Finite element method
History

While it is difficult to quote the date of the invention of the finite element method, the method originated from the need to solve complex elasticity and structural analysis problems in civil and aeronautical engineering. Its development can be traced back to work by Alexander Hrennikoff and Richard Courant in the early 1940s. Another pioneer was Ioannis Argyris. In the USSR, the introduction of the practical application of the method is usually connected with the name of Leonard Oganesyan. It was also independently rediscovered in China by Feng Kang in the later 1950s and early 1960s, based on the computations of dam constructions, where it was called the finite difference method based on variation principle. Although the approaches used by these pioneers are different, they share one essential characteristic: mesh discretization of a continuous domain into a set of discrete sub-domains, usually called elements.

Hrennikoff's work discretizes the domain by using a lattice analogy, while Courant's approach divides the domain into finite triangular subregions to solve second order elliptic partial differential equations that arise from the problem of torsion of a cylinder. Courant's contribution was evolutionary, drawing on a large body of earlier results for PDEs developed by Lord Rayleigh, Walther Ritz, and Boris Galerkin.

The finite element method obtained its real impetus in the 1960s and 1970s by the developments of J. H. Argyris with co-workers at the University of Stuttgart, R. W. Clough with co-workers at UC Berkeley, O. C. Zienkiewicz with co-workers Ernest Hinton, Bruce Irons and others at Swansea University, Philippe G. Ciarlet at the University of Paris 6 and Richard Gallagher with co-workers at Cornell University. Further impetus was provided in these years by available open-source finite element programs. NASA sponsored the original version of NASTRAN. UC Berkeley made the finite element programs SAP IV and later OpenSees widely available. In Norway, the ship classification society Det Norske Veritas (now DNV GL) developed Sesam in 1969 for use in the analysis of ships. A rigorous mathematical basis to the finite element method was provided in 1973 with the publication by Gilbert Strang and George Fix. The method has since been generalized for the numerical modeling of physical systems in a wide variety of engineering disciplines, e.g., electromagnetism, heat transfer, and fluid dynamics.
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