Review of Classical FEM Formulations and Discretizations
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.
- 1.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.Zienkiewicz OC, Taylor RL (2005) The finite element method for solid and structural mechanics. Butterworth-Heinemann, AmsterdamGoogle Scholar
- 4.Hughes TJR (2012) The finite element method: linear static and dynamic finite element analysis. Courier Corporation, North ChelmsfordGoogle Scholar
- 5.Belytschko T, Liu WK, Moran B, Elkhodary K (2013) Nonlinear finite elements for continua and structures. Wiley, New YorkGoogle Scholar
- 6.Crisfield MA, Remmers JJC, Verhoosel CC (2012) Nonlinear finite element analysis of solids and structures. Wiley, New YorkGoogle Scholar