Constitutive equations of viscoplasticity belong to the most complicated ones, hence optimal design of viscoplastic structures is usually performed in a purely numerical way, and the use of suitable discretization methods is necessary. In the present paper finite element method is used for optimal design of a rigid-viscoplastic bar under the impact of axial force. Minimal residual displacement is assumed as the design objective under the constraint of constant volume of the bar.

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... e allowed for and various shapes of force impulse are considered. Optimization of viscoplastic I-beams under dyna81ic loadings... is also mentioned. Introducti on structural design procedures. In some further results in optimal using suitable discretization Finite element method has been widely used to optimization of large and complicated structures, but under the restrictions to elastic response of such structures, usually subjected to static loadings. On the other hand many structural materials show inelastic properties before final failure. If dynamic loading is cosidered; then viscous effects are particulary important and a suitable viscoplastic material model should be applied. In such cases -view of complexity of the relevant constitutive equations -purely numerical optimization methods must often be employed even for simple structures. Literature devoted to optimal design of viscoplastic structures· is rather very scarce: it was reviewed in a survey paper by ivczkowSki .£13. We recall her·e brief.ly this review. Quasistatic loadings were investigated .by Cegielski [2], where optimal shapes. of a cantilever beam were considered as an example. The author analysed the dependence of optimal shapes on constitutive equations, on distribution of loading in space and in time, and on the type of· constraints adopted. The remaining papers were devoted to dynamic loadings: Cegielski and lyczkowski [31 discussed. para_tr.ic optimization of bars under axial impact within the range of small strains, Cegielski [4] considered op.timal beams for various implll.se shapes, Cegielski .and ZYli:zkowsld t5J found.optimal thickness distribution in circular cylindrical shells under dynamic combined loadings, lyczkowsld and Cegielski [6] optimized. beams. under tr'aT1!iYerse impact. In the present paper we give of viscoplastic structures by H. A. Eschenauer et al. (eds.), Discretization Methods and Structural Optimization -Procedures and Applications