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ME1401 – INTRODUCTION OF FINITE ELEMENT ANALYSIS
CONTENTS
UNIT – I
Fundamental Concepts
Syllabus
General Methods of the Finite Element Analysis
General Steps of the Finite Element Analysis
Boundary Conditions
Consideration during Discretization process
Rayleigh – Ritz Method (Variational Approach)
Problems (I set)
Weighted Residual method
Problems (II set)
Matrix Algebra
Matrix Operation
Gaussian Elimination Method
Problems (III set)
Advantages of Finite Element Method
Disadvantages of Finite Element Method
Applications of Finite Element Analysis
UNIT – II
One Dimension Problems
Syllabus
One Dimensional elements
Bar, Beam and Truss
Stress, Strain and Displacement
Types of Loading
Finite Element Modeling
Co – Ordinates

Natural Co – Ordinate (ε)
Shape function
Polynomial Shape function
Stiffness Matrix [K]
Properties of Stiffness Matrix
Equation of Stiffness Matrix for One dimensional bar element
Finite Element Equation for One dimensional bar element
The Load (or) Force Vector {F}
Problem (I set)
Trusses
Stiffness Matrix [K] for a truss element
Finite Element Equation for Two noded Truss element
Problem (II set)
The Galerkin Approach
Types of beam
Types of Transverse Load
Problem (III set)
UNIT – III
Two Dimension Problems – Scalar variable Problems
Syllabus
Two dimensional elements
Plane Stress and Plane Strain
Finite Element Modeling
Constant Strain Triangular (CST) Element
Shape function for the CST element
Displacement function for the CST element
Strain – Displacement matrix [B] for CST element
Stress – Strain relationship matrix (or) Constitutive matrix [D] for two dimensional
element
Stress – Strain relationship matrix for two dimensional plane stress problems

Stress – Strain relationship matrix for two dimensional plane strain problems
Stiffness matrix equation for two dimensional element (CST element)
Temperature Effects
Galerkin Approach
Linear Strain Triangular (LST) element
Problem (I set)
Scalar variable problems
Equation of Temperature function (T) for one dimensional heat conduction
Equation of Shape functions (N1 & N2) for one dimensional heat conduction
Equation of Stiffness Matrix (K) for one dimensional heat conduction
Finite Element Equations for one dimensional heat conduction
Finite element Equation for Torsional Bar element
Problem (II set)
UNIT – IV
AXISYMMETRIC CONTINUUM
Syllabus
Elasticity Equations
Axisymmetric Elements
Axisymmetric Formulation
Equation of shape function for Axisymmetric element
Equation of Strain – Displacement Matrix [B] for Axisymmetric element
Equation of Stress – Strain Matrix [D] for Axisymmetric element
Equation of Stiffness Matrix [K] for Axisymmetric element
Temperature Effects
Problem (I set)

UNIT – V
ISOPARAMETRIC ELEMENTS FOR TWO DIMENSIONAL CONTINUUM
Syllabus
Isoparametric element
Superparametric element
Subparametric element
Equation of Shape function for 4 noded rectangular parent element
Equation of Stiffness Matrix for 4 noded isoparametric quadrilateral element
Equation of element force vector
Numerical Integration (Gaussian Quadrature)
Problem (I set)

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