Ship Structures." Journal of Ship Research 34, no. 01 (March 1, 1990): 60–68. http://dx.doi.org/10.5957/jsr.1990.34.1.60.

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Statistical data are collected so as to quantify the probability of occurrence of voluntary course changes in heavy weather as well as their dependence on significant wave height and on ship heading. Decision rules are established about when and how to change course, on the basis of the analysis of operational data and of interviews with experienced shipmasters. A Monte Carlo simulation is performed so as to determine how an omnidirectional distribution of initial headings is changed by voluntary course changes depending on the significant wave height. Finally, the effect of the nonuniform distribution of headings on the mean wave-induced vertical bending moment is calculated. It is shown that although heavy weather maneuvering eases the ship motions, it can increase the wave-induced bending moments and thus increase the probability of structural failure.

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12

Zhu, Suji, Mingkang Wu, and Torgeir Moan. "Experimental and Numerical Study of Wave-Induced Load Effects of Open Ships in Oblique Seas." Journal of Ship Research 55, no. 02 (June 1, 2011): 100–123. http://dx.doi.org/10.5957/jsr.2011.55.2.100.

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Open ships inherently possess low torsional rigidity because of their open deck structural configuration. Some of the structural failures for open ships are caused by wave-induced torsional moment in combination with other load components in oblique seas. Relatively few experimental results about horizontal bending and torsional moments in oblique seas have been published, however. Further, test data for vertical shear force and vertical bending moment in oblique seas are quite scarce. A backbone model has been recently tested by the Center for Ships and Ocean Structures (CeSOS) in the towing tank and ocean basin at the Marine Technology Center. The model consists of 15 box-shaped segments, in addition to bow and stern segments, which are interconnected by an aluminum beam on the top. Model tests in oblique seas without forward speed were first carried out to provide basic comparisons. Tests in head and oblique seas with speeds were then conducted in regular waves. Irregular wave tests were also carried out to assess the spectral responses and peak distributions of cross-sectional load effects. Load effects at 7 longitudinal positions were measured through strain gauges, including vertical shear force (VSF), vertical bending moment (VBM), horizontal bending moment (HBM), and torsional moment (TM). The motivation of this paper is to perform a benchmark study by comparing numerical predictions of different computer codes with these test results. The uncertainties in the experiments and the computer codes are discussed, and conclusions are presented at the end of this paper.

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13

Gu, XueKang, JinWei Shen, and Torgeir Moan. "Efficient and Simplified Time Domain Simulation of Nonlinear Responses of Ships in Waves." Journal of Ship Research 47, no. 03 (September 1, 2003): 262–73. http://dx.doi.org/10.5957/jsr.2003.47.3.262.

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In this paper, a nonlinear time-domain strip theory is developed to predict nonlinear vertical ship motions and structural responses in severe waves. The effects of bottom impact, bow flare slamming, and green water on bending moments have been simulated. The flexible modes of the ship hull girder are accounted for by a Timoshenko beam theory. To validate the predicted responses, a model test was conducted for a ship with large bow flare and low bending rigidity, in both regular and irregular waves. The agreements between the calculated results and the model test are fairly good. The coupling effect between higher-order harmonic and the whipping components of vertical bending moments are verified by numerical calculations. Comparative studies with test and other theoretical results are also carried out for an S-175 containership with two kinds of bow flare forms. The causes of whipping and the variance in theoretical results are discussed. The good performance and high efficiency will make it possible to use the theory and its code for direct calculation of nonlinear bending moments in a long-term period and to develop a rule formula of design wave loads in the future.

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14

Pedley, T. J., and S. J. Hill. "Large-amplitude undulatory fish swimming: fluid mechanics coupled to internal mechanics." Journal of Experimental Biology 202, no. 23 (December 1, 1999): 3431–38. http://dx.doi.org/10.1242/jeb.202.23.3431.

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The load against which the swimming muscles contract, during the undulatory swimming of a fish, is composed principally of hydrodynamic pressure forces and body inertia. In the past this has been analysed, through an equation for bending moments, for small-amplitude swimming, using Lighthill's elongated-body theory and a ‘vortex-ring panel method’, respectively, to compute the hydrodynamic forces. Those models are outlined in this review, and a summary is given of recent work on large-amplitude swimming that has (a) extended the bending moment equation to large amplitude, which involves the introduction of a new (though probably usually small) term, and (b) developed a large-amplitude vortex-ring panel method. The latter requires computation of the wake, which rolls up into concentrated vortex rings and filaments, and has a significant effect on the pressure on the body. Application is principally made to the saithe (Pollachius virens). The calculations confirm that the wave of muscle activation travels down the fish much more rapidly than the wave of bending.

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15

Ćorak, Maro, Joško Parunov, and C. Guedes Soares. "Probabilistic Load Combination Factors of Wave and Whipping Bending Moments." Journal of Ship Research 59, no. 1 (March 1, 2015): 11–30. http://dx.doi.org/10.5957/josr.59.1.140052.

