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

This paper commemorates the eightieth anniversary of the finite element method (FEM), highlighting its evolution, revolutionary impact, and future potential across various engineering applications and scientific modeling. The objective is to provide a historical perspective on FEM, outlining its developments, applications, and the emergence of computational mechanics as a key discipline. The methodology employed involves a comprehensive analysis of the chronological advancements in FEM categorized into four distinct time periods: the early years (1941-1965), the golden age (1966-1991), the era of large-scale industrial applications (1992-2017), and the current state-of-the-art technology and future directions post-2018. Results indicate that FEM has fundamentally transformed scientific modeling and engineering design, influencing fields as diverse as material mechanics, fluid dynamics, and biological processes. The paper also acknowledges that the progression of FEM was not strictly linear, with significant interconnections across different time periods. Overall, this research highlights the substantial contributions of FEM to engineering and science, whilst suggesting areas for future exploration and development.