Šime Malenica

Some aspects of structural modelling and restoring stiffness in hydroelastic analysis of large container ships

The increase in world trade has largely contributed to the expansion of sea traffic. As a result, the market demand is leading to ultra-large container ships (ULCS), with expected capacity up to 18,000 TEU (twenty-foot equivalent unit) and length about 400 m, without changes in the operational requirements (speed up to 27 knots). The particular structural design of the container ships leads to open midship sections, resulting in increased sensitivity to torsional and horizontal bending loads that is much more complex to model numerically. At the same time, due to their large dimensions, the structural natural frequencies of ULCS become significantly lower so that the global hydroelastic structural responses (springing and whipping) can become a critical issue in the ship design and should be properly modelled by the simulation tools since the present classification rules do not cover described operating stages completely. There are several research projects worldwide aiming at solving this problem, and one of them is the EU FP7 project TULCS (tools for ultra-large container ships) for development of the integrated design tools, based on numerical procedures, model tests and full-scale measurements. This paper is based on research activities and results of the project, with particular emphasis on the part that deals with global hydroelastic loading and response. Special attention is paid to beam structural model based on the advanced beam theory. It includes shear influence on bending and torsion, contribution of transverse bulkheads to hull stiffness and an appropriate modelling of relatively short engine room structure of ULCS. Along with that, a hydrodynamic model is presented in a condensed form. Further on, a fully consistent formulation of restoring stiffness, which plays an important role in the hydrostatic model, is described. Theoretical contributions are illustrated within the numerical example, which includes a complete hydroelastic analysis of an 11,400 TEU container ship. In this case, validation of the one-dimensional (1D) finite-element method (FEM) model is done by a correlation analysis with the vibration response of the fine three-dimensional (3D) FEM model. The procedure related to determination of engine room effective stiffness is checked by a 3D FEM analysis of a ship-like pontoon, which has been made according to the 7800 TEU container ship properties. The obtained results confirm that the sophisticated beam model is a very useful numerical tool for the designer and represents a reasonable choice for determining wave load effects on ULCS, in preliminary design stage.

Semi-analytical models of hydroelastic sloshing impact in tanks of liquefied natural gas vessels

The present paper deals with the methods for the evaluation of the hydroelastic interactions that appear during the violent sloshing impacts inside the tanks of liquefied natural gas carriers. The complexity of both the fluid flow and the structural behaviour (containment system and ship structure) does not allow for a fully consistent direct approach according to the present state of the art. Several simplifications are thus necessary in order to isolate the most dominant physical aspects and to treat them properly. In this paper, choice was made of semi-analytical modelling for the hydrodynamic part and finite-element modelling for the structural part. Depending on the impact type, different hydrodynamic models are proposed, and the basic principles of hydroelastic coupling are clearly described and validated with respect to the accuracy and convergence of the numerical results.

Consistent Hydro-Structure Interface for Evaluation of Global Structural Responses in Linear Seakeeping

The difficulties related to the equilibration of the 3D FEM structural model, in the context of hydro-structure interactions in linear seakeeping are discussed. Different philosophies in modeling the structural and hydrodynamic parts of the problem, usually lead to very different meshes (hydro and structure) which results in unbalanced structural model and consequently in doubtful results for structural responses. The procedure usually employed consists in using different kinds of interpolation schemes to transfer the total hydrodynamic pressure from hydrodynamic panels to the centroids of the structural finite elements. This approach is both, very complex for complicated geometries, but also rather inaccurate. The method that we propose here is based on two main ideas: 1. Pressure recalculation instead of interpolation; 2. Separate transfer of different pressure components (incident, diffraction, radiation & hydrostatic variation). The first point removes the difficulties related to the interpolation techniques, and allows for a very robust method of pressure transfer. The second point ensures the perfect equilibrium because the body motions are calculated after integration over the structural mesh, which means that the equilibrium is implicitly imposed. It should be noted that this procedure is not completely straightforward and several numerical “tricks” need to be introduced. However, once these difficulties are solved, the final numerical code is extremely robust and can be easily coupled with any of the general 3D FEM packages.Copyright