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16

Mikulić, A., J. Parunov, and C. Guedes Soares. "Wave-Induced Vertical Motions and Bending Moments in Damaged Ships." Journal of Marine Science and Application 17, no. 3 (September 2018): 389–405. http://dx.doi.org/10.1007/s11804-018-0050-4.

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17

Ordonez-Sanchez, Stephanie, Matthew Allmark, Kate Porter, Robert Ellis, Catherine Lloyd, Ivan Santic, Tim O’Doherty, and Cameron Johnstone. "Analysis of a Horizontal-Axis Tidal Turbine Performance in the Presence of Regular and Irregular Waves Using Two Control Strategies." Energies 12, no. 3 (January 24, 2019): 367. http://dx.doi.org/10.3390/en12030367.

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The flow developed on a tidal site can be characterized by combinations of turbulence, shear flows, and waves. Horizontal-axis tidal turbines are therefore subjected to dynamic loadings that may compromise the working life of the rotor and drive train components. To this end, a series of experiments were carried out using a 0.9 m horizontal-axis tidal turbine in a tow tank facility. The experiments included two types of regular waveforms, one of them simulating an extreme wave case, the other simulating a more moderate wave case. The second regular wave was designed to match the peak period and significant wave height of an irregular wave which was also tested. Measurements of torque, thrust, and blade-bending moments were taken during the testing campaign. Speed and torque control strategies were implemented for a range of operational points to investigate the influence that a control mode had in the performance of a tidal stream turbine. The results showed similar average power and thrust values were not affected by the control strategy, nor the influence of either the regular or irregular wave cases. However, it was observed that using torque control resulted in an increase of thrust and blade root bending moment fluctuations per wave period. The increase in fluctuations was in the order of 40% when compared to the speed control cases.

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18

Thome, Michael, Ould el el Moctar, and Thomas E. Schellin. "Assessment of Hydrodynamic Loads on an Offshore Monopile Structure Considering Hydroelasticity Effects." Journal of Marine Science and Engineering 11, no. 2 (February 4, 2023): 350. http://dx.doi.org/10.3390/jmse11020350.

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Regular and irregular waves were numerically generated in a wave canal to investigate hydrodynamic loads acting on a wind turbine monopile and to predict its structural response. The monopile was implemented in the canal and modeled as a flexible structure, with the turbine blades and rotors considered as a point mass situated at the top of the monopile. Fluid–structure interaction (FSI) simulations were performed by coupling a structure solver based on a finite element method (FEM) with an unsteady Reynolds-averaged Navier–Stokes (URANS) equations solver of the finite volume method (FVM). The FSI simulations considered the two-way interaction between the deformable structure and the fluid flow. The URANS equations solver was coupled with the volume of fluid (VoF) method to account for the two-phase flow. In regular waves, numerically predicted total load coefficients occurring at the monopile’s first eigenfrequency compared favorably to experimental measurements. A deviation between calculations and measurements was observed for the total loads in irregular waves. This deviation occurred due to the smaller wave energy density of the numerically predicted irregular wave. Hydroelasticity effects increased wave-induced forces by about 6% and wave induced bending moments by about 16% in regular waves. A relatively strong whipping event was observed, which characterized the hydroelasticity response bending moment of the monopile in irregular long-crested waves. This whipping event also had a significant influence on the loads on the monopile. These investigations demonstrated the favorable use of FSI simulations to predict hydroelasticity effects on a monopile.

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19

Shindo, Y., I. Ohnishi, and S. Tohyama. "Flexural Wave Scattering at a Through Crack in a Conducting Plate Under a Uniform Magnetic Field." Journal of Applied Mechanics 64, no. 4 (December 1, 1997): 828–34. http://dx.doi.org/10.1115/1.2788988.

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Following a classical plate bending theory of magneto-elasticity, we consider the scattering of time-harmonic flexural waves by a through crack in a conducting plate under a uniform magnetic field normal to the crack surface. An incident wave giving rise to moments symmetric about the crack plane is applied. It is assumed that the plate has the electric and magnetic permeabilities of the free space. By the use of Fourier transforms we reduce the problem to solving a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic moment intensity factor versus frequency is computed and the influence of the magnetic field on the normalized values is displayed graphically. It is found that the existence of the magnetic field produces higher singular moments near the crack tip.

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20

Soares, C. Guedes. "Long term distribution of non-linear wave induced vertical bending moments." Marine Structures 6, no. 5-6 (January 1993): 475–83. http://dx.doi.org/10.1016/0951-8339(93)90033-y.

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21

Amin Rashidifar, Mohammad. "Analysis of Elastic Flexural Waves in Non-Uniform Beams Based on Measurement of Strains and Accelerations." Asian Journal of Electrical Sciences 5, no. 1 (May 5, 2016): 13–25. http://dx.doi.org/10.51983/ajes-2016.5.1.1969.

