Preben Terndrup Pedersen

Elements of Risk Analysis for Collision and Grounding of a RoRo Passenger Ferry

Newly developed software was applied to study the effects of damages due to collision and grounding. The annual risk of collision and grounding was computed for an example RoRo passenger ferry. Collision frequency was evaluated for a specified route taking into account traffic data. Grounding frequency was calculated for an artificial obstacle located close to the traffic route. The consequences of collision and grounding scenarios were estimated by introducing damage criteria that link the calculated distribution of damage size and damage location to monetary units. Loss of human life and reputation was not considered. It was shown that the main part of the calculated annual risk is caused by capsize of the vessel after severe damage.

Modelling of the internal mechanics in ship collisions

Abstract A method for analysis of the structural damage due to ship collisions is developed. The method is based on the idealized structural unit method (ISUM). Longitudinal/transverse webs which connect the outer and the inner hulls are modelled by rectangular plate units. The responses are determined by taking into account yielding, crushing, and rupture. Some plates of the outer and the inner shell subjected to large membrane tensions are modelled by membrane tension triangular/rectangular plate units, while the remaining shell panels are modelled by the usual plate units. The effect of stiffeners on the stiffness and the strength is considered as well. In order to include the coupling effects between local and global failure of the structure, the usual non-linear finite-element technique is applied. In order to deal with the gap and contact conditions between the striking and the struck ships, gap/contact elements are employed. Dynamic effects are considered by inclusion of the influence of strain-rate sensitivity in the material model. On the basis of the theory a computer program has been written. The procedure is verified by a comparison of experimental results obtained from test models of double-skin plated structures in collision/grounding situations with the present solutions. As an illustrative example the procedure has been used for analyses of a side collision of a double-hull tanker. Several factors affecting ship collision response, namely the collision speed and the scantlings/ arrangements of strength members, are discussed.

Ship grounding and hull-girder strength☆

Abstract A mathematical model for analysis of ship hull loading due to grounding on relatively plane sand, clay or rock sea bottoms is presented. The analysis model of the grounding event is separated into two phases. In the first phase the ship is subjected to an impulse caused by the sudden contact with the ground. This initial impulse is assumed to be completely inelastic and leads to a rapid change of the forward speed such that after the impact the ship has heave and pitch velocities which make its motion compatible with that of the contact point along the ground. In the second phase the ship is sliding with continuous contact to the ground. This means that the kinetic energy which is available after the end of the first impulse is, in this second phase, transformed into potential energy and into friction in the contact zone between the ground and the ship. In both phases the forces exerted on the ship bow are assumed to be governed by a Coulomb friction law. Grounding forces, sectional shear forces and bending moments caused by the grounding are determined and related to the ultimate capacity of the hull girder. First approximations to the ground reaction and the sectional forces are found to be proportional to the initial forward velocity of the ship. The results show that larger ships are more exposed to hull failure due to grounding than smaller ships. Finally, the mathematical grounding model is verified by model tests and controlled full-scale grounding experiments.

Collision Risk for Fixed Offshore Structures Close to High-density Shipping Lanes

Fixed offshore structures in the vicinity of intense ship traffic pose a potential collision hazard such as risk of loss of life, economic loss, environmental damage and other possible unwanted events. Therefore, one of the many performance goals in the design phase of such structures is to ensure that the risk of such major accidents and service disruptions is low enough to be acceptable to users, the public and those responsible for public safety. The present paper uses a risk analysis performed for a large suspension bridge with approach spans as an example of the key elements required in a rational risk analysis procedure for fixed offshore structures in shipping lanes with high traffic densities. It deals with the following items: the basic information and the navigational studies needed for a rational collision risk assessment, exemplification of target risk acceptance criteria for the bridge structure, an analysis procedure for ship collision frequencies as a function of the structural layout, elements in a calculation of the probabilistic distribution of collision forces on the fixed structure, given a collision has taken place, and finally it is shown how the consequences due to accidental ship collisions can be assessed, i.e. the risks that have to be compared to the target risk acceptance criteria. The main objective of the procedure is to provide the designers with the maximum flexibility to develop new cost effective offshore structures based on performance standards for the structural requirements and the requirements to the navigational arrangements, instead of basing the design on the more traditional prescriptive rules or codes. For the example bridge structure it is shown that fulfilment of the established risk criteria substantially influences the geometric requirements for the navigation clearance and the needed resistance to ship, impacts. In addition it was found necessary to establish a vessel traffic system (VTS).

Strength of ship plates under combined loading

Strength of ship plates plays a significant role in the ultimate strength analysis of ship structures. In recent years several authors have proposed simplified analytical methods to calculate the ultimate strength of unstiffened plates. The majority of these investigations deal with plates subjected to longitudinal compression only. For real ship structural plating, the most general loading case is a combination of longitudinal stress, transverse stress, shear stress and lateral pressure. In this paper, the simplified analytical method is generalized to deal with such combined load cases. The obtained results indicate that the simplified analytical method is able to determine the ultimate strength of unstiffened plates with imperfections in the form of welding-induced residual stresses and geometric deflections subjected to combined loads. Comparisons with experimental results show that the procedure has sufficient accuracy for practical applications in design.

