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

Mechanics of Solids Volume II: Linear Theories of Elasticity and Thermoelasticity, Linear and Nonlinear Theories of Rods, Plates, and Shells

146,99 €

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.06.1984

Herausgeber

C. Truesdell

Verlag

Springer Berlin

Seitenzahl

745

Maße (L/B/H)

24,4/17/4,1 cm

Gewicht

1286 g

Auflage

Softcover reprint of the original 1st edition 1973

Sprache

Englisch

ISBN

978-3-540-13161-8

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.06.1984

Herausgeber

C. Truesdell

Verlag

Springer Berlin

Seitenzahl

745

Maße (L/B/H)

24,4/17/4,1 cm

Gewicht

1286 g

Auflage

Softcover reprint of the original 1st edition 1973

Sprache

Englisch

ISBN

978-3-540-13161-8

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 Elasticity.- A. Introduction.- 1. Background. Nature of this treatise.- 2. Terminology and general scheme of notation.- B. Mathematical preliminaries.- I. Tensor analysis.- 3. Points. Vectors. Second-order tensors.- 4. Scalar fields. Vector fields. Tensor fields.- II. Elements of potential theory.- 5. The body B. The subsurfaces L1 and L2 of ?B.- 6. The divergence theorem. Stokes’ theorem.- 7. The fundamental lemma. Rellich’s lemma.- 8. Harmonic and biharmonic fields.- III. Functions of position and time.- 9. Class CM,N.- 10. Convolutions.- 11. Space-time.- C. Formulation of the linear theory of elasticity.- I. Kinematics.- 12. Finite deformations. Infinitesimal deformations.- 13. Properties of displacement fields. Strain.- 14. Compatibility.- II. Balance of momentum. The equations of motion and equilibrium.- 15. Balance of momentum. Stress.- 16. Balance of momentum for finite motions.- 17. General solutions of the equations of equilibrium.- 18. Consequences of the equation of equilibrium.- 19. Consequences of the equation of motion.- III. The constitutive relation for linearly elastic materials.- 20. The elasticity tensor.- 21. Material symmetry.- 22. Isotropic materials.- 23. The constitutive assumption for finite elasticity.- 24. Work theorems. Stored energy.- 25. Strong ellipticity.- 26. Anisotropic materials.- D. Elastostatics.- I. The fundamental field equations. Elastic states. Work and energy.- 27. The fundamental system of field equations.- 28. Elastic states. Work and energy.- II. The reciprocal theorem. Mean strain theorems.- 29. Mean strain and mean stress theorems. Volume change.- 30. The reciprocal theorem.- III. Boundary-value problems. Uniqueness.- 31. The boundary-value problems of elastostatics.- 32. Uniqueness.- 33. Nonexistence.- IV. The variational principles of elastostatics.- 34. Minimum principles.- 35. Some extensions of the fundamental lemma.- 36. Converses to the minimum principles.- 37. Maximum principles.- 38. Variational principles.- 39. Convergence of approximate solutions.- V. The general boundary-value problem. The contact problem.- 40. Statement of the problem. Uniqueness.- 41. Extension of the minimum principles.- VI. Homogeneous and isotropic bodies.- 42. Properties of elastic displacement fields.- 43. The mean value theorem.- 44. Complete solutions of the displacement equation of equilibrium.- VII. The plane problem.- 45. The associated plane strain and generalized plane stress solutions.- 46. Plane elastic states.- 47. Airy’s solution.- VIII. Exterior domains.- 48. Representation of elastic displacement fields in a neighborhood of infinity.- 49. Behavior of elastic states at infinity.- 50. Extension of the basic theorems in elastostatics to exterior domains.- IX. Basic singular solutions. Concentrated loads. Green’s functions.- 51. Basic singular solutions.- 52. Concentrated loads. The reciprocal theorem.- 53. Integral representation of solutions to concentrated-load problems.- X. Saint-Venant’s principle.- 54. The v. Mises-Sternberg version of Saint-Venant’s principle.- 55. Toupin’s version of Saint-Venant’s principle.- 56. Knowles’ version of Saint-Venant’s principle.- 56a. The Zanaboni-Robinson version of Saint-Venant’s principle.- XI. Miscellaneous results.- 57. Some further results for homogeneous and isotropic bodies.- 58. Incompressible materials.- E. Elastodynamics.- I. The fundamental field equations. Elastic processes. Power and energy. Reciprocity.- 59. The fundamental system of field equations.- 60. Elastic processes. Power and energy.- 61. Graffi’s reciprocal theorem.- II. Boundary-initial-value problems. Uniqueness.- 62. The boundary-initial-value problem of elastodynamics.- 63. Uniqueness.- III. Variational principles.- 64. Some further extensions of the fundamental lemma.- 65. Variational principles.- 66. Minimum principles.- IV. Homogeneous and isotropic bodies.- 67. Complete solutions of the field equations.- 68. Basic singular solutions.- 69. Love’s integral identity.