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Elastic flexural waves in an unloaded and unsupported segment of a non-uniform beam were considered. A method based on Timoshenko’s model was established for evaluation of shear force, transverse velocity, bending moment and angular velocity at an arbitrary section from four independent measurements of such quantities at one to four sections. From the evaluated quantities, shear stress, power transmission, etc. can be obtained. Experimental tests were carried out with an aluminium beam which had an abrupt change in height from 15 to 20 mm and was equipped with strain gauges and accelerometers at four uniformly distributed measurement sections and at three evaluation sections. The distance between the two outermost measurement sections was 600 mm, corresponding to 1.12 wave lengths at the upper end of the frequency interval 2500 Hz considered. Bending moments and transverse velocities evaluated from four measurements of any one of these quantities agreed well with those measured at evaluation sections located (i) centrally among the measurement sections and (ii) at a distance of 100 mm, or 0.17 wave lengths, outside. When it was located (iii) at a distance of 500 mm, or 0.83 wave lengths, outside, there was relatively large disagreement as expected from error analysis.

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22

Shindo, Y., I. Ohnishi, and S. Toyama. "Dynamic Singular Moments in a Perfectly Conducting Mindlin Plate With a Through Crack Under a Magnetic Field." Journal of Applied Mechanics 67, no. 3 (November 22, 1998): 503–10. http://dx.doi.org/10.1115/1.1311963.

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Following Mindlin’s theory of plate bending of magnetoelasticity, we consider the scattering of time-harmonic flexural waves by a through crack in a perfectly conducting plate under a uniform magnetic field normal to the crack surface. An incident wave giving rise to moments symmetric about the crack plane is applied. It is assumed that the plate has the electric and magnetic permeabilities of the free space. By the use of Fourier transforms we reduce the problem to solving a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic moment intensity factor versus frequency is computed and the influence of the magnetic field on the normalized values is displayed graphically. It is found that the existence of the magnetic field produces lower singular moments near the crack tip. [S0021-8936(00)02603-9]

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23

Hafiz, M. A., and A. Sulisetyono. "Structural Reliability Analysis for the Construction Design of the High-Speed Ship with CFRP Material." IOP Conference Series: Earth and Environmental Science 1081, no. 1 (September 1, 2022): 012041. http://dx.doi.org/10.1088/1755-1315/1081/1/012041.

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Abstract A high-speed ship mostly experiences the excessive motions in seaway that influence wave loads act to ship’s hull extremely. For this reason, the structure of a high-speed ship must be designed more strength than a low-speed vessel. In this paper, the construction design of the high-speed ship with material of CFRP are evaluated consider to the vertical bending moment under various wave excitation conditions. The eight design variations of the midship section are proposed to be evaluated against the uncertainty load stress due to the vertical motions of ship in random wave. The diffraction theory is adopted to solve the random wave loads due to various wave condition of heading angles, heights, and periods in which the maximum vertical bending moments of the rigid ship are obtained. Structural reliability analysis is applied for assessing structural safety and reliability of the ship’s structure. The structural strength of the construction design which are required for the reliability analysis have been developed based on permissible stress of BKI regulations. Safety levels associated with each mode of failure of all construction designs are determined and compared. Finally, the construction design is selected with the safety index 1.07.

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24

Guedes Soares, C. "On the definition of rule requirements for wave induced vertical bending moments." Marine Structures 9, no. 3-4 (January 1996): 409–25. http://dx.doi.org/10.1016/0951-8339(95)00033-x.

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25

Kim, Shinwoong, Benjamin Bouscasse, Guillaume Ducrozet, Sylvain Delacroix, Guillaume De Hauteclocque, and Pierre Ferrant. "Experimental investigation on wave-induced bending moments of a 6,750-TEU containership in oblique waves." Ocean Engineering 284 (September 2023): 115161. http://dx.doi.org/10.1016/j.oceaneng.2023.115161.

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26

NAZMY, ALY S. "SEISMIC ANALYSIS AND DESIGN EVALUATION OF CONTINUOUS PLATE-GIRDER BRIDGES: A CASE STUDY." International Journal of Structural Stability and Dynamics 03, no. 01 (March 2003): 91–106. http://dx.doi.org/10.1142/s021945540300077x.

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The currently-used AASHTO seismic design code for continuous plate-girder bridges built in areas of low to moderate seismicity is evaluated. The seismic behavior of a typical plate-girder bridge, designed according to the code, is studied in detail using a linear time-history analysis, and the peak response values of important parameters are computed. The effects of vertical ground excitation, seismic wave propagation, and change in support conditions on the bridge seismic response are investigated. The results are compared with those obtained using the current AASHTO seismic design code. The study concludes that the effect of vertical ground excitation on the plate-girder bending moments could be significant. It was found that the effect of seismic wave propagation on bending moments and shear forces in the bridge piers should be considered in the analysis of continuous plate girder bridges with several immovable supports when built in zones of low wave propagation speeds (e.g. 244 to 488 m/s). The study further concludes that AASHTO single mode spectral analysis slightly underestimates the forces in the bridge piers.

