FINITE ELEMENT METHOD

Although the foundations of the finite element method (FEM) date back to earlier times in the field of mathematics, it was first utilised in the field of engineering in the 1950s in order to realise stress analyses of complex structures in the aircraft and space industry.

The term “finite element” was first introduced by Clough in a study titled “Finite Elements Method (FEM) in Plane Stress Analysis” published in 1960 (Clough 1960, Barkanov 2001, Rao 2004, Chandrupatla and Belegundu 2011) .

As a result of the studies on the principles of the method and its applicability to the problems in different disciplines, it is employed today in the solution of almost all engineering problems (such as structural, heat transfer, electromagnetic, fluid dynamics, etc.).

With the ever-evolving technology, the power of computers and new generation software platforms has made this method widespread. Today, engineering analyses performed with FEM are also called Finite Elements Analysis (FEA).

An object/structure considered in FEA is tried to be described by taking its behaviour into predefined finite size elements. This is where the name of the method comes from. The logic of FEM can be demonstrated with the simplest approach in the area calculation of a circle shown in the figure below.

Here, the area of the circle can be approximated by dividing it into triangular elements. Increasing the number of elements gives a more approximate result to the real area of the circle (Liu 1998).

CLOUGH, R., W. 1960. Finite Element Method in Plane Stress Analysis. Proceedings American Society of Civil Engineers (2nd Conference on Electronic Compitation). Pitsburg, Pennsylvania, 23: 345-378.

BARKANOV, E. 2001. Introduction to Finite Element Method. Lecture Notes. Inst. of Materials and Structures, Fac. of Civil Engineering. Riga Technical University. Riga, Latvia, 70 p. Online: http://mmc.geofisica.unam.mx/Bibliografia/Matematicas/EDP/MetodosNumericos/IntroductionToTheFiniteElementMathod.pdf.

RAO, S., S. 2004. The Finite element Method in Engineering. 4th Ed. ,Elsevier Inc. ISBN: 0750678283, 663 p.

CHANDRUPATLA, T., R. and BELEGUNDU, A., D. 2011. Introduction to Finite Elements in Engineering. 4th Ed. Prentice Hall Publication, ISBN:0132162741, 448 p.

LIU, Y. 1998. Introduction to Finite Element Method. Lecture Notes, Dept. of Mechanical Engineering, University of Cincinnati, 178 p.