Calculation of Vertical Bending Moment Acting on an Ultra Large Containership in Large Amplitude Waves

2015 ◽  
Author(s):  
Suresh Rajendran ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Large Amplitude ◽  
Bending Moment ◽  
Regular Waves ◽  
Structural Dynamic ◽  
Strip Theory ◽  
Structural Dynamic Characteristics ◽  
Wetted Surface Area ◽  
The Time Domain ◽  
Hydroelastic Response ◽  
Vertical Bending Moment

The time domain method is further extended here in order to calculate the hydroelastic response of an ultra large containership in regular waves. Based on strip theory, the hydrodynamic and the hydrostatic forces are calculated for the instantaneous wetted surface area. Slamming forces are calculated using a Von Karman approach in which the water pile up during slamming is neglected. Timoshenko beam which takes into account the shear deformation and rotary inertia is used to model the structural dynamic characteristics of the hull. The beam is discretized using the finite element method and the ship vibration is solved using the modal analysis. The method is used to calculate the vertical bending moment acting on an ultra large containership in large amplitude regular waves. The results are compared with the experimental results measured in wave tank.

Whipping Response of Vessels With Large Amplitude Motions

2006 ◽  
Author(s):  
Nuno Fonseca ◽  
Eduardo Antunes ◽  
Carlos Guedes Soares
Keyword(s):  
Time Domain ◽  
Large Amplitude ◽  
Nonlinear Effects ◽  
Regular Waves ◽  
Structural Dynamic ◽  
Highly Nonlinear ◽  
Large Amplitude Motions ◽  
Structural Dynamic Characteristics ◽  
The Time Domain ◽  
Equations Of Motions

The paper presents a time domain method to calculate the ship responses in heavy weather, including the global structural loads due to whipping. Since large amplitude waves induce nonlinear ship responses, and in particular highly nonlinear vertical structural loads, the equations of motions and structural loads are solved in the time domain. The “partially nonlinear” time domain seakeeping program accounts for the most important nonlinear effects. Slamming forces are given by the contribution of two components: an initial impact due to bottom slamming and flare slamming due to the variation of momentum of the added mass. The hull vibratory response is calculated applying the modal analysis together with direct integration of the differential equations in the time domain. The structural dynamic characteristics of the hull are modeled by a finite element representation of a Timoshenko beam accounting for the shear deformation and rotary inertia. The calculation procedure is applied to a frigate advancing in regular waves. The contribution of whipping loads to the vertical bending moments on the ship structure is assessed by comparing this response with and without the hull vibration.

Time Domain Comparison With Experiments for Ship Motions and Structural Loads on a Container Ship in Abnormal Waves

2011 ◽  
Author(s):  
Suresh Rajendran ◽  
Nuno Fonseca ◽  
C. Guedes Soares ◽  
Gu¨nther F. Clauss ◽  
Marco Klein
Keyword(s):  
Time Domain ◽  
Bending Moment ◽  
Green Water ◽  
Ship Motions ◽  
Container Ship ◽  
Wave Elevation ◽  
Strip Theory ◽  
The Time Domain ◽  
Vertical Bending Moment ◽  
Comparison With Experiments

The paper presents experimental results from model tests with a containership advancing in abnormal wave conditions and comparisons with numerical simulations. A nonlinear time domain method based on strip theory is used for the calculation of vertical ship responses induced by abnormal waves. This code combines the linear diffraction and radiation forces with dominant nonlinear forces associated with vertical response arising from Froude-Krylov forces, hydrostatic forces and shipping of green water. The time domain simulations are compared directly with experimental records from tests with a model of a container ship in deterministic waves for a range of Froude numbers. Extreme sea conditions were replicated by the reproduction of realistic abnormal waves like the New Year Wave and abnormal wave from North Alwyn. Head sea condition is considered and the comparisons include the wave elevation, the vertical motions of the ship and the vertical bending moment at midship.

