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9780849398995

Advanced Mechanics Of Materials And Applied Elasticity

by ;
  • ISBN13:

    9780849398995

  • ISBN10:

    0849398991

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2005-08-19
  • Publisher: CRC Press

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Summary

This book presents both differential equation and integral formulations of boundary value problems for computing the stress and displacement fields of solid bodies at two levels of approximation - isotropic linear theory of elasticity as well as theories of mechanics of materials. Moreover, the book applies these formulations to practical solutions in detailed, easy-to-follow examples.Advanced Mechanics of Materials and Applied Elasticity presents modern and classical methods of analysis in current notation and in the context of current practices. The author's well-balanced choice of topics, clear and direct presentation, and emphasis on the integration of sophisticated mathematics with practical examples offer students in civil, mechanical, and aerospace engineering an unparalleled guide and reference for courses in advanced mechanics of materials, stress analysis, elasticity, and energy methods in structural analysis.

Table of Contents

Cartesian Tensors
1(52)
Vectors
1(10)
Dyads
11(1)
Definition and Rules of Operation of Tensors of the Second Rank
12(8)
Transformation of the Cartesian Components of a Tensor of the Second Rank upon Rotation of the System of Axes to Which They Are Referred
20(1)
Definition of a Tensor of the Second Rank on the Basis of the Law of Transformation of Its Components
21(1)
Symmetric Tensors of the Second Rank
22(1)
Invariants of the Cartesian Components of a Symmetric Tensor of the Second Rank
22(1)
Stationary Values of a Function Subject to a Constraining Relation
23(3)
Stationary Values of the Diagonal Components of a Symmetric Tensor of the Second Rank
26(5)
Quasi Plane Form of Symmetric Tensors of the Second Rank
31(2)
Stationary Values of the Diagonal and the Non-Diagonal Components of the Quasi Plane, Symmetric Tensors of the Second Rank
33(4)
Mohr's Circle for Quasi Plane, Symmetric Tensors of the Second Rank
37(6)
Maximum Values of the Non-Diagonal Components of a Symmetric Tensor of the Second Rank
43(1)
Problems
44(9)
Strain and Stress Tensors
53(54)
The Continuum Model
53(1)
External Loads
53(2)
The Displacement Vector of a Particle of a Body
55(1)
Components of Strain of a Particle of a Body
56(6)
Implications of the Assumption of Small Deformation
62(2)
Proof of the Tensorial Property of the Components of Strain
64(2)
Traction and Components of Stress Acting on a Plane of a Particle of a Body
66(2)
Proof of the Tensorial Property of the Components of Stress
68(3)
Properties of the Strain and Stress Tensors
71(9)
Components of Displacement for a General Rigid Body Motion of a Particle
80(2)
The Compatibility Equations
82(2)
Measurement of Strain
84(4)
The Requirements for Equilibrium of the Particles of a Body
88(3)
Cylindrical Coordinates
91(2)
Strain--Displacement Relations in Cylindrical Coordinates
93(1)
The Equations of Compatibility in Cylindrical Coordinates
94(1)
The Equations of Equilibrium in Cylindrical Coordinates
95(1)
Problems
96(11)
Stress--Strain Relations
107(48)
Introduction
107(1)
The Uniaxial Tension or Compression Test Performed in an Environment of Constant Temperature
108(7)
Strain Energy Density and Complementary Energy Density for Elastic Materials Subjected to Uniaxial Tension or Compression in an Environment of Constant Temperature
115(4)
The Torsion Test
119(2)
Effect of Pressure, Rate of Loading and Temperature on the Response of Materials Subjected to Uniaxial States of Stress
121(3)
Models of Idealized Time-Independent Stress--Strain Relations for Uniaxial States of Stress
124(2)
Stress--Strain Relations for Elastic Materials Subjected to Three-Dimensional States of Stress
126(2)
Stress--Strain Relations of Linearly Elastic Materials Subjected to Three-Dimensional States of Stress
128(2)
Stress-Strain Relations for Orthotropic, Linearly Elastic Materials
130(3)
Stress-Strain Relations for Isotropic, Linearly Elastic Materials Subjected to Three-Dimensional States of Stress
133(2)
Strain Energy Density and Complementary Energy Density of a Particle of a Body Subjected to External Forces in an Environment of Constant Temperature
135(7)
Thermodynamic Considerations of Deformation Processes Involving Bodies Made from Elastic Materials
142(4)
