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.

CONSTRUCTION OF SOLVING EQUATIONS OF SEMI-ANALYTICAL METHOD OF FINISHED ELEMENTS FOR PRISMATIC BODIES OF COMPLEX SHAPE

The article presents an effective numerical approach to the study of arbitrarily loaded massive and thin-walled prismatic bodies of complex shape, the deformation of which can take place beyond the elasticity of the material. The equations of the semi-analytical finite element method (SAFEM) when used to decompose the displacements of Fourier series. The main relations between the spatial problem of the theory of elasticity in a curvilinear coordinate system and the theory of plastic flow for an isotropically reinforcing material under the Mises fluidity condition are presented. In accordance with the method of the moment scheme of finite elements (MSFE), the expressions of deformations of the prismatic finite element due to the nodal values of amplitude displacements are obtained. Formulas for calculating the stiffness matrix coefficients of a finite element (FE) with variable and averaged in the cross-sectional plane mechanical and geometric parameters are derived.

Methodology of determining of the transfer function of engagement kinematics of accelerations of an aircraft and its elliptic coordinates used for thr guidance based on time difference of arrival

This paper discusses the problem of determining a kinematics (in terms of transfer function, as far as possible) of parameters of the motion of an aircraft expressed in the curvilinear coordinate system and control accelerations expressed in a rectangular coordinate system. Examples of curvilinear coordinate systems using in practice can be polar, biangular, two-center bipolar, elliptic, parabolic cylindrical, spherical, ellipsoidal, coordinate systems. A technique for obtaining a kinematic link for the control problem of an unmanned aerial vehicle in the elliptic coordinate system was described. It allowed to obtain simpler view of the kinematic link which could provide navigation an aircraft along the hyperbola deriving from the time difference of arrival navigation system. It can. As a result, it is possible to reduce the number of the navigation radio beacons.