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E-raamat: Introduction to Finite Element Analysis Using MATLAB and Abaqus [Taylor & Francis e-raamat]

(University of New South Wales, Canberra, Australia)
  • Formaat: 488 pages, 6 Tables, black and white; 360 Illustrations, black and white
  • Ilmumisaeg: 10-Jun-2013
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9780429166433
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  • Taylor & Francis e-raamat
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Introduction to Finite Element Analysis Using MATLAB and AbaqusSuurem pilt
  • Formaat: 488 pages, 6 Tables, black and white; 360 Illustrations, black and white
  • Ilmumisaeg: 10-Jun-2013
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9780429166433
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9780429166433
There are some books that target the theory of the finite element, while others focus on the programming side of things. Introduction to Finite Element Analysis Using MATLAB® and Abaqus accomplishes both. This book teaches the first principles of the finite element method. It presents the theory of the finite element method while maintaining a balance between its mathematical formulation, programming implementation, and application using commercial software. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. MATLAB is a high-level language specially designed for dealing with matrices, making it particularly suited for programming the finite element method, while Abaqus is a suite of commercial finite element software.

Includes more than 100 tables, photographs, and figures

Provides MATLAB codes to generate contour plots for sample results

Introduction to Finite Element Analysis Using MATLAB and Abaqus introduces and explains theory in each chapter, and provides corresponding examples. It offers introductory notes and provides matrix structural analysis for trusses, beams, and frames. The book examines the theories of stress and strain and the relationships between them. The author then covers weighted residual methods and finite element approximation and numerical integration. He presents the finite element formulation for plane stress/strain problems, introduces axisymmetric problems, and highlights the theory of plates. The text supplies step-by-step procedures for solving problems with Abaqus interactive and keyword editions. The described procedures are implemented as MATLAB codes and Abaqus files can be found on the CRC Press website.
List of Figures
xiii
List of Tables
xxv
Preface xxvii
Author xxix
Chapter 1 Introduction
1(4)
1.1 Prologue
1(1)
1.2 Finite Element Analysis and the User
1(1)
1.3 Aim of the Book
2(1)
1.4 Book Organization
2(3)
Chapter 2 Bar Element
5(58)
2.1 Introduction
5(1)
2.2 One-Dimensional Truss Element
5(4)
2.2.1 Formulation of the Stiffness Matrix: The Direct Approach
5(2)
2.2.2 Two-Dimensional Truss Element
7(2)
2.3 Global Stiffness Matrix Assembly
9(6)
2.3.1 Discretization
9(1)
2.3.2 Elements' Stiffness Matrices in Local Coordinates
9(1)
2.3.3 Elements' Stiffness Matrices in Global Coordinates
10(1)
2.3.3.1 Element 1
11(1)
2.3.3.2 Element 2
11(1)
2.3.3.3 Element 3
12(1)
2.3.4 Global Matrix Assembly
12(1)
2.3.4.1 Only Element 1 Is Present