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27

Andersen, Lars, Thomas Andersen, and Lance Manuel. "Model Uncertainties for Soil-Structure Interaction in Offshore Wind Turbine Monopile Foundations." Journal of Marine Science and Engineering 6, no. 3 (July 18, 2018): 87. http://dx.doi.org/10.3390/jmse6030087.

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Monopiles are the most common type of foundation used for bottom-fixed offshore wind turbines. This investigation concerns the influence of uncertainty related to soil–structure interaction models used to represent monopile–soil systems. The system response is studied for a severe sea state. Three wave-load cases are considered: (i) irregular waves assuming linearity; (ii) highly nonlinear waves that are merged into the irregular wave train; (iii) slamming loads that are included for the nonlinear waves. The extreme response and Fourier amplitude spectra for external moments and mudline bending moments are compared for these load cases where a simpler static pile-cap stiffness and a lumped-parameter model (LPM) are both considered. The fundamental frequency response of the system is well represented by the static pile-cap stiffness model; however, the influence of higher modes (i.e., the second and third modes with frequencies of about 1 Hz and 2 Hz, respectively) is significantly overestimated with the static model compared to the LPM. In the analyzed case, the differences in the higher modes are especially pronounced when slamming loads are not present.

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28

Ćorak, Maro, Joško Parunov, and Carlos Guedes Soares. "Long-term prediction of combined wave and whipping bending moments of container ships." Ships and Offshore Structures 10, no. 1 (September 20, 2013): 4–19. http://dx.doi.org/10.1080/17445302.2013.833022.

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29

Wang, Xiaozhi, and Torgeir Moan. "Stochastic and deterministic combinations of still water and wave bending moments in ships." Marine Structures 9, no. 8 (September 1996): 787–810. http://dx.doi.org/10.1016/0951-8339(95)00022-4.

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30

Gaylord, B., and M. Denny. "Flow and flexibility. I. Effects Of size, shape and stiffness in determining wave forces on the stipitate kelps eisenia arborea and pterygophora californica." Journal of Experimental Biology 200, no. 24 (December 1, 1997): 3141–64. http://dx.doi.org/10.1242/jeb.200.24.3141.

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Wave action on exposed rocky coasts can be severe, generating large hydrodynamic forces that have been proposed to constrain the size of intertidal animals and plants. In contrast, flows subtidally are more benign, and organisms, particularly seaweeds, may grow quite large. The large dimensions of these flexible macroalgae allow them to move during much or most of a passing wave cycle, reducing relative water velocities and modifying the forces the plants must endure. The consequences of such wave-induced motion are explored for the stipitate understory kelps Eisenia arborea and Pterygophora californica using a numerical model that approximates these seaweeds as vertically oriented cantilever beams subjected to lateral hydrodynamic forces acting at their stipe tips. Bending moments and peak stresses induced in the stipes of these species during the passage of waves are calculated as functions of plant size and shape and of water depth and sea state. Model predictions for a subset of conditions are validated against real-time measurements of bending moments acting on a Pterygophora individual in the field. The results suggest that the allometric patterns of growth exhibited by Eisenia and Pterygophora can greatly reduce the stresses generated in the stipes of these plants relative to isometric growth. Low stipe stiffness acts as a general, particularly effective, stress-lowering mechanism. The dynamic swaying associated with this low stiffness can also modulate the magnitudes of peak stresses induced in the stipes of these kelps. In particular, in shallow water under large waves, dynamic loading can substantially increase induced stress, suggesting that plant motion is an important factor affecting the loading regime encountered by these organisms.

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31

Boitsov, G. V., and M. A. Koudrin. "Drawbacks of the Present System of Unified Requirements for Ship Hull Global Strength and Potential Ways to Rectify Them." Marine Technology and SNAME News 37, no. 04 (October 1, 2000): 185–90. http://dx.doi.org/10.5957/mt1.2000.37.4.185.

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This paper considers inadequacies in the formulas for ship global hull strength currently approved by members of the International Associations of Classification Societies (IACS). Citing the results of several experimental and numerical studies, the author proposes modifications to the Rules formulas on ship hull vertical bending moments. Wave loading on the hull under steady wave conditions is studied for long-term ship operations, and the existing fatigue strength standards for hull longitudinals are also examined.

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32

Mei, C. "Free and Forced Wave Vibration Analysis of Axially Loaded Materially Coupled Composite Timoshenko Beam Structures." Journal of Vibration and Acoustics 127, no. 6 (April 18, 2005): 519–29. http://dx.doi.org/10.1115/1.2128643.