Linear Response of Bodies Made from Linearly Elastic Materials
146(1)
Time-Dependent Stress-Strain Relations
147(1)
The Creep and the Relaxation Tests
148(2)
Problems
150(5)
Yield and Failure Criteria
155(30)
Yield Criteria for Materials Subjected to Triaxial States of Stress in an Environment of Constant Temperature
155(4)
The Von Mises Yield Criterion
159(3)
The Tresca Yield Criterion
162(1)
Comparison of the Von Mises and the Tresca Yield Criteria
162(5)
Failure of Structures --- Factor of Safety for Design
167(6)
The Maximum Normal Component of Stress Criterion for Fracture of Bodies Made from a Brittle, Isotropic, Linearly Elastic Material
173(2)
The Mohr's Fracture Criterion for Brittle Materials Subjected to States of Plane Stress
175(4)
Problems
179(6)
Formulation and Solution of Boundary Value Problems Using the Linear Theory of Elasticity
185(36)
Introduction
185(1)
Boundary Value Problems for Computing the Displacement and Stress Fields of Solid Bodies on the Basis of the Assumption of Small Deformation
186(7)
The Principle of Saint Venant
193(3)
Methods for Finding Exact Solutions for Boundary Value Problems in the Linear Theory of Elasticity
196(1)
Solution of Boundary Value Problems for Computing the Displacement and Stress Fields of Prismatic Bodies Made from Homogeneous, Isotropic, Linearly Elastic Materials
196(20)
Problems
216(5)
Prismatic Bodies Subjected to Torsional Moments at Their Ends
221(50)
Description of the Boundary Value Problem for Computing the Displacement and Stress Fields in Prismatic Bodies Subjected to Torsional Moments at Their Ends
221(2)
Relations among the Coordinates of a Point Located on a Curved Boundary of a Plane Surface
223(1)
Formulation of the Torsion Problem for Prismatic of Arbitary Cross Section on the Basis of the Linear Theory of Elasticity
224(9)
Interpretation of the Results of the Torsion Problem
233(3)
Computation of the Stress and Displacement Fields of Bodies of Solid Elliptical and Circular Cross Section Subjected to Equal and Opposite Torsional Moments at Their Ends
236(5)
Multiply Connected Prismatic Bodies Subjected to Equal and Opposite Torsional Moments at Their Ends
241(8)
Available Results
249(1)
Direction and Magnitude of the Shearing Stress Acting on the Cross Sections of a Prismatic Body of Arbitrary Cross Section Subjected to Torsional Moments at Its Ends
249(2)
The Membrane Analogy to the Torsion Problem
251(7)
Stress Distribution in Prismatic Bodies of Thin Rectangular Cross Section Subjected to Equal and Opposite Torsional Moments at Their Ends
258(3)
Torsion of Prismatic Bodies of Composite Simply Connected Cross Sections
261(2)
Numerical Solutions of Torsion Problems Using Finite Differences
263(5)
Problems
268(3)
Plane Strain and Plane Stress Problems in Elasticity
271(56)
Plane Strain
271(2)
Formulation of the Boundary Value Problem for Computing the Stress and the Displacement Fields in a Prismatic Body in a State of Plane Strain Using the Airy Stress Function
273(5)
Prismatic Bodies of Multiply Connected Cross Sections in a State of Plane Strain
278(2)
The Plane Strain Equations in Cylindrical Coordinates
280(7)
Plane Stress
287(3)
Simply Connected Thin Prismatic Bodies (Plates) in a State of Plane Stress Subjected on Their Lateral Surface to Symmetric in x1 Components of Traction Tn2 and Tn3
290(5)
Two-Dimensional or Generalized Plane Stress
295(11)
Prismatic Members in a State of Axisymmetric Plane Strain or Plane Stress
306(16)
Problems
322(5)
Theories of Mechanics of Materials
327(64)
Introduction
327(2)
Fundamental Assumptions of the Theories of Mechanics of Materials for Line Members
329(8)
Internal Actions Acting on a Cross Section of Line Members
337(1)
Framed Structures
338(2)
Types of Framed Structures
340(2)
Internal Action Release Mechanisms
342(1)
Statically Determinate and Indeterminate Framed Structures
343(3)
Computation of the Internal Actions of the Members of Statically Determinate Framed Structures
346(9)
Action Equations of Equilibrium for Line Members
355(3)
Shear and Moment Diagrams for Beams by the Summation Method
358(4)
Stress-Strain Relations for a Particle of a Line Member Made from an Isotropic Linearly Elastic Material
362(3)
The Boundary Value Problems in the Theories of Mechanics of Materials for Line Members
365(3)
The Boundary Value Problem for Computing the Axial Component of Translation and the Internal Force in a Member Made from an Isotropic, Linearly Elastic Material Subjected to Axial Centroidal Forces and to a Uniform Change in Temperature
