## ME2353 FINITE ELEMENT ANALYSIS Lecture notes for MECH - Sixth (6th) semester- by R.Anirudhan

ME2353 Finite element analysis lecture notes

CONTENT :
INTRODUCTION (Not for examination)
Solution to engineering problems – mathematical modeling – discrete and continuum
modeling – need for numerical methods of solution – relevance and scope of finite
element methods – engineering applications of FEA

UNIT I FINITE ELEMENT FORMULATION OF BOUNDARY VALUE
PROBLEMS
Weighted residual methods –general weighted residual statement – weak formulation of
the weighted residual statement –comparisons – piecewise continuous trial functionsexample
of a bar finite element –functional and differential forms – principle of stationary
total potential – Rayleigh Ritz method – piecewise continuous trial functions – finite
element method – application to bar element

UNIT II ONE DIMENSIONAL FINITE ELEMENT ANALYSIS
General form of total potential for 1-D applications – generic form of finite element
equations – linear bar element – quadratic element –nodal approximation – development
of shape functions – element matrices and vectors – example problems – extension to
plane truss– development of element equations – assembly – element connectivity –
global equations – solution methods –beam element – nodal approximation – shape
functions – element matrices and vectors – assembly – solution – example problems

UNIT III TWO DIMENSIONAL FINITE ELEMENT ANALYSIS
Introduction – approximation of geometry and field variable – 3 noded triangular
elements – four noded rectangular elements – higher order elements – generalized
coordinates approach to nodal approximations – difficulties – natural coordinates and
coordinate transformations – triangular and quadrilateral elements – iso-parametric
elements – structural mechanics applications in 2-dimensions – elasticity equations –
stress strain relations – plane problems of elasticity – element equations – assembly –
need for quadrature formule – transformations to natural coordinates – Gaussian
quadrature – example problems in plane stress, plane strain and axisymmetric
applications

UNIT IV DYNAMIC ANALYSIS USING FINITE ELEMENT METHOD
Introduction – vibrational problems – equations of motion based on weak form –
longitudinal vibration of bars – transverse vibration of beams – consistent mass matrices
– element equations –solution of eigenvalue problems – vector iteration methods –
normal modes – transient vibrations – modeling of damping – mode superposition
technique – direct integration methods

UNIT V APPLICATIONS IN HEAT TRANSFER & FLUID MECHANICS
One dimensional heat transfer element – application to one-dimensional heat transfer
problems- scalar variable problems in 2-Dimensions – Applications to heat transfer in 2-
Dimension – Application to problems in fluid mechanics in 2-D