Global hydroelastic analysis of ultra large container ships by improved beam structural model

ABSTRACT Some results on the hydroelasticity of ultra large container ships related to the beam structural model and restoring stiffness achieved within EU FP7 Project TULCS are summarized. An advanced thin-walled girder theory based on the modified Timoshenko beam theory for flexural vibrations with analogical extension to the torsional problem, is used for formulation of the beam finite element for analysis of coupled horizontal and torsional ship hull vibrations. Special attention is paid to the contribution of transverse bulkheads to the open hull stiffness, as well as to the reduced stiffness of the relatively short engine room structure. In addition two definitions of the restoring stiffness are considered: consistent one, which includes hydrostatic and gravity properties, and unified one with geometric stiffness as structural contribution via calm water stress field. Both formulations are worked out by employing the finite element concept. Complete hydroelastic response of a ULCS is performed by coupling 1D structural model and 3D hydrodynamic model as well as for 3D structural and 3D hydrodynamic model. Also, fatigue of structural elements exposed to high stress concentration is considered.

Hydroelastic Response of a Ship Structural Detail to Seakeeping Loads Using a Top-Down Scheme

In order to investigate the local response of a ship structure, it is necessary to transfer the seakeeping loading to a 3DFEM model of the structure. A common approach is to transfer the seakeeping loads calculated by a BEM method to the FEM model. Following the need to take into account the dynamic response of the ship to the wave excitation, some methods based on a modal approach have been recently developed that include the dry structural modes in the hydro-structure coupling procedure and allow to compute the springing and whipping response of the ship structure to the seakeeping loads.In the context of the fatigue life assessment of a structural detail, a very fine FE model is required. A very large number of seakeeping loading cases also need to be considered to account for all the conditions encountered by the ship through its life. It becomes then clear that because of the CPU time issue, the whole FE model can not be very fine. This is why a hierarchical top-down analysis procedure is commonly used, in which the global ship structure is modelled in a coarse manner using one finite element between web frames. The structural details are modelled separately using a fine meshing. Such top-down methods are commonly used for the estimation of the quasi-static response of structural details to the seakeeping loads.This paper presents a methodology in which a top-down method is used to estimate the springing response of a ship structural detail loaded with wave pressure, and its fatigue life. The global dry structural modes are transferred to the detail fine model using the shape functions of the finite elements of the global model. The hydrodynamic pressures are computed directly on the fine mesh model, avoiding any interpolation error. The imposed displacements at the fine mesh boundary are computed using the same method that is used to transfer the structural mode shapes, and the local pressure induced loads and inertia loads are applied on the fine mesh nodes.This method is applied for the calculation of the elongation of a strain gauge which is installed in the passage way of an ultra large container ship.Copyright

A Novel Solution to Compute Stress Time Series in Nonlinear Hydro-Structure Simulations

Ship transport is growing up rapidly, leading to ships size increase, and particularly for container ships. The last generation of Container Ship is now called Ultra Large Container Ship (ULCS). Due to their increasing sizes they are more flexible and more prone to wave induced vibrations of their hull girder: springing and whipping. The subsequent increase of the structure fatigue damage needs to be evaluated at the design stage, thus pushing the development of hydro-elastic simulation models. Spectral fatigue analysis including the first order springing can be done at a reasonable computational cost since the coupling between the sea-keeping and the Finite Element Method (FEM) structural analysis is performed in frequency domain. On the opposite, the simulation of non-linear phenomena (Non linear springing, whipping) has to be done in time domain, which dramatically increases the computation cost. In the context of ULCS, because of hull girder torsion and structural discontinuities, the hot spot stress time series that are required for fatigue analysis cannot be simply obtained from the hull girder loads in way of the detail. On the other hand, the computation cost to perform a FEM analysis at each time step is too high, so alternative solutions are necessary. In this paper a new solution is proposed, that is derived from a method for the efficient conversion of full scale strain measurements into internal loads. In this context, the process is reversed so that the stresses in the structural details are derived from the internal loads computed by the sea-keeping program. First, a base of distortion modes is built using a structural model of the ship. An original method to build this base using the structural response to wave loading is proposed. Then a conversion matrix is used to project the computed internal loads values on the distortion modes base, and the hot spot stresses are obtained by recombination of their modal values. The Moore-Penrose pseudo-inverse is used to minimize the error. In a first step, the conversion procedure is established and validated using the frequency domain hydro-structure model of a ULCS. Then the method is applied to a non-linear time domain simulation for which the structural response has actually been computed at each time step in order to have a reference stress signal, in order to prove its efficiency.Copyright

