Estimation of hull girder vertical bending moments including non-linear and flexibility effects using closed form expressions

2009 ◽  
Vol 223 (3) ◽  
pp. 377-390 ◽  
Author(s):  
P T Pedersen ◽  
J J Jensen
Keyword(s):  
Closed Form ◽  
Linear Response ◽  
Bending Moment ◽  
Phase Lag ◽  
Bending Moments ◽  
Hull Girder ◽  
Strip Theory ◽  
Non Linear ◽  
Bow Flare ◽  
Wave Induced

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.

Wave induced extreme hull girder loads on containerships

2008 ◽  
Author(s):  
J. Juncher Jensen ◽  
Preben Terndrup Pedersen ◽  
Bill Shi ◽  
Sue Wang ◽  
Martin Petricic ◽  
...  
Keyword(s):  
Bending Moments ◽  
Wave Load ◽  
Spreadsheet Program ◽  
Hull Girder ◽  
Conceptual Design Phase ◽  
Strip Theory ◽  
Bow Flare ◽  
Analytical Formulas ◽  
Approximate Wave ◽  
Wave Induced

This paper provides simple but rational procedures for prediction of extreme wave – induced sectional hull girder forces with reasonable engineering accuracy. The procedures take into account main ship hull characteristics such as: length, breadth, draught, block coefficient, bow flare coefficient, forward speed and hull flexibility. The vertical hull girder loads are evaluated for specific operational profiles. Firstly a quadratic strip theory is presented which can give separate predictions for the hogging and sagging bending moments and shear forces and for hull girder loads. Then this procedure is used as a base to derive semi-analytical formulas such that approximate wave load calculations can be performed by a simple spreadsheet program. Due to the few input parameters this procedure can be used to estimate the wave-induced bending moments at the conceptual design phase. Since the procedure is based on rational methods it can be applied for novel single hull ship types not presently covered by the rules of the classification societies or to account for specific operational profiles.

On the Effect of Hull Girder Flexibility on the Vertical Wave Bending Moment for Ultra Large Container Vessels

2012 ◽  
Author(s):  
Ingrid Marie Vincent Andersen ◽  
Jørgen Juncher Jensen
Keyword(s):  
Bending Moment ◽  
Main Concern ◽  
Hull Girder ◽  
Numerical Predictions ◽  
Strip Theory ◽  
Reliability Method ◽  
Non Linear ◽  
Large Container ◽  
The Waves ◽  
Good Agreement

Currently, a number of very large container ships are being built and more are on order, and some concerns have been expressed about the importance of the reduced hull girder stiffness to the wave-induced loads. The main concern is related to the fatigue life, but also a possible increase in the global hull girder loads as consequence of the increased hull flexibility must be considered. This is especially so as the rules of the classification societies do not explicitly account for the effect of hull flexibility on the global loads. In the present paper an analysis has been carried out for the 9,400 TEU container ship used as case-ship in the EU project TULCS (Tools for Ultra Large Container Ships). A non-linear time-domain strip theory is used for the hydrodynamic analysis of the vertical bending moment amidships in sagging and hogging conditions for a flexible and a rigid modelling of the ship. The theory takes into account non-linear radiation forces (memory effects) through the use of a set of higher order differential equations. The non-linear hydrostatic restoring forces and non-linear Froude-Krylov forces are determined accurately at the instantaneous position of the ship in the waves. Slamming forces are determined by a standard momentum formulation. The hull flexibility is modelled as a non-prismatic Timoshenko beam. Generally, good agreement with experimental results and more accurate numerical predictions has previously been obtained in a number of studies. The statistical analysis is done using the First Order Reliability Method (FORM) supplemented with Monte Carlo simulations. Furthermore, strip-theory calculations are compared to model tests in regular waves of different wave lengths using a segmented, flexible model of the case-ship and good agreement is obtained for the longest of the waves. For the shorter waves the agreement is less good. The discrepancy in the amplitudes of the bending moment can most probably be explained by an underestimation on the effect of momentum slamming in the strip-theory applied.