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In this paper, wave vibration analysis of axially loaded bending-torsion coupled composite beam structures is presented. It includes the effects of axial force, shear deformation, and rotary inertia; namely, it is for an axially loaded composite Timoshenko beam. The study also includes the material coupling between the bending and torsional modes of deformations that is usually present in laminated composite beam due to ply orientation. From a wave standpoint, vibrations propagate, reflect, and transmit in a structure. The transmission and reflection matrices for various discontinuities on an axially loaded materially coupled composite Timoshenko beam are derived. Such discontinuities include general point supports, boundaries, and changes in section. The matrix relations between the injected waves and externally applied forces and moments are also derived. These matrices can be combined to provide a concise and systematic approach to vibration analysis of axially loaded materially coupled composite Timoshenko beams or complex structures consisting of such beam components. The systematic approach is illustrated through numerical examples for which comparative results are available in the literature.

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33

Teixeira, Angelo P., C. Guedes Soares, Nian-Zhong Chen, and Ge Wang. "Uncertainty Analysis of Load Combination Factors for Global Longitudinal Bending Moments of Double-hull Tankers." Journal of Ship Research 57, no. 01 (March 1, 2013): 42–58. http://dx.doi.org/10.5957/jsr.2013.57.1.42.

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The present article aims at assessing the probabilistic characteristics of the load combination factors for global longitudinal bending moments of double-hull tankers. The calculations are performed based on a sample of oil tankers representative of the range of application of the Association of Classification Societies' (IACS)–Common Structural Rules (CSR) design rules. The article starts by reviewing the probabilistic models that have been proposed to model stillwater and wave-induced loads and their characteristic extreme values. Different load combination methods are also reviewed including an analytical method that provides the combined characteristic value of stillwater and wave-induced bending moments based on the Poisson assumption for upcrossing events and using the first-order reliability method in combination with the point-crossing method. The predictions of the different load combination methods are assessed on the basis of a sample of five oil tankers adopted during the IACS-CSR design rules development process. A parametric and an uncertainty propagation study are then performed to identify the range of variation and the probabilistic models of the load combination factors that are applicable to double-hull tankers.

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Parunov, J., I. Senjanovi, and M. Paviaeeviae. "Use of Vertical Wave Bending Moments From Hydrodynamic Analysis In Design of Oil Tankers." International Journal of Maritime Engineering 146, a4 (2004): 10. http://dx.doi.org/10.3940/rina.ijme.2004.a4.5204.

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35

Fonseca, Nuno, Ricardo Pascoal, C. Guedes Soares, G. Clauss, and C. Schmittner. "Numerical and experimental analysis of extreme wave induced vertical bending moments on a FPSO." Applied Ocean Research 32, no. 4 (October 2010): 374–90. http://dx.doi.org/10.1016/j.apor.2010.08.001.

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36

Guedes Soares, C., and T. E. Schellin. "Long term distribution of non-linear wave induced vertical bending moments on a containership." Marine Structures 9, no. 3-4 (January 1996): 333–52. http://dx.doi.org/10.1016/0951-8339(95)00028-3.

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37

Liu, Tie Lin, Hui Wang, and Yang Yang Sun. "Response Analyses of High-Rise Steel Structure to Wave Passage Seismic Excitations." Applied Mechanics and Materials 256-259 (December 2012): 2024–27. http://dx.doi.org/10.4028/www.scientific.net/amm.256-259.2024.

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The earthquake responses of short span structures are usually obtained by using uniform excitations. Wave passage effects are often artificially neglected for short span structures. In this paper, a high-rise steel residence structure of 18-story is adopted to study the earthquake responses of high-rise steel structures to wave passage excitations and uniform excitations by using the software Midas/GEN. Two groups of earthquake acceleration records are chosen respectively from sites of hard soil and soft soil. Comparisons of the shear forces and the bending moments under uniform excitations and wave passage excitations shown that wave passage effects shouldn’t be neglected in the earthquake response analyses even for short span structures.

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38

Han, Xiaoshuang, Weiliang Qiao, and Bo Zhou. "Frequency Domain Response of Jacket Platforms under Random Wave Loads." Journal of Marine Science and Engineering 7, no. 10 (September 21, 2019): 328. http://dx.doi.org/10.3390/jmse7100328.

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This article presents a procedure that simplifies an offshore jacket platform as a non-uniform cantilever beam subjected to an axial force. A Ritz method combined with a pseudo-excitation method is then used to analyze the responses of the jacket platform under random wave loads with the associated power spectral densities, variances and higher spectral moments. The theoretical basis and pertinent governing equations are derived. The proposed procedure not only eases the process of determining the pseudo wave loads, but also requires only the rudimentary structural details that are typically available at the preliminary design stage. Additionally, the merit of the proposed procedure is that the process does not require one to compute the normal modes, which saves time and is particularly convenient for the dynamic-response analysis of a complex structure (such as an offshore platform). An illustrative example based on a three-deck jacket platform is presented to demonstrate the procedure used to obtain the power spectral densities, variances and second spectral moments of jacket-top displacement and the bending moment of the jacket at the mud line. The results obtained are compared with those obtained using a Finite Element Mothed (FEM) model. Based on the findings of the study and good agreement shown in the comparison of results, it is concluded that the proposed method is effective, simple and convenient, and can be a useful tool for the preliminary design analysis of offshore platforms.

