Nonlinear contact problems for thin-walled elements of constructions

Some one-dimensional contact problems for plates and shells are considered for one-side contact with a rigid base. Contrary to analogous papers about the zone of contact, we use applied theories of contraction of Winkler type, which are obtained from equations of elasticity theory by asymptotic methods together with bending equations of thin-walled elements. The possibility of deviation of shells needs a definition of a contact zone in the process of solution of the problem from the condition of continuity of bending and its derivatives up to the second order inclusive. Some conclusions are made with respect to the optimal projects of reinforcement of shells taking into account their deviation.Translated from Dinamicheskie Sistemy, No. 8, pp. 40–45, 1989.     

Clausius-Mossotti-Type relation for planar monolayers

The dielectric properties of a quasi-two-dimensional molecular monolayer are analyzed. The dielectric function of the monolayer is expressed in terms of molecular polarizability and monolayer characteristics. The expression is analogous to the well-known Clausius-Mossotti equation for three-dimensional systems. The response of the monolayer to an external field is calculated. The case of a planar array of nanoparticles is also considered. The solution is obtained in the framework of a local-field theory.     

Epoxidation of propyl- and isobutyl-β-alkylvinylketones

A study is made of the epoxidation of hepten-2-one-4, octen-3-one-5, nonen-4-one-6, 2-methylhepten-5-one-4, 2-methylocten-5-one-4, and 2-methylnonen-5-one-4 with alkaline methanolic hydrogen peroxide. 46–71% yield of the corresponding epoxy ketones are obtained. It is shown that treatment of the 2, 3-epoxyheptanone-4, 3, 4-epoxyoctanone-5, 4, 5-epoxynonanone-6, 2-methyl-5, 6-epoxyheptanone-4, 2-methyl-5, 6-epoxyoctanone-4 and 2-methyl-5, 6-epoxynonanone-4 with zinc chloride isomerizes them to, respectively, heptandione-3, 4, octandione-4, 5, nonandione-4, 5, 2-methylheptandione-4, 5, 2-methyloctandione-4, 5, and 2-methylnonandione-4, 5 in upto 78% yield.