Elastic-plastic behaviour of offshore steel structures under impact loads

Abstract This paper presents an accurate and efficient method for the collision analysis of offshore steel structures. A nonlinear force—displacement relationship is derived for the simulation of the local indentation in a hit tubular member and a three-dimensional beam—column element is developed for the modelling of the global behaviour of the struck structure. Large deformations, plasticity and strain-hardening of the beam—column elements are accounted for by combining an elastic large displacement analysis theory with the plastic node method. The dynamic elastic-plastic response of offshore platforms in typical ship collision situations is investigated. It is shown that strain-hardening plays an important role in the impact response. A large part of the impact energy is transformed into plastic deformation energy of the struck structure in a severe ship-platform collision. Therefore, a rational collision analysis should take into account the effects of large deformations, plasticity and strain-hardening. The presented procedure has the advantage that the number of elements in the analysis model need not be larger than the number of elements used in normal linear analysis procedures. Furthermore, the elastic-plastic stiffness matrices are derived without numerical integrations over the cross-sections.

Stability of the solutions to Mathieu-Hill equations with damping

SummaryThe Mathieu-Hill equations with the addition of the damping term are treated directly, and not as an extended problem of the undamped case. To some extent this in fact simplifies the problem, and the basic theorems are derived without too much mathematics. The aim of the paper is to analyse the stability of the solutions, and this object is obtained by the Bubnov-Galerkin procedure, which is rather unused in relation to Mathieu-Hill equations. For the specific periodic function cos 2τ + a4 cos 4τ stability diagrams are presented, including cases with “coexistent” solutions.ÜbersichtDie Mathieu-Hill-Gleichungen mit Dämpfungsglied werden unmittelbar, nicht nur als Erweiterung des Falles ohne Dämpfung, untersucht. In gewisser Weise vereinfacht sich die Aufgabe dadurch, so daß grundlegende Sätze ohne großen mathematischen Aufwand abgeleitet werden können. Ziel ist die Untersuchung der Stabilität der Lösungen. Hierzu wird das Verfahren von Bubnov-Galerkin verwendet. Für eine periodische Funktion cos 2τ + a4 cos 4τ werden Stabilitätsdiagramme angegeben, bei denen auch coexistierende Lösungen berücksichtigt sind.

On forward and backward precession of rotors

SummaryA study of the excitation of backward and forward precessional motion of rotors is presented. It is shown that if the rotor is supported in bearings with rotational symmetry, a rotating unbalance of the shaft cannot excite backward precessions, but if the bearings have even the slightest anisotropy, backward synchronous precessions are excited just as in the case of forward precessional motions. However, internal damping forces have a marked effect in reducing the amplitudes of the backward precessions.A rotating unbalanced non-uniform continuous circular shaft supported by anisotropic flexible bearings is studied. The governing equations of motion are derived taking into account the effects of transverse shear, gyroscopic moments, and internal and external damping.ÜbersichtEs wird die Erregung der gleich- und gegen-läufigen Präzessionen von Rotoren untersucht. Es wird gezeigt, daß bei Rotoren in rotationssymmetrischen Lagern eine Unsymmetrie der Welle keine gegenläufigen Präzessionea verursachen kann. Bei der geringsten Anisotropie der Lagerung werden jedoch synchrone gegenläufige Präzessionen in derselben Weise wie die gleichläufigen Präzessionen erregt. Allerdings werden die gegenläufigen Präzessionen durch innere Dämpfungskräfte stärker reduziert.Es wird weiterhin eine unwuchtige Welle mit nicht-konstantem Kreisquerschnitt untersucht, die in anisotropen, nachgiebigen Lagern gelagert ist. Die Bewegungsgleichungen werden für diesen Fall unter Berücksichtigung der Querkräfte, der Kreiselmomente und der inneren und äußeren Dämpfung abgeleitet.

Measures of model uncertainty in the assessment of primary stresses in ship structures

The paper considers various models and methods commonly used for linear elastic stress analysis and assesses the uncertainty involved in their application to the analysis of the distribution of primary stresses in the hull of a containership example, through statistical evaluations of the results of calculations performed by different methods.

Numerical prediction of slamming loads

It is important to include the contribution of the slamming-induced response in the structural design of large vessels with a significant bow flare. At the same time it is a challenge to develop rational tools to determine the slamming-induced loads and the prediction of their occurrence. Today it is normal practice to apply a standard sea-keeping procedure to determine the relative velocity distribution between the water surface and the hull and then to estimate the bottom slamming loads and the bow-flare slamming loads based on two-dimensional formulations similarly to water-entry problems. The pressure distribution as well as the total force is then determined by integration over a pseudo-three-dimensional presentation of the hull geometry. In this paper the evaluation of the slamming load is taken one step further by performing direct three-dimensional, fully non-linear numerical calculations in a realistic wave environment. Both the global and the local slamming loads are assessed numerically using a finite-volume formulation with the free surface captured by a volume-of-fluid technique. This numerical procedure is justified by comprehensive validation studies where numerically evaluated slamming pressures are compared with experimentally measured results. To obtain an insight into the three-dimensional flow effects the next step is to apply the validated numerical procedure to evaluate and compare the accuracy and performance of the traditionally used two-dimensional formulations by a comparison with three-dimensional numerical formulations for a fine-form Panamax container ship bow hitting a flat water surface at a constant trim angle. Finally, the slamming evaluation is carried out on the basis of a three-dimensional case study of the same container ship sailing in a head sea at half the service speed in a critical wave episode which is defined conditional on a given extreme response level of the hull girder bending moment.