SPATIAL PROBLEMS OF DYNAMIC STABILITY OF FRAME STRUCTURES

Periodic longitudinal forces in structural elements caused by operational or seismic influences, at certain values of the parameters of these forces can cause the occurrence and growing of transverse oscillations of these elements. This phenomenon is called parametric resonance or loss of dynamic stability. In the works of N. M. Belyaev, N. M. Krylov, М. М. Bogolyubov, E. Mettler, V. N. Chelomey, V. V. Bolotin flat problems of dynamic stability of frame structures were investigated. In this paper the modified Bolotin’s method, proposed to solve flat problems of dynamic stability of frames, is used. Instead of the deformation method used by V. V. Bolotin to construct analytical expressions of deflections of frame rods, in the modified method the numerical-analytical method of boundary elements is used. The article proposes a method for constructing domains of dynamic instability of frames in the space of parameters (frequency and amplitude) of seismic and operational dynamic influences that cause longitudinal forces in the rods, which periodically change over time and lead to unlimited growth of transverse oscillations amplitudes in the domains of instability. The proposed method is demonstrated in example, which considers the spatial problem of dynamic stability of a П-shaped frame with two concentrated masses located on it, which are under the action of vertical periodic forces. These forces create periodic longitudinal forces in the vertical rods of the frame. Areas of dynamic instability of the frame were constructed. Taking into account the destructive effect of oscillations is important for practical application. The most dangerous destructive effect of oscillations is observed in earthquakes and explosions. The study of this action makes it possible to avoid undesirable consequences of oscillations by limiting their level and to solve important practical problems of the dynamics of structures. Solving dynamics problems is a difficult problem. Dynamic calculation of structures provides their bearing capacity under the combined action of static and dynamic loads.

STUDY OF SPATIAL PROBLEMS OF DYNAMIC STABILITY OF REINFORCED CONCRETE FRAMES

The article proposes a method for constructing areas of dynamic instability of reinforced concrete frames in the space of parameters (frequency and amplitude) of seismic and operational dynamic impacts that cause the appearance of longitudinal forces in the bars of structures, which periodically change in time and lead to an unlimited increase in amplitudes of transverse vibrations when the values of these parameters are in the areas of instability. The proposed method is demonstrated by a specific example, which considers the spatial problem of dynamic stability of a П-shaped frame with two concentrated masses located on it, which are under the action of vertical periodic forces. These forces create periodic longitudinal forces in the vertical rods of the frame. Areas of dynamic instability of the frame are constructed. From the point of view of human activity, fluctuations can be both beneficial and harmful. We can observe vibrations of various buildings, structures, bridges, which cause additional stresses and deformations of these structures, have a harmful effect on their safe functioning. Too intense fluctuations lead to serious consequences. This leads to the destruction of individual elements of the structure and, as a result, to accidents. The most destructive effect of vibrations is observed during earthquakes and explosions. The study of vibrations is of great practical importance. This avoids the unwanted effects of fluctuations by limiting their level. Only on the basis of a deep study of various types of vibrations can important practical problems of the dynamics of structures be solved. Solving dynamics problems is a complex problem. In contrast to static calculation, when studying oscillations, one has to take into account an additional factor – time. The dynamic design of structures provides them with bearing capacity under the combined action of static and dynamic loads. A construction will be considered as a system with an infinite number of elementary masses distributed over it with an infinitely large number of dynamic degrees of freedom.

“It’s not rocket science” and “It’s not brain surgery”—“It’s a walk in the park”: prospective comparative study

