# CIRP Encyclopedia of Production Engineering

2019 Edition
| Editors: Sami Chatti, Luc Laperrière, Gunther Reinhart, Tullio Tolio

# Finite Element Analysis

Reference work entry
DOI: https://doi.org/10.1007/978-3-662-53120-4_16824

## Definition

Finite Element Analysis (FEA) is based on the Finite Element Method (FEM). The FEM is a mathematical method which transforms an analytically difficult to solve or unsolvable problem described by a variational formulation or by a system of differential equations into an algebraic problem. The under consideration overall system structure is replaced by a calculation model that divides the structure into a number of small subdivisions (finite elements). If the mechanical problem is described by a differential equation, the equation must be transformed into a variational formulation. The unknown and the variational function are then approximated by a simple interpolation polynomial. By determining that the coefficients of the variational function can take every possible value, an algebraic system of equations is obtained, with which the coefficients of the interpolation function for the unknown can be...
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## References

1. Altan T, Tekkaya AE (eds) (2012) Sheet metal forming: fundamentals. ASM International, Materials ParkGoogle Scholar
2. Cawthorn C, Loukaides EG, Allwood JM (2014) Comparison of analytical models for sheet rolling. In: Proceedings of the 11th international conference on technology of plasticity, ICTP 2014, 19–24 Oct 2014. Procedia engineering 12/2014, vol 81, pp 2451–2456Google Scholar
3. Doege E, Behrens B-A (2010) Handbuch Umformtechnik: Grundlagen, Technologien, Maschinen [Metal forming handbook: fundamentals, technologies, machines], 2nd edn. Springer, Berlin/Heidelberg. (in German)Google Scholar
4. Mori K, Akita K, Abe Y (2007) Springback behaviour in bending of ultra-high-strength steel sheets using CNC servo press. Int J Mach Tools Manuf 47(2):321–325
5. Zienkiewicz OC, Taylor RL, Zhu JZ (2005) The finite element method. Its basis and fundamentals, 6th edn. Oxford, Elsevier Butterworth-Heinemann 