13(1)
2.3.4.2 Only Element 2 Is Present
13(1)
2.3.4.3 Only Element 3 Is Present
13(1)
2.3.5 Global Force Vector Assembly
14(1)
2.4 Boundary Conditions
15(1)
2.4.1 General Case
15(1)
2.5 Solution of the System of Equations
16(1)
2.6 Support Reactions
17(1)
2.7 Members' Forces
18(1)
2.8 Computer Code: truss.m
19(8)
2.8.1 Data Preparation
20(1)
2.8.1.1 Nodes Coordinates
20(1)
2.8.1.2 Element Connectivity
20(1)
2.8.1.3 Material and Geometrical Properties
20(1)
2.8.1.4 Boundary Conditions
20(1)
2.8.1.5 Loading
21(1)
2.8.2 Element Matrices
21(1)
2.8.2.1 Stiffness Matrix in Local Coordinates
21(1)
2.8.2.2 Transformation Matrix
22(1)
2.8.2.3 Stiffness Matrix in Global Coordinates
22(1)
2.8.2.4 "Steering" Vector
22(1)
2.8.3 Assembly of the Global Stiffness Matrix
23(1)
2.8.4 Assembly of the Global Force Vector
23(1)
2.8.5 Solution of the Global System of Equations
23(1)
2.8.6 Nodal Displacements
23(1)
2.8.7 Element Forces
23(1)
2.8.8 Program Scripts
24(3)
2.9 Problems
27(8)
2.9.1 Problem 2.1
27(5)
2.9.2 Problem 2.2
32(3)
2.10 Analysis of a Simple Truss with Abaqus
35(28)
2.10.1 Overview of Abaqus
35(1)
2.10.2 Analysis of a Truss with Abaqus Interactive Edition
36(1)
2.10.2.1 Modeling
36(15)
2.10.2.2 Analysis
51(6)
2.10.3 Analysis of a Truss with Abaqus Keyword Edition
57(6)
Chapter 3 Beam Element
63(44)
3.1 Introduction
63(1)
3.2 Stiffness Matrix
63(4)
3.3 Uniformly Distributed Loading
67(4)
3.4 Internal Hinge
71(2)
3.5 Computer Code: beam.m
73(8)
3.5.1 Data Preparation
73(1)
3.5.1.1 Nodes Coordinates
73(1)
3.5.1.2 Element Connectivity
74(1)
3.5.1.3 Material and Geometrical Properties
74(1)
3.5.1.4 Boundary Conditions
74(1)
3.5.1.5 Internal Hinges
74(1)
3.5.1.6 Loading
75(1)
3.5.1.7 Stiffness Matrix
76(1)
3.5.2 Assembly and Solution of the Global System of Equations
76(1)
3.5.3 Nodal Displacements
76(1)
3.5.4 Element Forces
77(4)
3.6 Problems
81(9)
3.6.1 Problem 3.1
81(3)
3.6.2 Problem 3.2
84(3)
3.6.3 Problem 3.3
87(3)
3.7 Analysis of a Simple Beam with Abaqus
90(17)
3.7.1 Interactive Edition
90(13)
3.7.2 Analysis of a Beam with Abaqus Keyword Edition
103(4)
Chapter 4 Rigid Jointed Frames
107(28)
4.1 Introduction
107(1)
4.2 Stiffness Matrix of a Beam-Column Element
107(1)
4.3 Stiffness Matrix of a Beam-Column Element in the Presence of Hinged End
107(1)
4.4 Global and Local Coordinate Systems
108(1)
4.5 Global Stiffness Matrix Assembly and Solution for Unknown Displacements
109(1)
4.6 Computer Code: frame.m
109(15)
4.6.1 Data Preparation
109(1)
4.6.1.1 Nodes Coordinates
110(1)
4.6.1.2 Element Connectivity
110(1)
4.6.1.3 Material and Geometrical Properties
110(1)
4.6.1.4 Boundary Conditions
110(1)
4.6.1.5 Internal Hinges
111(1)
4.6.1.6 Loading
111(1)
4.6.2 Element Matrices
112(1)
4.6.2.1 Stiffness Matrix in Local Coordinates
112(1)
4.6.2.2 Transformation Matrix
113(1)
4.6.2.3 Stiffness Matrix in Global Coordinates
113(1)
4.6.2.4 "Steering" Vector
113(1)
4.6.2.5 Element Loads
113(1)
4.6.3 Assembly of the Global Stiffness Matrix
113(1)
4.6.4 Solution of the Global System of Equations
114(1)
4.6.5 Nodal Displacements
114(1)
4.6.6 Element Forces
114(10)
4.7 Analysis of a Simple Frame with Abaqus
124(11)
4.7.1 Interactive Edition
124(8)
4.7.2 Keyword Edition
132(3)
Chapter 5 Stress and Strain Analysis
