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NOTES OF LESSON

SEMESTER: VII BRANCH: MECHANICALSUBCODE: ME1401 SUBJECT: INTRODUCTION TO FEA.

UNIT I INTORDUCTION

Engineering Analysis:

Objectives and Methods

FEM History

Steps in FEA.

Advantages, Disadvantages, Application of FEM.

Matrix Algebra:

Various Matrix operation (Transpose,

Determinant,Inverse,Determinant of Inverse, Matrix

Differentiation, Matrix Integration, Solution to Simultaneous

Equation)

Discretization Process.

Raleigh Ritz Method (Variational Approach).

Gaussian Elimination Method.

UNIT II ONE DIMENSIONAL PROBLEM

Stress, Strain, Displacement and loading

Finite Element Modeling

Co-ordinates in FEM.

Shape Function derivation for one dimensional bar element.

Stiffness Matrix- Properties, Derivation for One dimensional bar element.

Derivation of Finite element equation for One dimensional Bar element.

Stiffness Matrix Assembly.

Problems on One Dimensional Bar element.

Temperature effect- Problems on it.

Shape Function derivation for one dimensional beam element.

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Stiffness Matrix- Properties, Derivation for One dimensional beam element.

Derivation of Finite element equation for One dimensional Beam element.

Stiffness Matrix Assembly.

Problems on One Dimensional Beam element.

UNIT-III TWO DIMENSIONAL CONTINUM

Trusses Stiffness Matrix derivation, Problems

Potential Energy Approach,

Galerkin Approach.

Plane stress & strain concept.

Finite element modeling.

Shape function derivation for Constant Strain triangle(CST)

Strain- Displacement matrix for CST.

Stress-Strain Relation or Constitutive matrix for two dimensional element.

Stiffness Matrix Derivation.

Assembly of matrix.

Problems on CST.

Temperature effect on CST- Problem.

Galerkin approach for two dimensional Problems.

UNIT IV AXISYMMETRIC CONTINUUM

Introduction.

Axisymmetric formulation.

Derivation of Shape functions for Axisymmetric Triangular element.

Strain- Displacement matrix for Axisymmetric Triangular element.

Stress-Strain Relation or Constitutive matrix for Axisymmetric Triangular

element.

Stiffness Matrix Derivation.

Assembly of matrix.

Problems on Axisymmetric Triangular element.

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Temperature effect and problems on it.

Galerkin Approach.

UNIT V ISOPARAMETRIC ELEMENT.

Introduction.

Shape function for 4-noded rectangular element.

Element stiffness matrix for 4-noded quadrilateral isoparametric element.

Assembly of matrix.

Numerical Integration or Gauss Quadrature Method.

Problems on 4-noded quadrilateral axisymmetric element.