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Primer for Finite Elements in Elastic Structures [Kõva köide]

(Emeritus, University of Central Florida)
  • Formaat: Hardback, 512 pages, kõrgus x laius x paksus: 259x185x37 mm, kaal: 1081 g
  • Ilmumisaeg: 17-Nov-1998
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 0471283452
  • ISBN-13: 9780471283454
Teised raamatud teemal:
Primer for Finite Elements in Elastic StructuresSuurem pilt
  • Formaat: Hardback, 512 pages, kõrgus x laius x paksus: 259x185x37 mm, kaal: 1081 g
  • Ilmumisaeg: 17-Nov-1998
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 0471283452
  • ISBN-13: 9780471283454
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780471283454.html
Märksõnad:
A textbook for a civil engineering course at the senior or first-year graduate level. Requires a knowledge of basic structural analysis, and recommends previous study of linear algebra but reviews the necessary elements of it in the first chapter. Explicates the entire finite element method in the context of elastic structures and the principle of virtual work, emphasizing its supportive theory and its mathematical and structural underpinnings. Leaves some of the higher mathematics to later courses. Uses MATLAB for calculations, but describes them such that other software can be used instead. Includes answers to the problems. Annotation c. by Book News, Inc., Portland, Or.

A thorough guide to the fundamentals--and how to use them--of finite element analysis for elastic structures

For elastic structures, the finite element method is an invaluable tool which is used most effectively only when one understands completely each of its facets. A Primer for Finite Elements in Elastic Structures disassembles the entire finite element method for civil engineering students and professionals, detailing its supportive theory and its mathematical and structural underpinnings, in the context of elastic structures and the principle of virtual work.

The book opens with a discussion of matrix algebra and algebraic equation systems to foster the basic skills required to successfully understand and use the finite element method. Key mathematical concepts outlined here are joined to pertinent concepts from mechanics and structural theory, with the method constructed in terms of one-dimensional truss and framework finite elements. The use of these one-dimensional elements in the early chapters promotes better understanding of the fundamentals. Subsequent chapters describe many two-dimensional structural finite elements in depth, including the geometry, mechanics, transformations, and mapping needed for them.

