Modern methods in ship structure analysis

Simulations are used commonly in ship design. Finite element simulations, for example, are used in the dimensioning of ship structures and systems, while computational fluid dynamics (CFD) simulations can be used in hull design to minimise ship drag and thereby reduce fuel consumption. CFD is also applied in propulsion design and propeller dimensioning. In this article, I discuss the use of simulations and finite element analysis in ship design.    

In the finite element method (FEM), a structure such as a ship hull is divided into small parts (elements), where displacements and strains can be defined with the help of mathematical equations. The equations reveal the stress levels in the elements. Very complex structures can be dimensioned extremely accurately without having to make the broad simplifications or assumptions associated with traditional analytical methods.

Modern simulation software programmes and powerful computers are used in simulations. This means that large entities can be modelled and analysed relatively quickly. In addition, changes and different structural solutions can be searched for rapidly. This allows engineers to ensure that the structure fulfils its defined requirements.

Ship dimensioning

Ship dimensioning has for long been, and still is, based on knowledge gained from experience, which is refined with analysis methods and structural solutions. Ships can be designed and dimensioned to a large degree based on classification society formulas and guidelines. This method is still used in the basic dimensioning of ships.

These dimensioning methods are appropriate when preliminary dimensioning is done, but they do not allow structural details to be examined, at least not easily. Classification societies also enable the use of more advanced methods. Of these methods, probably the most utilised is the finite element method.

Normally, and where the hull girder response cannot be sufficiently determined with beam theory, FE analysis is required. This is commonly the case, e.g. for ships with large deck openings like container ships, ships without or with limited transverse bulkhead structures like Ro-Ro vessels and car carries, and ships with partly effective superstructures like large passenger vessels.

Classification societies have also provided guidelines as to how analysis models should be created and what simplifications can be employed for the results to still be reliable, and if necessary, reproduced.

From a structural point of view, a ship is a big beam that floats on water. Differently spread masses and environmental stresses bend and twist this beam. The typical cross section dimensions of a ship can be defined based on the forces and torque caused by the ship structure and loads. These dimensions include, for example, the required shell plate thickness, as well as the scantlings of girders and frames.

These typical frames are then laid out, one after the other, with a specific frame spacing. More accurate dimensioning calculations naturally need to be made for transition zones. The effects of engine foundation, for example, and those of other systems, also need to be taken into consideration.

The downside of this is that structures are easily over-dimensioned or, in the worst case, under-dimensioned, when typical structures are used throughout the ship. Nowadays, the finite element method is generally used in ship dimensioning once the ship’s preliminary dimensions have been defined. Safety is, of course, behind all dimensioning actions. Without sufficient analysis one cannot be sure that a ship will withstand all stresses it is subjected to during its lifetime.

From global to local modellinG

Large cruise ships are not the most typical of vessels. They are expected to deliver something different, a WOW effect, with big open spaces and promenades to attract passengers. These structures are, however, very difficult to dimension based on formulas. It is for this reason that the use of the finite element method in ship dimensioning has grown so strongly and is employed at some stage in the dimensioning of every ship.

Modern computers and software are able to analyse increasingly large targets in greater detail with the finite element method. Typically, this is done by first creating a so-called global model of a ship. As the name indicates, a global model is a model of the entire ship, which can then be divided into elements.

The element division in the global model is usually very broad; typically, an element is the size of the space between main frames or between decks. The element size can, as such, be 3m x 3m. In this case, for example, smaller stiffeners of decks are not modeled geometrically at all, but should be taken into account in the stiffness of the elements in other ways. The model does not take all details into consideration, but rather aims to analyse the overall deformations and forces on the ship beam with sufficient accuracy. The model thus takes the stiffness of the structure into consideration with sufficient precision, but the stress field can be very inaccurate in places. As the computational power of computers increases, it will become possible to produce more accurate global models and stress results.

Typical element meshes of a local ship model. The element size is around 50x50mm and for smaller details the element size is typically t x t, where t is the plate thickness. 

