Informations générales
ECTSECTS
2
Goal(s)
Obtain a discretized then matrix version of a problem with initial and boundary conditions using a finite element method
Present hand-solved examples
Content(s)
CHAPTER 1
- Fundamental concepts using a 1-D example
- Weak and strong formulations
- Galerkin approximation, shape functions
- Matrix formulation
- Piecewise linear discretization
- Properties of the stiffness matrix
Problems :
- column submitted to a lineic density of forces parallel to its axis
- system of bars in a plane, truss
- beams in flexion : cubic Hermite polynomial
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CHAPTER 2
- thermal conduction
- Fourier law for conduction
- strong and weak formulation, Galerkin approximation, matrix formulation
- concept of node numbering in 2D and 3D
Problems :
- heat transfer with convection
- diffusion of a liquid through a dam
CHAPTER 3
- linear elastostatic
- strong and weak formulations, Galerkin approximation, matrix form
- 3D elastic constitutive law : plane deformation, plane stress, Voigt convention
- numbering of unknowns in 2D and 3D
Problems :
- dam under its own weight
- symmetry conditions
- elastic bases and imperfect supports
CHAPTER 4
- Finite element technology
- Sufficient conditions for the shape functions : regularity, continuity, completeness
- 4-node quadrilateral element Q4
- trilinear hexaedral element B8
- Lagrange polynomials and Serendip elements
- Gauss-Legendre quadrature
Prérequisites :
mechanics of continuous media, elasticity, resistance of materials
Test
final exam (2h)
Calendar
S1
Additional Information
28 h (12 h CM + 14 h TD + 2 h DS)
Bibliography
- The finite element method, T. JR. Hughes, Prentice Hall, 1987
- Finite element methods in mechanics, N. Kikuchi, Cambridge, 1986
- Finite element procedures in engineering analyses, K.J. Bathe, Prentice Hall, 1982
- The finite element method, O.C. Zienkiewicz, Mc Graw Hill, 1977
French State controlled diploma conferring a Master's degree
