Engineering Transactions, 40, 3, pp. 329-342, 1992

Discrete Model of Wave Propagation in a Rod with Rigid Unloading Characteristic

Z. Szcześniak
Military Technical Academy, Warszawa
Poland

A principle of construction and action of a discrete model of a rod with rigid characteristic of unloading is proposed. Its applications are shown for loading that varies arbitrarily with time. Propagating waves in this case cause multiple effects of rigid unloading and reloading in each cross-section of the rod. These effects are highly nonlinear and very difficult to describe analytically. Numerical algorithm is given. Its effectiveness is demonstrated on an example and solution errors are discussed.

Full Text: PDF

References

A.W.T.DANIEL, R.C.HARWEY and BURLEY, Stress-strain characteristics of sand, J. Geoteclm., Eng. Div., V, 1975.

Г.В.РЫКОВ, А.М.СКОБЕЕВ, Измрение напяжений в грунтах при кратковремекных нагрузках, Изд. Наука, Москва 1978.

F.DARVE, Une description du comportement cyclique des solides non visqueux, J. Mec. Tbeor. et Appl., 1982.

W.K.NOWACKI, Stress waves in nonelastic solids, Oxford, Pergamon Press, 1978.

W.K.NOWACKI, Ondes dans les milieux non-elastiques, Inst. de Mecanique de Grenoble, 1978.

Z.DŻYGADŁO, S.KALISKI, L.SOLARZ and E.WŁODARCZYK, Vibrations and waves in solids [in Polish], PWN, Warszawa 1966.

S.KALISKI and J .OSIECKI, Unloading wave for a body with rigid unloading characteristic, Proc. Vibr. Probl., 1, 1959, also in Polish in Biul. WAT, 2, 85, 1959.

E.WŁODARCZYK, Propagation and reflection of one- and two-dimensional stress waves in plastic media [in Polish], Suppl. to Biul. WAT, 2, 1969.

М.Д.БОДАНСКИЙ, Л.М.ГОРШКОВ, В.И.МОРОЗОВ и В.С.РАСТОРГУЕВ, Расчет конструкций удежищ, Стройиздат, Москва 1974.

Z.ŁĘGOWSKI, K.PODOLAK, E.WŁODARCZYK, Effect of explosion on a structure submerged in soil [in Polish], Biul. WAT, 7, 1975.

A.PAPLIŃSKI and E.WŁODARCZYK, Interaction of elastic-plastic stress waves with an incompressible plane baffle resting on an elastic halfspace [in Polish], Rozpr. lnź., 20, 2, 1972.

G.BĄK, Z.SZCZEŚNIAK, Method of discrete modelling of one-dimensional wave propagation process in elastic layered nonprismatic rods [in Polish], Rozpr. Inż., 35, 2, 1987.

G.BĄK, Z.SZCZEŚNIAK, Modelling of multiple collisions and spalling in elastic­brittle rods under tension [in Polish], Rozpr. Inż., 37, 1, 1989.

E.WŁODARCZYK, Models for soils and rocks in the wave propagation problems. Part I. Elastic and elastic-plastic models. Part II. Viscous and visco-plastic models [in Polish], Arch. Inż. Ląd., 3-4, 1991.

Г.М.ЛЯХОВ, Основы динамики взрыва в гурнтах и жидких средах, Изд. Иедра, Москва 1964.

Б.В.ЗАМЫШЛЯЕВ И Л.С.ЕВТЕРЕВ, Модеи динамического деформирования и разрушения грунтовых сред, Хаука, Москва 1990.

S.KALISKI, W.NOWACKI and E.WŁODARCZYK, On a certain closed solution for the shock-wave with rigid unloading, Bull. Acad. Polon. Sci., serie Sci. Techn., 15, 5, 1967.

R.C.SHIEH, G.A.HEGEMIER and W.PRAGER., Closed-form solutions to problems of wave propagation in a rigid, workhardening, locking rod, Int. J. Solids Struct., 5, 1969.

Х.А.РАХМАТУЛИН, О распространении волн в многокомпонентных средах, Р.М.М, 33, 4, 1969.

W.K.NOWACKI and B.RANIECKI, Theoretical analysis of dynamic compacting of soil around a spherical source of explosion, Arch. Mech., 39, 4, 1987.




Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland