A Treatise on the Mathematical Theory of Elasticity, المجلد 2University Press, 1893 An indispensable reference work for engineers, mathematicians, and physicists, this book is the most complete and authoritative treatment of classical elasticity in a single volume. Beginning with elementary notions of extension, simple shear and homogeneous strain, the analysis rapidly undertakes a development of types of strain, displacements corresponding to a given strain, cubical dilatation, composition of strains and a general theory of strains. A detailed analysis of stress including the stress quadric and uniformly varying stress leads into an exposition of the elasticity of solid bodies. Based upon the work-energy concept, experimental results are examined and the significance of elastic constants in general theory considered. Hooke's Law, elastic constants, methods of determining stress, thermo-elastic equations, and other topics are carefully discussed. --Back cover. |
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... element of plate . Stress - resultants and stress - couples . Effect of second approximation . General equations of equilibrium . Small displacements . CHAPTER XXI . GENERAL THEORY OF THIN ELASTIC 201 SHELLS . Arts . 328-342 . Geometry ...
... element of plate . Stress - resultants and stress - couples . Effect of second approximation . General equations of equilibrium . Small displacements . CHAPTER XXI . GENERAL THEORY OF THIN ELASTIC 201 SHELLS . Arts . 328-342 . Geometry ...
الصفحة 7
... element of it will be bent and twisted more or less like one of Saint - Venant's prisms , but neighbouring elements ... element with the coordinates of their unstrained positions referred to axes fixed in the element , and with the ...
... element of it will be bent and twisted more or less like one of Saint - Venant's prisms , but neighbouring elements ... element with the coordinates of their unstrained positions referred to axes fixed in the element , and with the ...
الصفحة 8
... elements , and the conclusion that the internal strain in an element may be determined without reference to the bodily forces . He proceeded to explain that certain modes of equilibrium of a prism under terminal tractions were known ...
... elements , and the conclusion that the internal strain in an element may be determined without reference to the bodily forces . He proceeded to explain that certain modes of equilibrium of a prism under terminal tractions were known ...
الصفحة 9
... element , and he gave an original proof that Saint - Venant's stress - conditions hold to the same order of approximation . M. Boussinesq's work is more general than that of Kirchhoff and Clebsch inasmuch as the solotropy of his rod is ...
... element , and he gave an original proof that Saint - Venant's stress - conditions hold to the same order of approximation . M. Boussinesq's work is more general than that of Kirchhoff and Clebsch inasmuch as the solotropy of his rod is ...
الصفحة 10
... element bounded by two normal sections near together " . The applications of the theory of thin rods are very numerous . Prominent among them are the theory of the flexure of a piece by continuous load , and the theory of a continuous ...
... element bounded by two normal sections near together " . The applications of the theory of thin rods are very numerous . Prominent among them are the theory of the flexure of a piece by continuous load , and the theory of a continuous ...
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angle approximation axis bending body boundary-conditions centre of inertia circular coefficients components compression const curve cylinder deflexion deformation differential equations direction-cosines displacements edge-line elastic central-line elastica element equations of equilibrium expression Ət² finite flexural couple flexural rigidity forces and couples formulæ functions G₁ G₂ given impact K₁ K₂ kinetic Kirchhoff's line-elements lines of curvature middle-surface modes N₁ normal section obtained order of approximation osculating plane P₁ P₂ parallel plane plate potential energy principal axes principal curvatures prism quantities radius referred shell shew shewn sin po small motion solution strained elastic central-line stress-couples stress-resultants stresses suppose surface tangent terminal theory thin rod twist U₁ U₂ unit length unstrained V₁ V₂ values vanish velocity wire Young's modulus θα ав дв дг ди ду дх მყ