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39

Hansen, P. Friis. "On Combination of Slamming-and Wave-Induced Responses." Journal of Ship Research 38, no. 02 (June 1, 1994): 104–14. http://dx.doi.org/10.5957/jsr.1994.38.2.104.

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Attempts to solve the combination problem of the low-frequency wave-induced bending and the high frequency slamming induced bending moments in ships have so far been based on a Poisson pulse train model for the occurrence of the slamming impacts. Embedded in the Poisson pulse model is the assumption that the time of occurrence and the intensity of a slamming impact are independent of the corresponding quantities of the previous impact. This assumption is not valid because the periodic character of the ship motion tends to concentrate the slamming impacts in clusters. Further, the times of occurrence of the slamming impact and the wave-induced stress peaks are highly correlated. Slamming impact usually generates the first peak of a compressive (sagging) slamming stress in the deck, as the wave-induced stress passes from hogging to sagging. The magnitude of the wave-induced and slamming-induced stress peaks, however, tends to be slightly negatively correlated. The work in the present paper is based on the so-called Slepian model process. This is a non-Gaussian and nonstationary process that gives a complete description of the original ergodic Gaussian process after an arbitrary upcrossing into a critical interval. By use of the Slepian model process, the joint distribution of the wave amplitude and the frequency is established at the occurrence of maximum slamming response within a cluster of slamming impacts. Thereafter the response is calculated for regular sinusoidal waves at selected wave amplitudes and frequencies. Response statistics are obtained by weighing the calculated response by the probability densities of the various pairs of wave amplitude and frequency.

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40

Gaspar, B., A. P. Teixeira, and C. Guedes Soares. "Effect of the nonlinear vertical wave-induced bending moments on the ship hull girder reliability." Ocean Engineering 119 (June 2016): 193–207. http://dx.doi.org/10.1016/j.oceaneng.2015.12.005.

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41

AlaviMehr, Javad, Jason Lavroff, Michael R. Davis, Damien S. Holloway, and Giles A. Thomas. "An Experimental Investigation of Ride Control Algorithms for High-Speed Catamarans Part 2: Mitigation of Wave Impact Loads." Journal of Ship Research 61, no. 02 (June 1, 2017): 51–63. http://dx.doi.org/10.5957/jsr.2017.61.2.51.

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High-speed craft frequently experience large wave impact loads due to their large motions and accelerations. One solution to reduce the severity of motion and impact loadings is the installation of ride control systems. Part 1 of this study investigates the influence of control algorithms on the motions of a 112-m highspeed catamaran using a 2.5-m model fitted with a ride control system. The present study extends this to investigate the influence of control algorithms on the loads and internal forces acting on a hydroelastic segmented catamaran model. As in Part 1, the model active control system consisted of a center bow T-Foil and two stern tabs. Six motion control feedback algorithms were used to activate the model-scale ride control system and surfaces in a closed loop system: local motion, heave, and pitch control, each in a linear and nonlinear application. The loads were further determined with a passive ride control system and without control surfaces fitted for direct comparison. The model was segmented into seven parts, connected by flexible links that replicate the first two natural frequencies and mode shapes of the 112-m INCAT vessel, enabling isolation and measurement of a center bow force and bending moments at two cross sections along the demi-hulls. The model was tested in regular head seas at different wave heights and frequencies. From these tests, it was found that the pitch control mode was most effective and in 60-mm model-scale waves it significantly reduced the peak slam force by 90% and the average slam induced bending moment by 75% when compared with a bare hull without ride controls fitted. This clearly demonstrates the effectiveness of a ride control system in reducing wave impact loads acting on high-speed catamaran vessels.

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42

Korshunov, V. А., R. S. Mudrik, D. А. Ponomarev, А. А. Rodionov, and М. А. Kuteinikov. "Comparative analysis of various models for predicting wave loads on ship hull." Transactions of the Krylov State Research Centre 2, no. 400 (May 16, 2022): 17–23. http://dx.doi.org/10.24937/2542-2324-2022-2-400-17-23.

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Object and purpose of research. The study deals with the problem of defining the integral external loads on the ship hull by various methods with subsequent comparison of system responses. Materials and methods. For determination of external forces in regular waves the strip method and panel method are used based on the boundary element technique. Main results. Response amplitude operators (RAO) of bending moments and shearing forces for different wave headings obtained by various methods are compared. Calculation procedures are analyzed. Conclusion. The problem of defining the external forces on the ship hull was solved and numerical hydrodynamic procedures were analyzed in the work. Results show that both methods are practical, while the panel method provides a wider range of possibilities to input and include non-linear parameters.

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43

Madsen, Freddy J., Antonio Pegalajar-Jurado, and Henrik Bredmose. "Performance study of the QuLAF pre-design model for a 10 MW floating wind turbine." Wind Energy Science 4, no. 3 (September 23, 2019): 527–47. http://dx.doi.org/10.5194/wes-4-527-2019.

