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  • Produktbild: Mechanics of Solids
  • Produktbild: Mechanics of Solids

Mechanics of Solids Volume III: Theory of Viscoelasticity, Plasticity, Elastic Waves, and Elastic Stability

136,99 €

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.06.1984

Herausgeber

C. Truesdell

Verlag

Springer Berlin

Seitenzahl

647

Maße (L/B/H)

24,4/17/3,6 cm

Gewicht

1127 g

Auflage

Softcover reprint of the original 1st ed. 1973

Sprache

Englisch

ISBN

978-3-540-13162-5

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.06.1984

Herausgeber

C. Truesdell

Verlag

Springer Berlin

Seitenzahl

647

Maße (L/B/H)

24,4/17/3,6 cm

Gewicht

1127 g

Auflage

Softcover reprint of the original 1st ed. 1973

Sprache

Englisch

ISBN

978-3-540-13162-5

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: GPSR Kontakt

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  • Produktbild: Mechanics of Solids
  • Produktbild: Mechanics of Solids
  • The Linear Theory of Viscoelasticity.- A. Introduction.- 1. Plan and scope of this article.- 2. Notation. Vectors, tensors, and linear transformations.- 3. Processes and histories.- 4. Convolutions.- 5. The Boltzmann operator.- B. Foundations of the linear theory.- 6. Linear hereditary laws.- 7. Boltzmann laws. Definitions.- 8. Characterization of Boltzmann laws.- 9. Constitutive relations. Linearly viscoelastic materials.- 10. Constitutive equations. Boltzmann laws. Stress relaxation.- 11. Relaxation and creep laws.- 12. Isotropic materials.- 13. Additional properties of Boltzmann laws. Mechanical forcing.- 14. Differential operator laws.- 15. Relaxation times and differential operator laws.- 16. Special differential operators.- 17. Field equations.- C. Quasi-static linear viscoelasticity.- 18. The quasi-static assumption.- 19. Quasi-static viscoelastic processes.- 20. Displacement equations of equilibrium.- 21. Equations of compatibility.- 22. Boundary data.- 23. The quasi-static boundary value problem.- 24. Synchronous and separable boundary data.- 25. Initial response. Elastic states.- 26. The past-history problem.- 27. Integral theorems.- 28. Uniqueness of quasi-static viscoelastic processes.- 29. Existence of quasi-static viscoelastic processes.- 30. Quasi-static variational principles.- 31. Elastic-viscoelastic correspondence.- 32. Stress functions for quasi-static viscoelastic processes.- 33. Singular solutions.- 34. Green’s processes and integral solutions.- 35. Saint-Venant’s principle.- D. Dynamic linear viscoelasticity.- 36. Dynamic viscoelastic processes.- 37. Field equations.- 38. Complete dynamic displacement generating functions.- 39. Power and energy.- 40. Uniqueness. Boundary value problem.- 41. Waves. Singular surfaces.- 42. Initial value problem. Uniqueness and existence of solutions.- 43. Oscillatory displacement processes. Free vibrations.- 44. Dynamic variational principles.- References.- Theory of Elastic Stability.- A. Introduction.- B. Abstract dynamical systems.- 1. Introduction.- 2. General features of a dynamical system.- 3. Definition of a dynamical system.- 4. The set of initial data and a related mapping.- C. Definitions of stability.- 5. Introduction.- 6. Definition of Liapounov stability.- 7. Further definitions.- 8. Continuous dependence.- 9. Instability in the sense of Liapounov.- 10. Boundedness and Liapounov stability.- 11. Instability in the sense of Lagrange.- 12. Stability and uniqueness.- D. Stability theorems for abstract dynamical systems.- 13. Introduction.- 14. Maximum principles.- 15. Liapounov’s theorems on stability. (The second method).- 16. Discussion of the theorems.- 17. Examples.- 18. Relation of stability to the calculus of variations.- 19. Theorems on instability.- 20. Boundedness and asymptotic stability.- E. Eigenfunction analyses.- F. Stability of elastic bodies.- 21. Introduction.- 22. Derivation of basic equations.- 23. The equations of perturbed motion. Isothermal linear elasticity.- 24. Incremental equations for thermoelasticity.- 25. Some causes of perturbations.- G. Liapounov functions for finite thermoelasticity.- 26. Introduction.- 27. Liapounov functions from the energy balance equation.- 28. Liapounov functions from the entropy production inequality.- H. Liapounov stability in the class of non-linear perturbations.- 29. Introduction.- 30. Sufficiency theorems.- I. The energy criterion for stability.- 31. Statement and history of the criterion.- 32. Necessary conditions.- 33. Sufficient conditions.- 34. Criticism of the energy criterion.- J. Stability for a fixed surface and under dead loads in the class of small incremental displacements.- 35. Stability of equilibrium.- 36. Stability of a body with time-dependent elasticities.- 37. Discussion of choice of measure.- 38. Stability with multipolar elasticity.- 39. Incompressible media.