Bending Moments and Shear Forces in Ships Sailing in Irregular Waves

1981 ◽  
Vol 25 (04) ◽  
pp. 243-251
Author(s):  
J. Juncher Jensen ◽  
P. Terndrup Pedersen
Keyword(s):  
Linear Part ◽  
Vertical Motion ◽  
Bending Moment ◽  
Irregular Waves ◽  
Bending Moments ◽  
Shear Forces ◽  
Strip Theory ◽  
Wave Heights ◽  
Exciting Forces ◽  
Wave Induced

This paper presents some results concerning the vertical response of two different ships sailing in regular and irregular waves. One ship is a containership with a relatively small block coefficient and with some bow flare while the other ship is a tanker with a large block coefficient. The wave-induced loads are calculated using a second-order strip theory, derived by a perturbational procedure in which the linear part is identical to the usual strip theory. The additional quadratic terms are determined by taking into account the nonlinearities of the exiting waves, the nonvertical sides of the ship, and, finally, the variations of the hydrodynamic forces during the vertical motion of the ship. The flexibility of the hull is also taken into account. The numerical results show that for the containership a substantial increase in bending moments and shear forces is caused by the quadratic terms. The results also show that for both ships the effect of the hull flexibility (springing) is a fair increase of the variance of the wave-induced midship bending moment. For the tanker the springing is due mainly to exciting forces which are linear with respect to wave heights whereas for the containership the nonlinear exciting forces are of importance.

Assessment of the Total Ship’s Hull Girder Bending Stresses When Unified Model of Sagging and Hogging Bending Moments is Used

2009 ◽  
Author(s):  
Lyuben D. Ivanov
Keyword(s):  
Life Span ◽  
Bending Moment ◽  
Extreme Value Statistics ◽  
Bending Moments ◽  
Hull Girder ◽  
Section Modulus ◽  
Probabilistic Distribution ◽  
Bending Stresses ◽  
Distribution Laws ◽  
Wave Induced

A method is proposed for calculating the hull girder bending stresses following the procedure in the class rules but in probabilistic terms, i.e. the still water and the wave-induced bending moments; the total hull girder bending moment; the hull girder section modulus and the hull girder bending stresses are treated as random variables with corresponding probabilistic distributions. The still water and wave-induced hull girder hogging and sagging loads are presented in probabilistic format as one phenomenon, i.e. using bi-modal probability density functions. The probabilistic distribution of the total hull girder load is calculated using the rules of the composition of the distribution laws of the constituent variables. After that, the hull girder geometric properties are presented in probabilistic format as annual distributions and distributions for any given life-span. Thus, it becomes possible to calculate both the annual probabilistic distributions and the probabilistic distribution for any given ship’s life span of the hull girder stresses. Individual amplitudes statistical analysis and extreme value statistics are used. Then, the probability of exceeding the permissible hull girder bending stresses in the class rules is calculated. An example is given for 25K DWT bulk carrier.

Time-Variant Reliability Assessment of FPSO Considering Corrosion and Collision

2006 ◽  
Author(s):  
Daokun Zhang ◽  
Wenyong Tang ◽  
Shengkun Zhang
Keyword(s):  
Oil And Gas ◽  
Bending Moment ◽  
Bending Moments ◽  
Hull Girder ◽  
Corrosion Defect ◽  
Direct Damage ◽  
Collision Condition ◽  
Inspection And Maintenance ◽  
Offshore Oil And Gas ◽  
Wave Induced

