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Advanced Mechanics of Solids: Analytical and Numerical Solutions with MATLAB® [Kõva köide]

(Iowa State University)
  • Formaat: Hardback, 578 pages, kõrgus x laius x paksus: 252x194x33 mm, kaal: 1370 g, Worked examples or Exercises; 300 Line drawings, black and white
  • Ilmumisaeg: 18-Feb-2021
  • Kirjastus: Cambridge University Press
  • ISBN-10: 110884331X
  • ISBN-13: 9781108843317
Teised raamatud teemal:
Advanced Mechanics of Solids: Analytical and Numerical Solutions with MATLAB®Suurem pilt
  • Formaat: Hardback, 578 pages, kõrgus x laius x paksus: 252x194x33 mm, kaal: 1370 g, Worked examples or Exercises; 300 Line drawings, black and white
  • Ilmumisaeg: 18-Feb-2021
  • Kirjastus: Cambridge University Press
  • ISBN-10: 110884331X
  • ISBN-13: 9781108843317
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781108843317.html
Märksõnad:
Build on the foundations of elementary mechanics of materials texts with this modern textbook that covers the analysis of stresses and strains in elastic bodies. Discover how all analyses of stress and strain are based on the four pillars of equilibrium, compatibility, stress-strain relations, and boundary conditions. These four principles are discussed and provide a bridge between elementary analyses and more detailed treatments with the theory of elasticity. Using MATLAB® extensively throughout, the author considers three-dimensional stress, strain and stress-strain relations in detail with matrix-vector relations. Based on classroom-proven material, this valuable resource provides a unified approach useful for advanced undergraduate students and graduate students, practicing engineers, and researchers.

Arvustused

'The book 'Advanced Mechanics of Solids' by Lester W. Schmerr Jr presents a comprehensive, modern, well-thought-out, and concise approach to the analysis of deformable bodies. The book presents both a detailed description of stated problems and a big picture of the mechanics of solids by highlighting basic principles governing deformable bodies. It shows solutions of elementary and advance systems, introduces analytical results and computational methods, and presents classical equilibrium and compatibility equations as well as a work-energy approach. The book is concluded with failure and stability theories. All that packed into six hundred well-written pages. Moreover, many problems are accompanied with Matlab® codes, the standard language of modern engineering computations. I can recommend this book with no hesitation.' Grzegorz Orzechowski, LUT University 'A considerable amount of detailed derivations of main relations alongside step-by-step solutions for multiple examples employing advanced theoretical approaches makes this book especially useful for self-learning and revision. The author consistently uses a set of basic principles, termed 'four pillars' (local stress equilibrium, strain compatibility equations, stressstrain relations, and boundary conditions), as a fundamental framework to cover the main topics of mechanics of solids and to solve multiple problems from elementary to advanced.' Vadim Silberschmidt, Loughborough University

