The contact problem in viscoelasticity is one in which different types of boundary conditions are prescribed depending on whether boundary points inside or outside the region of contact are considered. Since, in general, the contact region varies with time, this lends to a problem which cannot be treated directly by application of the Laplace transform, which has formed the basis for most published viscoelastic stress-distribution solutions. It is shown that the solution of the viscoelastic counterpart of the Hertz problem in elasticity can, however, be deduced from the elastic solution. A particular example is presented, and the marked effect of viscoelastic behavior on the pressure distribution in the contact region is illustrated. The problem also illustrates the tentative nature of the method of approach and the need for a separate confirmation of the solution. The solution is presented for general linear viscoelastic operators and offers the possibility of determining these from a contact test.

No abstract

No abstract

heated. In any case, it is clear that the most rapid convergence is obtained for small x and y and comparatively large t. Although the first term appears formidable, it turns out that in many instances the arctan and log terms are negligible. For example, if k = 103, a = 2, and xy < 4/106, the arctan and log may be neglected if an error within ±1/10 is satisfactory. Since the series is alternating, the error involved is less, in absolute value, than the first term not employed in the calculation. Thus, once k and a are fixed, one might check terms, beginning with the third, i.e., ka2xy/9&Tt3 [a2/3 + x2 + y2\, in order to obtain a range for x, y, and t so that a given error tolerance is not exceeded. From the form of each term, an inequality involving the product, xy, is simplest to handle and furnishes a good check for x and y small. As a usual occurrence the calculation of three or four terms gives sufficient accuracy for applied purposes provided a reasonable balance is maintained among the variables.

THIS is a volume honoring Dean L. M. K. Boeiter of UCLA on the occasion of his sixty-fifth birthday, and it-consists of thirty-four technical papers authored by his students, colleagues, and associates. In view of the number of papers involved, it is obvious that, no attempt toward individual review can be made here. Basically, the papers are divided into four categories: (a) Heat-mass transfer and thermodynamics; (6) Materials, mechanics, and design; (c) Engineering education; and (d) City planning.