Finite Element Method
Reference work entry
A numerical method used to approximate the solution of boundary- and initial-value problems characterized by partial differential equations.
The finite element method is a systematic procedure of approximating continuous functions as discrete models. This discretization involves finite number of points and subdomains in the problem’s domain. The values of the given function are held at the points, so-called nodes. The non-overlapping subdomains, so-called finite elements, are connected together at nodes on their boundaries and hold piecewise and local approximations of the function, which are uniquely defined in terms of values held at their nodes. The collection of discretized elements and nodes is called the mesh and the process of its construction is called meshing. A typical finite element partition of a two-dimensional domain with triangular finite elements is given in Fig. 1.
- Agwai A, Güven I, Madenci E (2009) Damage prediction for electronic package drop test using finite element method and peridynamic theory. In: Electronic components and technology conference, 2009. ECTC 2009. 59th, 565–569Google Scholar
- Childs THC, Maekawa K, Obikawa T, Yamane Y (2000) Metal machining: theory and applications. Arnold, LondonGoogle Scholar
- Clough RW (1960) The finite element method in plane stress analysis. In: Proceedings of ASCE 2nd conference on electronic computation, Conference papers American Society of Civil Engineers 2nd conference on electronic computation, 8–9 Sept 1960, PittsburghGoogle Scholar
- Luttge R (2011) Microfabrication for industrial applications. William Andrew, OxfordGoogle Scholar
- Okman O, Özmen M, Huwiler H, Tekkaya AE (2006) Free forming of locally heated specimens. Int J Mach Tool Manu 47(7–8):1197–1205Google Scholar
- Şimşir C, Gür CH (2010) Simulation of quenching process for prediction of temperature, microstructure and residual stresses. J Mech Eng 56(2):93–103Google Scholar
- Tekkaya AE (1998a) State-of-the-art of simulation in metal forming. In: 6th SheMet conference, University of Twente, Enschede/The Netherlands, 6–8 Apr 1998, vol I, pp 53–66Google Scholar
- Tekkaya AE (1998b) Status and developments in the simulation of forming processes. WIRE 48(1):31–36Google Scholar
- Wagoner RH, Chenot J-L (1997) Fundamentals of metal forming. Wiley, New YorkGoogle Scholar
© CIRP 2014