ED4251 Finite Element Methods in Mechanical Design Syllabus:

ED4251 Finite Element Methods in Mechanical Design Syllabus – Anna University PG Syllabus Regulation 2021

COURSE OBJECTIVES

1. To learn mathematical models for one dimensional problems and their numerical solutions
2. To learn two dimensional scalar and vector variable problems to determine field variables
3. To learn Iso parametric transformation and numerical integration for evaluation of element matrices
4. To study various solution techniques to solve Eigen value problems
5. To learn solution techniques to solve non-linear problems

UNIT-I FINITE ELEMENT ANALYSIS OF ONE DIMENSIONAL PROBLEMS

Historical Background – Weighted Residual Methods – Basic Concept of FEM – Variational Formulation of B.V.P. – Ritz Method – Finite Element Modelling – Element Equations – Linear and Higher order Shape functions – Bar, Beam Elements – Applications to Heat Transfer problems.

UNIT-II FINITE ELEMENT ANALYSIS OF TWO DIMENSIONAL PROBLEMS

Basic Boundary Value Problems in two-dimensions – Linear and higher order Triangular, quadrilateral elements – Poisson’s and Laplace’s Equation – Weak Formulation – Element Matrices and Vectors – Application to scalar variable problems – Introduction to Theory of Elasticity – Plane Stress – Plane Strain and Axisymmetric Formulation – Principle of virtual work – Element matrices using energy approach

UNIT-III ISO-PARAMETRIC FORMULATION

Natural Co-ordinate Systems – Lagrangian Interpolation Polynomials – Iso parametric Elements –Formulation – Shape functions -one dimensional , two dimensional triangular and quadrilateral elements -Serendipity elements- Jacobian transformation – Numerical Integration – Gauss quadrature – one, two and three point integration

UNIT-IV EIGEN VALUE PROBLEMS

Dynamic Analysis – Equations of Motion – Consistent and lumped mass matrices – Free Vibration analysis – Natural frequencies of Longitudinal, Transverse and torsional vibration – Solution of Eigenvalue problems – Introduction to transient field problems

UNIT-V NON-LINEAR ANALYSIS

Introduction to Non-linear problems – some solution techniques- computational procedure material non-linearity-Plasticity and visco plasticity, stress stiffening, contact interfaces- problems of gaps and contact – geometric non-linearity – modeling considerations – Free and Mapped meshing -Mesh quality- Error estimate

COURSE OUTCOMES:

On Completion of the course the student will be able to
 Develop mathematical models for one dimensional problems and their numerical solutions
 Determine field variables for two dimensional scalar and vector variable problems
 Apply Isoparametric transformation and numerical integration for evaluation of element matrices
 Apply various solution techniques to solve Eigen value problems
 Formulate solution techniques to solve non-linear problems

REFERENCES:

1. Bathe K.J., “Finite Element Procedures in Engineering Analysis”, Prentice Hall, 1990
2. David Hutton, “Fundamentals of Finite Element Analysis”, Tata McGrawHill, 2005
3. Rao, S.S., “The Finite Element Method in Engineering”, 6th Edition, ButterworthHeinemann,2018.
4. Reddy,J.N. “Introduction to the Finite Element Method”, 4 thEdition, Tata McGraw Hill, 2018
5. Seshu.P, “Text Book of Finite Element Analysis”, PHI Learning Pvt. Ltd., New Delhi, 2012.
6. Tirupathi R. Chandrupatla and Ashok D. Belegundu, “Introduction to Finite Elements inEngineering”, International Edition, Pearson Education Limited, 2014.