CAE333 Finite Element Methods Syllabus:
CAE333 Finite Element Methods Syllabus – Anna University Regulation 2021
COURSE OBJECTIVES:
Of this course are
1. To give exposure to various methods of solution, in particular the finite element method.
2. To expose the student to a wide variety of problems involving discrete and continuumelements
3. To impart knowledge in the basic theory of finite element formulation.
4. To allow the student to learn and understanding how element characteristic matrices aregenerated
5. To impart knowledge in assembly of finite element equations, and solve for the unknowns.
UNIT I INTRODUCTION
Review of various approximate methods – variational approach and weighted residual approach application to structural mechanic’s problems. finite difference methods- governing equation and convergence criteria of finite element method.
UNIT II DISCRETE ELEMENTS
Bar elements, uniform section, mechanical and thermal loading, varying section, 2D and 3D truss element. Beam element – problems for various loadings and boundary conditions – 2D and 3D Frame elements – longitudinal and lateral vibration. Use of local and natural coordinates.
UNIT III CONTINUUM ELEMENTS
Plane stress, plane strain and axisymmetric problems. Derivation of element matrices for constant and linear strain triangular elements and axisymmetric element.
UNIT IV ISOPARAMETRIC ELEMENTS
Definitions, Shape function for 4, 8 and 9 nodal quadrilateral elements, stiffness matrix and consistent load vector, evaluation of element matrices using numerical integration.
UNIT V FIELD PROBLEM AND METHODS OF SOLUTIONS
Heat transfer problems, steady state fin problems, derivation of element matrices for two dimensional problems, torsion problems. bandwidth- elimination method and method of factorization for solving simultaneous algebraic equations – Features of software packages, sources of error.
TOTAL: 45 PERIODS
COURSE OUTCOMES:
Upon completion of the course, Students will be able to
CO1: Have overall understanding of various approximate methods used for solving structural mechanics problems. Be able to understand the formulation of governing equation for the finite element method, convergence criteria and advantage over other approximate methods.
CO2: Have the capability to solve 1-D problems related to static analysis of structural members.
CO3: Formulate the elemental matrices for 2-D problems.
CO4:Get an exposure to isoperimetric element formulations and importance of numerical integration.
CO5: Solve Eigen value problems and scalar field problems.
TEXT BOOKS:
1. Reddy J.N., “An Introduction to Finite Element Method”, McGraw Hill, third edition, 2005.
2. Tirupathi.R. Chandrapatha and Ashok D. Belegundu, “Introduction to Finite Elements in Engineering”, Prentice Hall India, Fourth edition, 2012.
REFERENCES:
1. Bathe, K.J. and Wilson, E.L., “Numerical Methods in Finite Elements Analysis”, Prentice Hall of India, 1985.
2. Krishnamurthy, C.S., “Finite Element Analysis”, Tata McGraw Hill, 2000.
3. Rao. S.S., “Finite Element Methods in Engineering,” Butterworth and Heinemann, 2001.