The global model is used as the base for creating more accurate models, so-called local models, which take structural details into consideration. If necessary, one can progress to even more accurate models in a step-by-step fashion, in essence, by creating local models from local models.

In local models, even smaller stiffeners are modelled according to the geometry, which allows a very precise analysis of the structure’s stress condition. Local models are loaded on their edges by the deformations from the global model, whereby the global forces load this structural detail. In addition, local loads are also taken into consideration, such as the load on lifeboat davits. In the local model, detailed structural shapes can be more precisely defined, as well as e.g. plate strengths and local reinforcements.

Fatigue detail of a manhole edge.

A structure’s fatigue durability cannot be accurately defined in a global model, but in a local model, the fatigue durability of even a weld joint can be improved, if and when needed.

Several structural details can be analysed to ensure, for example, that plate thickness is the absolute mini-mum. However, even with FE analyses, one has to follow classification society rules for minimum plate and stiffener thickness. Structures can also be modified relatively quickly or analysed again to allow different alter-natives to be evaluated easily and reliably.

CFD used in a full scale self-propulsion test for propeller/hull interaction on a container ship.

Importance of comfort factor

Comfort factors are particularly important in cruise ships. Comfort has to be taken into consideration in many different areas, but with regards structures, the vibration level is a key aspect. The same element model used to analyse structural stress, can be employed to analyse vibration.

One can also study how vibrations spread through structures and try to reduce the resultant harmful impact by making structural changes. Vibration also causes noise, so vibration dampening can increase comfort levels greatly. Nowadays, attention is also increasingly paid to the noise transferred into water and the marine environment. The harmful noise transfer to water can be reduced by decreasing vibration and, for example, by insulating motor noise.

An example of a CFD simulation for a full scale wind tunnel test on a cruise ship to detect the comfort level in the superstructures and outer decks. 

IMPROVING PROCESSes

Structures can also be optimised with the help of technical analysis software. Once a mathematical model of a ship structure has been created, optimisation algorithms can be used to, for instance, maximise durability and minimise the vessel’s mass. This can result in significant construction savings. When this is coupled with the afore-mentioned ship hull and propulsion optimisation, one can see that large savings and reductions in pollution can be achieved over the life cycle of the vessel.

The finite element method is equally adept at analysing welding processes. The model can be used to analyse the effect that the heat generated by welding has on shape deformation and residual stress. The welding sequence can also be optimised to minimise shape deformations. This speeds up installation work at shipyards as parts do not need to be fitted, nor are harmful gaps formed between plate edges. This obviously requires very powerful computers to ensure that analysis times remain within reasonable boundaries.

SHIP SYSTEMS

A ship’s hull is naturally important in respect of durability, but finite element analysis can be used to study many other ship systems. It is, for example, used commonly in the dimensioning of ship engines. Power transmission dimensioning is another area where the finite element method is employed, be it for traditional shaft drive propulsion, or diesel-electric propulsion, where azimuthing propellers are used. See Figure below.

There are also many amusement park devices on cruise ships that can be beneficially dimensioned with the finite element method. The loads such devices will be exposed to, can also be analysed with dynamic simulations to get a significantly more accurate picture of the forces acting on the devices and the underlying ship structure. This also leads to more precise fatigue dimensioning.

An example of a traditional motor-gear-shaft type power transmission model used to calculate torsional vibration. 

SUMMARY

Growing computational performance and the developments in technical analysis software allow the modelling and analysis of entire ships. The finite element method is used widely in ship dimensioning. A good example of its application is the design of the Global Class cruise ship for MW Werften, where finite element analysis has been used by Elomatic to analyse several parts of the ship structure.

Based on the analyses, for example, structures have been modified and plate thickness defined. For other vessels, we have analysed transmission line durability under ice loads, conducted different vibration analyses and studied the effect of structural deformation on ship durability.

These analyses allow the optimisation of structures, the reduction of construction costs, enhanced safety and passenger comfort, as well as the reduction of harmful air and noise pollution into marine environments.