Muu info

Build on elementary mechanics of materials texts with this treatment of the analysis of stresses and strains in elastic bodies.
Preface xi
1 Introduction
1(27)
1.1 Axially Loaded Members
1(5)
1.2 Beam Bending
6(5)
1.2.1 Pure Bending
6(3)
1.2.2 Engineering Beam Theory
9(2)
1.3 Torsion of a Circular Shaft
11(5)
1.4 Limitations and Extensions of the Theories
16(1)
1.5 The Foundations of Deformable Body Problems
17(2)
1.6 About This Book
19(1)
1.7 Problems
20(7)
Reference
27(1)
2 Stress
28(41)
2.1 The Stress Vector
28(4)
2.1.1 Stress Vector on an Arbitrary Plane
30(2)
2.2 Normal and Shear Stresses on an Oblique Plane
32(9)
2.2.1 Stress Components on Oblique Planes
33(1)
2.2.2 Stress Transformation Equations
34(7)
2.3 A Relationship between the Normal Stress and Total Shear Stress
41(1)
2.4 Principal Stresses and Principal Stress Directions
42(11)
2.4.1 Special Case when I3 = 0, Plane Stress
50(1)
2.4.2 Special Case when Principal Stresses are Equal
51(2)
2.5 Mohr's Circle for Three-Dimensional States of Stress
53(7)
2.6 Stresses on the Octahedral Plane
60(1)
2.7 Stress Notations and the Concept of Stress -- A Historical Note
61(2)
2.8 Problems
63(5)
References
68(1)
3 Equilibrium
69(19)
3.1 Equations of Equilibrium -- Cartesian Coordinates
69(4)
3.1.1 Plane Stress
72(1)
3.2 Strength of Materials Solutions
73(3)
3.3 Force and Moment Equilibrium
76(4)
3.4 Equations of Equilibrium -- Cylindrical and Spherical Coordinates
80(4)
3.4.1 Plane Stress
84(1)
3.5 Problems
84(4)
4 Strain
88(31)
4.1 Definitions of Strains
88(3)
4.1.1 Normal Strain
88(1)
4.1.2 Shear Strain
89(2)
4.2 Strain--Displacement Relations and Strain Transformations
91(8)
4.2.1 Dilatation
98(1)
4.2.2 Plane-Strain Principal Strains
98(1)
4.3 Strain Compatibility Equations
99(5)
4.3.1 Plane-Strain and Plane-Stress Compatibility Equations
102(1)
4.3.2 Multiply Connected Bodies
103(1)
4.4 Satisfaction of Compatibility -- Strength of Materials Solutions
104(8)
4.5 Strains in Cylindrical Coordinates
112(2)
4.6 Problems
114(4)
References
118(1)
5 Stress--Strain Relations
119(27)
5.1 Linear Elastic Materials
119(10)
5.1.1 Linear Elastic Isotropic Materials
119(3)
5.1.2 General Linear Elastic Stress--Strain Relations
122(7)
5.2 Plane Stress and Plane Strain
129(2)
5.3 Transformation of Elastic Constants
131(8)
5.4 States of Stress and Strain on a Surface from Strain Gage Measurements
139(3)
5.5 Problems
142(4)
6 Governing Equations and Boundary Conditions
146(34)
6.1 Governing Equations in Three Dimensions
146(4)
6.2 Governing Equations in Two Dimensions
150(8)
6.2.1 Plane Stress
150(4)
6.2.2 Plane Strain
154(4)
6.3 Boundary Conditions
158(5)
6.3.1 Saint-Venant's Principle
160(3)
6.4 Governing Equations in Matrix--Vector Form
163(3)
6.5 Equivalent Algebraic Matrix--Vector Governing Equations for Structures
166(8)
6.5.1 Displacement Formulation
170(2)
6.5.2 Stress (Force) Formulation
172(2)
6.6 Structural Analysis -- A Brief Preview
174(2)
6.7 Problems
176(3)
References
179(1)
7 Analytical Solutions
180(44)
7.1 Displacement-Based Solutions
180(10)
7.1.1 Axisymmetric Solutions in Cylindrical Geometries
180(3)
7.1.2 Thick-Wall Pressure Vessel
183(4)
7.1.3 Shrink-Fits
187(3)
7.2 Airy Stress Function Solutions in Cartesian Coordinates
190(7)
7.2.1 Solutions of the Biharmonic Equation in Cartesian Coordinates
191(1)
7.2.2 A Simply Supported Beam
191(6)
7.3 Airy Stress Function Solutions in Polar Coordinates
197(17)
7.3.1 Michell's Solutions
197(1)
7.3.2 Stress Concentration at a Circular Hole in a Large Plate
198(4)
7.3.3 Pure Bending of a Curved Beam
202(3)
7.3.4 Comparison with a Curved Beam Strength of Materials Solution
205(3)
7.3.5 Concentrated Force on a Wedge
208(1)
7.3.6 Concentrated Force on a Planar Surface
209(3)
7.3.7 Elastic Bodies in Contact
212(2)
7.4 Stress Singularities
214(3)
7.5 Problems
217(6)
