A Treatise on the Mathematical Theory of Elasticityat the University Press, 1906 - 551 من الصفحات |
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طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
applied Article axis body forces central-line centre coefficients components of strain constants coordinates corresponding cos² couple cross-section curvature curve cylinder deflexion denote determined dilatation direction displacement dx dy elastic equations of equilibrium expressed formulæ given harmonic function integral isotropic load Lord Rayleigh Math middle surface motion normal obtained P₁ parallel Phil plane strain plane stress plate Poisson's ratio pressure principal axes problem quadratic function quadric quantities R₁ radius right angles rotation satisfy the equations shearing shearing stress sin² solid solid harmonics solution sphere spherical strain-components strain-energy-function stress stress-components stress-system surface tractions symmetry tangent tension theorem theory torsion unstrained values vanish velocity vibrations Young's modulus Z₂ θα λ+2μ λ+μ дах дв дг др дф дх дх ду
مقاطع مشهورة
الصفحة 2 - ... the power of any spring is in the same proportion with the tension thereof: that is, if one power stretch or bend it one space, two will bend it two, and three will bend it three, and so forward.
الصفحة 15 - An Essay on the application of Mathematical Analysis to the Theories of Electricity and Magnetism...
الصفحة 297 - It is not improbable that the surface waves here investigated play an important part in earthquakes, and in the collision of elastic solids. Diverging in two dimensions only, they must acquire at a great distance from the source a continually increasing preponderance.
الصفحة 4 - 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 188 - ... surface of the body, and the positive direction of the axis of z to- be that which goes into the interior of the body. The local effect of force applied at the origin being very great, we suppose the origin to be excluded by a hemispherical surface. The displacement expressed by (15) could be maintained in the body by tractions over the plane boundary, which are expressed by the equations ' AX Y = ^ Ay Z -0 ' *° 5' ^~U> and by tractions over the hemispherical boundary, which are expressed by...
الصفحة 4 - 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 11 - 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 170 - ... the equilibrium state) acting through the displacements from the unstressed state to the state of equilibrium.
الصفحة 42 - The strain quadric has the property that the reciprocal of the square of its central radius vector in any direction is proportional to the extension of a line in that direction. If the...