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E-raamat: Essentials of the Finite Element Method: For Mechanical and Structural Engineers

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(Professor, University of Stavanger, Stavanger, Norway)
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  • Ilmumisaeg: 14-Jul-2015
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780128026069
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Essentials of the Finite Element Method: For Mechanical and Structural EngineersSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 14-Jul-2015
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780128026069
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Fundamental coverage, analytic mathematics, and up-to-date software applications are hard to find in a single text on the finite element method (FEM). Dimitrios Pavlou’sEssentials of the Finite Element Method: For Structural and Mechanical Engineers makes the search easier by providing a comprehensive but concise text for those new to FEM, or just in need of a refresher on the essentials.

Essentials of the Finite Element Method explains the basics of FEM, then relates these basics to a number of practical engineering applications. Specific topics covered include linear spring elements, bar elements, trusses, beams and frames, heat transfer, and structural dynamics. Throughout the text, readers are shown step-by-step detailed analyses for finite element equations development. The text also demonstrates how FEM is programmed, with examples in MATLAB, CALFEM, and ANSYS allowing readers to learn how to develop their own computer code.

Suitable for everyone from first-time BSc/MSc students to practicing mechanical/structural engineers,Essentials of the Finite Element Method presents a complete reference text for the modern engineer.

  • Provides complete and unified coverage of the fundamentals of finite element analysis
  • Covers stiffness matrices for widely used elements in mechanical and civil engineering practice
  • Offers detailed and integrated solutions of engineering examples and computer algorithms in ANSYS, CALFEM, and MATLAB

