Synonyms
Definition
A numerical method used to approximate the solution of boundary- and initial-value problems characterized by partial differential equations.
Theory
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.
A 2D problem...
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References
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, 565–569
Argyris JH (1954) Energy theorems and structural analysis: a generalized discourse with applications on energy principles of structural analysis including the effects of temperature and non-linear stress–strain relations part I. Aircr Eng Aerosp Technol 26(10):347–356
Childs THC, Maekawa K, Obikawa T, Yamane Y (2000) Metal machining: theory and applications. Arnold, London
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, Pittsburgh
Courant R (1942) Variational methods for the solution of problems of equilibrium and vibrations. Bull Amer Math Soc 49:1–23
De Hoff PH, Anusavice KJ, Wang Z (1995) Three-dimensional finite element analysis of the shear bond test. Dent Mater 11(2):126–131
Lee CH, Kobayashi S (1973) New solution to rigid-plastic deformation problems using matrix methods. Trans ASME J Eng Ind 95(3):865–873
Lewis RW, Ravindran K (2000) Finite element simulation of metal casting. Int J Numer Methods Eng 47(1–3):29–59 (Special Issue: Richard H. Gallagher Memorial Issue)
Lindgren L-E (2001) Finite element modeling and simulation of welding. Part I: increased complexity. J Therm Stress 24(2):141–192
Luttge R (2011) Microfabrication for industrial applications. William Andrew, Oxford
McMeeking RM, Rice JR (1975) Finite-element formulations for problems of large elastic–plastic deformation. Int J Solids Struct 10:601–616
Nagtegaal JC (1982) On the implementation of inelastic constitutive equations with special reference to large deformation problems. Comp Meth Appl Mech Eng 33(1–3):469–484
Oden JT (1971) Finite elements of nonlinear continua. McGraw-Hill, New York
Oden JT, Reddy JN (1976) An introduction to the mathematical theory of finite elements. Wiley, New York
Okman O, Özmen M, Huwiler H, Tekkaya AE (2006) Free forming of locally heated specimens. Int J Mach Tool Manu 47(7–8):1197–1205
Şimşir C, Gür CH (2010) Simulation of quenching process for prediction of temperature, microstructure and residual stresses. J Mech Eng 56(2):93–103
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 53–66
Tekkaya AE (1998b) Status and developments in the simulation of forming processes. WIRE 48(1):31–36
Turner MJ, Clough RW, Martin HC, Topp LJ (1956) Stiffness and deflection analysis of complex structures. J Aeronaut Sci 23(9):805–823
Wagoner RH, Chenot J-L (1997) Fundamentals of metal forming. Wiley, New York
Wang N-M, Budiansky B (1978) Analysis of sheet metal stamping by a finite-element method. Trans ASME J Appl Mech 45:73–82
Zienkiewicz OC, Cheung YK (1965) The finite element method in continuum and structural mechanics. McGraw-Hill, New York
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Tekkaya, A.E., Soyarslan, C. (2014). Finite Element Method. In: Laperrière, L., Reinhart, G. (eds) CIRP Encyclopedia of Production Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20617-7_16699
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DOI: https://doi.org/10.1007/978-3-642-20617-7_16699
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