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.