Dynamics

Download Contact Mechanics by K. L. Johnson PDF

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By K. L. Johnson

This treatise is anxious with the stresses and deformation of strong our bodies in touch with one another, alongside curved surfaces which contact before everything at some extent or alongside a line. Examples are a railway wheel and rail, or a couple of substances wheel enamel. Professor Johnson first stories the advance of the idea of touch stresses because the challenge was once initially addressed through H. Hertz in 1882. subsequent he discusses the impact of friction and the topographical roughness of surfaces, and this can be integrated into the idea of touch mechanics. a massive characteristic is the remedy of our bodies which deform plastically or viscoelastically. as well as desk bound touch, an considerable portion of the ebook is anxious with our bodies that are in sliding or rolling touch, or which collide.

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4, i,e. the pressure distribution forms a plane facet de/. Any general polygonal region can be divided into triangular elements such as DEF. In this way a continuous distribution of pressure over the whole polygonal surface may be approximated by linear facets acting on triangular elements such as the one shown in Fig. 4, This representation of a continuous pressure distribution may be regarded as an improved approximation upon a series of boundary elements in each of which the pressure is taken to be uniform, since discontinuities in pressure along the sides of the elements have been eliminated and replaced by discontinuities in pressure gradient.

It is required to find the depression Uz at a general point B(x, y) on the surface and the stress components at a sub3urface point A(x ,y, z), BHh BB2 • etc. are perpendiculars of length h" h" etc. from B onto the sides of the polygon DE, EF respectively. 3 Fig. 3 E / / / / h, h,1 I / / / / V'/ B II, ~*-_ (x, y) \ F \ \ h, \ \ \ fr- - G ,,- III (a) D Ihl 54 Point loading of an elastic half-space eight right-angle triangles: DEFG = [BEH, + BEH, + BFH, + BFH,J -[BDH, + BDH, + BGH, + BGH,J A similar breakdown into rectangular triangles would have been possible if B had lain inside the polygon_ A typical triangular area is shown in Fig.

Tyz, Tzx. will appear. A special case arises when the loading is axi·symmetric about the z·axis. In cylindrical polar coordinates (r, 8, z) the pressure per) and the tangential traction q(r) are independent of 8 and q(r), if it is present, acts in a radial direction. The stress components T r 8 and T(Jz vanish and the other stress com· ponents are independent of O. The classical approach to finding the stresses and displacements in an elastic half·space due to surface tractions is due to Boussinesq (1885) and Cerruti (1882) who made use of the theory of potential.

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