Response Based Identification of Critical Wave Scenarios

2012 ◽  
Author(s):  
Günther F. Clauss ◽  
Marco Klein ◽  
Carlos Guedes Soares ◽  
Nuno Fonseca
Keyword(s):  
Linear Method ◽  
Bending Moment ◽  
Extreme Wave ◽  
Offshore Structure ◽  
Sea State ◽  
Worst Case ◽  
Strip Theory ◽  
Wave Conditions ◽  
Vertical Bending Moment ◽  
Method Approach

In the last years the identification and investigation of critical wave sequences regarding offshore structure responses became one of the main topics in the ocean engineering community. Thereby the area of interest covers the entire field of application spectra at sea — from efficient and economic offshore operations in moderate sea states to reliability as well as survival in extreme wave conditions. For most cases, the focus lies on limiting criteria for the design, such as maximum global loads, maximum relative motions between two or more vessels or maximum accelerations, at which the floating structure has to operate or to survive. These criteria are typically combined with a limiting characteristic sea state (Hs, Tp) or a rogue wave. For the investigation of offshore structures as well as the identification of critical wave sequences, different approaches are available — most of them are based on linear transfer functions as it is an efficient procedure for the fast holistic evaluation. But, for some cases the linear method approach implies uncertainties due to nonlinear response behavior, in particular in extreme wave conditions. This paper presents an approach to these challenges, a response based optimization tool for critical wave sequence detection. This tool, which has been successfully introduced for the evaluation of the applicability of a multi-body system based on the linear method approach, is adjusted to a nonlinear task — the vertical bending moment of a chemical tanker in extreme wave conditions. Therefore a nonlinear strip theory solver is introduced into the optimization routine to capture the nonlinear effects on the vertical bending moment due to steep waves acting on large bow flares. The goal of the procedure is to find a worst case wave sequence for a certain critical sea state. This includes intensive numerical investigation as well as model test validation.

Steep Wave Effects on Wave Induced Vertical Bending Moment Using a 3D Numerical Wave Tank

2017 ◽  
Author(s):  
Shivaji Ganesan Thirunaavukarasu ◽  
Debabrata Sen ◽  
Yogendra Parihar
Keyword(s):  
Comparative Study ◽  
Incident Wave ◽  
Bending Moment ◽  
Wave Steepness ◽  
Numerical Wave Tank ◽  
Wave Tank ◽  
Strip Theory ◽  
Numerical Wave ◽  
Wave Induced ◽  
Vertical Bending Moment

This paper presents a detail comparative study on wave induced vertical bending moment (VBM) between linear and approximate nonlinear calculations using a 3D numerical wave tank (NWT) method. The developed numerical approach is in time domain where the ambient incident waves can be defined by any suitable wave theory. Certain justifying approximations employed in the solution of the interaction hydrodynamics (diffraction and radiation) enabling the NWT to generate stable long duration time histories of all parameters of interest. This is an extension of our earlier works towards the development of a practical NWT based solution for wave-structure interactions [1]. After a brief outline of the implemented numerical details, a comprehensive validation and verification of vertical shear force (VSF) and bending moment RAOs computed using the linearized version of the NWT against the usual linear results of strip theory and 3D panel codes are presented. Next we undertake the comparative study between the fully linear and approximate nonlinear versions of the present code for different incident wave steepness. In the approximate nonlinear formulation, the ambient incident wave is defined by the full nonlinear numerical wave model based on Fourier approximation method which can generate very steep steady periodic nonlinear waves up to the near wave breaking limit. The nonlinearities associated with the incident Froude Krylov and hydrostatic restoring forces/moments are exact up to the instantaneous wetted surface at the displaced location, but the hydrodynamic diffraction and radiation effects are linearized around the mean wetted surface. The standard S175 container hull is considered for the comparative studies because of its geometric nonlinearities. Numerical simulations are performed for four different wave lengths with increasing wave steepness. It is observed that the computed wave induced VBM amidships from the approximate nonlinear results can be almost 30% higher compared to the results from a purely linear solution, which can be a critical issue from the safety point. Significant higher harmonics are also observed in the approximate nonlinear results which at some times may be responsible for exciting the undesirable whipping/springing responses.

