Read e-book online Advances in Applied Mechanics, Vol. 25 PDF

By Eds. Theodore Y. Wu & John W. Hutchinson

ISBN-10: 0120020254

ISBN-13: 9780120020256

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Extra resources for Advances in Applied Mechanics, Vol. 25

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1951). ” McGraw-Hill, New York. Todd, L. (1977). Some comments on steady, laminar flow through twisted pipes. J. Eng. Math. 11, 29-48. Todd, L. (1978). Steady, laminar flow through non-uniform, curved pipes of small cross-section. Tech. Rept. No. 78-19, Inst. Appl. Math. , Univ. British Columbia, Vancouver. Todd, L. (1979). Steady, laminar flow through curved pipes of small, constant cross-section. Tech. Rept. No. 79-1, Dept. , Sudbury, Canada. Todd, L. (1980). Steady, laminar flow through non-uniform, thin pipes.

The basic difficulty in getting solutions is due to the nonseparability of such problems. In an excellent survey published in Knopoff (1969), the various analytical methods that have been tried on these problems are reviewed. The survey ends on the sad note that none of the techniques tried (images, integral transforms, Weiner-Hopf method, iterations, and others) were successful. Knopoffs paper, however, is a very valuable contribution on this problem and its solution. Our survey in this area will focus on recent works in the two-dimensional elastic wedge and its special case the quarter-plane with their mixed or nonmixed edge conditions.

CURVEDCENTERLINE We turn now to slender three-dimensional shapes with curved centerlines. As in the corresponding plane problem, we restrict attention to unchanging cross sections, and it appears that in fact only such shapes have so far been treated in the literature. 1. Twist of an Elastic Ring Sector Gohner (1930, 1931a) has considered the elastic properties of a helical spring in tension or compression. He shows that if the pitch of the helix is small, it can be neglected with only very slight error.

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Advances in Applied Mechanics, Vol. 25 by Eds. Theodore Y. Wu & John W. Hutchinson

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