Finite element method

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MANISH RANJAN

it is ppt on finite element method.

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Contents
 Finite Elements methods
 Basic of FEM
 Potential energy approach
 Solution scheme of Spring system by FEM
 FEM Terminology: Discretization, Boundary condition, Strain-displacement model,
Stress-strain behaviors/Constitutive models , element stiffness, global stiffness, SLE
- iterative method s
 Limitation of FEM
9/6/2016 Dr. Ashok Jaiswal

Finite element method
9/6/2016 Dr. Ashok Jaiswal
F

Finite element method
Equilibrium condition
9/6/2016 Dr. Ashok Jaiswal
D
F

Minimum Potential Energy Approach
 Energy given to the system (F.D) = ET.E.
 Energy stored in the system (1/2 KD2) = ES.E.
 Potential energy of the system = EP.E.
ET.E. = ES.E. + EP.S.
EP.E. = ET.E. - ES.E.
Minimizing the Potential energy of the system to gain
the equilibrium condition.
9/6/2016 Dr. Ashok Jaiswal

Solution Scheme for Spring System
9/6/2016 Dr. Ashok Jaiswal
 Total Potential Energy :

Solution Scheme for Spring System
9/6/2016 Dr. Ashok Jaiswal
Global Stiffness Displacement Force
Matrix Matrix Matrix

Solution Scheme for Spring System
9/6/2016 Dr. Ashok Jaiswal

Discretization
Discretization view of different structures
9/6/2016 Dr. Ashok Jaiswal

Discretization
 Different types of elements (2-D)
9/6/2016 Dr. Ashok Jaiswal

Discretization
 Different types of elements (3-D)
9/6/2016 Dr. Ashok Jaiswal

Discretization
 Element
 Node
9/6/2016 Dr. Ashok Jaiswal

Strain Energy in the Element
S.E. = ½ [σ][ε]
9/6/2016 Dr. Ashok Jaiswal

Displacement – Strain – two dimensional case
9/6/2016 Dr. Ashok Jaiswal

Constant strain triangle (CST)
9/6/2016 Dr. Ashok Jaiswal

Isoperimetric representation
9/6/2016 Dr. Ashok Jaiswal

Jacobian Matrix
9/6/2016 Dr. Ashok Jaiswal

Element stiffness
9/6/2016 Dr. Ashok Jaiswal

Stress-Strain
Three dimensional
9/6/2016 Dr. Ashok Jaiswal

Stress-Strain
Two dimensional
Plane Stress
9/6/2016 Dr. Ashok Jaiswal

Stress-Strain
Two dimensional
Plane Strain
9/6/2016 Dr. Ashok Jaiswal

Boundary Conditions
9/6/2016 Dr. Ashok Jaiswal

Global Stiffness
9/6/2016 Dr. Ashok Jaiswal
d
d
[K][d] = [f]

Limitation of FEM
9/6/2016 Dr. Ashok Jaiswal

SLE Iterative Method
 Conjugate Gradient Method
 Gauss-Seidel Method
9/6/2016 Dr. Ashok Jaiswal

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Finite element method

2. Contents  Finite Elements methods  Basic of FEM  Potential energy approach  Solution scheme of Spring system by FEM  FEM Terminology: Discretization, Boundary condition, Strain-displacement model, Stress-strain behaviors/Constitutive models , element stiffness, global stiffness, SLE - iterative method s  Limitation of FEM 9/6/2016 Dr. Ashok Jaiswal

3. Finite element method 9/6/2016 Dr. Ashok Jaiswal F

4. Finite element method Equilibrium condition 9/6/2016 Dr. Ashok Jaiswal D F

5. Minimum Potential Energy Approach  Energy given to the system (F.D) = ET.E.  Energy stored in the system (1/2 KD2) = ES.E.  Potential energy of the system = EP.E. ET.E. = ES.E. + EP.S. EP.E. = ET.E. - ES.E. Minimizing the Potential energy of the system to gain the equilibrium condition. 9/6/2016 Dr. Ashok Jaiswal

6. Solution Scheme for Spring System 9/6/2016 Dr. Ashok Jaiswal  Total Potential Energy :

7. Solution Scheme for Spring System 9/6/2016 Dr. Ashok Jaiswal Global Stiffness Displacement Force Matrix Matrix Matrix

8. Solution Scheme for Spring System 9/6/2016 Dr. Ashok Jaiswal

9. Problem: 1 9/6/2016 Dr. Ashok Jaiswal

10. Discretization Discretization view of different structures 9/6/2016 Dr. Ashok Jaiswal

11. Discretization  Different types of elements (2-D) 9/6/2016 Dr. Ashok Jaiswal

12. Discretization  Different types of elements (3-D) 9/6/2016 Dr. Ashok Jaiswal

13. Discretization  Element  Node 9/6/2016 Dr. Ashok Jaiswal

14. Strain Energy in the Element S.E. = ½ [σ][ε] 9/6/2016 Dr. Ashok Jaiswal

15. Displacement – Strain – two dimensional case 9/6/2016 Dr. Ashok Jaiswal

16. Constant strain triangle (CST) 9/6/2016 Dr. Ashok Jaiswal

17. 9/6/2016 Dr. Ashok Jaiswal