- K. Stability under dead surface loads in the class of small incremental displacements.- 40. Introduction.- 41. Stability analysis I.- 42. Stability analysis II.- 43. Note on Korn’s inequality.- L. Instability under dead surface loads from the equations of linear incremental displacement.- 44. Instability from negative-definite total energy.- 45. Non-uniqueness and instability.- 46. The method of adjacent equilibrium.- 47. History and application of the test.- M. Logarithmic convexity.- 48. Introduction.- 49. Convexity of the function F(t; ?,t0).- 50. Applications.- N. Extension of stability analysis for traction boundary conditions.- 51. Stability without an axis of equilibrium.- 52. Stability with an axis of equilibrium.- 53. Instability analysis.- 54. Incompressible media.- O. Stability in special traction boundary value problems.- 55. Introduction.- 56. Isotropic compressible material under hydrostatic stress.- 57. Incompressible elastic material.- P. Stability in the class of linear thermoelastic displacements under dead loads.- 58. Introduction.- 59. Liapounov stability.- 60. Instability.- 61. Hölder stability.- 62. Asymptotic stability.- Q. Classification of stability problems with non-dead loading.- 63. Introduction.- 64. Group (a): Persistent stability.- 65. Group (b): Motion-dependent data.- R. Stability under weakly conservative loads.- 66. Definitions.- 67. Characterisations of weakly conservative forces.- 68. Stability analyses.- S. Stability with time-dependent and position-dependent data.- 69. Introduction.- 70. Prescribed surface traction with zero initial data.- 71. Prescribed surface traction with non-zero initial data.- 72. Prescribed surface displacement.- 73. Prescribed body force.- 74. Variation in the elasticities.- 75. Change in initial data under dead loading.- 76. Convexity arguments.- 77. Further arguments.- T. Stability under follower forces.- 78. Introduction.- 79. Examples using the Liapounov theory.- 80. Adjacent equilibrium method. Instability by divergence.- 81. Eigenfunction expansions. Analyses depending upon separation of variables.- U. Dissipative forces.- 82. Introduction.- 83. Snap-through.- References.- Growth and Decay of Waves in Solids.- I. Introduction.- 1. Nature of this article.- 2. General scheme of notation.- II. Preliminaries.- 3. Basic kinematical concepts.- 4. Theory of singular surfaces.- 5. Definition of shock waves and acceleration waves.- III. Acceleration waves in elastic bodies.- 6. Longitudinal waves in anisotropic elastic bodies.- 7. Transverse waves in anisotropic elastic bodies.- 8. Thermodynamic influences on waves in anisotropic elastic bodies.- 9. Waves in isotropic elastic bodies.- 10. Waves of arbitrary shape in isotropic elastic bodies.- 11. Thermodynamic influences on waves in isotropic elastic bodies.- IV. One dimensional waves in bodies of material with memory.- 12. Acceleration waves in bodies of material with memory.- 13. The local and global behavior of the amplitudes of acceleration waves.- 14. Acceleration waves entering homogeneously deformed bodies of material with memory.- 15. Thermodynamic influences on acceleration waves in bodies of material with memory.- 16. Shock waves entering unstrained bodies of material with memory.- 17. Consequences of the existence of steady shock waves.- V. One dimensional waves in elastic bodies.- 18. Acceleration waves in elastic bodies.- 19. Shock waves in elastic bodies.- VI. One dimensional waves in elastic non-conductors of heat.- 20. Acceleration waves in elastic non-conductors of heat.- 21. Acceleration waves entering deformed elastic non-conductors.- 22. Shock waves in elastic non-conductors of heat.- 23. Shock waves entering deformed elastic non-conductors.- VII. One dimensional waves in inhomogeneous elastic bodies.- 24. Acceleration waves in inhomogeneous elastic bodies.- 25. Acceleration waves in inhomogeneous elastic bodies at rest.- 26. Shock waves in inhomogeneous elastic bodies.- 27. Shock waves in inhomogeneous elastic bodies at rest.- 1. Existence of the one dimensional kinematical condition of compatibility.- 2. Proofs of Theorems 13.2, 13.3, 13.4 and 13.5.- 3. Derivation of (16.12).- References.- List of works cited.- Additional references.- Ideal Plasticity.- A. The basic equations.- I. The three-dimensional problem.- 1. Quadratic yield condition.- 2. Some basic formulas. Mohr circles.- 3. Plastic potential.- 4. Tresca’s yield criterion. “Singular” yield conditions.- 5. “Compatibility” relations.- 6. The flow equations of Prandtl and Reuss.- 7. Further stress strain laws.- 8. Remarks on some three-dimensional problems.- 8 bis. Remarks on uniqueness for rigid plastic solids.- II. Discontinuous solutions.- a) Characteristics. Application to the three-dimensional problem of the perfectly plastic body.- 9. Introduction.- 10. Examples.- 11. Systems of differential equations.