A Treatise on the Mathematical Theory of Elasticity, 第 2 巻University Press, 1893 |
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angle approximation axes axis Bdß boundary-conditions coefficients components const curve cylinder deflexion deformation differential equations direction-cosines displacements edge edge-line elastic central-line elastica element equations of equilibrium expression extension extensional Ət² finite flexural formulæ frequency functions G₁ G₂ given impact inertia K₁ K₂ kinetic line-elements lines of curvature Lord Rayleigh middle-surface modes N₁ normal section obtained order of approximation P₁ P₂ parallel plane plate potential energy principal principal curvatures prism quantities r₁ radius referred satisfied shell shew shewn sin po small motion solution stress-couples stress-resultants stresses suppose surface T₁ T₂ tangent theory thin rod torsional U₁ U₂ unit length unstrained V₁ V₂ values vanish velocity vibrations wire Young's modulus θα ав дв ди ди ду дх მყ
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127 ページ - jointly proportional to its strength and its toughness, and is " measured by the product of the mass and the square of the " velocity of a body capable of breaking it, or of the mass and the " height from which it must fall in order to acquire that velocity ; " while the strength is merely measured by the greatest pressure
8 ページ - the moment of inertia of the section about an axis through its centroid
14 ページ - the memoir of 1828. A large part of the investigation is reproduced in Todhunter and Pearson's History of the Elasticity and Strength of Materials, vol.
14 ページ - proposed to regard the work done in bending as proportional to the integral of the square of the sum of the principal curvatures taken over the surface. From this assumption and the principle of virtual work she deduced the equation of flexural vibration in the form now generally admitted. Later investigations have
66 ページ - of the theory of the motion of a rigid body about a fixed point
16 ページ - of the quantities defining the flexure of the middle-surface with a coefficient proportional to the cube of the thickness. The equations of small motion are deduced by an application of the principle of virtual work. When the displacement of a point on the middle-surface is
13 ページ - The success of theories of thin rods founded on special hypotheses appears to have given rise to hopes that a theory might be developed in the same way for
41 ページ - a curve whose ordinate at any point represents the bending moment at the corresponding
15 ページ - normal to the middle-surface after strain, and (2) that all the elements of the middle-surface remain unstretched. These assumptions enabled him to express the potential energy of the bent plate in terms of the curvatures produced in its middle-surface. The equations