Engineering Finite Element Analysis

Engineering Finite Element Analysis
اسم المؤلف
Ramana M. Pidaparti
التاريخ
18 نوفمبر 2019
المشاهدات
التقييم
(لا توجد تقييمات)
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Engineering Finite Element Analysis
Ramana M. Pidaparti
University of Georgia
Synthesis Lectures on Mechanical Engineering
Contents
Preface . Xiii
1 Introduction . 1
1.1 Overview 1
1.2 Computer-aided Engineering 1
1.3 Types of Numerical Methods . 2
1.4 Finite Element Analysis . 3
1.4.1 the Need for Fea . 4
1.4.2 Basic Steps in Fea . 6
1.5 Introduction to Ansys . 6
1.5.1 Ansys Modules 7
1.5.2 Using Ansys . 8
1.5.3 Graphical User Interface (Gui) . 9
1.5.4 Ansys Workbench . 11
1.5.5 Ansys Workbench Vs. Ansys Mechanical . 11
1.6 Exercise Problems . 13
2 Mathematical Preliminaries 17
2.1 Overview . 17
2.2 Matrix Algebra . 17
2.2.1 Matrix Addition and Subtraction . 18
2.2.2 Scalar Multiplication . 19
2.2.3 Transpose of a Matrix 19
2.2.4 Multiplication of Vectors . 20
2.2.5 Multiplication of Matrices 20
2.2.6 Multiplication of a Matrix With a Vector . 20
2.2.7 Determinant . 21
2.2.8 Inverse of a Matrix 21
2.3 System of Linear Equations . 22
2.3.1 Cramer’s Rule 22
2.3.2 Gaussian Elimination 22x
2.3.3 Cholesky’s Decomposition 23
2.4 Eigenvalues and Eigenvectors . 28
2.5 Numerical Integration . 30
2.6 Matrix Algebra Using Matlab Toolbox 32
2.7 Exercise Problems . 34
3 Finite Element Analysis–basics . 37
3.1 Overview . 37
3.2 Fem Formulations 37
3.2.1 Direct Formulation 37
3.2.2 the Minimum Total Potential Energy Formulation 39
3.2.3 Weighted Residual Formulation 40
3.3 Generic Fem Procedure . 42
3.4 Finite Element Modeling Techniques . 43
3.4.1 Types of Finite Elements . 43
3.4.2 Coordinate Systems . 44
3.4.3 Using Symmetry 45
3.4.4 Mesh Refining (Free Meshing Vs. Mapped Meshing) . 45
3.5 Verification of Fea Results . 47
3.6 Exercise Problems . 47
4 1d Finite Element Analysis 49
4.1 Overview . 49
4.2 1d Elements . 49
4.2.1 Finite Element Matrix Equations . 49
4.3 Shape Functions 50
4.3.1 Shape Function Properties 51
4.4 Stress Analysis . 51
4.4.1 Axial Bar Element . 52
4.4.2 Torsional Bar Element . 55
4.5 Heat Transfer Analysis . 59
4.5.1 Heat Transfer Element . 60
4.6 Fluid Analysis 65
4.7 Free Vibration Analysis 67
4.8 Exercise Problems . 70
4.9 Fea Activity Template 74xi
5 Truss, Beam, and Frame Analysis . 75
5.1 Overview . 75
5.2 Trusses . 75
5.3 Truss Finite Element 76
5.4 Space Trusses 85
5.5 Beams 87
5.6 Beam Finite Element Equations . 88
5.7 Frame Element Formulation 94
5.8 Exercise Problems 100
6 1d Fea Using Ansys . 107
6.1 Overview 107
6.2 Elements in Ansys for 1d Analysis 107
6.3 Axial Bar Under Tensile Load 107
6.4 Truss Analysis–example #1 120
6.5 Truss Analysis–example #2 124
6.6 Space Truss Analysis–example . 126
6.7 Beam Analysis–example 130
6.8 Frame Analysis–example 135
6.9 Static and Modal Analysis of a 3d Frame . 139
6.9.1 Structural Analysis . 139
6.9.2 Modal Analysis 145
6.10 1d Heat Transfer Analysis–example 150
6.11 Exercise Problems 153
7 2d Finite Element Analysis . 155
7.1 Overview 155
7.2 Element Types and Shape Functions . 155
7.2.1 Triangular Element . 155
7.3 Isoparametric Formulation . 158
7.4 Higher-order Elements . 160
7.4.1 Shape Functions for Higher-order Elements . 161
7.5 Axisymmetric Elements . 163
7.5.1 Axisymmetric Rectangular Element 164
7.6 Basics of 2d Stress Analysis (Plane Solids) 165
7.6.1 Examples of 2d Elements for Stress Analysis in Ansys . 168xii
7.7 Basics of 2d Heat Transfer Analysis . 171
7.7.1 Rectangular Element 171
7.7.2 Examples of 2d Elements for Heat Transfer Analysis in Ansys 177
7.8 Basics of Fluid Mechanics Analysis 181
7.8.1 Examples of 2d Elements for Fluid Analysis in Ansys . 182
7.8.2 Ansys Steps for 2d Drug Diffusion Analysis . 188
7.9 Exercise Problems 192
8 3d Finite Element Analysis . 199
8.1 Overview 199
8.2 3d Elements 199
8.3 Elements in Ansys for 3d Analysis 199
8.3.1 Solid Analysis Elements . 200
8.3.2 Heat Transfer/ Thermal Analysis Elements 200
8.3.3 Fluid Analysis Elements . 201
8.4 3d Solid Modeling for Import to Ansys 202
8.5 Multi-physics Problems . 220
8.6 Multi-physics (Fluid-solid Interaction) Example . 220
8.6.1 Governing Equations Defining the Physics of Airway Wall . 222
8.6.2 Governing Equations Defining the Physics of Fluid . 222
8.6.3 Input and Boundary Conditions . 223
8.7 Exercise Problems 242
9 Sample Project 245
9.1 Overview 245
9.2 Benefits in Conducting Analysis Through Projects 245
9.3 Sample Project—analysis of Wing Geometries for Mav 245
9.3.1 Objective . 246
9.3.2 Analysis Models . 246
9.3.3 Discussion 246
9.4 Example Projects for Analysis 249
Bibliography . 251
Author’s Biography
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