A Treatise on the Mathematical Theory of Elasticity, المجلد 1University 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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الصفحة 49
... dx + ( y1 − y ) dy + ( z1 − z ) dz - taken round the curve is 2P11 + 2P2w2 + 2P3w . From which it follows that we may interpret 1 as half the line - integral of the tangential displacement round a closed curve of unit area in the ...
... dx + ( y1 − y ) dy + ( z1 − z ) dz - taken round the curve is 2P11 + 2P2w2 + 2P3w . From which it follows that we may interpret 1 as half the line - integral of the tangential displacement round a closed curve of unit area in the ...
الصفحة 58
... dy dz , and let dS be an element of an arbitrary closed surface S drawn in the solid , and l , m , n the direction ... dx dydz = [ [ ( 15+ mn + n5 ) dS , ISS by η , Əz in which § , 7 , are functions of x , y , z , which are finite ...
... dy dz , and let dS be an element of an arbitrary closed surface S drawn in the solid , and l , m , n the direction ... dx dydz = [ [ ( 15+ mn + n5 ) dS , ISS by η , Əz in which § , 7 , are functions of x , y , z , which are finite ...
الصفحة 59
... dx dy dz = 0 ..... ............ . ( 3 ) . X ) dx dy dz дх ду дг Since this equation holds whatever the surface S may be , provided only that it is closed and altogether within the solid , it holds when S is reduced to a point , and thus ...
... dx dy dz = 0 ..... ............ . ( 3 ) . X ) dx dy dz дх ду дг Since this equation holds whatever the surface S may be , provided only that it is closed and altogether within the solid , it holds when S is reduced to a point , and thus ...
الصفحة 65
... dx dy dz + pZ ) Sw❘ dxdydz . The latter of these integrals vanishes identically in virtue of the equations of equilibrium , and therefore the work done in increasing the strain from e , f , g , a , b , c to e + de , ƒ + df ,. ... c + ...
... dx dy dz + pZ ) Sw❘ dxdydz . The latter of these integrals vanishes identically in virtue of the equations of equilibrium , and therefore the work done in increasing the strain from e , f , g , a , b , c to e + de , ƒ + df ,. ... c + ...
الصفحة 76
... Dy Jws + 2μ dz + pX = p at2 ბია as дог Jas ( 13 ) . ( λ + 2μ ) - 2μ + 2μ + pX = P ǝť2 - дх dy дг J2w θσι дог дг дх dy ΟΔ ( λ + 2μ ) 2μ + 2μ + _pZ = P ǝť2 The boundary - conditions are found from equations ( 12 ) of art . 14 , by ...
... Dy Jws + 2μ dz + pX = p at2 ბია as дог Jas ( 13 ) . ( λ + 2μ ) - 2μ + 2μ + pX = P ǝť2 - дх dy дг J2w θσι дог дг дх dy ΟΔ ( λ + 2μ ) 2μ + 2μ + _pZ = P ǝť2 The boundary - conditions are found from equations ( 12 ) of art . 14 , by ...
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عبارات ومصطلحات مألوفة
angle applied axis B₁ beam bodily forces boundary-conditions coefficients components const coordinates crystal cubical dilatation cylinder differential equations displacements distance elastic solid equal equations of equilibrium expressed extension Ət² finite function given Hence Hooke's Law isotropic isotropic solid Laplace's equation normal nẞ obtained P₁ parallel particular integrals planes of symmetry Poisson's ratio principal axes problem Prof quadratic function quadric radial radius ratio rigidity rotation Saint-Venant satisfy shear shearing stress shew shewn simple shear solution sphere spherical harmonic spherical solid harmonics strain stress suppose surface surface-tractions tangential theorem theory Thomson torsion traction transformation vanish vibrations w₁ W₂ Y₁ Young's modulus θα λ+μ ΟΔ дв дг ди ди дох др дф дх მყ
مقاطع مشهورة
الصفحة 339 - Mathematical and Physical Papers. By Sir W. THOMSON, LL.D., DCL, FRS, Professor of Natural Philosophy, in the University of Glasgow. Collected from different Scientific Periodicals from May, 1841, to the present time.
الصفحة 200 - 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 253 - In these expressions r is the distance of the point (x, y, z) from the centre of...
الصفحة 153 - 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 264 - ... 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.
الصفحة 120 - P, Q, R, S, T, U are linear functions of the strains e, f, g, a, b, c, and therefore W is a quadratic function of the strains.