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

W.K. Liu, S. Li and H.S. Park
Accepted for publication in Archives of Computational Methods in Engineering 2022

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.

This paper is available at Arxiv .


Moving Particle Finite Element Method

S. Hao, H.S. Park and W.K. Liu
International Journal for Numerical Methods in Engineering 2003; 53:1937-1958

Abstract

This paper presents the fundamental concepts behind the moving particle finite element method (MPFEM), which combines salient features of finite element and meshfree methods. The proposed method alleviates certain problems that plague meshfree techniques, such as essential boundary condition enforcement and the use of a separate background mesh to integrate the weak form. The method is illustrated via two-dimensional linear elastic problems. Numerical examples are provided to show the capability of the method in benchmark problems.

This paper is available in PDF form .