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E-grāmata: Finite Element Method for Mechanics of Solids with ANSYS Applications

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(Rutgers University, New Brunswick, New Jersey, USA)
  • Formāts: 508 pages
  • Sērija : Advances in Engineering Series
  • Izdošanas datums: 25-Aug-2011
  • Izdevniecība: CRC Press Inc
  • Valoda: eng
  • ISBN-13: 9781040162453
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Finite Element Method for Mechanics of Solids with ANSYS ApplicationsPalielināt
  • Formāts: 508 pages
  • Sērija : Advances in Engineering Series
  • Izdošanas datums: 25-Aug-2011
  • Izdevniecība: CRC Press Inc
  • Valoda: eng
  • ISBN-13: 9781040162453
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"The finite element method (FEM) has become the standard method used by engineers for the solution of static and dynamic problems for elastic and inelastic structures and machines. This volume explores the theory behind the method and instruction in use of ANSYS, a commonly used commercial finite element program. Totally, self contained, the book provides the necessary background on solid mechanics (elasticity, plasticity, viscoelasticity) and mathematics. It includes theory and examples and contains detailed instructions for solutions using ANSYS for small and large deformation elasticity, plasticity, viscoelasicity, vibrations, wave propagation, fracture mechanics, building, plates and shells, and contact problems"--

"The purpose of this book is to explain the application of finite the element method to problems in the mechanics of solids. It is intended for practicing engineers who use the finite element method for stress analysis and for graduate students in engineering who want to understand the finite element method for their research. It is also designed to be a textbook for a graduate course in engineering. The application of the finite element method is illustrated by using the ANSYS® computer program. Step bystep instructions for the use of ANSYS APDL and ANSYS Workbench in more than 40 examples are included. The required background material in the mechanics of solids is provided so that the work is self-contained for the knowledgeable reader. A more complete treatment of solid mechanics is provided in the book: Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity, by Ellis H. Dill, CRC Press, 2007. References to that book are abbreviated by 'Dill: Chapter --'"--



Recenzijas

" clearly written and addresses theory and solution of numerous example problems with the ANSYS software, including both ADPL and Workbench modules. a useful reference for practicing engineers and scientists in industry and academia." John D. Clayton, Ph.D., A. James Clark School of Engineering, University of Maryland, College Park, USA

Preface xiii
Author xv
Chapter 1 Finite Element Concepts 1(28)
1.1 Introduction
1(1)
1.2 Direct Stiffness Method
2(3)
1.2.1 Merging the Element Stiffness Matrices
3(2)
1.2.2 Augmenting the Element Stiffness Matrix
5(1)
1.2.3 Stiffness Matrix Is Banded
5(1)
1.3 The Energy Method
5(2)
1.4 Truss Example
7(6)
1.5 Axially Loaded Rod Example
13(5)
1.5.1 Augmented Matrices for the Rod
16(1)
1.5.2 Merge of Element Matrices for the Rod
17(1)
1.6 Force Method
18(3)
1.7 Other Structural Components
21(5)
1.7.1 Space Truss
21(1)
1.7.2 Beams and Frames
21(5)
1.7.2.1 General Beam Equations
24(2)
1.7.3 Plates and Shells
26(1)
1.7.4 Two- or Three-Dimensional Solids
26(1)
1.8 Problems
26(2)
References
28(1)
Bibliography
28(1)
Chapter 2 Linear Elasticity 29(24)
2.1 Basic Equations
29(13)
2.1.1 Geometry of Deformation
29(1)
2.1.2 Balance of Momentum
30(1)
2.1.3 Virtual Work
