Book Details

Finite Element Methods

Finite Element Methods

Published by uLektz

Course Code:10ME64

Author:uLektz

University: Visvesvaraya Technological University, Karnataka (VTU)

Regulation:2010

Categories:Mechanical

Format : ico_bookePUB3 (DRM Protected)

Type :eBook

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Description :Finite Element Methods of 10ME64 covers the latest syllabus prescribed by Visvesvaraya Technological University, Karnataka (VTU) for regulation 2010. Author: uLektz, Published by uLektz Learning Solutions Private Limited.

Note : No printed book. Only ebook. Access eBook using uLektz apps for Android, iOS and Windows Desktop PC.

Topics
UNIT-1 Introduction

1.1 Equilibrium equations in elasticity subjected to body force, traction forces, and stress-strain relations for plane stress and plane strains.

1.2 General description of Finite Element Method - Application and limitations.

1.3 Types of elements based on geometry.

1.4 Node numbering, Half band width.

UNIT-2 Basic Procedure:

2.1 Euler - Lagrange equation for bar, beam (cantilever / simply supported fixed)

2.2 Principle of virtual work

2.3 Principle of minimum potential energy

2.5 Direct approach for stiffness matrix formulation of bar element

2.6 Galerkin’s method

UNIT-3 Interpolation Models

3.1 Interpolation polynomials- Linear, quadratic and cubic.

3. 2 Simplex complex and multiplex elements.

3.3 2D PASCAL’s triangle.

3.4 CST elements-Shape functions and Nodal load vector, Strain displacement matrix and Jacobian for triangular and rectangular element.

UNIT-4 Solution of 1-D Bars

4.1 Solutions of bars and stepped bars for displacements

4.2 Reactions and stresses by using penalty approach and elimination approach.

4.3 Guass-elimination technique.

UNIT-5 Higher Order Elements

5.1 Langrange’s interpolation

5.2 Higher order one dimensional elements-Quadratic and cubic element and their shape functions.

5.3 Shape function of 2-D quadrilateral element-linear, quadric element Isoparametric, Sub parametric and Super parametric elements

5.4 Numerical integration : 1, 2 and 3 gauge point for 1D and 2D cases.

UNIT-6 Trusses

6.1 Stiffness matrix of Truss element.- Numerical problems.

UNIT-7 Beams

7.1 Hermite shape functions for beam element

7.2 Derivation of stiffness matrix.

7.3 Numerical problems of beams carrying concentrated, UDL and linearly varying loads.

UNIT-8 Heat Transfer

8.1 Steady state heat transfer

8.2 1D heat conduction governing equations

8.3 Functional approach for heat conduction

8.4 Galerkin’s approach for heat conduction - 1D heat transfer in thin fins.

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