Inclined Circular Punch Bonded to Transversely Isotropic Half‐Space
Publication: Journal of Engineering Mechanics
Volume 116, Issue 7
Abstract
A complete solution is given for the first time to the problem of an inclined circular punch bonded to a transversely isotropic elastic half‐space. Explicit expressions are derived for the field of stresses and displacements around such punch subjected to a shifting load and a tilting moment. The method of solution is based on the new results in potential theory obtained by the writer earlier. The complete solution is initially expressed in terms of three potential functions. The displacements are defined through first derivatives of the potential functions, while the stresses are given by second derivatives. The complete solution for an isotropic body is obtained as a limiting case of the general solution. Specific computations are performed in order to compare the elastic field in the vicinity of a bonded punch with similar parameters for a smooth punch. It is found that the influence of bonding on normal displacement is relatively small, while its influence on tangential displacements may be quite significant.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Elliott, H. A. (1948). “Three‐dimensional stress distributions in hexagonal aeolotropic crystals.” Proc. Cambridge Phil. Soc., 44, 522–533.
2.
Fabrikant, V. I. (1970). “Effect of concentrated force on a transversely isotropic elastic body.” Izvestiia Vysshikh Uchebnykh Zavedenii, Mashinostroenie, 3, 9–12 (Russian).
3.
Fabrikant, V. I. (1971a). “Axially symmetric problem of a stamp on a transverselt isotropic half‐space.” Mekhanika Tverdogo Tela, 6, 141–146 (in Russian);
English trans., Mechanics of Solids, 121–125.
4.
Fabrikant, V. I. (1971b). “Effect of shearing force and tilting moment on a cylindrical punch attached to a transversely isotropic half‐space.” Prikladnaia Matematika i Mekhanika, 35(1), 178–182 (in Russian);
English trans., J. Appl. Math. and Mech., 147–151.
5.
Fabrikant, V. I. (1986). “Four types of exact solutions to the problem of axisymmetric punch bonded to a transversely isotropic half‐space.” Int. J. Eng. Sci., 24, 785–801.
6.
Fabrikant, V. I. (1989). Applications of potential theory in mechanics. Selection of new results, Kluwer Academic, Dordrecht, Holland.
7.
Kapshivyi, A. A., and Masliuk, G. F. (1967). “The solution of the mixed axisymmetric problem from the theory of elasticity for a half‐space by the method of p-analytic functions.” Prikladnaia Mekhanika, 3(7), 21–27 (in Russian; English trans., Soviet Applied Mechanics, 13–16.
8.
Mossakovskii, V. I. (1954). “The fundamental mixed problem of the theory of elasticity for a half‐space with a circular line separating the boundary conditions.” Prikladnaia Matematika i Mekhanika, 18(2), 187–196 (in Russian).
9.
Ufliand, Ia. S. (1956). “The contact problem of the theory of elasticity for a die, circular in its plane, in the presence of adhesion.” Prikladnaia Matematika i Mekhanika, 20(5), 578–587 (in Russian).
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 116 • Issue 7 • July 1990
Pages: 1599 - 1617
Copyright
Copyright © 1990 ASCE.
History
Published online: Jul 1, 1990
Published in print: Jul 1990
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.