Objective To compare cognitive testing scores in neurosurgeons and aerospace engineers to help settle the age old argument of which phrase—“It’s not brain surgery” or “It’s not rocket science”—is most deserved. Design International prospective comparative study. Setting United Kingdom, Europe, the United States, and Canada. Participants 748 people (600 aerospace engineers and 148 neurosurgeons). After data cleaning, 401 complete datasets were included in the final analysis (329 aerospace engineers and 72 neurosurgeons). Main outcome measures Validated online test (Cognitron’s Great British Intelligence Test) measuring distinct aspects of cognition, spanning planning and reasoning, working memory, attention, and emotion processing abilities. Results The neurosurgeons showed significantly higher scores than the aerospace engineers in semantic problem solving (difference 0.33, 95% confidence interval 0.13 to 0.52). Aerospace engineers showed significantly higher scores in mental manipulation and attention (−0.29, −0.48 to −0.09). No difference was found between groups in domain scores for memory (−0.18, −0.40 to 0.03), spatial problem solving (−0.19, −0.39 to 0.01), problem solving speed (0.03, −0.20 to 0.25), and memory recall speed (0.12, −0.10 to 0.35). When each group’s scores for the six domains were compared with those in the general population, only two differences were significant: the neurosurgeons’ problem solving speed was quicker (mean z score 0.24, 95% confidence interval 0.07 to 0.41) and their memory recall speed was slower (−0.19, −0.34 to −0.04). Conclusions In situations that do not require rapid problem solving, it might be more correct to use the phrase “It’s not brain surgery.” It is possible that both neurosurgeons and aerospace engineers are unnecessarily placed on a pedestal and that “It’s a walk in the park” or another phrase unrelated to careers might be more appropriate. Other specialties might deserve to be on that pedestal, and future work should aim to determine the most deserving profession.

CONTACT PROBLEM FOR ORTHOTROPIC PLATES OF VARIABLE THICKNESS WITH A SPATIALLY INHOMOGENEOUS BASE

В работе приведено численное моделирование пространственной задачи контактного взаимодействия ортотропных плит переменной жесткости с упругими основаниями. Используемая методика расчета пригодна в случае любых известных контактных моделей упругих оснований. В качестве примера приведены численные результаты для пространственно-неоднородных оснований типа упругих слоев постоянной и переменной толщины. Система интегро-дифференциальных уравнений, к которой сводится задача, решается численно, сочетанием методов конечных разностей типа сквозного счета и граничных элементов. Найдены прогибы, изгибающие моменты и распределения контактных давлений прямоугольной плиты переменной жесткости, полностью примыкающей к основанию. Приводится анализ влияния на напряженно-деформированное состояние плиты, изменения ортотропных свойств ее материала и степень неравномерной сжимаемости толщи грунта. Разработанная методика позволяет эффективно моделировать работу плитных фундаментных конструкций, когда необходим учет неоднородности грунтов сжимаемой толщи в пределах габарита зданий или сооружений. The paper presents a numerical simulation of the spatial problem of contact interaction of orthotropic slabs of variable stiffness with elastic foundations. The calculation technique used is suitable for any known contact models of elastic foundations. As an example, numerical results are given for spatially inhomogeneous foundations such as elastic layers of constant and variable thickness. The system of integrodifferential equations, to which the problem is reduced, is solved numerically by a combination of finite difference methods such as end-to-end counting and boundary elements. Deflections, bending moments and contact pressure distributions of a rectangular slab of variable stiffness, completely adjacent to the base, are found. An analysis of the influence on the stress-strain state of the slab of changes in the orthotropic properties of its material and the degree of uneven compressibility of the soil thickness is given. The developed technique makes it possible to effectively simulate the operation of slab foundation structures when it is necessary to take into account the heterogeneity of the soil of the compressible strata within the dimensions of buildings or structures.

Parametric Studies of the Load Transfer Platform Reinforcement Interaction with Columns

When designing embankments on a soft ground improved with columns (rigid inclusions) and with a geosynthetically reinforced load transfer platform (LTP), the methods of determining strains in reinforcement reduce the spatial problem to a two-dimensional one, and analytical calculations are carried out for reinforcement strips in the directions along and across the embankment. In addition, the two-dimensional FEM models do not allow for a complete analysis of the behavior of the reinforcement material. The aim of this research was to analyze the work of the membrane in the 3D space modeling of the LTP reinforcement, depending on the interaction with the column, the shape of the column’s cap, the value of the Poisson’s ratio, the value of the stiffness of the elastic foundation (subgrade reaction k) modeling of the soft soil resistance between the columns and the load distribution over membranes that model the reinforcement. The membranes were modeled in the framework of the theory of large deformations using the finite element method and slender shell elements as three-dimensional objects. This modeling method allowed for the analysis of the behavior of the LTP reinforcement in various directions. The conducted analyses showed, among others, that in the absence of soil resistance between the columns, regardless of the shape of the cap (square, circle), the greatest strains are located near the edge of the cap in the diagonal direction between the columns.

