# Finite Element Analysis by G. Lakshmi Narasaiah full ebook in pdf format

Rajan Sharma | 04-Feb-2016 |

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Chapter 1
Introduction 1-34
1.1 Design and Analysis of a Component.. ............................................................ 1
1.2 Approximate Method vs. Exact Method ........................................................ 4
1.3 Weighted Residual Methods ........................................................................... 5
1.4 Variational Method or Rayleigh - Ritz Method ............................................ 12
1.5 Principle of Minimum Potential Energy ........................................................ 22
1.6 Origin ofFEM .............................................................................................. 26
1.7 Principle ofFEM .......................................................................................... 27
1.8, Classification ofFEM ................................................................................... 31
1.9 Types of Analyses ........................................................................................ 32
1.10 Summary ....................................................................................................... 33
Objective Questions .................................................................................................. 33
Chapter 2
Matrix Operations 35-60
2.1 Types of Matrices ........................................................................................ 35
2.2 MatrixAlgebra ....................................................................... ~ ..................... 37
2.3 Detenninant .................................................................................................. 39
2.4 Inversion of a Matrix .................................................................................... 41
2.5 Methods of Solution of Simultaneous Equations .......................................... 41
2.5.1 By Inversion of the Coefficient Matrix ............................................. 42
2.5.2 Direct Methods ................................................................................. 44
2.5.3 Iterative Methods .............................................................................. 53
2.6 Eigen Values and Eigen Vectors ................................................................... 55
2.7 Matrix Inversion Through Characteristic Equation ...................................... 59
2.8 Summary ....................................................................................................... 60
Chapter 3
Theory of Elasticity 61-84
3.1 Degrees of Freedom .................................................................................... 61
3.2 Rigid Body Motion ........................................................................................ 62
3.3 Discrete Structures ...................................................................................... 62
3.4 Continuum Structures ................................................................................... 62
3.5 Material Properties ....................................................................................... 63
3.6 Linear Analysis ............................................................................................. 63
3.7 Non-linear Analysis ...................................................................................... 63
3.8 Stiffness and Flexibility ................................................................................. 64
3.9 Principle of Minimum Potential Energy ........................................................ 65
3.10 Stress and Strain at a Point .......................................................................... 65
3.11 Principal Stresses ......................................................................................... 68
3.12 Mohr's Circle for Representation of 2-D Stresses ...................................... 68
3.13 VonMises Stress ........................................................................................... 71
3.14 Theory of Elasticity ...................................................................................... 72
3.15 Summary ....................................................................................................... 82
Chapter 4
Discrete (1-D) Elements 85-125
4.1 Degrees of Freedom of Different Elements ................................................ 85
4.2 Calculation of Stiffness Matrix by Direct Method ....................................... 86
4.3 Calculation of Stiffness Matrix by Variational Principle ............................... 88
4.4 Transformation Matrix .................................................................................. 92
, 4.5 Assembling Element Stiffness Matrices ...................................................... 94
4.6 Boundary Conditions .................................................................................... 96
4.7 Beam Element Stiffness Matrix by Variational Approach ............................ 98
4.8 General Beam Element .............................................................................. 100
4.9 Pipe Element ............................................................................................... 103
4.10 Summary ..................................................................................................... 104
Objective Questions ................................................................................................ 105
Solved Problems ...................................................................................................... 108
Chapter 5
Continuum (2-D & 3-D) Elements 127-158
5.1 2-D Elements Subjected to In-plane Loads ................................................ 127
5.2 Simplex, Complex and Multiplex Elements ................................................ 128
53 Stiffness Matrix of a CST Element ............................................................ 129
5.3.1 Stiffness Matrix of a Right Angled Triangle ................................... 131
5.4 Convergence Conditions ............................................................................. 133
5.5 Geometric Isotropy ..................................................................................... 136
5.6 Aspect Ratio ............................................................................................... 138
5.7 Inter-Element Compatibility ........................................................................ 139
5.8 2-D Elements Subjected to Bending Loads ................................................ 141
5.9 3-D Elements .............................................................................................. 143
5. JO Axi-symmetric Elements ............................................................................ 144
5.11 Summary ..................................................................................................... 146
Objective Que!t,tions .............................................................•.................................. 147
Solved Problen'!~ ...................................................................................................... 152
Chapter 6
Higher Order and Iso-Parametric Elements 159-199
6.1 Higher Order Elements .............................................................................. 159
6.2 Isoparametric Elements .............................................................................. 169
6.3 Stiffness Matrices of Some Iso-parametric Elements ................................ 170
6.4 Jacobian ...................................................................................................... 182
6.5 Strain-displacement Relations .................................................................... 184
6.6 Summary ..................................................................................................... 188
Objective Questions ................................................................................................ 189
Solvetl Problems ...................................................................................................... 190
Chapter 7
Factors Influencing Solution 201-236
7.3 Consistent Loads for a Few Common Cases ............................................. 206
7.4 Assembling Element Stiffness Matrices .................................................... 209
7.5 Automatic Mesh Generation ...................................................................... 214
7.6 Optimum Mesh Model ................................................................................ 215
7.7 Gaussian Points & Numerical Integration .................................................. 216
7.8 Modelling Techniques ................................................................................ 220
7.9 Boundary Conditions for Continuum Analysis ............................................ 224
7.10 Transition Element ...................................................................................... 228
7.11 Substructuring or Super Element Approach ............................................... 230
7.12 Deformed and Undeformed Plots .............................................................. 231
7.13 Summary ..................................................................................................... 232
Objective Questions ..........•.....•.•.......•....•................................•.........•.•.......•........... 233
Chapter 8
Dynamic Analysis (undamped free vibrations) 237-253
8.1 Normalising Eigenvectors ........................................................................... 239
8.2 Modelling for Dynamic Analysis ................................................................ 240
8.3 Mass Matrix ............................................................................................... 240
8.4 Summary ..................................................................................................... 251
Objective Questions .•...•.•......••.•.....................•........................................................ 252
Chapter 9
9.1 Governing Equations ................................................................................... 255
9.2 1-0 Heat Conduction ................................................................................. 257
9.2.1 Heat Conduction Through a Wall .................................................... 258
9.2.2 Heat Transfer Through a Fin .......................................................... 268
9.3 2-D heat Conduction in a Plate .................................................................. 273
9.4 Summary ..................................................................................................... 275
Objective Questions ....•......••......••......••..•................................•...........................•... 276
Chapter 10
Design Validation and Other Types of Analysis 277-291
10.1 Compliance with Design Codes ................................................................. 277
10.2 Transient Heat Condition ............................................................................ 281
10.3 Buckling of Columns .................................................................................. 282
10.4 FatigueAnalysis ......................................................................................... 283
10.5 Creep Analysis ........................................................................................... 285
10.6 Damped Free Vibration .............................................................................. 287
10.7 Forced Vibration ......................................................................................... 288
10.8 Torsion of a Non-circular Rod .................................................................... 289
Chapter 11
Computational Fluid Dynamics 293-307
11.1 Introduction ................................................................................................. 293
11.2 Governing Equation .................................................................................... 294
11.3 Finite Difference Method (FDM) .............................................................. 296
11.4 Elliptic Equations (or boundary value problems) ........................................ 297
11.5 Finite Volume Method (FVM) .................................................................... 305
11.6 FDM vs. FEM .......................................................................................... :. 307
Chapter 12
Practical Analysis Using a Software 309-329
12.1 Using a General Purpose Software ............................................................ 309
12.2 Some Examples with ANSYS .................................................................... 311