History of Finite Element Method: A Review

Abstract

Finite element method (FEM) is a numerical technique to obtain an approximate solution for problems involving elliptical partial differential equation by dividing the domain into n no of parts of smaller size and applying the boundary conditions to them. In more advance way, it is the analysis of any structure by dividing the whole body into number of small elements and applying the constraints and loads on them and finding the unknowns as per our analysis and the whole analysis are done by the software itself. Initially, the FEM concept was used for solving mathematical formulations in easier way but the development of the FEM concepts and various FEM software, like NASTRAN, ANSYS, etc., made its applications to reach into fields of statistical analysis of structures, linear and non-linear analysis, heat transfer problems and also in bio engineering, nuclear engineering, metallurgical and much more, and this is possible due to the advance types of element in the FEM software. So in the research, the origin and the history of FEM is been studied and the contribution of various researchers has been shown which gives a very clear development idea of FEM and applications of FEM in daily engineering applications from past date till today. The idea of discretization is very old, the mathematical papers on FEA by Schelbach and Courant show the same approach. Earlier, before 1922, also Courant used the finite element ideas in Dirchlet’s principle. The FEM we use today involves the contribution of many researchers, namely Turner, Clough, Martin and Topp, Argyris, Bubuska, Aziz, Irons, Melosh and many more, like M. J. Turner at being perfected the direct stiffness method, clough coined the term ‘Finite Elements’, contribution of B. M. Irons towards FEA was the introduction of shape functions, patch test, text books by Huges and Bathe, Zienkiewicz laid the foundation for further advancement of FEM, and thus the period of 1962–1972 is known as the golden age of FEM and so on.