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.     

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.