Confirmation of Lagrange Hypothesis for Twisted Elastic Rod

The history of structural optimization as an exact science begins possibly with the celebrated Lagrange problem: to find a curve which by its revolution about an axis in its plane determines the rod of greatest efficiency. The Lagrange hypothesis, that the optimal rod possesses the constant cross-section was abandoned for Euler buckling problem. In this Article the Lagrange hypothesis is proved to be valid for Greenhill's problem of torque buckling. The corresponding isoperimetric inequality is affirmed.Comment: 4 page

On body shapes providing maximum depth of penetration

The problem of maximization of the depth of penetration of rigid impactor into semi-infinite solid media (concrete shield) is investigated analytically and numerically using two-stage model and experimen- tal data of Forrestal and Tzou (Int J Solids Struct 34(31–32):4127–4146, 1997). The shape of the axisym- metric rigid impactor has been taken as an unknown design variable. To solve the formulated optimization problem for nonadditive functional, we expressed the depth of penetration (DOP) under some isoperimetric constraints. We apply approaches based on analyti- cal and qualitative variational methods and numerical optimization algorithm of global search. Basic atten- tion for considered optimization problem was given to constraints on the mass of penetrated bodies, ex- pressed by the volume in the case of penetrated solid body and by the surface area in the case of pene- trated thin-walled rigid shell. As a result of performed investigation, based on two-term and three-term two stage models proposed by Forrestal et al. (Int J Impact Eng 15(4):396–405, 1994), Forrestal and Tzou (Int J Solids Struct 34(31–32):4127–4146, 1997) and effectively developed by Ben-Dor et al. (Comp Struct 56:243–248, 2002, Comput Struct 81(1):9–14, 2003a, In

Some optimization problems foe bodies in quasi-steadi state wear

The problem of optimization of contact interaction of a moving rigid punch and an elastic half-space is investigated taking into account friction and wear. The punch shape is accepted as a desirable design variable and the volumetric wear rate under constraints on the friction dissipation power and the total load, applied to the punch, is taken as an optimized quality criterion. The ratio of the volumetric wear rate and the friction dissipation power under constraint on the total load is also considered as a suitable objective functional. A necessary condition for the optimality in quasi-steady state wear process is derived and discussed. The optimization problem is investigated analytically and exact solutions are obtained for the axysimmetric (stamp) punch which has a circular contact region and moves translationally with a constant velocity or rotates with constant angular velocit

Multiobjective Approach For Optimal Design Of Layered Plates Against Penetration Of Strikers

The study deals with the problem of layered plate multiobjective optimization against penetration of strikers having supersonic entry velocities. The plate is monolithic piecewise homogeneous and composed from several plate-like layers produced from various given materials. The number of considered materials is supposed to be finite and consequently the admissible design set consists of separate discrete values. The impactor is modeled as an axisymmetric rigid body with blunted nose. The ballistic limit velocity and the mass of the plate are taken as components of the vector-functional that is optimized in Pareto sense. Best distribution of given materials is found with the help of genetic algorithm