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Finite Elements Methods in Mechanics 2014 ed. [Kõva köide]

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  • Formaat: Hardback, 370 pages, kõrgus x laius: 235x155 mm, kaal: 7037 g, 130 Illustrations, black and white; XVI, 370 p. 130 illus., 1 Hardback
  • Sari: Solid Mechanics and Its Applications 216
  • Ilmumisaeg: 10-Jul-2014
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319080369
  • ISBN-13: 9783319080369
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Finite Elements Methods in Mechanics 2014 ed.Suurem pilt
  • Formaat: Hardback, 370 pages, kõrgus x laius: 235x155 mm, kaal: 7037 g, 130 Illustrations, black and white; XVI, 370 p. 130 illus., 1 Hardback
  • Sari: Solid Mechanics and Its Applications 216
  • Ilmumisaeg: 10-Jul-2014
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319080369
  • ISBN-13: 9783319080369
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319080369.html
Märksõnad:
This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams and elasticity with detailed derivations for the mass, stiffness and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson s equation. The second computer program handles the two dimensional elasticity problems and the third one presents the three dimensional

transient heat conduction problems. The programs are written in C++ environment.

Introduction and History.- Mathematical Foundations.- Finite Element of Elastic Membrane.- Elements and Local Coordinates.- Field Problems.- Conduction Heat Transfer in Solids.- Computer Methods.- Finite Elements of Beams.- Elasticity, Galerkin Formulations.- Elasticity, Variational Formulations.- Torsion of Prismatic Bars.- Thermoelasticity.- Incompressible Viscous Fluid Flow.- One-Dimensional Higher Order Elements.- Two-Dimensional Higher Order Elements.- Coupled Thermoelasticity.- Computer Programs.
1 Introduction and History
1(6)
1.1 Introduction
1(6)
References
4(3)
2 Mathematical Foundations
7(28)
2.1 Introduction
7(1)
2.2 Statement of Extremum Principle
8(1)
2.3 Method of Calculus of Variation
9(1)
2.4 Function of One Variable, Euler Equation
10(2)
2.5 Higher Order Derivatives
12(2)
2.6 Minimization of Functions of Several Variables
14(2)
2.7 Cantilever Beam
16(4)
2.8 Approximate Techniques
20(3)
2.8.1 A: Weighted Residual Methods
21(2)
2.8.2 B: Stationary Functional Method
23(1)
2.9 Further Notes on the Ritz and Galerkin Methods
23(3)
2.10 Application of the Ritz Method
26(6)
2.10.1 Non-homogeneous Boundary Conditions
28(4)
2.11 Problems
32(3)
Further Readings
34(1)
3 Finite Element of Elastic Membrane
35(22)
3.1 Introduction
35(1)
3.2 Poisson's Equation
36(2)
3.2.1 Physical Examples
36(2)
3.3 Weightless Elastic Membrane (Method I)
38(1)
3.4 Membrane Analysis (Method II)
39(2)
3.5 Strain Energy of Elastic Membrane
41(2)
3.6 Application of Calculus of Variation
43(1)
3.7 Introduction to the Finite Element Method
44(11)
3.7.1 The Elastic Membrane
45(1)
3.7.2 Boundary Value Problem
45(1)
3.7.3 Extremum Problem
45(8)
3.7.4 Boundary Conditions
53(2)
3.8 Problems
55(2)
Further Readings
55(2)
4 Elements and Local Coordinates
57(22)
4.1 Introduction
57(1)
4.2 Subparametric, Isoparametric, and Superparametric Elements
58(1)
4.3 One-Dimensional Elements
59(3)
4.3.1 Straight Linear Element
59(1)
4.3.2 Straight Quadratic Element
59(1)
4.3.3 Straight Cubic Element
60(1)
4.3.4 Curved Quadratic Element
61(1)
4.3.5 Curved Cubic Element
62(1)
4.4 Two-Dimensional Elements
62(4)
4.4.1 Linear Triangular Element
62(1)
4.4.2 Quadratic Element
63(1)
4.4.3 Cubic Element
63(1)
4.4.4 Curved Quadratic Element
64(1)
4.4.5 Curved Cubic Element
65(1)
4.4.6 Quadrilateral Element
65(1)
4.5 Three-Dimensional Elements
66(3)
4.5.1 Linear Tetrahedral Element
66(1)
4.5.2 Quadratic and Cubic Elements
67(1)
4.5.3 Quadratic and Cubic Curved Isoparametric Elements
67(1)
4.5.4 Six Sides Elements (Parallelepiped)
68(1)
4.6 Global and Local Coordinates
69(2)
4.7 Local Coordinates in One-Dimension
71(2)
4.8 Local Coordinates in Two-Dimensions
73(2)
4.9 Volume Integral
75(1)
4.10 Problems
76(3)
References
77(2)
5 Field Problems
79(16)
5.1 Introduction
79(1)
5.2 Governing Equations
79(5)
5.3 Axisymmetric Field Problems
84(3)
5.4 Biharmonic Field Problems
87(3)
5.5 Finite Element of Biharmonic Formulation
90(1)