135(40)
5.1 Introduction
135(1)
5.2 Stress Tensor
135(9)
5.2.1 Definition
135(2)
5.2.2 Stress Tensor-Stress Vector Relationships
137(2)
5.2.3 Transformation of the Stress Tensor
139(1)
5.2.4 Equilibrium Equations
139(1)
5.2.5 Principal Stresses
140(1)
5.2.6 von Mises Stress
141(1)
5.2.7 Normal and Tangential Components of the Stress Vector
141(2)
5.2.8 Mohr's Circles for Stress
143(1)
5.2.9 Engineering Representation of Stress
144(1)
5.3 Deformation and Strain
144(10)
5.3.1 Definition
144(1)
5.3.2 Lagrangian and Eulerian Descriptions
145(1)
5.3.3 Displacement
146(1)
5.3.4 Displacement and Deformation Gradients
147(1)
5.3.5 Green Lagrange Strain Matrix
148(1)
5.3.6 Small Deformation Theory
149(1)
5.3.6.1 Infinitesimal Strain
149(1)
5.3.6.2 Geometrical Interpretation of the Terms of the Strain Tensor
150(2)
5.3.6.3 Compatibility Conditions
152(1)
5.3.7 Principal Strains
152(1)
5.3.8 Transformation of the Strain Tensor
153(1)
5.3.9 Engineering Representation of Strain
153(1)
5.4 Stress-Strain Constitutive Relations
154(9)
5.4.1 Generalized Hooke's Law
154(1)
5.4.2 Material Symmetries
155(1)
5.4.2.1 Symmetry with respect to a Plane
155(2)
5.4.2.2 Symmetry with respect to Three Orthogonal Planes
157(1)
5.4.2.3 Symmetry of Rotation with respect to One Axis
157(1)
5.4.3 Isotropic Material
158(2)
5.4.3.1 Modulus of Elasticity
160(1)
5.4.3.2 Poisson's Ratio
160(1)
5.4.3.3 Shear Modulus
160(1)
5.4.3.4 Bulk Modulus
160(2)
5.4.4 Plane Stress and Plane Strain
162(1)
5.5 Solved Problems
163(12)
5.5.1 Problem 5.1
163(1)
5.5.2 Problem 5.2
164(3)
5.5.3 Problem 5.3
167(1)
5.5.4 Problem 5.4
168(2)
5.5.5 Problem 5.5
170(1)
5.5.6 Problem 5.6
171(1)
5.5.7 Problem 5.7
172(2)
5.5.8 Problem 5.8
174(1)
Chapter 6 Weighted Residual Methods
175(16)
6.1 Introduction
175(1)
6.2 General Formulation
175(1)
6.3 Galerkin Method
176(2)
6.4 Weak Form
178(1)
6.5 Integrating by Part over Two and Three Dimensions (Green Theorem)
179(4)
6.6 Rayleigh Ritz Method
183(8)
6.6.1 Definition
183(1)
6.6.2 Functional Associated with an Integral Form
183(1)
6.6.3 Rayleigh Ritz Method
183(2)
6.6.4 Example of a Natural Functional
185(6)
Chapter 7 Finite Element Approximation
191(20)
7.1 Introduction
191(1)
7.2 General and Nodal Approximations
191(2)
7.3 Finite Element Approximation
193(2)
7.4 Basic Principles for the Construction of Trial Functions
195(2)
7.4.1 Compatibility Principle
195(1)
7.4.2 Completeness Principle
196(1)
7.5 Two-Dimensional Finite Element Approximation
197(10)
7.5.1 Plane Linear Triangular Element for C° Problems
197(1)
7.5.1.1 Shape Functions
197(2)
7.5.1.2 Reference Element
199(3)
7.5.1.3 Area Coordinates
202(1)
7.5.2 Linear Quadrilateral Element for C° Problems
203(1)
7.5.2.1 Geometrical Transformation
203(3)
7.5.2.2 Construction of a Trial Function over a Linear Quadrilateral Element
206(1)
7.6 Shape Functions of Some Classical Elements for C° Problems
207(4)
7.6.1 One-Dimensional Elements
207(1)
7.6.1.1 Two-Nodded Linear Element
207(1)
7.6.1.2 Three-Nodded Quadratic Element
207(1)
7.6.2 Two-Dimensional Elements
207(1)
7.6.2.1 Four-Nodded Bilinear Quadrilateral
207(1)
7.6.2.2 Eight-Nodded Quadratic Quadrilateral
208(1)
7.6.2.3 Three-Nodded Linear Triangle
208(1)
7.6.2.4 Six-Nodded Quadratic Triangle
208(1)