30(1)
2.1.4 Constitutive Relations
31(2)
2.1.5 Boundary Conditions and Initial Conditions
33(1)
2.1.6 Incompressible Materials
33(1)
2.1.7 Plane Strain
34(1)
2.1.8 Plane Stress
34(1)
2.1.9 Tensile Test
35(1)
2.1.10 Pure Shear
36(1)
2.1.11 Pure Bending
36(1)
2.1.12 Bending and Shearing
37(1)
2.1.13 Properties of Solutions
38(2)
2.1.14 A Plane Stress Example with a Singularity in Stress
40(2)
2.2 Potential Energy
42(3)
2.2.1 Proof of Minimum Potential Energy
44(1)
2.3 Matrix Notation
45(3)
2.4 Axially Symmetric Deformations
48(2)
2.4.1 Cylindrical Coordinates
48(1)
2.4.2 Axial Symmetry
49(1)
2.4.3 Plane Stress and Plane Strain
50(1)
2.5 Problems
50(1)
References
51(1)
Bibliography
52(1)
Chapter 3 Finite Element Method for Linear Elasticity 53(28)
3.1 Finite Element Approximation
54(12)
3.1.1 Potential Energy
55(2)
3.1.2 Finite Element Equations
57(1)
3.1.3 Basic Equations in Matrix Notation
58(1)
3.1.4 Basic Equations Using Virtual Work
59(1)
3.1.5 Underestimate of Displacements
60(1)
3.1.6 Nondimensional Equations
61(2)
3.1.7 Uniaxial Stress
63(3)
3.2 General Equations for an Assembly of Elements
66(9)
3.2.1 Generalized Variational Principle
68(1)
3.2.2 Potential Energy
69(1)
3.2.3 Hybrid Displacement Functional
69(1)
3.2.4 Hybrid Stress and Complementary Energy
70(2)
3.2.5 Mixed Methods of Analysis
72(3)
3.3 Nearly Incompressible Materials
75(4)
3.3.1 Nearly Incompressible Plane Strain
78(1)
Bibliography
79(2)
Chapter 4 The Triangle and the Tetrahedron 81(22)
4.1 Linear Functions over a Triangular Region
81(3)
4.2 Triangular Element for Plane Stress and Plane Strain
84(4)
4.3 Plane Quadrilateral from Four Triangles
88(5)
4.3.1 Square Element Formed from Four Triangles
90(3)
4.4 Plane Stress Example: Short Beam
93(4)
4.4.1 Extrapolation of the Solution
96(1)
4.5 Linear Strain Triangles
97(1)
4.6 Four-Node Tetrahedron
98(1)
4.7 Ten-Node Tetrahedron
99(1)
4.8 Problems
99(4)
Chapter 5 The Quadrilateral and the Hexahedron 103(68)
5.1 Four-Node Plane Rectangle
103(12)
5.1.1 Stress Calculations
109(1)
5.1.2 Plane Stress Example: Pure Bending
110(2)
5.1.3 Plane Strain Example: Bending with Shear
112(1)
5.1.4 Plane Stress Example: Short Beam
112(3)
5.2 Improvements to Four-Node Quadrilateral
115(15)
5.2.1 Wilson–Taylor Quadrilateral
115(3)
5.2.2 Enhanced Strain Formulation
118(4)
5.2.3 Approximate Volumetric Strains
122(3)
5.2.4 Reduced Integration on the k Term
125(1)
5.2.5 Reduced Integration on the λ Term
126(1)
5.2.6 Uniform Reduced Integration
127(3)
5.2.7 Example Using Improved Elements
130(1)
5.3 Numerical Integration
130(3)
5.4 Coordinate Transformations
133(1)
5.5 Isoparametric Quadrilateral
134(5)
5.5.1 Wilson-Taylor Element
138(1)
5.5.2 Three-Node Triangle as a Special Case of Rectangle
138(1)
5.6 Eight-Node Quadrilateral
139(10)
5.6.1 Nodal Loads
144(1)
5.6.2 Plane Stress Example: Pure Bending
145(1)
5.6.3 Plane Stress Example: Bending with Shear
145(3)
5.6.4 Plane Stress Example: Short Beam
148(1)
5.6.5 General Quadrilateral Element
148(1)
5.7 Eight-Node Block
149(3)
5.8 Twenty-Node Solid
152(1)
5.9 Singularity Element
152(2)
5.10 Mixed U-P Elements
154(9)
5.10.1 Plane Strain
154(4)
5.10.2 Alternative Formulation for Plane Strain
158(2)
5.10.3 3D Elements
160(3)
5.11 Problems
163(5)
References
168(1)
Bibliography
169(2)
Chapter 6 Errors and Convergence of Finite Element Solution 171(10)
6.1 General Remarks
171(2)
6.2 Element Shape Limits
173(3)
6.2.1 Aspect Ratio
173(1)
6.2.2 Parallel Deviation for a Quadrilateral
174(1)
6.2.3 Large Corner Angle
175(1)
6.2.4 Jacobian Ratio
175(1)
6.3 Patch Test
176(4)
6.3.1 Wilson-Taylor Quadrilateral
178(2)
References
180(1)
Chapter 7 Heat Conduction in Elastic Solids 181(10)
7.1 Differential Equations and Virtual Work