Most chapters end with questions and problems which review the text material. Answers for many of these are at the end of the book. An appendix describes how to use MATLAB(r), a popular matrix-manipulation software platform necessary to perform the many matrix operations required for the finite element method, such as matrix addition, multiplication, inversion, partitioning, rearrangement, and assembly. As an added extra, the m-files discussed can be downloaded from the Wiley FTP server.
PREFACE xiii
CHAPTER 1 Finite Element Method Prerequisites
1(33)
1.1. Introduction
1(1)
1.2. Matrix Operations for the Finite Element Method
1(20)
1.2.1. Basic Matrix Definitions
2(1)
1.2.2. Basic Matrix Operations
3(6)
1.2.3. Determinants
9(1)
1.2.4. Adjoint Method of Matrix Inversion
10(4)
1.2.5. Gauss-Jordan Method of Matrix Inversion
14(4)
1.2.6. Choleski's Method of Matrix Inversion
18(3)
1.3. Algebraic Equation Systems
21(7)
1.3.1. Reduction Solution Procedure
21(3)
1.3.2. Submatrix Solution Procedure
24(2)
1.3.3. Solution without Rearrangement
26(1)
1.3.4. Penalty Solution Procedure
27(1)
1.4. Closing Remarks
28(6)
Bibliography
28(1)
Problems
29(5)
CHAPTER 2 The Finite Element Method
34(11)
2.1. Introduction
34(1)
2.2. Nodes, Equilibrium, and Continuity
34(2)
2.3. Degrees of Freedom
36(1)
2.4. Stiffness Equations
36(4)
2.4.1. Element Stiffness Equations
37(1)
2.4.2. Global Stiffness Equations
38(1)
2.4.3. Global and Local Reference Axes
39(1)
2.5. System Restraints: Boundary Conditions
40(2)
2.5.1. Essential Boundary Conditions
40(1)
2.5.2. Natural Boundary Conditions
40(1)
2.5.3. Mixed Boundary Conditions
41(1)
2.5.4. Restraint Sufficiency
42(1)
2.6. Steps in the Finite Element Process
42(2)
Bibliography
44(1)
CHAPTER 3 Element Stiffness Equations by Direct Methods
45(23)
3.1. Direct Determination of Element Stiffness Equations
45(10)
3.1.1. Element Stiffness Matrix: Global Axes
45(5)
3.1.2. Element Stiffness Matrix: Local Axes
50(3)
3.1.3. Element Load Vector
53(2)
3.2. Transformation of Element Stiffness Equations: 1D Elements in 2D and 3D Space
55(7)
3.2.1. Displacement Transformation
55(3)
3.2.2. Force and Moment Transformation
58(3)
3.2.3. Element Stiffness Matrix Transformation
61(1)
3.3. Closing Remarks
62(1)
Bibliography
62(1)
Problems
62(6)
CHAPTER 4 Global Stiffness Equations
68(31)
4.1. Introduction
68(1)
4.2. Assembly of Global Stiffness Matrix
69(4)
4.2.1. Equilibrium and Compatibility at Nodes
69(3)
4.2.2. A Process for the Assembly
72(1)
4.3. Assembly of Global Load Vector
73(2)
4.3.1. Applied Loads
74(1)
4.3.2. Support reactions
74(1)
4.4. Global Displacement Vector
75(1)
4.5. Solution of Global Stiffness Equations
75(11)
4.5.1. Plane Truss Example
76(4)
4.5.2. Plane Frame Example
80(6)
4.6. Element Internal Forces
86(1)
4.7. Banded Global Stiffness Matrix
87(4)
4.8. Closing Remarks
91(1)
Bibliography
91(1)
Problems
92(7)
CHAPTER 5 Element Stiffness Equations by Displaced State Virtual Work Applications
99(32)
5.1. Displaced State of the Structure
99(7)
5.1.1. Global Displacement Basis Functions
99(3)
5.1.2. Element Displacement Shape Functions
102(4)
5.2. Virtual Work Basis of Element Stiffness Equations
106(20)
5.2.1. Principle of Virtual Work
107(2)
5.2.2. Element Stiffness Equations
109(7)
5.2.3. Beam Finite Element on an Elastic Foundation
116(3)
5.2.4. Axial Finite Elements
119(7)
5.3. Closing Remarks
126(1)
Bibliography
126(1)
Problems
127(4)
CHAPTER 6 General Approach to Element Stiffness Equations
131(25)
6.1. Introduction
131(1)
6.2. Stress and Strain
131(6)
6.3. Strain and Stress Displacement Relationships
137(2)
6.4. Element Stiffness Equations
139(4)
6.4.1. Virtual Strain Displacement Relationships
139(1)
6.4.2. Virtual Strain Energy
140(1)
6.4.3. Virtual Work of External Actions
141(1)
6.4.4. General Expressions for Element Stiffness Equations
142(1)
6.5. Generalized Stress and Strain
143(3)
6.6. Generalized dof
146(7)
6.7. Closing Remarks
153(1)
Bibliography
154(1)
Problems
154(2)
CHAPTER 7 Plane Stress and Plane Strain
156(20)
7.1. Introduction
156(1)
7.2. Isotropic Plane Stress and Plane Strain
156(1)
7.3. Biaxial Stress Transformation
157(4)
7.4. Biaxial Strain Transformation
161(3)
7.5. Orthotropic Plane Stress
164(6)
7.6. Orthotropic Plane Strain
170(2)
7.7. Closing Remarks
172(1)
Bibliography
173(1)
Problems
173(3)
CHAPTER 8 Plane Stress Structural Triangular Finite Elements