368(10)
The Boundary Value Problem for Computing the Angle of Twist and the Internal Torsional Moment in Members of Circular Cross Section Made from an Isotropic, Linearly Elastic Material Subjected to Torsional Moments
378(6)
Problems
384(7)
Theories of Mechanics of Materials for Straight Beams Made from Isotropic, Linearly Elastic Materials
391(108)
Formulation of the Boundary Value Problems for Computing the Components of Displacement and the Internal Actions in Prismatic Straight Beams Made from Isotropic, Linearly Elastic Materials
391(14)
The Classical Theory of Beams
405(9)
Solution of the Boundary Value Problem for Computing the Transverse Components of Translation and the Internal Actions in Prismatic Beams Made from Isotropic, Linearly Elastic Materials Using Functions of Discontinuity
414(7)
The Timoshenko Theory of Beams
421(9)
Computation of the Shearing Components of Stress in Prismatic Beams Subjected to Bending without Twisting
430(14)
Build-Up Beams
444(4)
Location of the Shear Center of Thin-Walled Open Sections
448(6)
Members Whose Cross Sections Are Subjected to a Combination of Internal Actions
454(6)
Composite Beams
460(13)
Prismatic Beams on Elastic Foundation
473(4)
Effect of Restraining the Warping of One Cross Section of a Prismatic Member Subjected to Torsional Moments at Its Ends
477(9)
Problems
486(13)
Non-Prismatic Members --- Stress Concentrations
499(12)
Computation of the Components of Displacement and Stress of Non-Prismatic Members
499(1)
Stresses in Symmetrically Tapered Beams
500(5)
Stress Concentrations
505(4)
Problems
509(2)
Planar Curved Beams
511(26)
Introduction
511(1)
Derivation of the Equations of Equilibrium for a Segment of Infinitesimal Length of a Planar Curved Beam
511(3)
Computation of the Circumferential Component of Stress Acting on the Cross Sections of Planar Curved Beams Subjected to Bending without Twisting
514(14)
Computation of the Radial and Shearing Components of Stress in Curved Beams
528(6)
Problems
534(3)
Thin-Walled, Tubular Members
537(44)
Introduction
537(1)
Computation of the Shearing Stress Acting on the Cross Sections of Thin-Walled, Single-Cell, Tubular Members Subjected to Equal and Opposite Torsional Moments at Their Ends
538(2)
Computation of the Angle of Twist per Unit Length of Thin-Walled, Single-Cell, Tubular Members Subjected to Equal and Opposite Torsional Moment at Their Ends
540(6)
Prismatic Thin-Walled, Single-Cell, Tubular Members with Thin Fins Subjected to Torsional Moments
546(5)
Thin-Walled, Multi-Cell, Tubular Members Subjected to Torsional Moments
551(4)
Thin-Walled, Single-Cell, Tubular Beams Subjected to Bending without Twisting
555(10)
Thin-Walled, Multi-Cell, Tubular Beams Subjected to Bending without Twisting
565(7)
Single-Cell, Tubular Beams with Longitudinal Stringers subjected to Bending without Twisting
572(4)
Problems
576(5)
Integral Theorems of Structural Mechanics
581(76)
A Statically Admissible Stress Field and an Admissible Displacement Field of a Body
581(1)
Derivation of the Principle of Virtual Work for Deformable Bodies
582(5)
Statically Admissible Reactions and Internal Actions of Framed Structures
587(1)
The Principle of Virtual Work for Framed Structures
588(9)
The Unit Load Method
597(9)
The Principle of Virtual Work for Framed Structures, Including the Effect of Shear Deformation
606(4)
The Strong Form of One-Dimensional, Linear Boundary Value Problems
610(3)
Approximation of the Solution of One-Dimensional, Linear Boundary Value Problems Using Trial Functions
613(2)
The Classical Weighted Residual Form for Second Order, One-Dimensional, Linear Boundary Value Problems
615(2)
The Classical Weighted Residual Form for Fourth Order, One-Dimensional, Linear Boundary Value Problems
617(2)
Discretization of Boundary Value Problems Using the Classical Weighted Residual Methods
619(1)
The Modified Weighted Residual (Weak) Form of One-Dimensional, Linear Boundary Value Problems
620(9)
Total Strain Energy of Framed Structures
629(1)
Castigliano's Second Theorem
630(7)
Betti-Maxwell Reciprocal Theorem
637(2)
Proof That the Center of Twist of a Cross Section Coincides with Its Shear Center
639(1)
The Variational Form of the Boundary Value Problem for Computing the Components of Displacement of a Deformable Body --- Theorem of Stationary Total Potential Energy
640(11)
Comments on the Modified Gallerkin Form and the Theorem of Stationary Total Potential Energy
651(1)
Problems
651(6)
Analysis of Statically Indeterminate Framed Structures
