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Review of Classical FEM Formulations and Discretizations

  • Julien YvonnetEmail author
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 258)

Abstract

The objective of this first chapter is to recall the basics of Finite Elements for simple problems, here, the steady-state and linear elasticity problems, in order to use it as a solver for the localization problems required in computational homogenization in the next chapters. We do not intend to provide a complete framework on FEM here, but present a short introduction and practical aspects which can be used to directly implement a FEM program. For more in-depth about FEM formulations, we refer to classical books on Finite Elements such as [1, 2, 3, 4] for linear problems and [5, 6] for nonlinear problems.

References

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    Akin JE (2005) Finite element analysis with error estimators: an introduction to the FEM and adaptive error analysis for engineering students. Butterworth-Heinemann, AmsterdamGoogle Scholar
  2. 2.
    Zienkiewicz OC, Taylor RL (2005) The finite element method for solid and structural mechanics. Butterworth-Heinemann, AmsterdamGoogle Scholar
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    Fish J, Belytschko T (2007) A first course in finite elements. Wiley, New YorkCrossRefGoogle Scholar
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    Hughes TJR (2012) The finite element method: linear static and dynamic finite element analysis. Courier Corporation, North ChelmsfordGoogle Scholar
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    Belytschko T, Liu WK, Moran B, Elkhodary K (2013) Nonlinear finite elements for continua and structures. Wiley, New YorkGoogle Scholar
  6. 6.
    Crisfield MA, Remmers JJC, Verhoosel CC (2012) Nonlinear finite element analysis of solids and structures. Wiley, New YorkGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.MSME LaboratoryUniversité Paris-Est Marne-la-ValléeMarne-la-Vallée Cedex2France

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