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# Finite Element Methods

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Course type: Online Instructor led Course

Platform: Skype

Course ID: 21800

Course type: Online Instructor led Course

Platform: Skype

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The Finite Element Method is a well established technique for analysing the behaviour of structures subjected to a variety of loads. These may be static or dynamic, and the structural responses may be linear or non-linear, with varying degrees of complexity.

The underlying theory of the method is now well understood, with many books and courses providing adequate explanations of this aspect. The major problem facing the structural analyst contemplating the use of Finite Elements, lies in acquiring appropriate knowledge to provide assurance that the Finite Element model produced gives a reasonably reliable representation of the "real life" structure, and that errors introduced by the modelling process can be identified and, if possible, quantified.

## Topics Covered

INTRODUCTION
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 functions- example 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
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
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

## Who should attend

The course is aimed at Engineers who intend to use commercially available Finite Element packages to analyse structures in the Aeronautical, Mechanical, Civil and other Engineering industries. The examples are run on ANSYS 14.5.

Participants are assumed to have knowledge of the basic principles of structural mechanics. Some knowledge of Finite Elements is an advantage, but not essential. The course is designed for engineers faced with the modelling of actual structures in the commercial environment using modern Finite Element systems.

## Pre-requisites

An undergraduate degree in engineering or science.
An engineer working in automobile, aerospace and marine fields.
Research candidates.

## What you need to bring

Theoretical class and practicals which involve minimum stationery items.

## Key Takeaways

Practical and theoretical knowledge.

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Kirthan .L.J

PhD in Mechanical Engineering

Having 9 years experience in teaching and research in mechanical engineering.

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