On the solution singularity in the plane elasticity problem for a cantilever strip

The plane elasticity problem of bending of a cantilever strip whose material is assumed to be incompressible in the transverse direction is solved. It is shown that, in the classical statement of of the boundary condition for the fixed edge of the strip, the solution has a singularity at the corner points of the edge. Several cases of the strip fixation and loading characterized by the presence or absence of the solution singularity are considered. The strength of glass beams of three types, for which the theory of elasticity predicts whether the normal stress has a singularity, is studied experimentally. It is shown that the limit stresses for the beams of the types under study are practically the same, which testifies that the solution singularity does not have any physical nature.     

Analytic description of the domain of existence of triple configurations with a negative slope of reflected shock

We consider triple configurations of compression shocks in supersonic flows of an inviscid perfect gas. The boundaries of the domain of existence of shock-wave structures of a new type (triple configurations with a negative slope of the reflected shock or negative triple configurations) on a set of flow parameters have been theoretically investigated.     

Method for calculating the potential of spacecraft elements in 3D space

We propose a method for calculating the potentials of the spacecraft surface, based on triangulation approximation of surfaces, the area method, and analytic calculations of the matrix elements of the Coulomb interaction. The technique described here has a wide range of applications including low, as well as geostationary and polar orbits, and increases the calculating speed and accuracy.