INTRODUCTION TO THE FINITE ELEMENT METHOD G.P.NIKISHKOV
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INTRODUCTION TO THE FINITE ELEMENT METHOD G.P.NIKISHKOV
je ne sais pas si l'on a déjà posté ce document mais il est très intéressant:
INTRODUCTION TO THE FINITE ELEMENT METHOD G.P.NIKISHKOV
1Introduction
1.1 What is the finite element method
1.2 How the FEM works
1.3 Formulation of finite element equations
1.3.1 Galerkin method
1.3.2 Variational formulation
2 Finite Element Equations for Heat Transfer
2.1 Problem Statement
2.2 Finite element discretization of heat transfer equations
2.3 Different Type Problems
3 FEM for Solid Mechanics Problems
3.1 Problem statement
3.2 Finite element equations
3.3 Assembly of the global equation system
4 Finite Elements
4.1 Two-dimensional triangular element
4.2 Two-dimensional isoparametric elements
4.2.1 Shape functions
4.2.2 Strain-displacement matrix
4.2.3 Element properties
4.2.4 Integration in quadrilateral elements
4.2.5 Calculation of strains and stresses
4.3 Three-dimensional isoparametric elements
4.3.1 Shape functions
4.3.2 Strain-displacement matrix
4.3.3 Element properties
4.3.4 Efficient computation of the stiffness matrix
4.3.5 Integration of the stiffness matrix
4.3.6 Calculation of strains and stresses
4.3.7 Extrapolation of strains and stresses
5 Discretization
5.1 Discrete model of the problem
5.2 Mesh generation
5.2.1 Mesh generators
5.2.2 Mapping technique
5.2.3 Delaunay triangulation
6 Assembly and Solution
6.1 Disassembly and assembly
6.2 Disassembly algorithm
6.3 Assembly
6.3.1 Assembly algorithm for vectors
6.3.2 Assembly algorithm for matrices
6.4 Displacement boundary conditions
6.4.1 Explicit specification of displacement BC
6.4.2 Method of large number
6.5 Solution of Finite Element Equations
6.5.1 Solution methods
6.5.2 Direct LDU method with profile matrix
6.5.3 Preconditioned conjugate gradient method
7 Nonlinear Problems
7.1 Physical and geometrical nonlinearity
7.2 Constitutive relations for elastic-plastic material
7.3 Computing finite stress increments
7.3.1 Determining elastic fraction of stress increment
7.3.2 Subincrementation for computing stress increment
7.3.3 Midpoint integration of constitutive relations
7.4 Nonlinear solution procedure
7.4.1 Newton-Raphson method
7.4.2 Initial stress method
7.4.3 Convergence criteria
8 Visualization
8.1 Introduction
8.2 Overview of algorithm
8.3 Geometry and results data
8.3.1 Geometry relations for 20-node element
8.3.2 Surface of the finite element model
8.3.3 Continuous field of secondary results
8.4 Subdivision of quadratic surfaces
8.4.1 Curvature-based subdivision
8.4.2 Results-based subdivision
8.4.3 Delaunay triangulation
8.5 Using Java3D API for visualization
voici le lien de ce document:
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on peut visiter ce lien:
http://www.u-aizu.ac.jp/~niki/feminstr/feminstr.html
INTRODUCTION TO THE FINITE ELEMENT METHOD G.P.NIKISHKOV
1Introduction
1.1 What is the finite element method
1.2 How the FEM works
1.3 Formulation of finite element equations
1.3.1 Galerkin method
1.3.2 Variational formulation
2 Finite Element Equations for Heat Transfer
2.1 Problem Statement
2.2 Finite element discretization of heat transfer equations
2.3 Different Type Problems
3 FEM for Solid Mechanics Problems
3.1 Problem statement
3.2 Finite element equations
3.3 Assembly of the global equation system
4 Finite Elements
4.1 Two-dimensional triangular element
4.2 Two-dimensional isoparametric elements
4.2.1 Shape functions
4.2.2 Strain-displacement matrix
4.2.3 Element properties
4.2.4 Integration in quadrilateral elements
4.2.5 Calculation of strains and stresses
4.3 Three-dimensional isoparametric elements
4.3.1 Shape functions
4.3.2 Strain-displacement matrix
4.3.3 Element properties
4.3.4 Efficient computation of the stiffness matrix
4.3.5 Integration of the stiffness matrix
4.3.6 Calculation of strains and stresses
4.3.7 Extrapolation of strains and stresses
5 Discretization
5.1 Discrete model of the problem
5.2 Mesh generation
5.2.1 Mesh generators
5.2.2 Mapping technique
5.2.3 Delaunay triangulation
6 Assembly and Solution
6.1 Disassembly and assembly
6.2 Disassembly algorithm
6.3 Assembly
6.3.1 Assembly algorithm for vectors
6.3.2 Assembly algorithm for matrices
6.4 Displacement boundary conditions
6.4.1 Explicit specification of displacement BC
6.4.2 Method of large number
6.5 Solution of Finite Element Equations
6.5.1 Solution methods
6.5.2 Direct LDU method with profile matrix
6.5.3 Preconditioned conjugate gradient method
7 Nonlinear Problems
7.1 Physical and geometrical nonlinearity
7.2 Constitutive relations for elastic-plastic material
7.3 Computing finite stress increments
7.3.1 Determining elastic fraction of stress increment
7.3.2 Subincrementation for computing stress increment
7.3.3 Midpoint integration of constitutive relations
7.4 Nonlinear solution procedure
7.4.1 Newton-Raphson method
7.4.2 Initial stress method
7.4.3 Convergence criteria
8 Visualization
8.1 Introduction
8.2 Overview of algorithm
8.3 Geometry and results data
8.3.1 Geometry relations for 20-node element
8.3.2 Surface of the finite element model
8.3.3 Continuous field of secondary results
8.4 Subdivision of quadratic surfaces
8.4.1 Curvature-based subdivision
8.4.2 Results-based subdivision
8.4.3 Delaunay triangulation
8.5 Using Java3D API for visualization
voici le lien de ce document:
http://www.zshare.net/download/2469569c6f5ce8/
on peut visiter ce lien:
http://www.u-aizu.ac.jp/~niki/feminstr/feminstr.html
nassima- Expert
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Re: INTRODUCTION TO THE FINITE ELEMENT METHOD G.P.NIKISHKOV
une autre fois merci imane
t_salim- Expert
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ibrahim74- MGCien Special
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Re: INTRODUCTION TO THE FINITE ELEMENT METHOD G.P.NIKISHKOV
de rien mes frères...
nassima- Expert
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Re: INTRODUCTION TO THE FINITE ELEMENT METHOD G.P.NIKISHKOV
MErci Nassima super ton document
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Re: INTRODUCTION TO THE FINITE ELEMENT METHOD G.P.NIKISHKOV
de rien khti ....
nassima- Expert
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Re: INTRODUCTION TO THE FINITE ELEMENT METHOD G.P.NIKISHKOV
merci! ke de splendide doc
RAKOTOJAONA Tovo- Membre
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