MTech Finite Element Method syllabus for 3 Sem 2020 scheme 20MAU333

Module-1 Introduction to Finite Element Methods 0 hours

Introduction to Finite Element Methods:

Engineering analysis, History, advantages and disadvantages, classification, basic concepts, convergence criteria. Role of finite element analysis in computer aided design, mathematical preliminaries, and differential equation formulation. Variational formulations, weighted residual methods

Module-2 One Dimensional Elements 0 hours

One Dimensional Elements:

Analysis of bars and trusses, basic equations and Potential Energy functional. 1D Bar Element, Admissible displacement function, strain matrix, stress recovery, Element equation, stiffness matrix. Consistent nodal force vectors: Body force, initial strain, assembly procedure, Boundary and constraint conditions, single point constraint, multi point constraint, truss element , shape functions for higher order elements, C0, C-1 elements

A d v e r t i s e m e n t
Module-3 Two Dimensional Elements 0 hours

Two Dimensional Elements:

Analysis of Plane Elasticity Problems: Triangular element, four noded quadrilateral Element( QUAD4), shape functions for higher order elements ( LST and QUAD 8), Lagrange element, stain –displacement matrix, stiffness matrix and Jacobian of CST and QUAD4 elements.

 

Axi-symmetric Solid elements:

Analysis of Bodies of revolution under axi-symmetric loading, Axisymmetric Triangular and Quadrilateral Ring Elements, StrainDisplacement matrix, stiffness matrix

Module-4 Three dimensional elements 0 hours

Three dimensional elements:

Applications to Solid mechanics Problems: Basic Equations and Potential Energy Functional, Four Noded Tetrahdral Element, Eight - Noded Hexahedral Element, LaGrange family, Shape Functions for Higher Order Elements.

 

Beam elements

Analysis of beam and frames: 1-D Beam element Problems.

Module-5 Dynamic Considerations 0 hours

Dynamic Considerations:

Formulation of point mass and distributed mass, Consistent element mass matrix of one dimensional bar element, truss element, beam element , Lumped mass matrix, Evaluation of eigen values and eigen vectors. Applications to bars and beam element

 

Heat Transfer:

Steady state heat transfer, 1D heat conduction governing quations. Functional approach for heat conduction. Galerkin’s approach for heat conduction. 1D heat transfer in thin fins

 

Course outcomes:

At the end of the course the student will be able to:

CO1:Understand and explain the fundamentals of structural mechanics and finite elementmethod

CO2: Develop element stiffness matrix for different elements using variousmethods.

CO3: Illustrate different methods of deriving shape functions for variouselements.

CO4: Design, analyse and create simple structural elements,

CO5:Design,analyse and create simple heat transfer conduction problems

 

Question paper pattern:

The SEE question paper will be set for 100 marks and the marks scored will be proportionately reduced to 60.

  • The question paper will have ten full questions carrying equal marks.
  • Each full question is for 20 marks.
  • There will be two full questions (with a maximum of four sub questions) from each module.
  • Each full question will have sub question covering all the topics under a module.
  • The students will have to answer five full questions, selecting one full question from each module.

 

Textbook/ Textbooks

T. R. Chandrupatla, A. D. Belegundu, Finite Elements in Engineering , 3rd Ed PHI. 3rd Edition

S. S. Rao, Finite Elements in Engineering, 4th Edition, Elsevier, 6th Edition,

 

Reference Books

(1) U.S. Dixit, Finite Element Methods for Engineers, Cengage Learning, 1st Edition 2009

(2) R. D. Cook, D. S Maltus, M. E. Plesha, R. J. Witt,, Concepts and applications of Finite Element Analysis Wiley 4th Ed 4th Edition 2001

(3) 4 th Edition 2001, Finite Element Methods, Thomson Learning 3rdedition, 5th Edition 2012 J. N. Reddy,, Finite Element Method, McGraw -Hill , 3rd Edition 2006International Edition.

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