Eighty Years of the Finite Element Method: Birth, Evolution, and Future

Wing Kam Liu, Shaofan Li*, Harold S. Park

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

105 Scopus citations

Abstract

This document presents comprehensive historical accounts on the developments of finite element methods (FEM) since 1941, with a specific emphasis on developments related to solid mechanics. We present a historical overview beginning with the theoretical formulations and origins of the FEM, while discussing important developments that have enabled the FEM to become the numerical method of choice for so many problems rooted in solid mechanics.

Original languageEnglish (US)
Pages (from-to)4431-4453
Number of pages23
JournalArchives of Computational Methods in Engineering
Volume29
Issue number6
DOIs
StatePublished - Oct 2022

Funding

The authors would like to acknowledge the sources of some historic facts cited in this paper, which are taken from the following finite element history articles and books: (1) Oden, J.T. (1990). Historical comments on finite elements. In A history of scientific computing , 152–166. (2) Lax, P. (1993). Feng Kang. SIAM News , 26 (11). (3) Clough, R.W., and Wilson, E.L. (1999), August. Early finite element research at Berkeley. In Fifth US National Conference on Computational Mechanics , 1–35. (4) Felippa, C.A. (2004). Introduction to finite element methods. University of Colorado , 885.(5) Owen, D.R.J. and Feng, Y.T. (2012). Fifty years of finite elements—a solid mechanics perspective. Theoretical and Applied Mechanics Letters , 2 (5), p.051001. (6) Stein, E. (2014). History of the finite element method–mathematics meets mechanics–part I: Engineering developments. In The History of Theoretical, Material and Computational Mechanics-Mathematics Meets Mechanics and Engineering (pp. 399–442). Springer, Berlin, Heidelberg. (7) Clough, R.W. (1980). The finite element method after twenty-five years: a personal view. Computers & Structures , 12 (4), 361–370. (8) Wikipedia: Finite Element Method, https://en.wikipedia.org/wiki/Finite_element_method.

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics

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