Muu info

A unified presentation of finite element analysis with detailed step-by-step analytic procedures for equations for mechanical and structural engineers
Preface xiii
Acknowledgments xv
Chapter 1 An Overview of the Finite Element Method
1(18)
1.1 What Are Finite Elements?
1(1)
1.2 Why Finite Element Method Is Very Popular?
1(1)
1.3 Main Advantages of Finite Element Method
1(1)
1.4 Main Disadvantages of Finite Element Method
1(1)
1.5 What Is Structural Matrix?
2(1)
1.5.1 Stiffness Matrix
2(1)
1.5.2 Transfer Matrix
3(1)
1.6 What Are the Steps to be Followed for Finite Element Method Analysis of Structure?
3(1)
1.6.1 Step
1. Discretize or Model the Structure
4(1)
1.6.2 Step
2. Define the Element Properties
4(1)
1.6.3 Step
3. Assemble the Element Structural Matrices
4(1)
1.6.4 Step
4. Apply the Loads
4(1)
1.6.5 Step
5. Define Boundary Conditions
4(1)
1.6.6 Step
6. Solve the System of Linear Algebraic Equations
4(1)
1.6.7 Step
7. Calculate Stresses
4(1)
1.7 What About the Available Software Packages?
4(1)
1.8 Physical Principles in the Finite Element Method
5(2)
1.9 From the Element Equation to the Structure Equation
7(1)
1.10 Computer-Aided Learning of the Finite Element Method
7(12)
1.10.1 Introduction to CALFEM
7(3)
1.10.2 Spring elements
10(1)
1.10.3 Bar Elements for Two-Dimensional Analysis
11(1)
1.10.4 Bar Elements for Three-Dimensional Analysis
12(1)
1.10.5 Beam Elements for Two-Dimensional Analysis
13(1)
1.10.6 Beam Elements for Three-Dimensional Analysis
14(1)
1.10.7 System Functions
15(1)
1.10.8 Statement Functions
15(1)
1.10.9 Graphic Functions
16(1)
1.10.10 Working Environment in ANSYS
16(1)
References
17(2)
Chapter 2 Mathematical Background
19(22)
2.1 Vectors
19(5)
2.1.1 Definition of Vector
19(1)
2.1.2 Scalar Product
19(2)
2.1.3 Vector Product
21(1)
2.1.4 Rotation of Coordinate System
22(1)
2.1.5 The Vector Differential Operator (Gradient)
23(1)
2.1.6 Green's Theorem
23(1)
2.2 Coordinate Systems
24(4)
2.2.1 Rectangular (or Cartesian) Coordinate System
24(1)
2.2.2 Cylindrical Coordinate System
25(1)
2.2.3 Spherical Coordinate System
25(1)
2.2.4 Component Transformation
26(2)
2.2.5 The Vector Differential Operator (Gradient) in Cylindrical and Spherical Coordinates
28(1)
2.3 Elements of Matrix Algebra
28(6)
2.3.1 Basic Definitions
28(1)
2.3.2 Basic Operations
29(5)
2.4 Variational Formulation of Elasticity Problems
34(7)
2.4.1 Definition of the Variation of a Function
34(1)
2.4.2 Properties of Variations
35(1)
2.4.3 Derivation of the Functional from the Boundary Value Problem
35(5)
References
40(1)
Chapter 3 Linear Spring Elements
41(16)
3.1 The Element Equation
41(2)
3.1.1 The Mechanical Behavior of the Material
41(1)
3.1.2 The Principle of Direct Equilibrium
42(1)
3.2 The Stiffness Matrix of a System of Springs
43(14)
3.2.1 Derivation of Element Matrices
43(1)
3.2.2 Expansion of Element Equations to the Degrees of Freedom of the Structure
44(1)
3.2.3 Assembly of Element Equations
44(1)
3.2.4 Derivation of the Field Values
44(11)
References
55(2)
Chapter 4 Bar Elements and Hydraulic Networks
57(24)
4.1 Displacement Interpolation Functions
57(3)
4.1.1 Functional Form of Displacement Distribution
57(2)
4.1.2 Derivation of the Element Equation
59(1)
4.2 Alternative Procedure Based On the Principle of Direct Equilibrium
60(1)
4.2.1 The Mechanical Behavior of the Material
60(1)
4.2.2 The Principle of Direct Equilibrium
61(1)
4.3 Finite Element Method Modeling of a System of Bars
61(6)
4.3.1 Derivation of Element Matrices
62(1)
4.3.2 Expansion of Element Equations to the Degrees of Freedom of the Structure
62(1)
4.3.3 Assembly of Element Equations
63(1)
4.3.4 Derivation of the Field Values
63(4)
4.4 Finite Elements Method Modeling of a Piping Network
67(14)
References
79(2)
Chapter 5 Trusses
81(54)
5.1 The Element Equation for Plane Truss Members
81(2)
5.2 The Element Equation for 3D Trusses
83(2)
5.3 Calculation of the Bar's Axial Forces (Internal Forces)
85(50)
References
133(2)
Chapter 6 Beams
135(78)
6.1 Element Equation of a Two-Dimensional Beam Subjected to Nodal Forces
135(15)
6.1.1 The Displacement Function
135(2)
6.1.2 The Element Stiffness Matrix
137(13)
6.2 Two-Dimensional Element Equation of a Beam Subjected to a Uniform Loading
150(3)
6.3 Two-Dimensional Element Equation of a Beam Subjected to an Arbitrary Varying Loading
153(23)
6.4 Two-Dimensional Element Equation of a Beam on Elastic Foundation Subjected to Uniform Loading
176(5)
6.5 Engineering Applications of the Element Equation of the Beam on Elastic Foundation
181(11)
6.5.1 Beam Supported on Equispaced Elastic Springs
181(1)
6.5.2 Cylindrical Shells Under Axisymmetric Loading
181(11)
6.6 Element Equation for a Beam Subjected to Torsion
192(2)
6.6.1 The Mechanical Behavior of the Material
192(1)
6.6.2 The Principle of Direct Equilibrium
193(1)
6.7 Two-Dimensional Element Equation For a Beam Subjected To Nodal Axial Forces, Shear Forces, Bending Moments, and Torsional Moments
194(2)
6.8 Three-Dimensional Element Equation for a Beam Subjected to Nodal Axial Forces, Shear Forces, Bending Moments, and Torsional Moments
196(17)
References
212(1)
Chapter 7 Frames
213(66)
7.1 Framed Structures
213(1)
7.2 Two-Dimensional Frame Element Equation Subjected to Nodal Forces
213(4)
7.3 Two-Dimensional Frame Element Equation Subjected to Arbitrary Varying Loading
217(13)
7.4 Three-Dimensional Beam Element Equation Subjected to Nodal Forces
230(4)
7.5 Distribution of Bending Moments, Shear Forces, Axial Forces, and Torsional Moments of Each Element
234(45)
References
278(1)
Chapter 8 The Principle of Minimum Potential Energy for One-Dimensional Elements
