Coarse mesh finite element model for cruise ship global and local vibration analysis

Funding Information: The research work carried out in this paper was funded by Aalto University and Meyer Turku Oy. The financial support is gratefully appreciated. Publisher Copyright: © 2021This paper presents a practical procedure for creating finite element (FE) model for vibration analysis of cruise ships. The most preferable FE modelling approaches are studied and discussed through case studies of common ship structures, which cover the range from low to high frequencies. The application of homogenized equivalent single layer (ESL) theory based equivalent element for stiffened panel is extended to local forced vibration analysis, where inertia induced interaction between plate and stiffener occurs. Modal method is used with an energy-based correction for accounting the plate-stiffener interaction into modal properties. Case study results reveal that mesh density of one 4-node element per web frame spacing is suitable for global FE-model when vibration analysis is limited to global hull girder modes. For such modes it is sufficient to only include the membrane stiffness of stiffened panels. For investigating the response at higher frequencies, bending properties of stiffened panel should be included and mesh density should be at least two elements per web frame spacing. Then forced vibration analysis can be performed with an excellent accuracy up to frequencies about one third of the local plate natural frequencies between the stiffeners. Beyond that, the influence of the local plate vibration becomes more significant in panel vibration, making the ESL-theory based element limited. With the applied correction method, the validity of the ESL-model can be extended to approximately two thirds of the local plate natural frequency.Peer reviewe

Optimisation of passenger ship structures in concept design stage

This paper presents an optimization method for concept design state of passenger ship with focus on utilisation of efficient Finite Element Modelling, evolutionary optimisation algorithm and indirect constraint relaxation. The response is analysed using 3D coarse mesh global finite element (FE) model, where stiffened panels are modelled using equivalent single layer (ESL) elements and the primary stiffeners are modelled with offset beam elements. The simplifications on stiffened panels and beams enable exploration of design space without changing the FE-mesh. The strength is defined based on classification society rules. Local stress peaks are allowed to exceed the rule-based strength limits, i.e. stress constraints are relaxed indirectly. Instead of increasing the allowed stress levels, the amount of material exceeding strength criteria is utilised. Optimization is based on Particle Swarm Optimization (PSO) algorithm with objective to reduce steel weight. The results show that stress relaxation has significant effect on the obtained total mass.Peer reviewe

Influence of weld-induced distortions on the stress magnification factor of a thin laser-hybrid welded ship deck panel

The limited knowledge about fatigue behavior and lack of analytical solutions for distorted thin plates are predominantly limiting their application today. This paper focuses on finding the most influential distortion parameter that dictates the fatigue strength at the butt weld of a laser-hybrid welded 4 mm thin ship deck panel. A FEA based sensitivity analysis method is employed to identify the influence of the distortion parameters. The results from the experimental validation showed that the distortions of the distorted deck plate on either side of the butt weld could be simplified with 4-point and 3-point splines on longitudinal and transversal direction, respectively. The most important distortion parameters are local angular misalignment, the distortion magnitude and location of local maximum distortion close to the butt weld. The distortion parameters further away from the weld has a minor influence on the structural stress at the butt weld. Furthermore, the results showed that the local angular misalignment can independently provide a better estimate of stress magnification factor km compared to any other distortion parameters.Peer reviewe

Fatigue strength of high-strength steel after shipyard production process of plasma cutting, grinding, and sandblasting

This paper investigates experimentally the fatigue strength of high-strength steel, which has undergone the normal shipyard production process of plasma cutting, grinding, and sandblasting. The study includes steels with the yield strength of 355 and 690 MPa. The tested specimens are of dog-bone shape and represent the large-scale situation of a cruise ship balcony opening corner, loaded in shear or tension. The influence of surface roughness, internal inclusions, hardness, and residual stress on the fatigue strength are studied and discussed. Compared to the design curve as well as to the untreated surfaces, the results show significantly improved fatigue strength under constant amplitude loading at a load ratio of R = 0.1. However, very flat or even rising slope of the S-N curve indicates variations in the material and surface quality as well as in the residual stress. Surprisingly, internal defects even up to 100 μm in size did not decrease the fatigue strength.Peer reviewe

Limit state analyses in design of thin-walled marine structures - Some aspects on length-scales

This paper gives an overview of the factors that affect the strength and structural design of advanced thin-walled marine structures with reduced plate thickness or alternative topologies to those used today in the marine industry. Due to production-induced initial deformations and resulting geometrical non-linearity, the classical division between primary, secondary, and tertiary responses becomes strongly coupled. Volume-averaged, non-linear response of structural element can be used to define the structural stress-strain relation that enables analysis at the next, larger, length scale. This, today's standard homogenization process, needs to be complemented with localization, where the stresses are assessed at the details, such as welds for fatigue analysis. Due to this, the production-induced initial distortions need to be considered with high accuracy. Another key question is the length-scale interaction in terms of continuum description. Non-classical continuum mechanics are needed when consecutive scales are close. Strain-gradients are used to increase the accuracy of the kinematical description of beams, plates, and shells. The paper presents examples of stiffened and sandwich panels covering limit states such as fatigue, non-linear buckling, and fracture.Peer reviewe

Fatigue strength of laser-welded thin-plate ship structures based on nominal and structural hot-spot stress approach

To improve the energy efficiency, the demand for new light-weight solutions has been increased significantly in the last decades. The weight reduction of the current ship structures is possible using thinner plates, that is, plate thickness between 3 and 4 mm. However, at present this is, in normal cases, not possible due to the 5 mm minimum plate thickness requirement given by classification societies. The present paper investigates the fatigue strength of thin-plated ship structures. In the European research project BESST – ‘Breakthrough in European Ship and Shipbuilding Technologies’ – the extensive fatigue test programme was carried out for butt- and fillet-welded specimens, which were manufactured by the arc, laser and laser-hybrid welding methods. The test programme also covered the different production quality and thus a large variation of misalignments was included. Fatigue test results were analysed using the nominal as well as the structural stress approach, where the actual geometry of the specimens was taken into account. The results show that the present design S–N curve with slope value of 3 is applicable to thin plates, but it is slightly non-conservative. The fatigue test results for thin plates show better agreement with the slope value of 5. For thin plates and slender ship structures, the secondary bending stress due to angular misalignment plays an important part and changes in a non-linear way with the applied tension load. Therefore, it is important to consider the plate straightening effect in structural stress analysis