Finite
element method is a method of solving a problem by dividing the problem in to
small problems by dividing or breaking up the geometric model into small pieces
that are easier to analyze called discretization. In the case of the cylinder
it might be broken up into small cubes or plates called elements. All of the
elements make up the mesh. Each of these elements can be easily solved for by
using simple equations for stress and strain. As the number of elements
increases (increasing mesh size), their size decreases and the solution will
grow more accurate.

An excellent
comparison to finite element analysis is the solution for area under the curve.
If one is trying to find the area under the curve, breaking the curve up into a
series of rectangles and adding their areas can approximate the solution. The
no of rectangular divisions increase the accuracy.

With the
recent increases in the speed and processing power of computers, finite element
analysis has become a practical way to solve many problems. The increase in
computer capabilities has allowed for even greater numbers of elements and
higher order elements to be used so that calculated solutions will be fairly
accurate.

Unfortunately,
due to incorrect meshing and constraining, the structure does not simulate the
actual structure being analyzed. Depending on the subject being modelled the
method used can become extremely important.

One
application of finite element analysis is for pressure vessels. The pressure
vessels may be different types. Domestic gas cylinder is one made in two half
and welded at centre. Other types are cylinders with separate cap at ends.

There are several ways to model pressure vessels
using finite element analysis. If modelled correctly these methods should
result in the same solution, but the time spent in calculating solutions can be
different. If the finite element analysis solution has an error of five percent
and takes an hour to run, that solution may be considered acceptable when
compared to a solution with a one percent error that takes twenty hours to run
depending on the particular use of the structure and factor of safety. So
element selection, approach and size of elements used are much critical during
analysis.