 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| E. E. Pavlovskaya and Yu. V. Petrov, "On some specific features of solutions of dynamic problems of elasticity," Mech. Solids. 37 (4), 31-36 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
4 |
Pages |
31-36 |
| Title |
On some specific features of solutions of dynamic problems of elasticity |
| Author(s) |
E. E. Pavlovskaya (St. Petersburg)
Yu. V. Petrov (St. Petersburg) |
| Abstract |
Three problems of linear elasticity are considered to illustrate
the importance of essential dynamic features- a specific behavior
of the energy, the inertia, and time factor. The solutions of
these problems (obtained in closed form) are analyzed. Some paradoxes
of the behavior of dynamical systems appearing when treating the results
obtained in quasistatic terms are indicated and explained.
We present an exact closed form solution for the problem
of two-sided tension of a one-dimensional elastic rod by constant
stresses. On the basis of this solution, we find the time history
of the rod total mechanical energy and show that in the dynamic case,
this energy essentially depends on time and periodically
vanishes.
In the problem of dynamic cyclic loading of an elastic half-space
with a semi-infinite crack, we constructed an analytical expression
for the time history of the stress intensity factor at the crack tip.
It is shown that the ideally elastic model allows for the fatigue effect
that manifests itself in the fact that the failure determined by
a prescribed critical value of the stress intensity factor does
not occur at the first cycle of the loading but can occur at some
Nth cycle.
For the problem of dynamic loading of a system of remote rigid punches
in an ideally elastic half-space, we present model equations
governing the dynamics of these punches with allowance for
their interaction with the half-space and with one another.
This model is shown to cover dissipative phenomena the existence
of which in a conservative system looks paradoxically.
The dynamic processes of loading and failure of solids have
a number of specific features that make these processes essentially
different from the quasi-static analogues. In some cases,
the stress-strain state of elastic media subjected to a dynamic
loading demonstrates a paradoxical behavior that leads to
fine effects that look somewhat unusually when interpreted
in terms of classical principles. Such effects can be explained
by taking into account the dynamic features, such as
a specific behavior of the mechanical energy, the inertia,
and time factor. |
| References |
| 1. | O. P. Barsukov, L. A. Vaisberg, B. V. Semkin,
and V. A. Tsukerman, "On the energy relations for an impact
action on a rod," Izv. Vysh. Uchebn. Zavedenii, Fizika,
No. 7, pp. 96-101, 1972. |
| 2. | G. P. Cherepanov, Mechanics of Brittle Fracture [in Russian],
Nauka, Moscow, 1974. |
| 3. | P. A. Martynyuk, "On the diffraction of a plane wave by
a penny-shaped crack," Dinamika Sploshnoi Sredy, No. 25,
pp. 82-91, 1976. |
| 4. | P. G. Richards, "Elementary solutions to Lamb's problem
for a point source and their relevance to three-dimensional
studies of spontaneous crack propagation," Bull. Seism. Soc. Amer.,
Vol. 69, No. 4, pp. 947-956, 1979. |
| 5. | N. A. Lavrov and E. E. Pavlovskaya, "Dynamics of a system of remote
punches on an elastic half-space," Zhurnal Prikl. Mekhaniki i
Tekhn. Fiziki, No. 6, pp. 204-210, 1999. |
| 6. | W. Nowacky, Elasticity [Russian translation], Mir, Moscow, 1975. |
| 7. | L. A. Galin, Contact Problems of Elasticity and Viscoelasticity
[in Russian], Nauka, Moscow, 1980. |
|
| Received |
25 January 2000 |
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