5.6 Finite Element Solution
91(3)
5.7 Problems
94(1)
Further Readings
94(1)
6 Conduction Heat Transfer in Solids
95(24)
6.1 Introduction
95(1)
6.2 Galerkin Formulations
96(4)
6.3 Variational Formulations
100(5)
6.4 One-Dimensional Conduction
105(2)
6.5 Two-Dimensional Conduction
107(4)
6.6 Three-Dimensional Conduction
111(4)
6.7 Transient Heat Conduction
115(1)
6.8 Problems
116(3)
References
117(2)
7 Computer Methods
119(38)
7.1 Introduction
119(1)
7.2 Assembly of the Global Matrices
120(4)
7.3 Bandwidth Calculation
124(2)
7.4 Boundary Conditions
126(10)
7.5 Gauss Elimination
136(11)
7.6 Skyline Method, Static Problems
147(1)
7.7 Solution of Transient Problems
148(2)
7.8 Solution of Dynamic Problems
150(5)
7.8.1 The Central Difference Method
150(2)
7.8.2 The Houbolt Method
152(1)
7.8.3 The Newmark Method
153(1)
7.8.4 The Wilson-fl Method
154(1)
7.9 Problems
155(2)
References
156(1)
8 Finite Element of Beams
157(30)
8.1 Introduction
157(1)
8.2 Euler Beam, Variational Formulation
157(2)
8.3 Euler Beam, Galerkin Formulation
159(2)
8.4 Axial Vibration of Bars and Beams
161(3)
8.5 Torsional Vibration of Bars and Beams
164(2)
8.6 Lateral Vibration of Beams
166(12)
8.7 Timoshenko Beam
178(6)
8.8 Problems
184(3)
References
186(1)
9 Elasticity, Galerkin Formulations
187(22)
9.1 Introduction
187(1)
9.2 Basic Equations of Elasticity
187(4)
9.3 Galerkin Finite Element Formulation
191(3)
9.4 Two-Dimensional Elasticity
194(6)
9.5 Two-Dimensional Simplex Element
200(6)
9.6 Problems
206(3)
References
207(2)
10 Elasticity, Variational Formulations
209(20)
10.1 Introduction
209(1)
10.2 Hamilton's Principle
209(3)
10.3 Basic Relations of Linear Elasticity
212(2)
10.4 Finite Element Approximation
214(5)
10.5 Two-Dimensional Elasticity
219(3)
10.5.1 Plane Strain Condition
219(2)
10.5.2 Plane Stress Condition
221(1)
10.6 Axisymmetric Elasticity
222(5)
10.7 Problems
227(2)
References
228(1)
11 Torsion of Prismatic Bars
229(8)
11.1 Introduction
229(1)
11.2 Equilibrium Equation for Torsion of Bars
230(4)
11.3 Finite Element Solution
234(2)
11.4 Problems
236(1)
Further Readings
236(1)
12 Thermoelasticity
237(18)
12.1 Introduction
237(1)
12.2 Governing Equations
238(2)
12.3 Displacement Formulation
240(2)
12.4 Temperature Distribution for Zero Thermal Stress
242(1)
12.5 Finite Element Formulation
243(8)
12.6 Problems
251(4)
References
252(3)
13 Incompressible Viscous Fluid Flow
255(30)
13.1 Introduction
255(1)
13.2 Continuity Equation
256(1)
13.3 Equation of Motion
257(2)
13.4 Incompressible Newtonian Fluid Flow
259(1)
13.5 Stokes Equation
260(1)
13.6 Dimensionless Form of Equations
261(1)
13.7 Galerkin Finite Element Formulations
262(2)
13.8 Two-Dimensional Fluid Flow
264(3)
13.9 Boundary Conditions
267(1)
13.10 Element Selection
268(2)
13.11 Vorticity Transport
270(2)
13.12 Finite Element Modelling
272(4)
13.13 Linearization Technique
276(1)
13.14 Triangular Simplex Element
277(3)
13.15 Boundary Conditions
280(3)
13.16 Problems
283(2)
References
283(2)
14 One-Dimensional Higher Order Elements
285(28)
14.1 Introduction
285(1)
14.2 One-Dimensional Quadratic Element
285(2)
14.3 Natural Coordinates, Jacobian Matrix
287(2)
14.4 Application to the Field Problems
289(2)
14.5 Straight Cubic Element
291(10)
14.6 Layer-Wise Theory of Composite Beams
301(9)
14.7 Problems
310(3)
References
311(2)
15 Two-Dimensional Higher Order Elements
313(18)
15.1 Introduction
313(1)
15.2 Triangular Element
314(1)
15.3 Jacobian Matrix
315(3)
15.4 Quadratic Element
318(4)
15.5 The Quadrilateral Elements
322(2)
15.6 Bilinear Quadrilateral Element
324(2)
15.7 Application to the Field Problems
326(3)
15.8 Problems
329(2)
Further Readings
330(1)
16 Coupled Thermoelasticity
331(32)
16.1 Introduction
331(1)
16.2 Galerkin Finite Element
332(8)
16.3 Functionally Graded Layers
340(6)
16.4 Coupled Thermoelasticity of Thick Spheres
346(8)
16.5 Higher Order Elements
354(5)
16.6 Problems
359(4)
References
359(4)
17 Computer Programs
363
17.1 Description of the Membrane Computer Program
363(2)
17.1.1 Preprocessor
363(1)
17.1.2 Processor
364(1)
17.1.3 Postprocessor
365(1)
17.2 Description of the Static Elasticity Computer Program
365(2)
17.2.1 Preprocessor
366(1)
17.2.2 Processor
366(1)
17.2.3 Postprocessor
366(1)
17.3 Description of the 3D Transient Heat Conduction Computer Program
367
References
370