- 12. Characteristics of the v. Mises plasticity equations.- 13. Further results and comments.- b) Continuation.- 14. Characteristic surfaces. Characteristic condition.- 15. Compatibility conditions.- 16. Discontinuous solutions.- 17. Preliminary comments on discontinuous solutions in plasticity.- c) Hadamard’s theory.- 18. Moving surfaces.- 19. Geometrical and kinematical discontinuity conditions.- 19 bis. Continuation.- 20. Application to a system of equations.- 21. Compatibility conditions.- d) Shock conditions. Stress discontinuities.- 22. “ Shock conditions ”.- 23. On the classification of discontinuities.- 24. Stress discontinuities.- B. Plane problems.- I. Plane strain, plane stress, and generalizations.- 25. Plane strain with v. Mises’ or with Tresca’s yield condition derived from three-dimensional problem.- 26. Plane strain under general yield condition.- 27. Plane stress with quadratic yield condition.- 27 bis. Plane stress. Continued.- 28. Generalized plane stress.- II. The theory of plane strain.- a) Differential relations.- 29. Basic equations.- 30. Continuation. Slip line field.- b) Integration. Particular solutions.- 31. Integration.- 32. Examples of exact particular solutions.- 33. Discontinuities.- C. The general plane problem.- I. Basic theory.- a) The equations.- 34. Linearization.- 35. Various yield conditions.- b) Characteristics of the complete plane problem.- 36. Characteristic directions and compatibility relations.- 37. Continuation. Relation to O. Mohr’s theory. Differential equations in characteristic coordinates.- 38. Examples for Sects. 36 and 37.- c) Remarks on integration. Examples.- 39. On integration.- II. Singular solutions and various remarks.- a) Limit line singularities and branch line singularities.- 40. Limit line singularities.- 41. Limit line singularities. Continuation.- 42. Branch line singularities.- b) Simple waves.- 43. Definition.- 44. Simple waves. Continuation.- 45. Simple waves for particular yield conditions.- c) Various remarks.- 46. Remarks on the approximate solution of initial-value problems.- 47. Summary remarks on some further problems.- D. Boundary-value problems.- I. Some elastic-plastic problems.- a) The torsion problem.- 48. Fully elastic and fully plastic torsion.- 49. Elastic-plastic torsion.- 50. Examples, further problems and concluding remarks.- b) The thick walled tube.- 51. Expansion of a cylindrical tube.- 52. Partly plastic tube.- 53. Further solutions. Comments.- c) Flat ring and flat sheet in plane stress. Further elastic-plastic problems.- 54. Flat ring radially stressed as a problem of plastic-elastic equilibrium.- 55. Continuation: Plastic-elastic equilibrium.- 56. Expansion of a circular hole in an infinite sheet.- 57. A few further elastic-plastic problems.- II. Some plastic-rigid problems.- a) Various remarks.- 58. The plastic-rigid body.- 58 bis. Axial symmetry. A few remarks.- b) Wedge with pressure on one face.- 59. General discussion and velocity distribution.- c) Plastic mass between rough rigid plates.- 60. Infinite slab.- 61. Slab of material with overhanging ends between rough plates.- Some reference books.- Topics in the Mathematical Theory of Plasticity.- A. Introduction.- B. Foundation of the theory.- I. Thermodynamics for elastic-plastic materials.- 1. Motion and deformation history.- 2. Constitutive functionals.- 3. Elastic-plastic resolution of deformations.- 4. Consequences of the Clausius-Duhem inequality.- 5. Rate independent materials.- 6. Isotropy and principle of frame indifference.- II. Prandtl-Reuss theory.- 7. Flow rule.- 8. Prandtl-Reuss equations.- III. St. Venant-Lévy-v. Mises theory.- IV. Theory of Hencky.- C. General theorems.- I. Intrinsic formulation of the variational principle.- II. Examples.- 9. Elastic-plastic torsion in the sense of Hencky.- 10. Stationary creep deformation of a plate.- 11. Plane stress and plane deformation problems.- III. Existence of certain steady plastic flows.- 12. Formulation of a weak problem.- 13. Existence of solution of certain weak problems.- D. Torsion problems.- I. Completely plastic torsion.- 14. Variational formulation of the problem.- 15. Solution of the problem.- 16. St. Venant’s conjecture and its extension.- II. Elastic-plastic torsion.- 17. Formal statement of the problem.- 18. Variational formulation of the problem.- 19. Existence and uniqueness of the extremal.- 20. Holder continuity of the extremal.- 21. The existence of an elastic core.- 22. Continuity of stress.- 23. Natural partition of the cross section.- 24. Some properties of E and P.- 25. Elastic-plastic boundary.- 26. Dependence upon angle of twist.- 27. Dependence upon the yield strength.- 28. Dependence upon the angle of twist, continued.- References.- Namenverzeichnis — Author Index.- Sachverzeichnis (Deutsch-Englisch).- Subject Index (English-German).