Abnormal Loading on Structures: Experimental and Numerical Modelling
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Ten inner iterations were used for the convergence of the flow field equations within each time step. The second part is the convergence monitoring of numerical calculation, which mainly includes the monitoring of residual, physical quantity and flow field data. This technique can also be useful when comparing to residuals that cannot be exhibiting a converged solution.
In this case, visualizing the solution and observing any changes in the flow field that are happening at a location in the domain far from any geometry or solution feature of interest, can help determine that a satisfactory solution has been obtained.
In the wind load numerical simulation and added resistance due to combined wind-wave loads numerical simulation part of the paper, through the results of residual, monitoring engineering quantity and visualizing the flow field, it is shown that the numerical part of this paper is convergent. A comparison of wind-load coefficients obtained using empirical calculations prescribed in models proposed independently by Isherwood and Hong, CFD calculations, and wind-tunnel experiments under conditions of different wind angles are shown in Fig 9.
These regression coefficients were subsequently used to acquire longitudinal and lateral wind-load coefficients and the yawing moment at different wind angles. Based on this, an empirical equation for calculation of wind-load coefficients was proposed via wind-tunnel experiments and regression of experimental data obtained for actual ships.
Variables considered in this approach are mutually independent and include basic parameters concerning each ship type with most major ship types being sampled, thereby providing a high degree of computational accuracy. In accordance with the method prescribed by B.
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Hong [ 2 ], Fourier-series expansions were performed on wind-load coefficients acquired from wind-tunnel data concerning 50 ship models, thereby obtaining fifth-order harmonic expressions as functions of the wind angle. In particular, Fourier coefficients were obtained by solving a coefficient matrix obtained via multivariate quadratic regression. As observed in Fig 9 , values of longitudinal wind-load coefficients obtained via CFD are only slightly different from those determined experimentally; i.
Values of wind-load coefficients obtained from wind-tunnel experiments are generally slightly higher compared to those obtained via CFD. Wind-tunnel experiments are amongst the most reliable methods for studying wind-loads acting on ship structures. The results of these experiments and those obtained via CFD calculations and empirical methods are different for each procedure. Overall, values obtained from CFD calculations were observed to demonstrate the highest agreement with those determined experimentally.
Figs 10 — 12 show numerically obtained distribution of streamlines, vortex traces, and pressure fields around superstructure containers at different wind angles. Additionally, compared to the bow region, there exists a low-pressure zone at the stern. The air viscosity causes incoming flows to disperse along the ship superstructure, thereby resulting in creation of very large detached-eddy zones the largest among the cases considered on the leeward side.
From Figs 11 and 12 , we observe that as the wind angle is increased, the ship model tends to get increasingly affected by lateral winds, thereby resulting in stronger flows around the superstructure and expansions within the low-pressure, detached-eddy zone on the leeward side.
Therefore, it can be inferred that values of transverse wind-load coefficients for ship structures generally exceed those of longitudinal ones. Relationships between resistance and ship speed under calm-water and a variety of wave conditions are shown in Fig Under calm-water conditions, the CFD-calculated value of resistance nearly equals that obtained experimentally.
Under wave conditions, CFD results generally demonstrate good agreement with experimental trends, especially at low ship speeds, with error values measuring less than 1. With increase in ship speed, CFD-calculated values tend to become smaller compared to those determined experimentally. In addition, the ship resistance was observed to be significantly higher under wave conditions compared to the calm-water case, and the added resistance due to wave loads increased with increase in ship speed. The added resistance of ship motion caused by wave is an important component of the total ship resistance in wave Fig 14 shows periodic patterns exhibited by the pitch and heave motions.
The pitch curve Fig 14 A indicates the occurrence of head trim under wavy conditions, thereby resulting in the bow dipping under water.
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The average head trim of the ship under wavelengths of 0. Heave curves, on the other hand, indicate existence of a greater draft at 0. The observed heave was greater in magnitude at 0. The first part is the sinkage values caused by the hydrodynamic pressure corresponding to the ship speed, literature [ 39 ]; the second part is the ship heave caused by wave surface under the wave conditions.
When the ship sails in calm water with a higher speed, the container ship will in the state of sinkage. The sinkage value is related to the hydrodynamic pressure distribution around the ship. During simulation of combined wind—wave loads, the direction of waves and the wind were considered to be aligned with the ship bow. Additionally, interactions and the coupling between wind- and wave-induced loads were considered to affect wave parameters, thereby altering the additional resistance faced by the ship.
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Prior to calculating the added resistance under combined presence of wind and wave loads, loads acting on the ship were simulated under conditions of combined wind—wave action and wave loads alone. This allowed the authors to ascertain the accuracy of wind- and wave-load simulations.
As shown in Fig 15 A , changes in the wave surface during wave load alone demonstrate a good fit with the theoretical curve with peak values exactly coinciding theoretically determined ones, whereas trough values were observed to be slightly lower compared to those predicted theoretically.
