finite element method

Finite Element Method

Finite Element Methodfor solid mechanics

1Dr. Ashok JaiswalDr. Ashok Jaiswal

Contents Finite Elements methodsBasic of FEMPotential energy approach Solution scheme of Spring system by FEMFEM Terminology: Discretization, Boundary condition, Strain-displacement model, Stress-strain behaviors/Constitutive models , element stiffness, global stiffness, SLE - iterative method s Limitation of FEM

8/5/2016Dr. Ashok Jaiswal


Finite element method

8/5/2016Dr. Ashok JaiswalF


Finite element method Equilibrium condition

8/5/2016Dr. Ashok JaiswalDF


Minimum Potential Energy ApproachEnergy 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 gainthe equilibrium condition.



Solution Scheme for Spring System 8/5/2016Dr. Ashok Jaiswal

Total Potential Energy :


Global Stiffness Displacement Force Matrix Matrix Matrix


Problem: 1


DiscretizationDiscretization view of different structures



DiscretizationDifferent types of elements (2-D)



DiscretizationDifferent types of elements (3-D)



DiscretizationElementNode



Strain Energy in the Element

S.E. = [][]8/5/2016Dr. Ashok Jaiswal

Displacement Strain two dimensional case



Constant strain triangle (CST)8/5/2016Dr. Ashok Jaiswal


Isoperimetric representation 8/5/2016Dr. Ashok Jaiswal




Jacobian Matrix8/5/2016Dr. Ashok Jaiswal




Element stiffness8/5/2016Dr. Ashok Jaiswal




Stress-StrainThree dimensional



Stress-StrainTwo dimensional Plane Stress



Stress-StrainTwo dimensional Plane Strain






Boundary Conditions



Boundary Conditions



Element Stiffness8/5/2016Dr. Ashok Jaiswal

Global Stiffness 8/5/2016Dr. Ashok Jaiswal

d

d

[K][d] = [f]

Limitation of FEM


SLE Iterative Method

Conjugate Gradient MethodGauss-Seidel Method 8/5/2016Dr. Ashok Jaiswal

THANK YOU8/5/2016Dr. Ashok Jaiswal

finite element method

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