Generalisations of Heyman's and Foulkes' theorems using dual formulation

Existing duality principles in structural optimisation are briefly reviewed and then they are extended to structures with segment-wise constant cross-sections. All theories are discussed in the particular context of optimal plastic beam design with symmetric convex specific cost functions and are confirmed by independent calculations on illustrative examples. It is shown that the optimal solution is always associated with a displacement field in which the mean absolute curvature value for each segment equals the subgradient of the specific cost function, with respect to the maximum absolute moment value for that segment. Moreover, the dual problem consists of the maximisation of the difference of two terms: the first one is the integral of the product of load and deflection (external work), and the second is the sum of products of segment lengths and the mean complementary cost values (taken with respect to the mean absolute curvature for that segment). Finally, some tentative proposals for a class of non-convex optimisation problems are presented. For special cases, the proposed general statements reduce to theorems by Heyman, Foulkes and Hemp.     

Dosimetric characteristic of VVR-M reactor with respect to tritium

Translated from Atomnaya Énergiya, Vol. 67, No. 2, pp. 111–113, August, 1989.     

Computing hysteresis points of nonlinear equations depending on two parameters

A direct method is described for computing a hysteresis point (double turning point) corresponding to a cusp point of a system ofn nonlinear equations inn variables depending on two parameters. By addition of two equations a minimally extended system ofn+2 nonlinear equations is constructed for which the hysteresis point is an isolated solution. An efficient implementation of Newton's method is presented not requiring evaluations of second derivatives of the original problem. Two numerical examples show the efficiency of theQ-quadratically convergent method.     

Multifactor Experiments under Superdeep-Penetration Conditions

Consideration is given to the possibility of controlling the efficiency of the process of superdeep penetration of a high-velocity microstriker flux into metal obstacles due to the employment of ballast elements in the jet and to additional supply of energy in compression by an explosive charge along the external perimeter.     

Special features of the periodic-pulse-train laser radiation confinement in doped gallium arsenide and zinc selenide

Experimental data on the pulsed laser radiation confinement in compensated GaAs and ZnSe with deep impurity levels are reported for the laser wavelength λ=1.55 μm and a pulse repetition frequency of up to 100 kHz. It is demonstrated that an increase in the pulse repetition rate is accompanied by a decrease in the energy confinement threshold and by an increase in the radiation attenuation coefficient. These effects are explained by the accumulation of nonequilibrium charge carriers related to a dependence of the recombination time constant on the concentration of free impurity centers.     

High-voltage bridge for measuring spontaneous polarization,dielectric constants,and conductivity of ferroelectric crystals

Translated from Izmeritel'naya Tekhnika, No. 9, pp. 34–35, September, 1989.