- V. Wave propagation.- 70. The acoustic tensor.- 71. Progressive waves.- 72. Propagating surfaces. Surfaces of discontinuity.- 73. Shock waves. Acceleration waves. Mild discontinuities.- 74. Domain of influence. Uniqueness for infinite regions.- VI. The free vibration problem.- 75. Basic equations.- 76. Characteristic solutions. Minimum principles.- 77. The minimax principle and its consequences.- 78. Completeness of the characteristic solutions.- References.- Linear Thermoelasticity.- A. Introduction.- 1. The nature of this article.- 2. Notation.- B. The foundations of the linear theory of thermoelasticity.- 3. The basic laws of mechanics and thermodynamics.- 4. Elastic materials. Consequences of the second law.- 5. The principle of material frame-indifference.- 6. Consequences of the heat conduction inequality.- 7. Derivation of the linear theory.- 8. Isotropy.- C. Equilibrium theory.- 9. Basic equations. Thermoelastic states.- 10. Mean strain and mean stress. Volume change.- 11. The body force analogy.- 12. Special results for homogeneous and isotropic bodies.- 13. The theorem of work and energy. The reciprocal theorem.- 14. The boundary-value problems of the equilibrium theory. Uniqueness.- 15. Temperature fields that induce displacement free and stress free states.- 16. Minimum principles.- 17. The uncoupled-quasi-static theory.- D. Dynamic theory.- 18. Basic equations. Thermoelastic processes.- 19. Special results for homogeneous and isotropic bodies.- 20. Complete solutions of the field equations.- 21. The theorem of power and energy. The reciprocal theorem.- 22. The boundary-initial-value problems of the dynamic theory.- 23. Uniqueness.- 24. Variational principles.- 25. Progressive waves.- List of works cited.- Existence Theorems in Elasticity.- 1. Prerequisites and notations.- 2. The function spaces $$\mathop H\limits^ \circ$$m and Hm.- 3. Elliptic linear systems. Interior regularity.- 4. Results preparatory to the regularization at the boundary.- 5. Strongly elliptic systems.- 6. General existence theorems.- 7. Propagation problems.- 8. Diffusion problems.- 9. Integro-differential equations.- 10. Classical boundary value problems for a scalar 2nd order elliptic operator.- 11. Equilibrium of a thin plate.- 12. Boundary value problems of equilibrium in linear elasticity.- 13. Equilibrium problems for heterogeneous media.- Boundary Value Problems of Elasticity with Unilateral Constraints.- 1. Abstract unilateral problems: the symmetric case.- 2. Abstract unilateral problems: the nonsymmetric case.- 3. Unilateral problems for elliptic operators.- 4. General definition for the convex set V.- 5. Unilateral problems for an elastic body.- 6. Other examples of unilateral problems.- 7. Existence theorem for the generalized Signorini problem.- 8. Regularization theorem: interior regularity.- 9. Regularization theorem: regularity near the boundary.- 10. Analysis of the Signorini problem.- 11. Historical and bibliographical remarks concerning Existence Theorems in Elasticity.- The Theory of Shells and Plates.- A. Introduction.- 1. Preliminary remarks.- 2. Scope and contents.- 3. Notation and a list of symbols used.- B. Kinematics of shells and plates.- 4. Coordinate systems. Definitions. Preliminary remarks.- 5. Kinematics of shells: I. Direct approach.- ?) General kinematical results.- ?) Superposed rigid body motions.- ?) Additional kinematics.- 6. Kinematics of shells continued (linear theory): I. Direct approach.- ?) Linearized kinematics.- ?) A catalogue of linear kinematic measures.- ?) Additional linear kinematic formulae.- ?) Compatibility equations.- 7. Kinematics of shells: II. Developments from the three-dimensional theory.- ?) General kinematical results.- ?) Some results valid in a reference configuration.- ?) Linearized kinematics.- ?) Approximate linearized kinematic measures.- ?) Other kinematic approximations in the linear theory.- C. Basic principles for shells and plates.- 8. Basic principles for shells: I. Direct approach.- ?) Conservation laws.- ?) Entropy production.- ?) Invariance conditions.- ?) An alternative statement of the conservation laws.- ?) Conservation laws in terms of field quantities in a reference state.- 9. Derivation of the basic field equations for shells: I. Direct approach.- ?) General field equations in vector forms.- ?) Alternative forms of the field equations.- ?) Linearized field equations.- ?) The basic field equations in terms of a reference state.- 10. Derivation of the basic field equations of a restricted theory: I. Direct approach.- 11. Basic field equations for shells: II. Derivation from the three-dimensional theory.- ?) Some preliminary results.- ?) Stress-resultants, stress-couples and other resultants for shells.- ?) Developments from the energy equation. Entropy inequalities.