INTRODUCTION OF FINITE ELEMENT METHOD

INTRODUCTION OF FINITE ELEMENT METHOD (FEM / FEA)

1) The FEM is a numerical procedure for solving Boundary Value Problems (BVP’s) and structural & solid mechanics problems in engineering.

2) The method had its birth in the aerospace industry in the early 1950s and then with applications to structural and solid mechanics.

In 1963 it was shown that the FEM was a variation of Raleigh-Ritz Method (which produces a set of linear equations by minimizing the potential energy of the system). This lead to its application in different areas of heat transfer, fluid flow, etc.

In 1969 it was shown that element equations could also be derived using a weighted residual procedure such as Galerkin’s Method or the least squares approach. This allows application to any BVP and therefore enlarged its use and application.

3) Fundamental Concept of FEM

Any continuous quantity, such as temperature, pressure, or displacement, can be approximated by a discrete model composed of a set of piecewise continuous functions (polynominals) defined over a finite number of subdomains or elements.

Discretization:

It means dividing an object into an equivalent system of many smaller bodies or units (finite elements) interconnected at points common to two or more elements (nodes or nodal points) and/or boundary lines and/or surfaces.

FEA Applications:
1) Mechanical/Aerospace/Civil/Automotive Engineering.
2) Structural/Stress Analysis.
3) Static/Dynamic.
4) Linear/Nonlinear.
5) Fluid Flow.
6) Heat Transfer.
7) Electromagnetic Fields.
8) Soil Mechanics.
9) Acoustics.
10) Biomechanics.