279(10)
8.1 The Basic Concept
279(1)
8.2 Application of the MPE Principle on Systems of Spring Elements
280(1)
8.3 Application of the MPE Principle on Systems of Bar Elements
281(3)
8.4 Application of the MPE Principle on Trusses
284(1)
8.5 Application of the MPE Principle on Beams
284(5)
References
288(1)
Chapter 9 From "Isotropic" to "Orthotropic" Plane Elements: Elasticity Equations for Two-Dimensional Solids
289(22)
9.1 The Generalized Hooke's Law
289(7)
9.1.1 Effects of Free Thermal Strains
292(1)
9.1.2 Effects of Free Moisture Strains
293(2)
9.1.3 Plane Stress Constitutive Relations
295(1)
9.2 From "Isotropic" to "Orthotropic" Plane Elements
296(3)
9.2.1 Coordinate Transformation of Stress and Strain Components for Orthotropic Two-Dimensional Elements
298(1)
9.3 Hooke's Law of an Orthotropic Two-Dimensional Element, with Respect to the Global Coordinate System
299(1)
9.4 Transformation of Engineering Properties
300(5)
9.4.1 Elastic Properties of an Orthotropic Two-Dimensional Element in the Global Coordinate System
300(3)
9.4.2 Free Thermal and Free Moisture Strains in Global Coordinate System
303(2)
9.5 Elasticity Equations for Isotropic Solids
305(6)
9.5.1 Generalized Hooke's Law for Isotropic Solids
305(2)
9.5.2 Correlation of Strains with Displacements
307(1)
9.5.3 Correlation of Stresses with Displacements
307(1)
9.5.4 Differential Equations of Equilibrium
308(1)
9.5.5 Differential Equations in Terms of Displacements
308(1)
9.5.6 The Total Potential Energy
308(1)
References
309(2)
Chapter 10 The Principle of Minimum Potential Energy for Two-Dimensional and Three-Dimensional Elements
311(62)
10.1 Interpolation and Shape Functions
311(21)
10.1.1 Linear Triangular Elements (or CST Elements)
316(2)
10.1.2 Quadratic Triangular Elements (or LST Elements)
318(3)
10.1.3 Bilinear Rectangular Elements (or Q4 Elements)
321(1)
10.1.4 Tetrahedral Solid Elements
322(4)
10.1.5 Eight-Node Rectangular Solid Elements
326(2)
10.1.6 Plate Bending Elements
328(4)
10.2 Isoparametric Elements
332(5)
10.2.1 Definition of Isoparametric Elements
332(1)
10.2.2 Lagrange Polynomials
332(1)
10.2.3 The Bilinear Quadrilateral Element
333(4)
10.3 Derivation of Stiffness Matrices
337(36)
10.3.1 The Linear Triangular Element (or CST Element)
337(2)
10.3.2 The Quadratic Triangular Element (or LST Element)
339(1)
10.3.3 The Bilinear Rectangular Element (or Q4 Element)
339(1)
10.3.4 The Tetrahedral Solid Element
339(1)
10.3.5 Eight-Node Rectangular Solid Element
339(1)
10.3.6 Plate Bending Element
339(1)
10.3.7 Isoparametric Formulation
340(31)
References
371(2)
Chapter 11 Structural Dynamics
373(40)
11.1 The Dynamic Equation
373(1)
11.2 Mass Matrix
374(14)
11.2.1 Bar Element
374(2)
11.2.2 Two-Dimensional Truss Element
376(3)
11.2.3 Three-Dimensional Truss Element
379(3)
11.2.4 Two-Dimensional Beam Element
382(1)
11.2.5 Three-Dimensional Beam Element
383(2)
11.2.6 Inclined Two-Dimensional Beam Element (Two-Dimensional Frame Element)
385(2)
11.2.7 Linear Triangular Element (CST Element)
387(1)
11.3 Solution Methodology for the Dynamic Equation
388(2)
11.3.1 Central Difference Method
388(1)
11.3.2 Newmark-Beta Method
389(1)
11.4 Free Vibration---Natural Frequencies
390(23)
References
412(1)
Chapter 12 Heat Transfer
413(66)
12.1 Conduction Heat Transfer
413(4)
2D Steady-State Heat Conduction Equation in Cartesian Coordinates
415(1)
3D Steady-State Heat Conduction Equation in Cartesian Coordinates
415(1)
3D Steady-State Heat Conduction Equation in Cylindrical Coordinates
416(1)
3D Steady-State Heat Conduction Equation in Spherical Coordinates
417(1)
Heat conduction of orthotropic materials
417(3)
12.2 Convection Heat Transfer
420(59)
12.3 Finite Element Formulation
420(1)
12.3.1 One-Dimensional Heat Transfer Modeling Using a Variational Method
420(15)
12.3.2 Two-Dimensional and Three-Dimensional Heat Transfer Modeling Using a Variational Method
435(42)
References
477(2)
Index 479
Dimitrios Pavlou is Professor of Mechanics at University of Stavanger in Norway, and Elected Academician of the Norwegian Academy of Technological Sciences. He has had over twenty-five years of teaching and research experience in the fields of Theoretical and Applied Mechanics, Fracture Mechanics, Finite and Boundary Elements, Structural Dynamics, Anisotropic Materials, and their applications in Engineering Structures.

Professor Pavlou is the author of titles, "Essentials of the Finite Element Method" (Elsevier) and "Composite Materials in Piping Applications" (Destech Publications), and guest co-editor of several international journal Special Issues and conference proceedings.

His research portfolio includes over 120 publications in the areas of Applied Mechanics and Engineering Mathematics (majority as single or first author). Since January 2020, Professor Pavlou joined the Editorial Board of the journal "Computer-Aided Civil and Infrastructure Engineering" (IF=11.775, 1st of 134 journals in Civil Engineering 2020 Journal Citation Reports).

He works as Editor for the journals Maritime Engineering” (IF=5.952); Nondestructive Testing and Evaluation” (IF=2.098); Advances in Civil Engineering” (IF= 1.843); Aerospace Technology and Management” (IF= 0.713);

Dynamics”; Aeronautics and Aerospace Open Access Journal” and Journal of Materials Science and Research”.

He is also an Editorial Board Member for the International Journal of Structural Integrity,” the International Journal of Ocean Systems Management” and Journal of Materials Science and Research”.
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