Floating production, storage, and offloading (FPSO) system has been widely used in the offshore oil and gas exploitations. Since it has long intervals of docking for thorough inspection and maintenance, and is exposed to collision risk at sea, the time-variant reliability of FPSO becomes very important as for the risks of corrosion and collision. The corrosion defect is modeled as the exponential function of time. The Idealized Structural Unit Method is also proposed to predict ultimate strength of hull girder. Still water and wave-induced bending moments are also combined into stochastic processes. Reliabilities of intact hull during the service are calculated as references to those of collided hulls with effect of corrosion defect. Collision condition is a focus in this paper, where collided hulls are modeled according to ABS instructions. According to the instructions, the section with highest bending moment, which almost locates at the mid ship, should be noticed. Therefore still water bending moments of mid section of collided hulls are achieved and divided into two groups based on collision positions. One is that the mid section is broken, which is named as “direct damage”. Another is that other else section is broken, which is named as “influence”. Result shows that “influence” condition has higher still water bending moment than “direct damage”, which is usually neglected in previous researches. Finally, reliabilities of collided hulls throughout the service life are obtained, which can become references to further inspection and maintenance plan.

Ship Operational and Safety Aspects of Ballast Water Exchange at Sea

1994 ◽  
Vol 31 (04) ◽  
pp. 315-326
Author(s):  
John B. Woodward ◽  
Michael G. Parsons ◽  
Armin W. Troesch
Keyword(s):  
Bending Moment ◽  
Bending Moments ◽  
University Of Michigan ◽  
Bulk Carrier ◽  
Rough Water ◽  
Design Values ◽  
Wave Heights ◽  
Ballast Tanks ◽  
The University ◽  
Wave Induced

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.

Experimental Assessment of Form Based Approach for Predicting Extreme Value Distribution of Hull Girder Bending Moment in a Ship

2019 ◽  
Author(s):  
Tomoki Takami ◽  
Yusuke Komoriyama ◽  
Takahiro Ando ◽  
Kazuhiro Iijima
Keyword(s):  
Estimation Method ◽  
Bending Moment ◽  
Extreme Value Distribution ◽  
Irregular Waves ◽  
Extreme Wave ◽  
Scaled Model ◽  
Element Analysis ◽  
Hull Girder ◽  
Reliability Method ◽  
Wave Induced

Abstract This paper describes a series of towing tank tests using a scaled model of a recent container ship for validating the First Order Reliability Method (FORM) based approach to predict the maximum response. The FORM based approach is adopted in conjunction with the nonlinear strip method as an estimation method for the most probable wave episodes (MPWEs) leading to the given extreme wave-induced vertical bending moments (VBMs). Tank tests under the pre-determined MPWEs are conducted to evaluate the extreme wave-induced VBMs. Numerical simulations based on the coupled Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) are also conducted and are compared with the test results under the MPWEs. Furthermore, to estimate the extreme VBM statistics, tank tests under random irregular waves are conducted. A series of validations of the probability of exceedances (PoEs) of the VBM evaluated from the FORM based approach is carried out. The effect of hydroelastic (whipping) vibrations on the extreme VBM statistics are finally discussed.

Evaluation of Sealing Performance of Pipe Flange Connection Subjected to External Bending Moments

2009 ◽  
Author(s):  
Yoshio Takagi ◽  
Hiroyasu Torii ◽  
Toshiyuki Sawa ◽  
Kensuke Funada
Keyword(s):  
Bending Moment ◽  
Bending Moments ◽  
Stress Strain ◽  
Flange Connection ◽  
Strain Behavior ◽  
Leakage Test ◽  
Bolt Preload ◽  
Sealing Performance ◽  
Non Linear

The sealing performance of pipe flange connection subjected to an external bending moment was evaluated with the FEM and the experiments. The experimental leakage test using water revealed that the bending moment had an important effect on the sealing performance. The FE analyses suggested that the contact gasket stress, which was a function of the bolt preload, determines the leakage. The changes in contact gasket stress at tension side and compression side when the external bending moment applied were not symmetrical. The reduction in the contact gasket stress of tension side was larger than that of compression side due to the non-linear stress-strain behavior of the gasket. In addition, the hub stress of the flange when external bending moment applied, was evaluated from FE result and the discussion for optimizing the flange design subjected to external bending moment was done in this paper.

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.

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