181(4)
7.2 Example Problem: One-Dimensional Transient Heat Flux
185(2)
7.3 Example: Hollow Cylinder
187(1)
7.4 Problems
188(3)
Chapter 8 Finite Element Method for Plasticity 191(14)
8.1 Theory of Plasticity
191(6)
8.1.1 Tensile Test
194(1)
8.1.2 Plane Stress
195(1)
8.1.3 Summary of Plasticity
196(1)
8.2 Finite Element Formulation for Plasticity
197(4)
8.2.1 Fundamental Solution
198(1)
8.2.2 Iteration to Improve the Solution
199(2)
8.3 Example: Short Beam
201(2)
8.4 Problems
203(1)
Bibliography
204(1)
Chapter 9 Viscoelasticity 205(16)
9.1 Theory of Linear Viscoelasticity
205(10)
9.1.1 Recurrence Formula for History
210(1)
9.1.2 Viscoelastic Example
211(4)
9.2 Finite Element Formulation for Viscoelasticity
215(4)
9.2.1 Basic Step-by-Step Solution Method
216(1)
9.2.2 Step-by-Step Calculation with Load Correction
217(1)
9.2.3 Plane Strain Example
218(1)
9.3 Problems
219(1)
Bibliography
220(1)
Chapter 10 Dynamic Analyses 221(34)
10.1 Dynamical Equations
221(3)
10.1.1 Lumped Mass
221(1)
10.1.2 Consistent Mass
222(2)
10.2 Natural Frequencies
224(1)
10.2.1 Lumped Mass
224(1)
10.2.2 Consistent Mass
225(1)
10.3 Mode Superposition Solution
225(2)
10.4 Example: Axially Loaded Rod
227(9)
10.4.1 Exact Solution for Axially Loaded Rod
227(2)
10.4.2 Finite Element Model
229(3)
10.4.2.1 One-Element Model
229(1)
10.4.2.2 Two-Element Model
230(2)
10.4.3 Mode Superposition for Continuum Model of the Rod
232(4)
10.5 Example: Short Beam
236(1)
10.6 Dynamic Analysis with Damping
237(4)
10.6.1 Viscoelastic Damping
238(1)
10.6.2 Viscous Body Force
239(1)
10.6.3 Analysis of Damped Motion by Mode Superposition
240(1)
10.7 Numerical Solution of Differential Equations
241(8)
10.7.1 Constant Average Acceleration
241(2)
10.7.2 General Newmark Method
243(1)
10.7.3 General Methods
244(1)
10.7.3.1 Implicit Methods in General
244(1)
10.7.3.2 Explicit Methods in General
244(1)
10.7.4 Stability Analysis of Newmark's Method
245(1)
10.7.5 Convergence, Stability, and Error
246(1)
10.7.6 Example: Numerical Integration for Axially Loaded Rod
247(2)
10.8 Example: Analysis of Short Beam
249(2)
10.9 Problems
251(2)
Bibliography
253(2)
Chapter 11 Linear Elastic Fracture Mechanics 255(14)
11.1 Fracture Criterion
255(5)
11.1.1 Analysis of Sheet
257(1)
11.1.2 Fracture Modes
258(2)
11.1.2.1 Mode I
258(1)
11.1.2.2 Mode II
259(1)
11.1.2.3 Mode III
259(1)
11.2 Determination of K by Finite Element Analysis
260(3)
11.2.1 Crack Opening Displacement Method
260(3)
11.3 J-Integral for Plane Regions
263(4)
11.4 Problems
267(1)
References
268(1)
Bibliography
268(1)
Chapter 12 Plates and Shells 269(22)
12.1 Geometry of Deformation
269(1)
12.2 Equations of Equilibrium
270(1)
12.3 Constitutive Relations for an Elastic Material
271(2)
12.4 Virtual Work
273(3)
12.5 Finite Element Relations for Bending
276(4)
12.6 Classical Plate Theory
280(2)
12.7 Plate Bending Example
282(5)
12.8 Problems
287(1)
References
288(1)
Bibliography
289(2)
Chapter 13 Large Deformations 291(36)
13.1 Theory of Large Deformations
291(18)
13.1.1 Virtual Work
292(1)
13.1.2 Elastic Materials
293(4)
13.1.3 Mooney-Rivlin Model of an Incompressible Material
297(1)
13.1.4 Generalized Mooney-Rivlin Model
298(3)
13.1.5 Polynomial Formula
301(2)
13.1.6 Ogden's Function
303(1)
13.1.7 Blatz-Ko Model
304(2)
13.1.8 Logarithmic Strain Measure
306(1)
13.1.9 Yeoh Model
307(1)
13.1.10 Fitting Constitutive Relations to Experimental Data
308(1)
13.1.10.1 Volumetric Data
308(1)
13.1.10.2 Tensile Test
308(1)
13.1.10.3 Biaxial Test
309(1)
13.2 Finite Elements for Large Displacements
309(8)
13.2.1 Lagrangian Formulation
311(1)
13.2.2 Basic Step-by-Step Analysis
312(1)
13.2.3 Iteration Procedure
312(1)
13.2.4 Updated Reference Configuration