176(49)
8.1. Introduction
176(1)
8.2. Constant-Strain Triangular Element (3-Node, 6-dof)
176(17)
8.2.1. Shape and Displacement Functions
177(4)
8.2.2. Element Stiffness Matrix
181(3)
8.2.3. Loads between Nodes
184(5)
8.2.4. Plane Stress Plate Example Analysis
189(4)
8.3. Natural Coordinates and Quadrature for Triangular Elements
193(6)
8.3.1. Natural Coordinates for Triangular Elements
194(3)
8.3.2. Quadrature for Triangular Elements
197(1)
8.3.3. Example Body Force
197(2)
8.4. Natural Coordinates and Quadrature for Line Segments
199(5)
8.4.1. Natural Coordinates for Lines
199(3)
8.4.2. Quadrature for a Line Segment
202(1)
8.4.3. Example Line Load
202(2)
8.5. Linear Strain Triangular Element (6-Node, 12-dof)
204(13)
8.5.1. Shape and Displacement Functions
204(2)
8.5.2. Element Stiffness Matrix
206(2)
8.5.3. Numerical Quadrature over Triangular Area
208(2)
8.5.4. Loads between Nodes
210(1)
8.5.5. Linear Strain Element Example Analysis
210(7)
8.6. Closing Remarks
217(1)
Bibliography
218(1)
Problems
219(6)
CHAPTER 9 Isoparametric Plane Stress Structural Quadrilateral Finite Elements
225(63)
9.1. Introduction
225(1)
9.2. Bilinear Rectangular Element (4-Node, 8-dof)
226(8)
9.2.1. Shape and Displacement Functions
226(4)
9.2.2. Element Stiffness Matrix
230(4)
9.3. Quadrilateral Element (4-Node, 8-dof)
234(7)
9.3.1. Isoparametric Transformation
235(5)
9.3.2. Element Stiffness Matrix
240(1)
9.4. Quadrature Rules
241(12)
9.4.1. Nodal Point Quadrature
242(2)
9.4.2. Gaussian Quadrature: Functions of One Variable
244(3)
9.4.3. Gaussian Quadrature: Functions of Two Variables
247(6)
9.5. Element Mapping and Master Element Calculations
253(19)
9.5.1. Element Mapping
254(4)
9.5.2. Master Element Stiffness Calculations
258(7)
9.5.3. Master Element Equivalent Nodal Loads
265(7)
9.6. Quadratic Quadrilateral Elements
272(5)
9.6.1. Serendipity Element (8-Node, 16-dof)
272(2)
9.6.2. Lagrange Element (9-Node, 18-dof)
274(3)
9.7 Closing Remarks
277(1)
Bibliography
277(1)
Problems
278(10)
CHAPTER 10 Flat Plate Flexural Finite Elements
288(57)
10.1. Introduction
288(1)
10.2. Thin, Flat Plate Small Deflection Flexure Theory
289(7)
10.3. Rectangular Thin Plate Element (4-Node, 12-dof)
296(26)
10.3.1. Shape and Displacement Functions
298(3)
10.3.2. Element Stiffness Matrix: Physical Displacements
301(7)
10.3.3. Element Stiffness Matrix: Generalized dof
308(3)
10.3.4. Nodal Actions
311(5)
10.3.5. Effect of an Elastic Foundation
316(4)
10.3.6. Restraints and Boundary Conditions
320(1)
10.3.7. Shape Functions and the Generalized dof Form
321(1)
10.4. Other Flat Plate Flexure Finite Elements
322(16)
10.4.1. Rectangular Thin Plate Element (4-Node, 16-dof)
322(4)
10.4.2. Triangular Thin Plate Element (3-Node, 9-dof)
326(6)
10.4.3. Rectangular Thick Plate Element (4-Node, 12-dof)
332(6)
10.5. Quadrilateral Thick Flat Plate Flexure Element
338(1)
10.6. Closing Remarks
339(1)
Bibliography
339(1)
Problems
340(5)
CHAPTER 11 Axisymmetric Structural Finite Elements
345(40)
11.1. Introduction
345(1)
11.2. Axisymmetric Stress, Strain, and Elastic Properties
346(1)
11.3. Axisymmetric Structural Finite Elements
347(1)
11.4. Triangular Finite Element (3-Node, 6-dof)
348(9)
11.4.1. Shape and Displacement Functions
349(1)
11.4.2. Element Stiffness Matrix: Physical dof
350(4)
11.4.3. Element Stiffness Matrix: Generalized dof
354(3)
11.5. Quadrilateral Finite Element (4-Node, 8-dof)
357(7)
11.5.1. Shape and Displacement Functions
358(1)
11.5.2. Isoparametric Transformation
359(1)
11.5.3. Element Stiffness Matrix
359(5)
11.6. Nodal Actions
364(11)
11.6.1. Concentrated Axial Force
364(1)
11.6.2. Uniform Line Force
364(2)
11.6.3. Distributed Surface Force
366(3)
11.6.4. Distributed Body Force
369(3)
11.6.5. Equivalent Force Calculations
372(3)
11.7. Closing Remarks
375(1)
Bibliography
376(1)
Problems
377(8)
CHAPTER 12 Structural Finite Elements in Perspective
385(4)
12.1. Introduction
385(1)
12.2. Modeling Structures with Finite Elements
385(2)
12.3. Linear Algebra Basis
387(1)
12.4. The Finite Element Method
387(1)
12.5. The Finite Element
388(1)
APPENDIX Matrix Operations for the Finite Element Method Using MATLAB 389(58)
ANSWERS TO SELECTED PROBLEMS 447(38)
INDEX 485
W. F. CARROLL is Professor Emeritus in the Department of Civil and Environmental Engineering at the University of Central Florida.