Finite element analysis.......

not only in finite element analysis, but almost modern engineering and theory solution will need this matrix tool.

at first you have to solve equation group at many situation, the matrix is a wonderful solution tool. using it, you can easily get the solution.

of cause , if you insist to use primary method, you can also solve the equaiton.

none so foolish to face with practice problem

In the general way FEA is the same thing that you have to calculate a regular beam(it is an general example) with its supports and forces, it just cuts the beam in little pieces, and calcule it for each piece(finite element), obviusly, you use FEA to calculate a irregular geometry but it is the same pattern.

When you cut it. You must to remind than you only have a exact answer for the point where you cut (nodes). in the other infinite numbers of points, between the "cuts", you only have an aproxxx... according to a funtion, (linear, parabolic, etc, you choose) As well as, you can see, here start to game the accurance and other stuff, but now if you need 3 exact displacement in the beam, then you need to cut it in 3 pieces,so you have 4 nodes you have 2 posibble movents in each one, so you have 8 equations, and it is only for a beam you cut it in 3, if you have a bigger body and it can move in 6 ways.

Well Matrix is the easier way to solve problems with 10000 equations, and of course, program a computer to do it, if you solve it with other methods probably you need more operations on your program to solve it. An differencial calculus have the same role that in the normal calculus, and in FEA it play with the accurrance of the results too.

The primary reason a Matrix is used is because a computer can solve a matrix very effiecently and it's relative easy to get the information into that format.

sir, could u give me a practical casesyudy (step by step solution for particular problem) on Finite element analysis.

Another reason for using a finite element method is that the elements are interrelated

, each element is affected by its neighbours, The results must therefore be iterated until all equations are in balance.

A ring main reticulation pipeline is a good example.

One of my first assignments of computing finite elements was for a conical floor for a sewage care works. There were no programs to buy at that stage.