Some Aspects of Hydro-Structure Coupling for Combined Action of Seakeeping and Sloshing

The techniques for hydrodynamic load transfer from combined action of waves (seakeeping) and internal liquid flow (sloshing), onto 3DFEM structural model are discussed. The problem is relevant both for a ship transporting liquids in tanks (LNG carriers, tankers...) as well as for any ship sailing in ballast conditions. Correct pressure transfer to the FEM model is essential for spectral fatigue assessment of structural details. The methods that are used in practice do not appear to be very clear and different levels of approximations based on some empirical considerations are usually employed. In this paper, a fully consistent method is proposed in the context of the linear frequency domain model.Copyright

Maximum stress of stiff elastic plate in uniform flow and due to jet impact

The liquid jet impact onto a clamped elastic plate is investigated. The two-dimensional jet of constant thickness and with flat vertical front is initially advancing towards the elastic plate along a flat, rigid, and horizontal plane at a constant uniform speed. The elastic plate of variable thickness is mounted perpendicular to the rigid plane. The maximum stress during the early impact stage is estimated for a given retardation time and a given relaxation time of the plate material. The stresses during the initial impact stage are compared with the static stresses in the plate placed in an equivalent uniform flow. It is shown that the static stresses are always smaller than the bending stresses during the early stage of impact for a given speed and thickness of the jet. This implies that if the stresses in the plate are smaller than the yield stress of the plate material with no plastic deformations in the plate occurring during the unsteady impact stage, then the plate behaves elastically after the imp...

Rational Assessment of Fluid Impact Loads

The safe operation of ships is a high priority task in order to protect the ship, the personnel, the cargo and the wider environment. A methodology for the rational and reliable assessment of the structural integrity and thus safety of ships and their cargos at sea has been developed. Central to this methodology is a set of mathematical models, the conditions of their use, and the links between them, which were designed to improve the predictions of wave impact loads acting on ships. The models, together with the methodology of their use, were utilised by the ship certification industry bringing benefits through recognised quality assurance systems and certification.

Improvements of beam structural modelling in hydroelasticity of Ultra Large Container Ships

Increase in global ship transport induces building of Ultra Large Container Ships (ULCS), which have a capacity up to 14000 TEU with length up to 400 m, without changes of the operational requirements (speed around 27 knots). Natural frequencies of such ships can fall into the range of encounter frequencies in an ordinary sea spectrum. Present Classification Rules for ship design and construction don’t cover such conditions completely and hydroelastic analysis of ULCS seems to be the appropriate solution for analysis of their response in waves. This paper deals with numerical procedure for ship hydroelastic analysis with particular emphasis on improvements of the present beam structural model. The structural model represents a constitutive part of hydroelastic mathematical model and generally it can be formulated either as 1D FEM or 3D FEM model. For the preliminary design stage hydroelastic model derived by coupling 1D FEM structural model and 3D BEM hydrodynamic one seems to be an appropriate choice. Within the paper the importance of hydroelastic approach and methodology of hydroelastic analysis are elaborated. Further on, structural model based on advanced beam theory is described in details. The improvements include taking into account shear influence on torsion, contribution of bulkheads to hull stiffness as well as determination of effective stiffness of engine room structure. Along with that, hydrodynamic and hydrostatic models are presented in a condensed form. Numerical example, which includes complete hydroelastic analysis of a large container ship, is also added. In this case, validation of 1D FEM model is checked by correlation analysis with the vibration response of the fine 3D FEM model. The procedure related to determination of engine room effective stiffness is checked by 3D FEM analysis of ship-like pontoon which has been made according to the considered ship characteristics.Copyright