- 12. Basic field equations for shells continued: II. Derivation from the three-dimensional theory.- ?) General field equations.- ?) An approximate system of equations of motion.- ?) Linearized field equations.- ?) Relationship with results in the classical linear theory of thin shells and plates.- 12 A. Appendix on the history of derivations of the equations of equilibrium for shells.- D. Elastic shells.- 13. Constitutive equations for elastic shells (nonlinear theory): I. Direct approach.- ?) General considerations. Thermodynamical results.- ?) Reduction of the constitutive equations under superposed rigid body motions.- ?) Material symmetry restrictions.- ?) Alternative forms of the constitutive equations.- 14. The complete theory. Special results: I. Direct approach.- ?) The boundary-value problem in the general theory.- ?) Constitutive equations in a mechanical theory.- ?) Some special results.- ?) Special theories.- 15. The complete restricted theory: I. Direct approach.- 16. Linear constitutive equations: I. Direct approach.- ?) General considerations.- ?) Explicit results for linear constitutive equations.- ?) A restricted form of the constitutive equations for an isotropic material.- ?) Constitutive equations of the restricted linear theory.- 17. The complete theory for thermoelastic shells: II. Derivation from the three-dimensional theory.- ?) Constitutive equations in terms of two-dimensional variables. Thermodynamical results.- ?) Summary of the basic equations in a complete theory.- 18. Approximation for thin shells: II. Developments from the three-dimensional theory.- ?) An approximation procedure.- ?) Approximation in the linear theory.- 19. An alternative approximation procedure in the linear theory: II. Developments from the three-dimensional theory.- 20. Explicit constitutive equations for approximate linear theories of plates and shells: II. Developments from the three-dimensional theory.- ?) Approximate constitutive equations for plates.- ?) The classical plate theory. Additional remarks.- ?) Approximate constitutive relations for thin shells.- ?) Classical shell theory. Additional remarks.- 21. Further remarks on the approximate linear and nonlinear theories developed from the three-dimensional equations.- 21 A. Appendix on the history of the derivation of linear constitutive equations for thin elastic shells.- 22. Relationship of results from the three-dimensional theory and the theory of Cosserat surface.- E. Linear theory of elastic plates and shells.- 23. The boundary-value problem in the linear theory.- ?) Elastic plates.- ?) Elastic shells.- 24. Determination of the constitutive coefficients.- ?) The constitutive coefficients for plates.- ?) The constitutive coefficients for shells.- 25. The boundary-value problem of the restricted linear theory.- 26. A uniqueness theorem. Remarks on the general theorems.- F. Appendix: Geometry of a surface and related results.- A.1. Geometry of Euclidean space.- A.2. Some results from the differential geometry of a surface.- ?) Definition of a surface. Preliminaries.- ?) First and second fundamental forms.- ?) Covariant derivatives. The curvature tensor.- ?) Formulae of Weingarten and Gauss. Integrability conditions.- ?) Principal curvatures. Lines of curvature.- A.3. Geometry of a surface in a Euclidean space covered by normal coordinates.- A.4. Physical components of surface tensors in lines of curvature coordinates.- References.- The Theory of Rods.- A. Introduction.- 1. Definition and purpose of rod theories. Nature of this article.- 2. Notation.- 3. Background.- B. Formation of rod theories.- I. Approximation of three-dimensional equations.- 4. Nature of the approximation process.- 5. Representation of position and logarithmic temperature.- 6. Moments of the fundamental equations.- 7. Approximation of the fundamental equations.- 8. Constitutive relations.- 9. Thermo-elastic rods.- 10. Statement of the boundary value problems.- 11. Validity of the projection methods.- 12. History of the use of projection methods for the construction of rod theories.- 13. Asymptotic methods.- II. Director theories of rods.- 14. Definition of a Cosserat rod.- 15. Field equations.- 16. Constitutive equations.- III. Planar problems.- 17. The governing equations.- 18. Boundary conditions.- C. Problems for nonlinearly elastic rods.- 19. Existence.- 20. Variational formulation of the equilibrium problems.- 21. Statement of theorems.- 22. Proofs of the theorems.- 23. Straight and circular rods.- 24. Uniqueness theorems.- 25. Buckled states.- 26. Integrals of the equilibrium equations. Qualitative behavior of solutions.- 27. Problems of design.- 28. Dynamical problems.- References.- Namenverzeichnis. — Author Index.- Sachverzeichnis (Deutsch-Englisch).- Subject Index (English-German).