References
223(1)
8 Work--Energy Concepts
224(52)
8.1 Work Concepts
224(2)
8.1.1 Work for a Deformable Body
224(2)
8.2 Work--Strain Energy
226(7)
8.2.1 Linear Elastic Material
227(3)
8.2.2 Isotropic Case
230(2)
8.2.3 Distortional Strain Energy
232(1)
8.3 Complementary Strain Energy
233(1)
8.3.1 Linear Elastic Material
234(1)
8.4 Strain Energy for Strength of Materials Problems
234(5)
8.4.1 Axial Loads
235(1)
8.4.2 Bending
236(2)
8.4.3 Torsion
238(1)
8.5 Principle of Virtual Work and Minimum Potential Energy
239(10)
8.5.1 General Deformable Body
239(10)
8.6 Principle of Complementary Virtual Work and Minimum Complementary Potential Energy
249(5)
8.6.1 General Deformable Body
249(5)
8.7 Work-Energy Principles and Discrete Forces and Moments
254(13)
8.7.1 Virtual Work and Potential Energy
255(4)
8.7.2 Complementary Virtual Work and Complementary Potential Energy
259(4)
8.7.3 Principle of Least Work
263(4)
8.8 Reciprocity
267(3)
8.9 Problems
270(5)
References
275(1)
9 Computational Mechanics of Deformable Bodies
276(96)
9.1 Numerical Solutions -- Axial Loads
277(4)
9.1.1 Principles of Virtual Work and Complementary Virtual Work
277(4)
9.2 Stiffness-Based Finite Elements for Axial-Load Problems
281(14)
9.3 Force-Based Finite Elements for Axial-Load Problems
295(17)
9.3.1 A Summary and Discussion
307(5)
9.4 Generation of the Compatibility Equations
312(3)
9.5 Numerical Solutions -- Beam Bending
315(5)
9.5.1 Principles of Virtual Work and Complementary Virtual Work
316(4)
9.6 Stiffness-Based Finite Elements for Beam Bending
320(9)
9.7 Force-Based Finite Elements for Beam Bending
329(8)
9.8 Some Extensions of a Force-Based Approach
337(19)
9.9 Finite Elements for General Deformable Bodies
356(5)
9.9.1 Stiffness-Based Finite Elements
356(2)
9.9.2 Force-Based Finite Elements
358(3)
9.10 The Boundary Element Method
361(5)
9.11 Problems
366(5)
References
371(1)
10 Unsymmetrical Beam Bending
372(37)
10.1 Multiple Axis Bending of Nonsymmetrical Beams
372(12)
10.2 Shear Stresses in Thin, Open Cross-Section Beams
384(4)
10.3 The Shear Center for Thin, Open Cross-Section Beams
388(14)
10.4 Thin, Closed Cross-Section Beams
402(2)
10.5 Problems
404(5)
11 Uniform and Nonuniform Torsion
409(66)
11.1 Torsion of Circular Cross-Sections -- A Summary
409(2)
11.2 Uniform Torsion of Noncircular Cross-Sections -- Warping Function
411(6)
11.3 Uniform Torsion of Noncircular Cross-Sections -- Prandtl Stress Function
417(9)
11.4 Nonuniform Torsion
426(14)
11.5 General Solution of the Nonuniform Torsion Problem
440(2)
11.6 Torsion of Thin, Open Cross-Sections
442(12)
11.7 Torsion of Thin, Closed Cross-Sections
454(13)
11.8 Problems
467(7)
References
474(1)
12 Combined Deformations
475(21)
12.1 Bending and Torsion of Thin, Open Cross-Sections
475(2)
12.2 Bending and Torsion of Thin, Closed Cross-Sections
477(11)
12.2.1 Single-Cell Cross-Sections
477(2)
12.2.2 Multiple-Cell Cross-Sections
479(9)
12.3 Twisting Induced by Axial Stresses
488(6)
12.4 Problems
494(1)
References
495(1)
13 Material Failure and Stability
496(31)
13.1 Theories of Static Failure
496(6)
13.1.1 Maximum Normal-Stress Theory
496(1)
13.1.2 Maximum Shearing-Stress Theory
497(2)
13.1.3 Maximum Distortional Strain Energy Theory
499(3)
13.2 Fatigue Failure
502(6)
13.3 Fracture Mechanics
508(7)
13.4 Stability
515(5)
13.5 Problems
520(5)
References
525(2)
Appendix A Cross-Section Properties 527(2)
A.1 Parallel Axis Theorem 529(2)
A.2 Area Moments in Rotated Coordinates and Principal Axes 531(2)
A.3 Calculating Centroids and Area Moments in MATLAB® 533(4)
Appendix B The Beltrami--Michell Compatibility Equations 537(1)
B.1 Compatibility Equations for Stresses 537(3)
Appendix C The Sectorial Area Function 540(17)
Appendix D MATLAB® Files 557(8)
Index 565
Lester W. Schmerr, Jr, is Emeritus Professor of Aerospace Engineering at Iowa State University.