FINITE ELEMENT METHODS (BME701)

FINITE ELEMENT METHODS

Course Code BME701 
CIE Marks 50
Teaching Hours/Week (L:T:P: S) 3:0:2:0 
SEE Marks 50
Total Hours of Pedagogy 40 hours Theory + 8­10 Lab slots 
Total Marks 100
Credits 04 
Exam Hours 3
Examination nature (SEE) Theory

MODULE­ 1

Introduction to FEM:

Introduction to FEM, engineering applications, advantages, General steps, Element types, Convergence

criteria, Coordinate systems, commercial packages­pre­processor, solver and post processor. Principles of Elasticity: Strain­ displacement relations, Stress­strain relations for 1D, 2D, and 3D cases,

Plain stress and Plain strain conditions,

Introduction to Numerical Methods, Potential energy method, Rayleigh­Ritz method and Galerkin

method­applied to simple problems on axially loaded members, cantilever, simply supported beams, with

point loads and distributed loads.

MODULE­ 2

One Dimensional Element:

Formulation of a linear bar element, Shape Functions­ Polynomial, The Potential Energy Approach,

derivation of stiffness matrix, Properties of stiffness matrix, Assembly of Global Stiffness Matrix and Load

Vector, Boundary conditions­ elimination method and penalty method. Numerical Problems on straight

and stepped bars. (Problems with 2 elements only).

MODULE­ 3

rTrusses and Beams:

Formulation plane trusses element, Stiffness matrix (No derivation), Numerical Problems on point load,

Formulation beam element, derivation of Hermite shape functions, stiffness matrix and load vector (No

derivations), Numerical Problems on beams carrying concentrated, UDL and couples.(Problems with 2 elements only).

MODULE ­4

Two dimensional Element:

Formulation of triangular and quadrilateral elements. Displacement models and shape functions for

linear and higher order elements, Lagrangian and serendipity elements, Iso parametric – sub parametric

– super parametric elements, Introduction to axisymmetric– triangular elements. Convergence criteria,

pascal triangle. (No numerical problems)

MODULE­ 5

Dynamic considerations and Heat Transfer:

Dynamic considerations: Formulation for point mass and distributed masses, Consistent mass matrices

for 1­D bar element, computation of eigen values and eigen vectors. Numerical Problems on straight and

stepped bars.

Heat Transfer Problems: Steady state heat transfer, 1D heat conduction governing equation, boundary

conditions, Numerical problems on composite wall, 1D heat transfer in thin fins.

PRACTICAL COMPONENT OF IPCC

Experiments

1 Bars of constant cross section area, tapered cross section area and stepped bar with different

materials

2 Trusses – (Minimum 3 exercises of different areas of cross sections of links, different supports

such as fixed support, rolling support)

3 Beams – Simply supported, cantilever, beams with point load, UDL, beams with varying load

etc. (Minimum 6 exercises)

4 Stress analysis of a rectangular plate with a circular hole

5 Thermal Analysis – 1D & 2D problem with conduction and convection boundary conditions

(Heat transfer through composite section) Minimum of 2 exercises

6 Natural frequency of beam with fixed – fixed end condition

7 Response of beam with fixed – fixed end conditions subjected to forcing function

8 Demonstrate the use of graphics standards (IGES, STEP etc) to import the model from

modeler to solver

9 Can be Demo experiments for CIE

Demonstrate the use of graphics standards ( IGES, STEP etc ) to import the model from

modeler to solver

10 Can be Demo experiments for CIE

Demonstrate one example of contact analysis to learn the procedure to carry out contact

analysis.

11 Can be Demo experiments for CIE

Demonstrate at least two different type of example to model and analyze bars or plates made

from composite material

Suggested Learning Resources:

Text Books:

1. Logan, D. L., A first course in the finite element method,6th Edition, Cengage Learning, 2016.

2. Rao, S. S., Finite element method in engineering, 5th Edition, Pergaman Int. Library of Science, 2010.

3. Chandrupatla T. R., Finite Elements in engineering, 2nd Edition, PHI, 2013.

4. O. C. Zienkiewicz and Y.K. Cheung, The Finite Element Method in Structural and Soild Mechanics,

McGraw Hill, London

Reference Books:

1. J.N.Reddy, “Finite Element Method”­ McGraw ­Hill International Edition.Bathe K. J. Finite Elements

Procedures, PHI.

2. Cook R. D., et al. “Conceptsand Application of Finite Elements Analysis”­ 4th Edition, Wiley & Sons,

2003.

3. C.S.Krishnamoorty, Finite ElementAnalysis, Tata McGraw­Hill David V. Hutton, Fundamentals of

Finite ElementAnalysis, McGraw Hill

4. D. Maity, Computer Analysis of Framed Structures, I.K. International Pvt. Ltd. New Delhi

5. Erik G. Thompson, Introduction to the Finite Element Method: Theory, Programming and

Applications, John Wiley