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Abstract. This paper presents a comparison study of the simplified model QuLAF (Quick Load Analysis of Floating wind turbines) and a FAST model of the Technical University of Denmark (DTU) 10 MW reference wind turbine mounted on the LIFES50+ OO-Star Wind Floater Semi 10 MW floating substructure. The purpose is to investigate how accurate results can be obtained from this simplified model for different load cases. The two models are briefly presented and the limitations of QuLAF are discussed. These are (a) an under-prediction of the wave excitation loads for large sea states; (b) a simplified representation of the rotor-induced forcing and damping; (c) an over-predicted aerodynamic damping for the tower mode motion and (d) restriction to planar motion. All the limitations are linked to approximations applied for achieving the substantial model speedup relative to the state-of-the-art model. The comparative study is based on the planar version of design load cases (DLCs) 1.2, 1.3, 1.6, 2.1 and 6.1, and the overall analysis shows that the simplified model is generally good at estimating the bending moment at the tower base and the floater motions in heave and pitch. The largest tower-base bending moments are slightly over-predicted, but it is observed that while stronger wind leads to an over-prediction, stronger waves lead to an under-prediction. Thus, in DLC 1.6, where the largest load was obtained at 10.3 m s−1, a good match in tower-base bending moments between the two models is found. The nacelle acceleration, however, is generally under-predicted, which is linked to an over-prediction of the aerodynamic damping on the tower mode. Furthermore, the floater response in large sea states is influenced by the omission of viscous hydrodynamic drag forcing, which leads to an under-prediction of the wave excitation loads. A further investigation of the model limitations confirms these findings with respect to the tower mode damping and viscous drag loads, while the simplified approach to rotor-induced loads is found to provide remarkably accurate forcing results. Although a full design load basis evaluation with a state-of-the-art model must be carried out for the final design, the present results show the potential of applying simplified models in the preliminary design phase.

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44

Huang, Shu, Jian Zhong Zhou, X. D. Yang, Hong Yan Ruan, Deng Hui Wei, and J. R. Fan. "Investigation on the Effect of Thickness to Sheet Metal Treated by Laser Peen Forming." Key Engineering Materials 464 (January 2011): 33–37. http://dx.doi.org/10.4028/www.scientific.net/kem.464.33.

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After the mechanisms of laser peen forming (LPF) were analyzed, the effect of sheet metal’s thickness on LPF was discussed in theory. The analysis model that residual stresses brought sheet bending was established, and the relationship between thickness and arc height of sheet metal was obtained. The process of laser shock wave loading during LPF was modeled, and then the residual stresses and deformation of the peened sheet were simulated by ABAQUS software. The results indicated that LPF use bending moments caused by residual stress to induce deformation, which was agreed with the theory analysis. The curvature of sheet metal induced by LPF decreased as the thickness increased, the arc height formed by bending was inversely proportional to thickness square of sheet metal on the whole. This research also has significance for the control of LPF and the investigation of further experiment

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45

Németh, Csaba, and Ján Brodniansky. "Silo with a Corrugated Sheet Wall." Slovak Journal of Civil Engineering 21, no. 3 (September 1, 2013): 19–30. http://dx.doi.org/10.2478/sjce-2013-0013.

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Abstract Silos and tanks are currently being used to create reserves of stored materials. Their importance is based on balancing the production and consumption of bulk materials to establish an adequate reserve throughout the year. The case study introduced within the framework of this paper focuses on thin-walled silos made of corrugated sheets and on an approach for designing these types of structures. The storage of bulk materials causes compression or tensile stresses in the walls of a silo structure. The effect of a frictional force in the silo walls creates an additional bending moment in a wave, which ultimately affects the resulting bending moments. Several mathematical and physical models were used in order to examine various types of loading and their effects on a structure. Subsequently, the accuracy of the computational models was verified by experimental measurements on a grain silo in Bojničky, Slovakia. A comparison of the experimental and mathematical models shows a reasonable match and confirms the load specifications, while indicating that the mathematical model was correct.

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46

Zarzalejos, J. M., J. J. Aznárez, L. A. Padrón, and O. Maeso. "Influences of type of wave and angle of incidence on seismic bending moments in pile foundations." Earthquake Engineering & Structural Dynamics 43, no. 1 (June 26, 2013): 41–59. http://dx.doi.org/10.1002/eqe.2330.

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47

Wei, Yujia, Atilla Incecik, and Tahsin Tezdogan. "A Fully Coupled CFD-DMB Approach on the Ship Hydroelasticity of a Containership in Extreme Wave Conditions." Journal of Marine Science and Engineering 10, no. 11 (November 18, 2022): 1778. http://dx.doi.org/10.3390/jmse10111778.

