A Treatise on the Mathematical Theory of Elasticity, المجلد 1
University Press, 1892 - 681 من الصفحات
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 applied axis beam bodily forces body boundary coefficients complementary solutions components const coordinates corresponding crystal cubical dilatation curvilinear coordinates cylinder determine differential equations direction distance dx dy dy dz elastic constants elastic limits elastic solid energy-function equal equations of equilibrium expressed finite flexure formula frequency-equation function given harmonic inequality harmonic of order hemihedral forms Hence Hooke's Law incompressible isotropic isotropic solid Laplace's equation load material motion normal notation obtained parallel particular integrals planes of symmetry Poisson's Poisson's ratio potential principal axes problem produced Prof quadratic function quadric quantities radial displacement radius ratio rigidity rotation Saint-Venant satisfy the boundary-conditions satisfy the equations shearing stress shew shewn simple shear sphere spherical harmonic spherical solid harmonics strain suppose surface surface-displacements surface-tractions system of displacements tangential stresses theorem theory Thomson torsion traction transformation vanish vibrations Young's modulus zero
الصفحة 214 - Dyck's models of surfaces representing the real and imaginary parts of a function of a complex variable at and near a singular value should be studied by every reader of Mr.
الصفحة 12 - In whatever way the elements of any material system may act upon each other, if all the internal forces exerted be multiplied by the elements of their respective directions, the total sum for any assigned portion of the mass will always be the exact differential of some function.
الصفحة 269 - In these expressions r is the distance of the point (x, y, z) from the centre of...
الصفحة 155 - Now a, yl + a2 yl -|- etc. is the sum of the products obtained by multiplying each infinitesimal part of the area of the cross-section by the square of its distance from the neutral axis; hence, it is the moment of inertia of the cross-section with respect to the neutral axis. If this...
الصفحة 280 - ... suppose the gas not to be subject to the action of external forces. Let the gas be referred to the rectangular axes of x, y, z, and let u, v, w be the components of the velocity. Since the gas is at rest except as to the disturbance communicated to it from the sphere, u, v, w are by a well-known theorem the partial differential coefficients with respect to x, y, z of a function...
الصفحة 5 - The modulus of the elasticity of any substance is a column of the same substance, capable of producing a pressure on its base which is to the weight causing a certain degree of compression, as the length of the substance is to the diminution of its length.
الصفحة 12 - Analytique, and which appears to be more especially applicable to problems that relate to the motions of systems composed of an immense number of particles mutually acting upon each other. One of the advantages of this method, of great importance, is, that we are necessarily led by the mere process of the calculation, and with little care on our part, to all the equations and conditions which are requisite and sufficient for the complete solution of any problem to which it may be applied.
الصفحة 5 - This introduction of a definite physical concept, associated with the coefficient of elasticity, which descends as it were from a clear sky on the reader of mathematical memoirs, marks an epoch in the history of the science.