Engineering Transactions, 40, 4, pp. 483-500, 1992

Discrete Modelling of Wave Propagation in Bars with Piecewise-Linear Characteristics

Z. Szcześniak
Military Technical Academy, Warszawa
Poland

A method is proposed to model one-dimensional wave propagation problems in a discrete manner as applied to the material with piecewise-linear stress-strain relationship in loading and rigid-elastic behaviour in unloading. The method consists in a simple combination of basic models, i.e. an elastic model and a plastic model with rigid unloading to obtain a combined model. It turns out to be accurate and effective. Numerical algorithm is described. Errors are discussed and an example of unloading stress wave is given.

Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

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

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

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

E.WŁODARCZYK, Propagation and reflection of one- and two-dimensional stress waves in plastic media [in Polish], Biul. WAT, 2, 198, 1969.

W.BoGUSZ, Z.DŻYGADŁO, S.KALISKI, D.ROGULA, CZ.RYMARZ, K.SOBCZYK, L. SOLARZ and E.WŁODARCZYK, Technical mechanics Vol. III. Vibrations and waves [in Polish], PWN, Warszawa 1986.

Z.ŁĘGOWSKI and E.WŁODARCZYK, Effect of linearly elastic unloading on the dynamics an object immersed in an elastic-plastic soil [in Polish], Rozpr. Inż., 21, 4, 1973.

K.PODOLAK, On the propagation of stress waves in a plastic medium separated by a rigid plate [in Polish], Rozpr. Inż., 22, 1, 1974.

S.KALISKI, W.K.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.

Х.А.РАХМАТУЛИН, Ю.А.ДЕМЯНОВ, Прочность при интенсивных кратковременных нагрузках, Гос. Издат. Физ. Мат. Лит., Москва 1962.

А.М.СКОБЕЕВ, К теории волны разгрузки, ЛММ, 6, 26, 1962.

D.R.BLAND, Wave theory and applications, Clarendon Press, Oxford 1988.

T.YOKOYAMA and M.TSUZUKI, Finite element analysis of plastic wave propagation in tapered bar, Technology Reports of the Osaka University, 31, 1597, Osaka 1981.

J.GALLEGO, R.ALVAREZ, W.K.NOWACKI and E.ALARCON, Application del metodo de las caracteristicas a problemas de impacto en medios viscoplasticos, Primer Congreso Iberoarnericano de Metodos Computacionales en Ingenieria, Madrid, Julio, 1985.

R.ALVAREZ, J.MOLINA, W.K.NOWACKI and E.ALARCON, Los metodos de las caracteristicas y elementos finitos en propagacion des ondas, lngenieria Mecanica, 2, Madrid 1985.

S.GOMEZ-LERA, P.GUELIN, W.K.NOWACKI and E.ALARCON, Respuesta sismica de suelos con histeresis y viscosidad, Primer Congreso Iberoarnericano de Metodos Computationa.les en Ingenieria, Madrid, Julio, 1985.

W.K.NOWACKI and B.RANIECKI, Theoretical and numerical analysis of dynamic compacting of soil around a spherical source of explosion, Second World Congress on Computational Mechanics, FRG, Stuttgart, August 1990.

W.K.NOWACKI, Propagation des ondes dans un sol elastoplastique, Symposium franco-polonaise, Problems Non-lineaires de Mechanique, Cracovie 1977.

E.WŁODARCZYK, Dynamics of rigid plate resting on an elastic-plastic foundation [in Polish], Biul. WAT, 7, 203, 1969.

E.WŁODARCZYK, Effect of linearly-elastic unloading on the motion of a rigid plate resting on an elastic-plastic soil [in Polish], Biul. WAT, 7, 203, 1969.

A.PAPLIŃSKI and E.WŁODARCZYK, interaction of elastic-plastic stress waves with an incompressible fiat diaphragm resting on an elastic half-space [in Polish], Rozpr. Inż., 20, 2, 1972.

G.BĄK and Z.SZCZEŚNIAK, Discrete modelling of one-dimensional wave propagation problems in elastic layered nonprismatic bars [in Polish], Rozpr. Inż., 35, 2, 1987.

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

Z.SZCZEŚNIAK, Discrete model of wave propagation in a bar with rigid unloading characteristic, Engng. Trans., 401 3, 1992.

Г.В.РЫКОВ, А.М.СКОБЕЕВ, Измерение напряжений в грунтах при кратковременных нагрузках, Наука, Москва 1978.

Х.А.РАХМАТУЛИН, А.Я.САГАМОНЯН, Н.А.АЛЕКСЕЕВ, Вопросы динамики грунтов, Москва 1964.

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

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

E.WŁODARCZYK, Soil and rock models in wave propagation problems [in Polish], Arch. Inż. Ląd., 3-4, 1991.

P.GUELIN, W.K.NOWACKI, Stress waves in elastic-plastic solids with discrete memory, J. Tech. Phys., 2, 33, 1992.