Overall, the simulated wave field demonstrated an adequate level of accuracy. Fig 15 B illustrates results obtained for simulated wind and wave loads. In this figure, wave parameters can be observed to have been altered by the action of turbulent wind fields on the wave surface. Consequently, peak values were observed to increase relative to those shown in Fig 15 A , and lengths of the crest and trough regions can be observed to have been shortened and lengthened, respectively, thereby resulting in sharper peaks and rounded troughs.
Results obtained via numerical simulation of wind and wave loads— a Time history of wave surface under isolated wave loads; b Time history of wave surface under combined wind—wave loads.
Ship speeds considered during simulation were identical to those considered for the isolated wave-load case. Results obtained from these simulations are shown in Fig 16 , wherein the solid and dotted lines represent the resistance due to combined wind—wave loads and the sum of individual wind and wave resistances, respectively.
The colors black and red, represent cases corresponding to wavelengths of 0. The purpose of Fig 16 is to compare the resistance to ship motion under combined wind and wave load against that observed under isolated wave- and wind-load conditions. The figure also demonstrates the effect of the combined action of wind- and wave-load on ship resistance. As observed, the resistance under conditions of combined wind—wave loads was greater compared to the sum of resistances due to individual wind and wave loads, and this enhancement in resistance increases with increase in ship speed.
In fact, the resistance under the combined action of wind and wave is more than twice that under the action of wave alone. Figs 13 and 16 show resistances observed under all conditions calm-water, wave action, and wind action at the model scale. Wind resistance of the ship-scale superstructure was calculated in accordance with the wind-resistance formula, and the non-dimensional wind resistance coefficients formula [ 40 ]:. Under actual navigation conditions, frontal area A s of the full-scale ship model equaled Using these values, the total wind resistance of the full-scale superstructure equaled Ship resistance observed under the calm-water condition was also converted to its full-scale equivalent using the Froude method two-dimensional method , and the resulting value equaled Results obtained for case involving combined wind—wave loads— a Time history of ship pitch; b Time history of ship heave.
Fig 17 shows the time evolution of ship-motion characteristics in the presence of combined wind—wave loads. Figs 18 and 19 illustrates the relative frequency counter of pitch and heave value of Fig 17 , and the frequency domain curve after FFT of time history pitch and heave value of Fig 17 , respectively.
Based on the pitch and heave curves shown in Fig 17 and relative frequency counter shown in Figs 18 and 19 , it may be inferred that amplitudes of ship motion increase under combined wind—wave loads. Compared to the average head trim shown in Fig 14 , significantly greater dipping of the bow can be observed in this case.
The average draft also demonstrates an increase, which further increases the resistance to ship motion. Furthermore, effects of the fluctuating wind field on waves tend to alter wave parameters over the course of the voyage, thereby increasing the height and speed of waves. The relative frequency counter of pitch value a. The relative frequency counter of heave value a.
As observed, pitching torque of the fluctuating wind load acting on the ship is positively correlated with the square of the wind speed, and ship motions under the said wave loads exhibit the same frequency as that of the pitching torque. Therefore, motion responses of the ship resonate with the fluctuating wind field in the presence of combined wind—wave loads. This, in turn, increases the magnitude of the ship motion. To investigate the effect of fluctuating wind fields on ship-motion resistance, motion resistance of the fixed ship model under combined wind and wave load was compared to that of a free model to analyze the overall resistance caused by the combined load.
Draft and trim angles of the fixed model were set equal to those of the free model. Fig 21 shows resistance curves obtained for the fixed and free models subjected to the aforementioned combined load with wavelengths of 0. In the figure, the solid curve with blue solid dots represents the algebraic sum of calm-water- and wind-load-induced resistances. The sum of resistances denoted by solid red and black curves in the free-model case under combined wind and wave load was considered as the target total resistance, whereas that of resistances denoted by red and black dotted lines in the fixed-model case under identical load conditions was considered as the target total resistance upon removal of the influence of model movement.
The algebraic sum of calm-water and wind resistances was considered the total model resistance after removal of the influence of model motion, wave resistance, and resistance offered by the coupled wind—wave effect, which is known from the difference in the above resistance. The effect of the wave added resistance and the added resistance under the wind-wave coupling effect is greater than the resistance of the model motion. Fig 22 shows the VOF distribution of water and air components under combined wind and wave load at wavelengths of 0.
Fig 23 shows the ship and free surface interaction phenomenon diagrams corresponding to different wavelength cases. Usually, the breaking of waves must lead to formation of vorticity and loss of kinetic energy; however, in the present case, the wave did not break automatically. Instead, it was broken by fluctuating winds. The presence of fluctuating wind increases wave velocity at the crest, which in turn, increases the wave kinetic energy. Additionally, fluctuating winds destroy the original wave shape, thereby altering wave parameters. This subsequently led to the formation of plunging waves.
Considering the results shown in Fig 14 B , it may be inferred that waves are rapidly "lifted" by the wind prior to breaking at the crest.