This paper proposes a design strategy of a hydro-structural model considering the vertical-bending and torsional vibration mode shapes. A ship with large opening decks, such as a container ship, has its shear center below its bottom hull. In the proposed design strategy, such a shear center location is achieved for a ship model by imparting appropriate stiffness to its hull.We built a box-shaped model, whose length was 2 m, with urethane foam and polyethylene resin based on the proposed design strategy. A three-point bending test, a torsion test, and a decay test of the model were conducted to investigate its elastic properties. The vertical-bending and torsional moments were estimated from the strains measured with gauges based on the fiber Bragg grating (FBG) technology. The validation of the test results with finite element simulations revealed that the elastic responses were successfully measured using the model designed based on the proposed strategy with the FBG strain gauges.
This paper is the second of the two companion papers dealing with ultimate longitudinal strength analysis of container ships considering the effects of bottom local loads. The major causes of reduction of ultimate hull girder strength due to local loads were discussed based on the finite element analysis of a hold model in the Part 1. The objective of this paper is to develop a practical method of progressive collapse analysis of a hull girder subjected to combined longitudinal bending and bottom local loads.Smith's method is widely used to estimate the hull girder ultimate strength under pure bending. It however cannot consider the local deformations such as double-bottom bending because it assumes that a hull-girder cross section remains plane. A new methodology is therefore proposed, which idealizes the double bottom structures as a plane grillage consisting of longitudinal and transverse beams and extending over a hold length in the longitudinal direction. The rest part of a hull-girder cross section, such as a ship side and a bilge, is modeled as a unit beam and connected with the grillage model along the bilge parts using multi-point constraints. The calculation of the stiffness of longitudinal beam elements is based on the original Smith's method, including the definition of plate and stiffened-panel elements and the application of a concept of average stress-average strain relationship for each element. The proposed model may be called an "extended Smith's method". The progressive collapse behaviors and hull girder ultimate strength predicted by the extended Smith's method are compared with the result of nonlinear finite element analysis.
In this study, the feasibility of Fiber Bragg Gratings (FBG) pressure sensors is verified for hull structural strength evaluation. To investigate the effectiveness of FBG pressure sensors for the strength evaluation, the towing tank test is carried out with a pure hydro-structural (PHS) ship model, which is capable of elastic deformation. FBG pressure sensors are installed on the outer hull surface and FBG strain sensors are installed inside the hull to calculate a vertical bending moment (VBM). Measured water pressure is interpolated on the whole hull surface by using the weighted average approach based on relative distance. Finite Element Analysis (FEA) is carried out based on interpolated water pressure. In FEA, inertia force is considered according to the inertia relief method, and VBM is calculated by FEA results. The strain measured by FBG strain sensors is transformed to VBM based on the calibration coefficient obtained by the vertical bending test. Finally, VBM obtained by the measured water pressure and strain are compared. As a result, VBM obtained by the measured water pressure is consistent with ones obtained by the measured strain. Therefore, the availability of water pressure measured by the FBG pressure sensors is validated for the hull structural strength evaluation in terms of VBM.
In this study, the authors have developed the simple and accurate formulae of the Froude-Krylov forces of 6-DOFs based on the linear theory, as a fundamental study to develop a closed formula of ship motion in waves. The proposed formulae have been developed by approximating the hull-form under waterline by the function uniquely determined by the principal particulars of the ship; length L, breadth B, draft d, block coefficient Cb, waterplane area coefficient Cw, midship section area coefficient Cm, height of center of gravity KG, longitudinal center of floatation LCF. Therefore, the proposed formulae are expressed as the explicit function determined by only principal particulars as well as the wave condition parameters. It was confirmed that the proposed formulae have high accuracy for all merchant ship types in any wave condition (wave angle and wave length) through validation compared with numerical calculation by using actual hull-forms of 77 ships × 2 conditions.
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