Engineering Transactions, 29, 1, pp. 27-37, 1981

Parametric Optimization of Viscoplastic Bars Under Dynamic Axial Loading

E. Cegielski
Institute of Mechanics and Machine Design, Kraków

M. Życzkowski
Institute of Mechanics and Machine Design, Kraków

The paper formulates the problem of the parametric optimal design of a viscoplastic bar under the impact of axial force, Eq. (4.4), and gives some solutions. The dual approach to the problem has been applied, the minimal residual deflection being the design objective, under the constraint of a constant volume of the bar. The governing equation (2.4) has been derived under the assumption of a power physical law and arbitrarily variable cross section; however, effective calculations have been performed for the linear law (0=1) and for bars of truncated cone shape. Two parameters describe the cross section of this bar, Eq. (3.1), but one of them can be determined from the condition of constant volume of the bar. Hence the parameter of tapering of the cone (A) remains the only design variable in this case. The influence of various parameters which describe the shape of the force impulse (Fig. 2) on the parameter Aopt has been investigated (Figs. 3, 4 and 5).
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W. F. AMES, Numerical method for partial differential equations, ed. Academic Press, New York-San Francisco 1977.

G. J. BARENBLATT, A. JU. ISZLINSKU, Ob udare wiazko-plasticeskogo sterżnia o zestkuju pregradu, Prikl. Mat. Mech., 26, 497-502, 1962.

R. J. CLIFTON, Plastic waves; theory and experiment, in: Mechanics Today, vol.1, ed. Nemat - Nasser, Pergamon Press, 102-167, London 1974.

N. CRISTESCU, Dynamic plasticity, 164-169, Amsterdam 1967.

T. HAYASHI, H. FUKUOKA, H. TODA, Axial impact of law carbon mild steel rod, Bull. ISME, 14, 75, 901-908, 1971.

В. Н. КУКУДЖАНОВ, Распростраиение волн упругой ралрузкш в стержилх из упруго-пла­стического материала, Bull. Acad. Polon. Sci., Serie Sci. techn., 13, 3, 143-152, 1965.

В. Н. КУКУДЖАНОВ, Л. В. НИКИТИН, Распрострапение волu в стернснлх из неодиородного упруго-влжо-пластического материала, Изв. АН СССР, Механика ц машиностроение, 4, 53-59, 1960.

L. E. MALVERN, The propagation of longitudinal waves of plastic deformation in a bar of material exhibiting a strain-rate effect, J. Appl. Mech., 18, 3, 203-208, 1951.

P. PERZYNA, Teoria lepkoplastyczności, PWN, Warszawa 1966.

И. М. РАБШЮВИЧ, К расчету ферм и балоrе минималыюго объема на действия динами­ческих нагрузок и собственного веса, Иссл. по теории сооружевий, 15, 151-158, 1967.

М. И. РЕЙТМАН, Приблuженный метод проектирования упруго-пластических конструк­ций мuнимальиого веса при динамическом нагружетш, Иссл. по теории сооружений, 19, 41-46, 1972.

В. В. СОКОЛОВСКИЙ, Распростраиенuе упруго-вязко-пластических волu в стерJJснях, При-кл. Мех., 12, 3, 1948.

P. S. SYMONDS, T. C. T. TING, Longitudinal impact on viscoplastic rods - approximate method and comparisons, J. Appl. Mech., 31, 611-620, 1964.

T. C. T. TING, Impact of a nonlinear viscoplastic rod on a rigid wall, J. Appl. Mech., 33, 3, 505-513, 1966.

T. C. T. TING, P. S. SYMONDS, Longitudinal impact on viscoplastic rods-linear stress-strain law, J. Appl. Mech., 31, 2, 199-207, 1964.

D. WALLACE, A. SHIREG, Optimum design of prismatic bars subjected to longitudinal impact, Pap. ASME DE-G, 8, 1970.

M. ŻYCZKOWSKI, Optimal structural design in rheology, Trans. ASME E38, 1, 39-46, 1971.

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