7.6.3 Three-Dimensional Elements
208(1)
7.6.3.1 Four-Nodded Linear Tetrahedra
208(1)
7.6.3.2 Ten-Nodded Quadratic Tetrahedra
209(1)
7.6.3.3 Eight-Nodded Linear Brick Element
209(1)
7.6.3.4 Twenty-Nodded Quadratic Brick Element
210(1)
Chapter 8 Numerical Integration
211(20)
8.1 Introduction
211(1)
8.2 Gauss Quadrature
211(5)
8.2.1 Integration over an Arbitrary Interval [ a, b]
214(1)
8.2.2 Integration in Two and Three Dimensions
215(1)
8.3 Integration over a Reference Element
216(1)
8.4 Integration over a Triangular Element
217(2)
8.4.1 Simple Formulas
217(1)
8.4.2 Numerical Integration over a Triangular Element
218(1)
8.5 Solved Problems
219(12)
8.5.1 Problem 8.1
219(2)
8.5.2 Problem 8.2
221(5)
8.5.3 Problem 8.3
226(5)
Chapter 9 Plane Problems
231(122)
9.1 Introduction
231(1)
9.2 Finite Element Formulation for Plane Problems
231(3)
9.3 Spatial Discretization
234(1)
9.4 Constant Strain Triangle
235(28)
9.4.1 Displacement Field
236(1)
9.4.2 Strain Matrix
237(1)
9.4.3 Stiffness Matrix
237(1)
9.4.4 Element Force Vector
237(1)
9.4.4.1 Body Forces
238(1)
9.4.4.2 Traction Forces
238(1)
9.4.4.3 Concentrated Forces
239(1)
9.4.5 Computer Codes Using the Constant Strain Triangle
240(1)
9.4.5.1 Data Preparation
241(2)
9.4.5.2 Nodes Coordinates
243(1)
9.4.5.3 Element Connectivity
243(1)
9.4.5.4 Material Properties
243(1)
9.4.5.5 Boundary Conditions
243(1)
9.4.5.6 Loading
243(1)
9.4.5.7 Main Program
243(2)
9.4.5.8 Element Stiffness Matrix
245(1)
9.4.5.9 Assembly of the Global Stiffness Matrix
246(1)
9.4.5.10 Solution of the Global System of Equations
246(1)
9.4.5.11 Nodal Displacements
246(1)
9.4.5.12 Element Stresses and Strains
246(1)
9.4.5.13 Results and Discussion
247(2)
9.4.5.14 Program with Automatic Mesh Generation
249(4)
9.4.6 Analysis with Abaqus Using the CST
253(1)
9.4.6.1 Interactive Edition
253(7)
9.4.6.2 Keyword Edition
260(3)
9.5 Linear Strain Triangle
263(16)
9.5.1 Displacement Field
264(1)
9.5.2 Strain Matrix
265(1)
9.5.3 Stiffness Matrix
266(1)
9.5.4 Computer Code: LST_PLANE_STRESS_MESH.m
266(4)
9.5.4.1 Numerical Integration of the Stiffness Matrix
270(1)
9.5.4.2 Computation of the Stresses and Strains
271(1)
9.5.5 Analysis with Abaqus Using the LST
272(1)
9.5.5.1 Interactive Edition
272(6)
9.5.5.2 Keyword Edition
278(1)
9.6 The Bilinear Quadrilateral
279(25)
9.6.1 Displacement Field
280(1)
9.6.2 Strain Matrix
281(1)
9.6.3 Stiffness Matrix
282(1)
9.6.4 Element Force Vector
282(2)
9.6.5 Computer Code: Q4_PLANE_STRESS.m
284(1)
9.6.5.1 Data Preparation
284(3)
9.6.5.2 Main Program
287(2)
9.6.5.3 Integration of the Stiffness Matrix
289(1)
9.6.5.4 Computation of the Stresses and Strains
290(1)
9.6.5.5 Program with Automatic Mesh Generation
291(4)
9.6.6 Analysis with Abaqus Using the Q4 Quadrilateral
295(1)
9.6.6.1 Interactive Edition
295(7)
9.6.6.2 Keyword Edition
302(2)
9.7 The 8-Node Quadrilateral
304(22)
9.7.1 Formulation
304(3)
9.7.2 Equivalent Nodal Forces
307(1)
9.7.3 Program Q8_PLANE_STRESS.m
307(1)
9.7.3.1 Data Preparation
307(4)
9.7.3.2 Main Program
311(3)
9.7.3.3 Integration of the Stiffness Matrix
314(1)
9.7.3.4 Results with the Coarse Mesh
314(1)
9.7.3.5 Program with Automatic Mesh Generation
315(6)
9.7.4 Analysis with Abaqus Using the Q8 Quadrilateral
321(5)
9.8 Solved Problem with MATLAB®
