CE3007 Introduction to Finite Element Method Syllabus:

CE3007 Introduction to Finite Element Method Syllabus – Anna University Regulation 2021

COURSE OBJECTIVE

 To develop a thorough understanding of the finite element analysis techniques with an ability to effectively use the tools of the analysis for solving practical problems arising in Civil Engineering.

UNIT I INTRODUCTION

Historical Background – Mathematical Modeling of field problems in Engineering –Governing Equations – Discrete and continuous models – Boundary, Initial and Eigen Value problems– Weighted Residual Methods – Variational Formulation of Boundary Value Problems – Ritz Technique – Basic concepts of the Finite Element Method.

UNIT II STIFFNESS MATRIX FORMULATION

Introduction to Discrete and Continua elements – Discrete Elements – Direct stiffness method – Special characteristics of stiffness matrix – Assemblage of elements – Boundary condition & reaction – 2D – truss element – 2D – beam element – Analysis of framed Structures – Basic steps in finite element analysis – Differential equilibrium equations – strain displacement relation – linear constitutive relation – Numerical methods in finite element analysis- Gauss elimination method.

UNIT III ONE DIMENSIONAL PROBLEMS

One Dimensional Second Order Equations – Discretization – Element types- Linear and Higher order Elements – Continua Elements – Displacement models – convergence requirements. Natural coordinate systems – Shape function. Interpolation function. Linear and quadratic elements – Lagrange & Serendipity elements. Strain displacement matrix – element stiffness matrix and nodal load vector. Natural frequencies of longitudinal vibration and mode shapes.

UNIT IV TWO DIMENSIONAL PROBLEMS

Two dimensional isoparametric elements – Four noded quadrilateral elements – triangular elements. Computation of stiffness matrix for isoparametric elements – numerical integration (Gauss quadrature) Convergence criteria for isoparametric elements.

UNIT V ANALYSIS OF PLATES

Introduction to Plate Bending Problems – displacement functions – Analysis of Thin Plate – Analysis of Thick Plate – Analysis of Skew Plate, Finite Element Analysis of Shell, plane stress and plane strain analysis, Example problem using any general-purpose finite element software

TOTAL: 45 PERIODS
COURSE OUTCOMES:

CO1 to understand the basics of finite element formulation.
CO2 to formulate the stiffness matrix for beam, truss and framed structures.
CO3 :to apply finite element formulations to solve one-dimensional problems.
CO4: to apply finite element method to solve two dimensional problems.
CO5 to apply finite element method to analyze plate bending problems.

TEXT BOOKS:

1. Rao, S.S., “The Finite Element Method in Engineering”, 6th Edition, ButterworthHeinemann,2018.
2. Reddy,J.N. “Introduction to the Finite Element Method”, 4thEdition, Tata McGrawHill,2018.

REFERENCES

1. Krishnamoorthy, C. S, Finite Element Analysis – Theory and Programming, McGraw – Hill, 1995.
2. David Hutton, Fundamentals of Finite Element Analysis, Tata McGraw Hill Publishing Company Limited, New Delhi, 2005.
3. G.R. Liu and S.S.Quek, Finite Element Method: A Practical Course, Butterworth-Heinemann; 1st edition (21 February 2003)
4. Chennakesava R. Alavala Finite Element Methods: Basic Concepts and Applications, Prentice Hall Inc., 2010.
5. R. T. Chandrupatla and A. D. Belegundu, Introduction to Finite Elements in Engineering, PHI Learning Pvt Ltd, New Delhi, 1997.
6. S. S. Bhavikatti, Finite Element Analysis, New Age Publishers, 2007.