A Treatise on Mathematical Theory of Elasticity其它

彈性波理論方面的經(jīng)典專箸。"When rods made of classic elastic materials are subject to deformations of this type, the curves formed by their axes at the equilibrium are called elastic curves or elastica (cf., e.g.: Thomson and Tait, 1879; Love, 1944). On the basis of Kirchhoff's kinetic analogue that identifies the equilibrium equations of a rod with the motion equations of a pendulum, the elastica can be classified into two categories (Love, 1944) that correspond to the two classes of planar motions of a pendulum, i.e., oscillating and revolving motions. Accordingly, the curves formed by the rod axes at the equilibrium are distinguished in: i ) inflexional elastica, that contain inflexions, i.e., points of the axis where the curvature and the moment vanish, and are held in equilibrium by terminal forces alone without couples; the end points, to which the forces are applied, are inflexions and all the inflexions lie on the line of action of the terminal forces and are equallyspaced along the axial curve; ii ) non-inflexional elastica which do not have points in which the curvature vanishes, and whose equilibrium requires the presence of terminal forces and couples; if there are only terminal couples, the rod is bent into an arc of circle. "