Numerical algorithm for the Mayer problem for nonlinear dynamic systems

An algorithm is proposed for numerical construction of optimal programmed controls in the Mayer problem for a nonlinear dynamic system. In each step of the optimization process, the algorithm uses the method of successive linearization with subsequent projection of the objective functional gradient on the constraints and recovery of violated boundary conditions and constraints. Solutions of some test problems are reported.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 107–114, 1985.     

Analysis of the stress-strain state of a ring-reinforced cylindrical section of an underground pipe

A method is presented for solving the problem of determining the stress-strain state of closed circular cylindrical shells in an elastic medium. The problem relates to the design of underground pipelines. The work of cylindrical shells is examined from the viewpoint of the theory of thin-walled three-dimensional systems, with allowance being made for the unilateral character of the interaction with the elastic medium. The stress-strain state of a cylindrical section of an underground pipe reinforced in the middle by a ring is investigated. It is shown that different factors influence the stress-strain state of the shell of the pipe.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 66–72, 1987.     

Study of formation mechanism of 1,3-benzodioxanes from tertiary phenoloalcohols and carbonyl compounds using labeled atoms

It was shown that the reaction of o-hyroxyphenyldiphenylmethanol with benzaldehyde labeled with ¹⁷O and ¹⁸O isotopes proceeds in such a way that oxygen atoms of the starting phenoloalcohol are retained.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 632–633, May, 1991.     

Ductile-to-ductile transition in dispersely filled composites based on thermoplastic polymers

The fracture mechanism for rubber-filled composites based on gutta-percha, LDPE, medium-density PE, and rubber particles has been studied. An increase in the concentration of filler particles leads to a change in the stress-strain behavior of the composites from neck propagation to homogeneous plastic deformation. For the filled composites, the criterion for the ductile-to-ductile transition is the equality of yield and draw stresses. The critical concentration of rubber particles at the ductile-to-ductile transition is controlled by the ratio between the yield stress of matrix polymer and the neck propagation stress. Transition from neck propagation to homogeneous plastic flow of the material is accomplished under two conditions: the breaking strength of the polymer matrix should be higher than the yield stress, and stretching of the composite should not be accompanied by the formation of diamond cracks. The latter condition is fulfilled when the dimensions of rubber particles are below a certain critical value, which is determined by the ductility of the matrix.