# Finite Element Method (ME-504)

## Syllabus

UNIT 1:
Introduction
Structural analysis, objectives, static, Dynamic and kinematics analyses, Skeletal and continuum structures, Modeling of infinite d.o.f. system into finite d.o.f. system, Basic steps in finite element problem formulation, General applicability of the method.

UNIT 2:
Element Types and Characteristics
Discretization of the domain, Basic element shapes, Aspect ratio, Shape functions, Generalized co-ordinates and nodal shape functions. ID spar and beam elements, 2D rectangular and triangular elements, Axisymmetirc elements.

UNIT 3:
Assembly of Elements and Matrices
Concept of element assembly, Global and local co-ordinate systems, Band width and its effects, Banded and skyline assembly, Boundary conditions, Solution of simultaneous equations, Gaussian elimination and Choleksy decomposition methods, Numerical integration, One and 2D applications.

UNIT 4:
Higher Order and Isoparametric Elements
One dimensional quadratic and cubic elements, Use of natural co-ordinate system, Area co-ordinate system continuity and convergence requirements, 2D rectangular and triangular requirement.

UNIT 5:
Static & Dynamic Analysis
Analysis of trusses and frames, Analysis of machine subassemblies, Use commercial software packages, Advantages and limitations Hamilton's principle, Derivation of equilibrium, Consistent and lumped mass matrices, Derivation of mass matrices for ID elements, Determination of natural frequencies and mode shapes, Use of commercial software packages.

• Unit 1
• Unit 2
• Unit 3
• Unit 4
• Unit 5

## Books Recommended

Rao, S.S., The Finite Element Method in Engineering, 2nd ed.., Peragamon Press, Oxford.
 Robert, D. Cook., David, S. Malkins, and Michael E. Plesha, Concepts and Application of Finite Element Analysis 3rd ed., John Wiley.
 Chandrupatla, T.R. an Belegundu, A.D., Introduction to Finite Elements in Engineering, Prentice Hall of India Pvt. Ltd.
 Zienkiewicz O C, The Finite Element Method, 3rd ed, Tata McGraw Hill

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