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.

The partial banana mapping: a robust linear method for impact probability estimation

ABSTRACT This paper presents a robust linear method for impact probability estimation of near-Earth asteroids with the Earth. This method is a significantly modified and improved method, which uses a special curvilinear coordinate system associated with the nominal orbit of an asteroid. One of the coordinates of this system is the mean anomaly in the osculating orbit of an asteroid. A normal distribution of errors of coordinates and velocities of this system is assumed. Because of the usage of the curvilinear coordinate system, the fact that the confidence region is curved and stretched mainly along the nominal asteroid orbit is taken into account. On the main axis of the curvilinear confidence ellipsoid the virtual asteroid, which is the closest to the Earth, is found. The part of the curvilinear confidence ellipsoid, around the found virtual asteroid, is obtained and mapped on to its target plane. The impact probability is calculated as the probability of the asteroid being in the region of the found virtual asteroid multiplied by the probability of a collision of the found virtual asteroid with the Earth. This approach is shown to give more accurate and trustworthy results than the target plane method.

Vector Approximation in the Roller Shells Nonlinear Calculations on the Fem Basis

In the curvilinear coordinate system, an approximation of the finite element required quantities in the vector formulation is developed with the implementation of the stiffness matrix of the volumetric finite element of the shell of rotation taking into account the geometric nonlinearity.