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**A treatise on the mathematical theory of elasticity. 4th ed.**
*(English)*
Zbl 0063.03651

New York: Dover Publications. xviii, 643 p. (1944).

Publisher’ s description: This Dover edition, first published in 1944 (and reissued in 2011), is an unabridged republication of the fourth (1927) edition of the work [JFM 53.0752.01], originally published by Cambridge University Press in 1892/93 [JFM 24.0939.04; JFM 25.1555.09].

Combining a wealth of practical applications with a thorough, rigorous discussion of fundamentals, this work is recognized as an indispensable reference tool for mathematicians and physicists as well as mechanical, civil, and aeronautical engineers. The American Mathematical Monthly hailed it as “the standard treatise on elasticity,” praising its significant content, originality of treatment, vigor of exposition, and valuable contributions to the theory.

Starting with a historical introduction, the author discusses the analysis of strain and stress, the elasticity of solid bodies, the equilibrium of isotropic elastic solids, elasticity of crystals, vibration of spheres and cylinders, propagation of waves in elastic solid media, torsion, the theory of continuous beams, the theory of plates, and other topics. A wide range of practical material includes coverage of plates, beams, shells, bending, torsion, vibrations of rods, impact, and more.

Contents:

Historical introduction (1–31).

Ch. I: Analysis of strain (32–58). Appendix to Ch. I. General theory of strain (59–73).

Ch. II: Analysis of stress (74–91).

Ch. III: The elasticity of solid bodies (92–111).

Ch. IV: The relation between the mathematical theory of elasticity and technical mechanics (112–124).

Ch. V: The equilibrium of isotropic elastic solids (125–148).

Ch. VI: Equilibrium of æolotropic elastic solid bodies (149–165).

Ch. VII: General theories (166-182).

Ch. VIII: The transformation of force (183–203).

Ch. IX: wo-dimensional elastic systems (204–220). Appendix to Ch. VIII and IX: Volterra’s theory of dislocation (221–228).

Ch. X: Theory of the integration of the equations of equilibrium of an isotropic elastic solid body (229–248).

Ch. XI: The equilibrium of an elastic sphere and related problems (249–277).

Ch. XII: Vibrations of spheres and cylinders (278–292).

Ch. XIII: The propagation of waves in elastic solid media (293–309).

Ch. XIV: Torsion (310–328).

Ch. XV: The bending of a beam by terminal transversal load (329–348).

Ch. XVI: The bending of a beam loaded uniformly along its length (349–364).

Ch. XVII: The theory of continuous beams (365–380).

Ch. XVIII: General theory of the bending and twisting of thin rods (381–398).

Ch. XIX: Problems concerning the equilibrium of thin rods (399–426).

Ch. XX: Vibrations of rods. Problems of dynamical resistance (427–443).

Ch. XXI: Small deformation of naturally curved rods (444-454).

Ch. XXII: The stretching and bending of plates (455–464); Theory of moderately thick plates (465-487); Approximate theory of thin plates (487–498).

Ch. XXIII: Inextensional deformation of curved plates or shells (499–514).

Ch. XXIV: General theory of thin plates and shells (515–552).

Ch. XXIV\(_{\text{A}}\): Equilibrium of thin plates and shells (553–563); Equilibrium of thin shells (564–567); Cylindrical shells (568–582); Spherical shell (583–589); Conical shell (590–613).

Notes (614–632). Index (633–643).

The third ed. appeared in (1920); see JFM 47.0750.09.

External reviews: 4th ed. (1927) by Edwin B. Wilson, Bull. Am. Math. Soc. 34, 242–243 (1928).

Combining a wealth of practical applications with a thorough, rigorous discussion of fundamentals, this work is recognized as an indispensable reference tool for mathematicians and physicists as well as mechanical, civil, and aeronautical engineers. The American Mathematical Monthly hailed it as “the standard treatise on elasticity,” praising its significant content, originality of treatment, vigor of exposition, and valuable contributions to the theory.

Starting with a historical introduction, the author discusses the analysis of strain and stress, the elasticity of solid bodies, the equilibrium of isotropic elastic solids, elasticity of crystals, vibration of spheres and cylinders, propagation of waves in elastic solid media, torsion, the theory of continuous beams, the theory of plates, and other topics. A wide range of practical material includes coverage of plates, beams, shells, bending, torsion, vibrations of rods, impact, and more.

Contents:

Historical introduction (1–31).

Ch. I: Analysis of strain (32–58). Appendix to Ch. I. General theory of strain (59–73).

Ch. II: Analysis of stress (74–91).

Ch. III: The elasticity of solid bodies (92–111).

Ch. IV: The relation between the mathematical theory of elasticity and technical mechanics (112–124).

Ch. V: The equilibrium of isotropic elastic solids (125–148).

Ch. VI: Equilibrium of æolotropic elastic solid bodies (149–165).

Ch. VII: General theories (166-182).

Ch. VIII: The transformation of force (183–203).

Ch. IX: wo-dimensional elastic systems (204–220). Appendix to Ch. VIII and IX: Volterra’s theory of dislocation (221–228).

Ch. X: Theory of the integration of the equations of equilibrium of an isotropic elastic solid body (229–248).

Ch. XI: The equilibrium of an elastic sphere and related problems (249–277).

Ch. XII: Vibrations of spheres and cylinders (278–292).

Ch. XIII: The propagation of waves in elastic solid media (293–309).

Ch. XIV: Torsion (310–328).

Ch. XV: The bending of a beam by terminal transversal load (329–348).

Ch. XVI: The bending of a beam loaded uniformly along its length (349–364).

Ch. XVII: The theory of continuous beams (365–380).

Ch. XVIII: General theory of the bending and twisting of thin rods (381–398).

Ch. XIX: Problems concerning the equilibrium of thin rods (399–426).

Ch. XX: Vibrations of rods. Problems of dynamical resistance (427–443).

Ch. XXI: Small deformation of naturally curved rods (444-454).

Ch. XXII: The stretching and bending of plates (455–464); Theory of moderately thick plates (465-487); Approximate theory of thin plates (487–498).

Ch. XXIII: Inextensional deformation of curved plates or shells (499–514).

Ch. XXIV: General theory of thin plates and shells (515–552).

Ch. XXIV\(_{\text{A}}\): Equilibrium of thin plates and shells (553–563); Equilibrium of thin shells (564–567); Cylindrical shells (568–582); Spherical shell (583–589); Conical shell (590–613).

Notes (614–632). Index (633–643).

The third ed. appeared in (1920); see JFM 47.0750.09.

External reviews: 4th ed. (1927) by Edwin B. Wilson, Bull. Am. Math. Soc. 34, 242–243 (1928).

### MSC:

74-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids |