REVIEW OF FINITE ELEMENT ANALYSIS & EVOLUTION OF FINITE ELEMENT ANALYSIS

REVIEW OF FINITE ELEMENT ANALYSIS

INTRODUCTION

In the analysis and design field the finite element method (FEM) has become a powerful tool for the solution of complicated engineering problems, as the  existing mathematical tool will not be sufficient to fine even an approximate solution for some practical problems, it necessitates to for alternate method FEM.

The basic idea in the FEM is to find the solution of complicated problem by replacing it by a simper one and then analyzing the simper one to find an approximate solution for the required problem.

EVOLUTION OF FINITE ELEMENT ANALYSIS

An analytical solution mathematical expression that gives the values of the desired unknown quantity at any locations of a body, and as consequence it is valid  for an infinite number of locations in the body. It is not possible to obtain analytical mathematical solution for many engineering problems. Analytical solutions can be obtained only for certain simplified situations.

Therefore for problem involving complex material properties and boundary conditions, the engineer resorts to numerical methods that provides approximate but acceptable solution. In most of the numerical methods the solutions yield approximate values of the unknown quantities only at discrete number of points in the body. In these methods, instead of solving the problem for the entire body, the solutions are formulated for each smaller unit, which are obtained  by dividing the entire body. For a large number of these subdivision it is formidable task to handle the date manual, and recourse must be made to automatic electronic computation.

In contrast to the all other numerical techniques, the finite element method essentially a product of the electronic digital computer ages. This method possesses certain characteristics  that take advantage of the special facilities offered by the high speed computers. In particular, the method can be systematically programmed to accommodate such complex, and difficult problems as non-homogeneous materials, non linear stress strain behavior, and complicated boundary conditions. It is difficult to accommodate these complexities in the other methods. Another favorable aspect of the FEM is the variety of levels at which may develop and understanding of the technique.

One may take a very physical or intuitive approach to the learning and Using of the method. On the other hand, one may develop a rigorous mathematical interpretation of the method. The fem as know today was first suggested in a technical paper published in 1956.

 

Historical Background

 

Ancient mathematicians found the circumferences (s) of the circle by approximating  as a polygon inscribed i.e., lower bonds  S (L) or circumscribed each side of the polygon can be called a finite to the true values. This also holds well in any finite elements application.

In 1943 an approach similar to the FEM, involving the use of use continuous functions defined over triangular regions was first suggested by. COURANT.

In 1956 TURNER, CLOUGH, MATRIN & TOPP today have a presented the FEM as known. This paper presents the applications of simple finite elements for analysis of aircraft structure and is considered as one of the key contribution in the development of FEM.

In the early 1960’s engineers used the method for approximate solution of problems in stress analysis, fluid flow, heat transfer etc. the first book on finite element by ZIENKIEWICZ and CHUNG was published in 1967. In the early 1970’s finite element analysis was applied to non-liner problems and large deformation.