Prediction of Ship Responses in Large Amplitude Waves Using a Body Nonlinear Time Domain Method With 2nd Order Froude-Krylov Pressure

2014 ◽  
Author(s):  
Suresh Rajendran ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Surface Area ◽  
Time Domain ◽  
Time Instant ◽  
The Body ◽  
Regular Waves ◽  
Time Step ◽  
Strip Theory ◽  
Practical Engineering ◽  
Wetted Surface Area ◽  
Nonlinear Time Domain

The paper analyzes the effect of 2nd order waves on the vertical ship responses in extreme seas. The numerical simulations are carried out using a body nonlinear time domain code based on strip theory. The radiation, diffraction, Froude-krylov and hydrostatic forces are calculated for the exact wetted surface area of the ship for each time step. A practical engineering approach is followed to calculate the body nonlinear radiation and diffraction forces. First order Froude Krylov pressures are replaced with a second order model for the present study. The 2nd order Froude-Krylov pressures are integrated upto the exact wetted surface area for each time instant. The ship responses in regular waves with varying steepness are analyzed. Finally, the vertical ship responses are compared with the responses in design waves measured in the wave tank.

Influence of Whipping on Long-term Vertical Bending Moment

2004 ◽  
Vol 48 (04) ◽  
pp. 261-272
Author(s):  
Gro Sagli Baarholm ◽  
Jørgen Juncher Jensen
Keyword(s):  
Nonlinear Response ◽  
Extreme Values ◽  
Bending Moment ◽  
Sea Waves ◽  
Short Term ◽  
Strip Theory ◽  
Long Time ◽  
Wave Induced ◽  
Vertical Bending Moment

This paper is concerned with estimating the response value corresponding to a long return period, say 20 years. Time domain simulation is required to obtain the nonlinear response, and long time series are required to limit the statistical uncertainty in the simulations. It is crucial to introduce ways to improve the efficiency in the calculation. A method to determine the long-term extremes by considering only a few short-term sea states is applied. Long-term extreme values are estimated using a set of sea states that have a certain probability of occurrence, known as the contour line approach. Effect of whipping is included by assuming that the whipping and wave-induced responses are independent, but the effect of correlation of the long-term extreme value is also studied. Numerical calculations are performed using a nonlinear, hydroelastic strip theory as suggested by Xia et al (1998). Results are presented for the S-175 containership (ITTC 1983) in head sea waves. The analysis shows that whipping increases the vertical bending moment and that the correlation is significant.

NON LINEAR ANALYSIS OF SHIP MOTIONS AND LOADS IN LARGE AMPLITUDE WAVES

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
G Mortola ◽  
A Incecik ◽  
O Turan ◽  
S.E. Hirdaris
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Large Amplitude ◽  
Linear Time ◽  
Ship Motions ◽  
Wave Loads ◽  
Time Step ◽  
Strip Theory ◽  
Non Linear ◽  
The Time Domain

A non linear time domain formulation for ship motions and wave loads is presented and applied to the S175 containership. The paper describes the mathematical formulations and assumptions, with particular attention to the calculation of the hydrodynamic force in the time domain. In this formulation all the forces involved are non linear and time dependent. Hydrodynamic forces are calculated in the frequency domain and related to the time domain solution for each time step. Restoring and exciting forces are evaluated directly in time domain in a way of the hull wetted surface. The results are compared with linear strip theory and linear three dimensional Green function frequency domain seakeeping methodologies with the intent of validation. The comparison shows a satisfactory agreement in the range of small amplitude motions. A first approach to large amplitude motion analysis displays the importance of incorporating the non linear behaviour of motions and loads in the solution of the seakeeping problem.