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In this paper, we present a fully coupled computational fluid dynamic (CFD) and discrete module beam (DMB) method for the numerical prediction of nonlinear hydroelastic responses of a ship advancing in regular and focused wave conditions. A two-way data communication scheme is applied between two solvers, whereby the external fluid pressure exported from the CFD simulation is used to derive the structural responses in the DMB solver, and the structural deformations are fed back into the CFD solver to deform the mesh. We first conduct a series of verification and validation studies by using the present CFD–DMB method to investigate the global ship motion, vertical bending moments (VBMs), and green water phenomenon of the ship in different regular wave conditions. The numerical results agreed favourably with the CFD–FEA model and experimental measurements. Then, the extreme ship motions are studied in focused wave conditions to represent extreme sea conditions that a ship may experience in a real sea state. According to the conclusion drawn from the numerical simulations, it is founded that the focused wave case will lead to the increase of the longitudinal responses of the hull compared to regular wave condition, i.e., the heave, pitch, and total VBMs rise about 25%, 20% and 9%, respectively. In focused wave conditions, intensive ship responses and severe waves cause stronger slamming phenomena. It is found that the instantaneous impact pressure from the focused wave is higher and sharper compared to the regular waves and comes along with the obvious green-water-on-deck phenomena.

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48

Clukey, E. C., A. V. Maller, J. D. Murff, R. H. Goodwin, M. C. Miller, and R. J. Ebelhar. "Wave Attenuation, Mudslide, and Structural Analyses for Mississippi Delta/Main Pass Caisson." Journal of Offshore Mechanics and Arctic Engineering 112, no. 1 (February 1, 1990): 6–13. http://dx.doi.org/10.1115/1.2919838.

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The environmental loads associated with the design of a caisson-type structure in a mudslide region are largely dependent upon the interaction of waves with the seabottom. This wave-seabottom interaction results in both an attenuation of wave energy as the waves propagate over the soft soils, as well as the generation of mudslide loads at the platform site. These effects were investigated for the design of a 14-ft-dia caisson in the Main Pass region of the Mississippi Delta. The proposed structure was planned for installation in about 100-ft water depth in very soft underconsolidated soils, typical of the Mississippi Delta region. The potential for wave attenuation was investigated analytically by considering the change in response spectra from deep water to the platform site. Regional soil conditions were used for this part of the investigation. The results obtained from the analytical modeling were in good agreement with field measurements obtained from another part of the Delta. Mudslide thicknesses were determined based on site specific soil data and the design wave for the platform site. The predicted mudslides also agreed favorably with the geological interpretations for the area. Once the design waves and mudslide thicknesses were determined, structural analyses were performed to determine the bending moments and dynamic response for the caisson. Overall, the improved analytical methodology used in the investigation and the availability of field data to verify the results allowed for a more economic platform design.

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49

Pierson, Willard J. "Oscillatory Third-Order Perturbation Solutions for Sums of Interacting Long-Crested Stokes Waves on Deep Water." Journal of Ship Research 37, no. 04 (December 1, 1993): 354–83. http://dx.doi.org/10.5957/jsr.1993.37.4.354.

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Oscillatory third-order perturbation solutions for sums of interacting long-crested Stokes waves on deep water are obtained. A third-order perturbation expansion of the nonlinear free boundary value problem, defined by the coupled Bernoulli equation and kinematic boundary condition evaluated at the free surface, is solved by replacing the exponential term in the potential function by its series expansion and substituting the equation for the free surface into it. There are second-order changes in the frequencies of the first-order terms at third order. The waves have a Stokes-like form when they are high. The phase speeds are a function of the amplitudes and wave numbers of all of the first-order terms. The solutions are illustrated. A preliminary experiment at the United States Naval Academy is described. Some applications to sea keeping are bow submergence and slamming, capsizing in following seas and bending moments.

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50

Abdel Raheem, Shehata E., and Elsayed M. A. Abdel Aal. "Finite Element Analysis for Structural Performance of Offshore Platforms under Environmental Loads." Key Engineering Materials 569-570 (July 2013): 159–66. http://dx.doi.org/10.4028/www.scientific.net/kem.569-570.159.

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Offshore structures for oil and gas exploitation are subjected to various ocean environmental phenomena which can cause highly nonlinear action effects. Offshore structures should be designed for severe environmental loads and strict requirements should set for the optimum performance. The structural design requirements of an offshore platform subjected to wave induced forces and moments in the jacket can play a major role in the design of the offshore structures. For an economic and reliable design; good estimation of wave loadings are essential. The structure is discretized using the finite element method, wave force is determined according to linearized Morison equation. Hydrodynamic loading on horizontal and vertical tubular members and the dynamic response of fixed offshore structure together with the distribution of displacement, axial force and bending moment along the leg are investigated for regular and extreme conditions, where the structure should keep production capability in conditions of the one year return period wave and must be able to survive the 100 year return period storm conditions. The results show that the nonlinear response analysis is quite crucial for safe design and operation of offshore platform. Fixed Jacket type offshore platforms under extreme wave loading conditions may exhibit significant nonlinear behavior. The effect of current with different angles when hitting the offshore structure with the wave and wind forces, is very important for calculate the stress, the response displacement and deformation shapes. As the current increase or decrease the effect of wave force according to the hitting angle of current.

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