ANNA University Finite Elements Analysis Notes
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Syllabus:
UNIT II ONE DIMENSIONAL FINITE ELEMENT ANALYSIS 8+4
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 10+4
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 8+4
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 6+3
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
You Can Download The Material Of FEA From The Below Link
Syllabus:
UNIT I FINITE ELEMENT FORMULATION OF BOUNDARY VALUE
PROBLEMS 5+3
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
PROBLEMS 5+3
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 8+4
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 10+4
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 8+4
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 6+3
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
You Can Download The Material Of FEA From The Below Link