Influence of Wave Group Characteristics on Loads in Severe Seas

2011 ◽  
Author(s):  
Gu¨nther F. Clauss ◽  
Matthias Dudek ◽  
Marco Klein
Keyword(s):  
Critical Loads ◽  
Target Position ◽  
Bending Moment ◽  
Ship Design ◽  
Main Question ◽  
Wave Group ◽  
Regular Waves ◽  
Worst Case ◽  
Bow Flare ◽  
Vertical Bending Moment

The precise knowledge of loads and motions in extreme sea states is indispensable to ensure reliability and survival of ships and floating offshore structures. In the last decades, several accidents in severe weather with disastrous consequences have shown the need for further investigations. Besides the sea state behavior and the local structural loads, one key parameter for safe ship design is the vertical bending moment. Previous investigations revealed that different ship design criteria, such as bow geometry and wave board height, affect the global loads significantly. Investigations in regular waves as well as in single high waves of vessels with different bow flares and freeboard heights show that the vertical bending moment increases significantly with increasing bow flare and freeboard height. Furthermore it became apparent that critical loads and motions do not have to come along with the highest wave which results in the main question of this paper: What is the worst case scenario — the highest rogue wave or a wave group with certain frequency characteristics? Which sea states have to be taken into account for the experimental evaluation of limiting criteria? This paper presents investigations in different critical wave sequences, i.e. two real-sea registrations accompanied by results in regular waves to evaluate the influence of the encountering wave characteristics on the vertical bending moment. For the model tests in the seakeeping basin of the Technical University Berlin a segmented RoRo vessel with large bow flare has been built at a scale of 1:70 and equipped with force transducers. The paper proves that critical loads and motions depend most notably on combinations of wave height, wave group sequences, crest steepness, encountering speed and the ships target position: Even small wave heights with unfavorable wave lengths can cause a critical situation.

Determination of global design loads for large high-speed catamarans

2002 ◽  
Vol 216 (1) ◽  
pp. 79-94
Author(s):  
S E Heggelund ◽  
T Moan ◽  
S Oma
Keyword(s):  
High Speed ◽  
Bending Moment ◽  
Wave Loads ◽  
Strip Theory ◽  
Non Linear ◽  
Design Loads ◽  
Linear Effects ◽  
Operational Criteria ◽  
Vertical Bending Moment

Methods for calculation of design loads for high-speed vessels are investigated. The influence of operational restrictions on design loads is emphasized. Relevant operational criteria for high-speed displacement vessels are discussed. Procedures and criteria for numerical calculation of operational limits are incomplete and should be further investigated. Operational limits and design loads for a 60 m catamaran are calculated on the basis of linear strip theory. Non-linear effects on design loads are assessed from calculations in regular waves. Simplified formulae commonly used by classification societies for prediction of operational limits seem to over-predict the reduction of motions and wave loads at reduced speed. When operational limits typically given by the shipmaster or the operator are used, the design loads found by direct calculations are comparable with design loads given by classification societies. For vertical bending moment and torsion, the use of active foils is found to increase the linear loads. Owing to reduced motions, the foils reduce the non-linear loads and hence the total loads. The effect of non-linear horizontal loads is not investigated but can be important for transverse bending moment.

Time-Domain Analysis of Large-Amplitude Vertical Ship Motions and Wave Loads

1998 ◽  
Vol 42 (02) ◽  
pp. 139-153 ◽  
Author(s):  
N. Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Large Amplitude ◽  
Surface Condition ◽  
Memory Effects ◽  
Wave Loads ◽  
Strip Theory ◽  
Large Amplitude Motions ◽  
Free Surface Oscillations ◽  
The Time Domain

The vertical motions and wave induced loads on ships with forward speed are studied in the time domain, considering non-linear effects associated with large amplitude motions and hull flare shape. The method is based on a strip theory, using singularities distributed on the cross sections which satisfy the linear free surface condition. The solution is obtained in the time domain using convolution to account for the memory effects related to the free surface oscillations. In this way the linear radiation forces are represented in terms of impulse response functions, infinite frequency added masses and radiation restoring coefficients. The diffraction forces associated with incident wave scattering are linear. The hydrostatic and Froude-Krylov forces are evaluated over the instantaneous wetted surface of the hull to account for the large amplitude motions and hull flare. The radiation contribution for wave loads is also obtained in the time domain using convolution to account for the memory effects related to the free surface oscillations. Results of motions and wave loads for the S175 container ship are presented and analyzed. The results from the present method are compared with linear results.

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