657(14)
The Basic Force or Flexibility Method
657(7)
Computation of Components of Displacement of Points of Statically Indeterminate Structures
664(2)
Problems
666(5)
The Finite Element Method
671(92)
Introduction
671(1)
The Finite Element Method for One-Dimensional, Second Order, Linear Boundary Value Problems as a Modified Galerkin Method
671(6)
Element Shape Functions
677(3)
Assembly of the Stiffness Matrix for the Domain of One-Dimensional, Second Order, Linear Boundary Value Problems from the Stiffness Matrices of Their Elements
680(3)
Construction of the Force Vector for the Domain of One-Dimensional, Second Order, Linear Boundary Value Problems
683(2)
Direct Computation of the Contribution of an Element to the Stiffness Matrix and the Load Vector of the Domain of One-Dimensional, Second Order, Linear Boundary Value Problems
685(4)
Approximate Solution of Linear Boundary Value Problems Using the Finite Element Method
689(10)
Application of the Finite Element Method to the Analysis of Framed Structures
699(37)
Approximate Solution of Scalar Two-Dimensional, Second Order, Linear Boundary Value Problems Using the Finite Element Method
736(22)
Problems
758(5)
Plastic Analysis and Design of Structures
763(44)
Strain--Curvature Relation of Prismatic Beams Subjected to Bending without Twisting
763(2)
Initiation of Yielding Moment and Fully Plastic Moment of Beams Made from Isotropic, Linearly Elastic, Ideally Plastic Materials
765(4)
Distribution of the Shearing Component of Stress Acting on the Cross Sections of Beams Where M2y<M2<M2p
769(3)
Location of the Elastoplastic Boundaries --- Moment--Curvature Relation
772(6)
Computation of the Deflection of Beams Made from Isotropic, Linearly Elastic, Ideally Plastic Materials
778(2)
Effect of Stress Concentrations on the Design of Line Members
780(2)
Elastic and Plastic Design for Strength of Statically Determinate Structures
782(3)
Plastic Analysis and Design of Planar Statically Indeterminate Beams and Frames
785(5)
Direct Computations of the Collapse Load of Beams and Frames
790(3)
Derivation of the Equations of Equilibrium for a Structure Using the Principle of Virtual Work
793(2)
Theorems for Limit Analysis
795(2)
Systematic Procedure for Plastic Analysis of Structures
797(5)
Problems
802(5)
Mechanics of Materials Theory for Thin Plates
807(54)
Introduction
807(2)
Fundamental Assumptions of the Theories of Mechanics of Materials for Thin Plates
809(3)
Internal Action Intensities Acting on an Element of a Plate
812(3)
Internal Action Intensities Acting on Planes Which Are Inclined to the x1 and x2 Axes
815(1)
Equations of Equilibrium for a Plate
816(3)
Boundary Conditions for Plates
819(6)
Analysis of Simply Supported Rectangular Plates Subjected to a General Distribution of Transverse Forces
825(7)
The Method of Levy for Computing the Deflection of Rectangular Plates Having a Simply Supported Pair of Parallel Edges
832(7)
Bending of Circular Plates
839(6)
Use of the Weighted Residual Methods to Construct Approximate Expressions for the Deflection of Plates
845(11)
The Theorem of Total Stationary Potential Energy for Plates
856(2)
Problems
858(3)
Instability of Elastic Structures
861(44)
States of Unstable Equilibrium of Structures
861(11)
The Non-Linear Theory of Elasticity and the Theory of Moderate Rotations
872(3)
Criterion for the Stability or Instability of an Equilibrium Configuration of Structures
875(1)
Investigation of the Beginning of Buckling
875(1)
Buckling of Structures Having One Degree of Freedom
876(12)
Buckling of Structures Having Infinite Degrees of Freedom --- The Direct Equilibrium Approach
888(7)
Buckling of Structures Having Infinite Degrees of Freedom --- The Stationary Total Potential Energy Approach
895(2)
Determination of the Critical Load at Buckling of Infinite Degree of Freedom Structures by Investigating the Beginning of Buckling
897(3)
Columns Subjected to Eccentric Axial Compressive Forces at Their Ends
900(4)
Local Buckling of Columns
904(1)
Problems
904(1)
Appendices
905(62)
A Mechanical Properties of Materials
907(2)
B Stress--Strain Relations for Orthotropic and Isotropic Materials
909(10)
C Centroid, Moments and Products of Inertia of Plane Surfaces
919(10)
D Method of Finite Differences
929(14)
E Elements of Calculus of Variations
943(8)
F Derivation of the Expression for the Plane Stress Functions X(x1, x2, x3)
951(6)
G Functions of Discontinuity
957(4)
H Properties of Rolled Shapes
961(6)
Index 967

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