Alexander von Graefe ISMT, University Duisburg-Essen, Bismarckstrasse 69, Duisburg 47057, Germany e-mail: alexander.von-graefe@dnvgl.com Ould el Moctar ISMT, University Duisburg-Essen, Bismarckstrasse 69, Duisburg 47057, Germany e-mail: ould.ei-moctar@uni-due.de Jan Oberhagemann DNV GL, Brooktorkai 18, Hamburg 20457, Germany e-mail: jan.oberhagemann@dnvgl.com Vladimir Shigunov1 DNV GL, Brooktorkai 18, Hamburg 20457, Germany e-mail: vladimir.shigunov@dnvgl.com Linear and Nonlinear Sectional Loads With Potential and Field Methods A Rankine source method is applied to predict linear and weakly nonlinear sectional loads o f a modern container ship. The method uses solution in the frequency domain, lin earized with respect to wave amplitude about the nonlinear steady flow due to forward speed, which accounts for the nonlinear free-surface conditions, ship wave, and dynamic trim and sinkage. Weak nonlinearity of the sectional loads in waves (e.g., hogging sagging asymmetry) is taken into account by pressure extrapolation and integration up to the estimated actual water line. The sectional forces obtained with this method are com pared with the results of other methods, including (1) linear Rankine panel method, where flow due to waves is linearized about the double-body flow, (2) linear zero-speed Green function method with correction for forward speed, (3) fully nonlinear simulations based on field-based solution of Reynolds-averaged Navier-Stokes (RANS) equations, and (4) model tests. Comparison with RANS solution and model tests shows, that the pro posed method can accurately predict sectional loads for small to moderate wave heights. [DOI: 10.1115/1.4026885] " Introduction A ship hull girder is dimensioned with respect to extreme loads and required fatigue life. Extreme loads strongly depend on non linear effects; sometimes, nonlinearities are classified as weak nonlinearity (taking into account real wet surface) and strong nonlinearity (impact loads and whipping). Accurate computation of strong nonlinear effects is only possible with field-based meth ods, such as finite-volume methods for Reynolds-averaged Navier-Stokes equations, and therefore requires much computing time. Besides, there are no straightforward statistical techniques for the definition of long-term extreme loads using such methods. Therefore, simplified approaches, based on a combination of lin ear hydrodynamic analysis (and linear statistics) with nonlinear analysis in selected regular design waves, are currently used in design and approval. Current developments of this technique include nonlinear simulations in irregular design wave trains [1] and nonlinear Monte Carlo simulations in selected irregular “design seaways” [2]. All these methods are based on the assump tion that linear computations are an accurate identifier of the com binations of seaway conditions and operational parameters that lead to extreme nonlinear responses. Therefore, accurate calcula tion of linear responses in the frequency domain is an important prerequisite for the assessment of nonlinear maximum global loads when such methods are used. For the estimation of fatigue life, the loads are frequently sepa rated into two components: so called wave loads (i.e., rigid-body responses) and dynamic loads (elastic responses, such as springing and whipping). Wave loads produce the main contribution to fa tigue damage; besides, it is important for the designer and ap proval body to know what contribution to fatigue damage comes from rigid-body responses and what from elastic reactions. Calculation of elastic responses will be addressed elsewhere; for fatigue-relevant rigid-body loads, linear loads are again important. ’Corresponding author. Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the Journal of Offshore M echanics and A r c t ic E ngineering . Manuscript received June 18, 2013; final manuscript received February 11, 2014; published online April 1, 2014. Assoc. Editor: Dominique Roddier. Finally, an efficient way to take into account weak nonlinearity in potential methods is to use linear hydrodynamic analysis in the frequency domain to compute added masses, damping, and wave excitation forces (and use impulse-response theory or state-space model to compute linear hydrodynamic forces in the time do main), combined with the calculation of nonlinear forces and moments due to the incident wave and nonlinear hydrostatic restoring forces and moments by pressure integration over the in stantaneous wetted surface in the time domain; when using this approach, accurate linear analysis in the frequency domain is required. Therefore, the aim of this paper is to address the prediction of linear sectional loads. Nonlinear loads and their accurate predic tion are not considered here; however, a simple nonlinear correc tion in the frequency domain is tested to check its applicability. Two linear methods are used: (1) the zero forward speed free- surface Green function with encounter-frequency correction to consider forward speed effect and (2) the new Rankine source method [3]. The Rankine source method directly takes into account the effect of forward speed, whereas the zero-speed Green function approach uses a simple approximate correction to take this effect into account; comparison of these two methods is one of the aims of this paper. Both methods are implemented in the code GL Rankine (GL stands for Germanischer Lloyd). Few open benchmarking data for linear methods in the fre quency domain are available. Reference [4] compares strip-theory computations from 24 organizations of midship vertical shear force and bending moment in head and following waves, and mid ship lateral force, bending moment, and torsional moment in quar tering (60 deg off stem) and bow (30 deg off bow) waves with model tests for an S-175 container ship at Fr = 0.275. Vertical shear force and bending moment in head waves show moderate scatter between different calculations and agree with the measure ments. In following waves, different computational results show significant scatter in the entire frequency range; the tendency of numerical results with increasing frequency differs from the meas urements. Midship lateral shear force and bending moment, as well as torsional moment, show moderate scatter between differ ent computations in bow waves but significant scatter and Journal of Offshore Mechanics and Arctic Engineering AUGUST 2014, Vol. 136 / 031602-1 Copyright © 2014 by ASME