Interfacing conditions in the pipeline mathematical model with a kink of profile

Сформулирована замкнутая краевая задача расчета напряженно-деформированного состояния трубопровода как оболочки Власова с линией излома поверхности. Выведены разрешающие уравнения оболочки в перемещениях в избранной криволинейной системе координат; в локальных координатах, связанных с линией излома, выведены кинематические условия сопряжения; на линии излома поверхности наложены и доказаны условия сопряжения для моментов и усилий в оболочке. Условия сопряжения выведены в перемещениях оболочки на линии излома, не являющейся координатной линией. Доказано наличие сингулярности в условиях сопряжения. Установлена согласованность результатов численного анализа с известными результатами. A closed-ended formulation of the boundary-value problem of calculating the pipeline stress-strain state as a Vlasov shell with a kink line of surface was given. The resolving equations of the shell in displacements in the chosen curvilinear coordinate system were derived; in the local coordinates associated with the kink line, the kinematic conjugation conditions on this line were derived; conjugation conditions for moments and forces in the shell on the surface kink line were stated and proved. All conjugation conditions were deduced in the displacements of the shell on the kink line, which is not a coordinate line. The presence of a singularity in the obtained conjugation conditions was proved. The consistency of the numerical analysis results with known results was established.

VARIOUS EVALUATION IN PHYSICS AND MATHEMATICS FACULTIES OF GENERAL EDUCATIONAL SCIENCES

The article analyzes the integration of physics and mathematics in general secondary schools. KEY WORDS: continuity, optimized curriculum, quadratic equation, coordinate line, thermometer, surface, pressure, volume, density, parabola, exponential function, logarithmic function, modular function.

Complexes of elliptic cylinders with a characteristic manifold of the generator element in the form of coordinate straight lines

The complex (three-parameter family) of elliptic cylinders is investigated in the three-dimensional affine space, in which the characteristic multiplicity of the forming element consists of three coordinate axes. The focal variety of the forming element of the considered variety is geometrically characterized. Geometric properties of the complex under study were obtained. It is shown that the studied manifold exists and is determined by a completely integrable system of differential equations. It is proved that the focal variety of the forming element of the complex consists of four geometrically characterized points. The center of the ray of the straight-line congruence of the axes of the cylinder, the indicatrix of the second coordinate vector, the second coordinate line and one of the coordinate planes are fixed. The indicatrix of the first coordinate vector describes a one-parameter family of lines with tangents parallel to the second coordinate vector. The end of the first coordinate vector describes a one-parameter family of lines with tangents parallel to the third coordinate vector. The indicatrix of the third coordinate vector and its end describe congruences of planes parallel to the first coordinate plane. The points of the first coordinate line and the first coordinate plane describe one-parameter families of planes parallel to the coordinate plane indicated above.