Finite Element Analysis of Ship Structures

 

Finite Element Method(FEM) is a mathematical technique used to solve complex problems in engineering and physical sciences. In this method the complex problem domain is discretized into a finite number of  relatively simple problem domains and the solution to these so called simple problems are then use to obtain a solution to the original complex problem. The finite element method changes the continuous problem into an approximated discrete version of the problem.

In Finite Element Analysis of structures the problem domain is the given structure of a particular material with loads at given locations on the structure. We try to obtain the deformation of the structure under the given loading condition. In order to do that, we divide the structure into a number of smaller units called 'finite elements' , find out what loads are acting on the individual finite elements from the given load distribution. From the loading condition and geometry of the finite elements we can evaluate the stresses arising in the individual finite elements for eg. Direct Stress, Shear Stress etc and then we use these stresses to obtain the value of strains in the individual finite elements. Thus we can obtain how a structure will deform under a given load. 

Computer programs are used to implement this technique on ship structures since large number of repetitions of same steps are involved. Let us see how this is done.

To apply FEA on ship structures, we require the following:

1. Structure description

2. Material description

3. Load Description

Structure Description 

In this we require the hull geometry and every structural detail. In case of ships that would mean lines plan, position of bulkheads arrangement of stiffeners transverses as well as longitudinals, bottom tanks and wing tanks if any.

Material Description

We will require the Material properties out of which our structure is made to obtain an expression for the response of the structure under given loading conditions. 

Load Description

The loads that act on Ships in general can be broadly classified into two types.

1. Static Loads

2. Dynamic Loads

Static Loads are the loads that do not vary with time and are roughly constant for a given structure.

These would be: 

i. Still Water Load (Buoyancy)

ii. Cargo Load

iii. Lightweight or Self Weight

Dynamic Loads are time varying loads that are highly probabilistic in nature which are:

i. Wave Load

ii. Impact Load

With the help of load description we obtain loadcases which are combined to obtain loadsets and applied on the structure.

The Ship is modeled into finite elements using a finite element modeler or Pre-Processor as we call it in some well known programs such as ANSYS , NASTRAN etc. Certain rules are followed in modelling the structure the description of which would be beyond the scope of this article. 

The ships structure is then divided into smaller blocks to reduce the running time of the Computer Program. These smaller blocks are more correctly described as "three-hold models" assuming our ship is composed of holds divided by bulkheads. Then certain boundary conditions are imposed on the model depending on the loads acting and/or type of analysis for eg: longitudinal strength, transverse strength etc.Load cases are applied on the model to obtain the values of stresses arising in the finite elements and strains are used to model the deformation in the structure.