313(2)
13.2.5 Example I
315(1)
13.2.6 Example II
315(2)
13.3 Structure of Tangent Modulus
317(1)
13.4 Stability and Buckling
318(1)
13.4.1 Beam-Column
319(1)
13.5 Snap Through Buckling
319(5)
13.5.1 Shallow Arch
323(1)
13.6 Problems
324(2)
References
326(1)
Bibliography
326(1)
Chapter 14 Constraints and Contact 327(22)
14.1 Application of Constraints
327(6)
14.1.1 Lagrange Multipliers
327(2)
14.1.2 Perturbed Lagrangian Method
329(2)
14.1.3 Penalty Functions
331(1)
14.1.4 Augmented Lagrangian Method
332(1)
14.2 Contact Problems
333(8)
14.2.1 Example: A Truss Contacts a Rigid Foundation
333(4)
14.2.1.1 Load Fy> 0 Is Applied with Fx = 0
335(1)
14.2.1.2 Loads Are Ramped Up Together: Fx = 27a, Fy = 12.8a
336(1)
14.2.2 Lagrange Multiplier, No Friction Force
337(1)
14.2.2.1 Stick Condition
338(1)
14.2.2.2 Slip Condition
338(1)
14.2.3 Lagrange Multiplier, with Friction
338(2)
14.2.3.1 Stick Condition
339(1)
14.2.3.2 Slip Condition
339(1)
14.2.4 Penalty Method
340(1)
14.2.4.1 Stick Condition
341(1)
14.2.4.2 Slip Condition
341(1)
14.3 Finite Element Analysis
341(5)
14.3.1 Example: Contact of a Cylinder with a Rigid Plane
342(1)
14.3.2 Hertz Contact Problem
343(3)
14.4 Dynamic Impact
346(1)
14.5 Problems
347(1)
References
348(1)
Bibliography
348(1)
Chapter 15 ANSYS APDL Examples 349(122)
15.1 ANSYS Instructions
349(4)
15.1.1 ANSYS File Names
351(1)
15.1.2 Graphic Window Controls
352(27)
15.1.2.1 Graphics Window Logo
352(1)
15.1.2.2 Display of Model
352(1)
15.1.2.3 Display of Deformed and Undeformed Shape White on White
352(1)
15.1.2.4 Adjusting Graph Colors
352(1)
15.1.2.5 Printing from Windows Version of ANSYS
353(1)
15.1.2.6 Some Useful Notes
353(1)
15.2 ANSYS Elements SURF153, SURF154
353(1)
15.3 Truss Example
354(3)
15.4 Beam Bending
357(3)
15.5 Beam with a Distributed Load
360(1)
15.6 One Triangle
361(3)
15.7 Plane Stress Example Using Triangles
364(2)
15.8 Cantilever Beam Modeled as Plane Stress
366(3)
15.9 Plane Stress: Pure Bending
369(2)
15.10 Plane Strain Bending Example
371(5)
15.11 Plane Stress Example: Short Beam
376(3)
15.12 Sheet with a Hole
379(2)
15.12.1 Solution Procedure
379(2)
15.13 Plasticity Example
381(6)
15.14 Viscoelasticity Creep Test
387(4)
15.15 Viscoelasticity Example
391(3)
15.16 Mode Shapes and Frequencies of a Rod
394(3)
15.17 Mode Shapes and Frequencies of a Short Beam
397(1)
15.18 Transient Analysis of Short Beam
398(2)
15.19 Stress Intensity Factor by Crack Opening Displacement
400(2)
15.20 Stress Intensity Factor by J-Integral
402(3)
15.21 Stretching of a Nonlinear Elastic Sheet
405(3)
15.22 Nonlinear Elasticity: Tensile Test
408(4)
15.23 Column Buckling
412(3)
15.24 Column Post-Buckling
415(2)
15.25 Snap Through
417(3)
15.26 Plate Bending Example
420(3)
15.27 Clamped Plate
423(2)
15.28 Gravity Load on a Cylindrical Shell
425(4)
15.29 Plate Buckling
429(3)
15.30 Heated Rectangular Rod
432(2)
15.31 Heated Cylindrical Rod
434(4)
15.32 Heated Disk
438(4)
15.33 Truss Contacting a Rigid Foundation
442(4)
15.34 Compression of a Rubber Cylinder between Rigid Plates
446(5)
15.35 Hertz Contact Problem
451(5)
15.36 Elastic Rod Impacting a Rigid Wall
456(4)
15.37 Curve Fit for Nonlinear Elasticity Using Blatz-Ko Model
460(4)
15.38 Curve Fit for Nonlinear Elasticity Using Polynomial Model
464(5)
Bibliography
469(2)
Chapter 16 ANSYS Workbench 471(11)
16.1 Two- and Three-Dimensional Geometry
471(1)
16.2 Stress Analysis
472(1)
16.3 Short Beam Example
473(4)
16.3.1 Short Beam Geometry
473(1)
16.3.2 Short Beam, Static Loading
474(2)
16.3.3 Short Beam, Transient Analysis
476(1)
16.4 Filleted Bar Example
477(3)
16.5 Sheet with a Hole
480(2)
Bibliography 482(1)
Index 483
Ellis H. Dill
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