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.

The problem of normal oscillations of a viscous stratified fluid with an elastic membrane

Normal oscillations of a viscous stratified fluid partially filling an arbitrary vessel and bounded above by an elastic horizontal membrane are studied. In this case, we consider a scalar model problem that reflects the main features of the vector spatial problem. The characteristic equation for the eigenvalues of the model problem is obtained, the structure of the spectrum and the asymptotics of the branches of the eigenvalues are studied. Assumptions are made about the structure of the oscillation spectrum of a viscous stratified fluid bounded by an elastic membrane for an arbitrary vessel. It is proved that the spectrum of the problem is discrete, located in the right complex half-plane symmetrically with respect to the real axis, and has a single limit point $+\infty$. Moreover, the spectrum is localized in a certain way in the right half-plane, the location zone depends on the dynamic viscosity of the fluid.

THE MAIN PARAMETERS OF THE STRENGTH CALCULATION OF NOVIKOV GEARING WITH STANDARD BASIC RACK PROFILE

The article shows the expediency of using Novikov gearing with standard basic rack profile and with hardened teeth for general purpose gearboxes, also with thermally improved teeth for special purpose gearboxes. It sets out the principled approach for solving the problem definition of basic parameters of the strength calculation of these gears, consisting of two stages: a) definitions of both basic bending, contact stresses and tooth rigidity, and phase taking into account the coefficients of influence of the gear face; b) modeling the process of real multipoint engagement with finding the criterial stress in dangerous sections of the teeth, which determine the load-bearing capacity and service life of the gearbox. Implementing this approach, we obtained generalizing results of solving a spatial problem of the stress-strain state of teeth at any position of the contact area along their length and the way of obtaining partial efforts at the contact area and criterion stresses is indicated. The dependencies, convenient for embedding in the developed computing programs, tables, approximating the power polynomials for determining the basic parameters of the contact were obtained. The completed studies are supposed to be issued in the form allows to offer the method of strength calculation of Novikov gearing with standard basic rack profile domestic machine-building enterprises, producing drives for general engineering and special purpose.

Investigation of the second main problem of elasticity for a layer with n cylindrical inclusions

When designing structures in the form of a reinforced layer, one has to deal with the situation when the reinforcement bars are located close to each other. In this case, their influence on each other increases. In order to obtain the stress-strain state in the contact zone of the layer and the inclusion, it is necessary to have a method that would allow obtaining a result with high accuracy. In this work, an analytical-numerical approach to solving the spatial problem of the theory of elasticity for a layer with a given number of longitudinal cylindrical inclusions and displacements given at the boundaries of the layer has been proposed. The solution of the problem has been obtained by the generalized Fourier method with respect to the system of Lame's equation in local cylindrical coordinates associated with inclusions and Cartesian coordinates associated with layer boundaries. Infinite systems of linear algebraic equations obtained by satisfying the boundary conditions and conjugation conditions of a layer with inclusions have been solved by the reduction method. As a result, displacements and stresses have been obtained at different points of the considered medium. When the order of the system of equations is 6, the accuracy of fulfilling the boundary conditions was 10-2 for values from 0 to 1. Numerical studies of the algebraic system of equations give grounds to assert that its solution can be found with any degree of accuracy by the reduction method, which is confirmed by the high accuracy of fulfilling the boundary conditions. In the numerical analysis, variants of the layer with 1 and 3 inclusions have been compared. The result has shown that close placement of reinforcement bars increases stresses on the surface of these inclusions. The values of stresses on the layer contact surfaces with inclusions have also been obtained. The proposed solution algorithm can be used in the design of structures, the computational scheme of which is the layer with longitudinal cylindrical inclusions and displacements specified at the layer boundaries.