A Treatise on the Mathematical Theory of Elasticity, 第 2 巻University 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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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