326(27)
9.8.1 Strip Footing with the CST Element
326(5)
9.8.2 Strip Footing with the LST Element
331(5)
9.8.3 Bridge Pier with the Q8 Element
336(17)
Chapter 10 Axisymmetric Problems
353(26)
10.1 Definition
353(1)
10.2 Strain-Displacement Relationship
353(1)
10.3 Stress-Strain Relations
354(1)
10.4 Finite Element Formulation
355(3)
10.4.1 Displacement Field
355(1)
10.4.2 Strain Matrix
355(1)
10.4.3 Stiffness Matrix
356(1)
10.4.4 Nodal Force Vectors
356(1)
10.4.4.1 Body Forces
356(1)
10.4.4.2 Surface Forces Vector
356(1)
10.4.4.3 Concentrated Loads
357(1)
10.4.4.4 Example
357(1)
10.5 Programming
358(14)
10.5.1 Computer Code: AXI_SYM_T6.m
359(3)
10.5.1.1 Numerical Integration of the Stiffness Matrix
362(1)
10.5.1.2 Results
363(2)
10.5.2 Computer Code: AXI_SYM_Q8.m
365(3)
10.5.2.1 Numerical Integration of the Stiffness Matrix
368(2)
10.5.2.2 Results
370(2)
10.6 Analysis with Abaqus Using the 8-Node Quadrilateral
372(7)
Chapter 11 Thin and Thick Plates
379(40)
11.1 Introduction
379(1)
11.2 Thin Plates
379(4)
11.2.1 Differential Equation of Plates Loaded in Bending
379(3)
11.2.2 Governing Equation in terms of Displacement Variables
382(1)
11.3 Thick Plate Theory or Mindlin Plate Theory
383(2)
11.3.1 Stress-Strain Relationship
384(1)
11.4 Linear Elastic Finite Element Analysis of Plates
385(4)
11.4.1 Finite Element Formulation for Thin Plates
385(1)
11.4.1.1 Triangular Element
385(2)
11.4.1.2 Rectangular Element
387(1)
11.4.2 Finite Element Formulation for Thick Plates
388(1)
11.5 Boundary Conditions
389(1)
11.5.1 Simply Supported Edge
389(1)
11.5.2 Built-in or Clamped Edge
390(1)
11.5.3 Free Edge
390(1)
11.6 Computer Program for Thick Plates Using the 8-Node Quadrilateral
390(10)
11.6.1 Main Program: Thick_plate_Q8.m
390(5)
11.6.2 Data Preparation
395(1)
11.6.2.1 Stiffness Matrices
395(1)
11.6.2.2 Boundary Conditions
395(1)
11.6.2.3 Loading
396(1)
11.6.2.4 Numerical Integration of the Stiffness Matrix
397(1)
11.6.3 Results
398(1)
11.6.3.1 Determination of the Resulting Moments and Shear Forces
398(1)
11.6.3.2 Contour Plots
399(1)
11.7 Analysis with Abaqus
400(19)
11.7.1 Preliminary
400(1)
11.7.1.1 Three-Dimensional Shell Elements
401(1)
11.7.1.2 Axisymmetric Shell Elements
401(1)
11.7.1.3 Thick versus Thin Conventional Shell
401(1)
11.7.2 Simply Supported Plate
401(5)
11.7.3 Three-Dimensional Shells
406(13)
Appendix A List of MATLAB® Modules and Functions 419(26)
Appendix B Statically Equivalent Nodal Forces 445(2)
Appendix C Index Notation and Transformation Laws for Tensors 447(6)
References and Bibliography 453(2)
Index 455
Dr. Amar Khennane is a senior lecturer in the School of Engineering and Information Technology at the University of New South Wales, Canberra, Australian Capital Territory, Australia. He earned his PhD in civil engineering from the University of Queensland, Australia; a Master of Science in structural engineering from Heriot-Watt University, United Kingdom; and a bachelors degree in civil engineering from the University of Tizi-Ouzou, Algeria. His teaching experience spans 20 years, and two continents. He has taught structural analysis, structural mechanics, and the finite element method at various universities.
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