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.

DETAILS OF NORMAL SECTIONS STRENGTH CALCULATION OF FLEXIBLE REINFORCED CONCRETE STRUCTURES BY THE WOOD’S METHOD IN PC "LIRA SAPR"

Problem statement. The problem of realization of the calculation method of normal cross-sections strength of reinforced concrete constructions under flat bending, which is established in the current building codes of Ukraine, is considered. The main attention is paid to atypical and practically not considered calculation cases, typical for automated algorithms in the environment of SP "LIRA SAPR". The purpose of the article. Analysis of the feasibility of using the calculation method of current building codes with further development of recommendations, based on the specifics of computerized calculations. Methodology. Within the framework of the performed research, rectangular cross-sections of reinforced concrete structures with single and double reinforcement (provided a significant increase in the area of reinforcement of the compressed cross-sectional area) with variation of concrete classes, reinforcement coefficient and ratio of reinforcement areas were considered. The stress-strain diagrams of concrete and reinforcement are bilinear with characteristic values set for the first group of limit states. The character of change of cross-sections’ status diagrams "M - εc(1) " is investigated. Research results. It is found that for single-reinforced sections with decreasing reinforcement area there is a decrease of the value of deformation of the compressed fiber of concrete, which is used to find solutions for systems of nonlinear equilibrium equations of the deformation method. This leads to an increase of the execution time of calculations of the flat elements’ reinforcement by the Wood method. It is established that for sections with double reinforcement at relatively large values of the ratios of the reinforcement areas, the equilibrium of the section is at the maximum deformations of the compressed concrete fiber. Conclusions. An approach aimed at accelerating the calculation of sections with single reinforcement, which is based on the use of the relationship between the percentage (area) of reinforcement and the deformation of the most compressed fiber of the reinforced concrete element. Features of analytical algorithms for calculating the selected sections are taken into account by implementing this technique in the PC "LIRA SAPR", optimization and acceleration of automated algorithms for calculating reinforced concrete structures.

A Hybrid Model Method for Accurate Surface Deformation and Incision Based on FEM and PBD

In some simulations like virtual surgery, an accurate surface deformation method is needed. Many deformation methods focus on the whole model swing and twist. Few methods focus on surface deformation. For the surface deformation method, two necessary characteristics are needed: the accuracy and real-time performance. Some traditional methods, such as position-based dynamics (PBD) and mass-spring method (MSM), focus more on the real-time performance. Others like the finite element method (FEM) focus more on the accuracy. To balance these two characteristics, we propose a hybrid mesh deformation method for accurate surface deformation based on FEM and PBD. Firstly, we construct a hybrid mesh, which is composed of a coarse volume mesh and a fine surface mesh. Secondly, we implement FEM on coarse volume mesh and PBD on fine surface mesh, and the deformation of fine surface mesh is constrained by the displacement of the coarse volume mesh. Thirdly, we introduced a small incision process for our proposed method. Finally, we implemented our method on a simple deformation simulation and a small incision simulation. The result shows an accurate surface deformation performance by implementing our method. The incision effect shows the compatibility of our proposed method. In conclusion, our proposed method acquires a better trade-off between accuracy and real-time performance.

Internal Damage Detection of Composite Structures Using Passive RFID Tag Antenna Deformation Method: Basic Research

This manuscript deals with the detection of internal cracks and defects in aeronautical fibreglass structures. In technical practice, it is problematic to accurately determine the service life or MTBF (Mean Time Between Failure) of composite materials by the methods used in metallic materials. The problem is mainly the inhomogeneous and anisotropic structure of composites, possibly due to the differences in the macrostructure during production, production processes, etc. Diagnostic methods for detecting internal cracks and damage are slightly different, and in practice, it is more difficult to detect defects using non-destructive testing (NDT). The article deals with the use of Radio frequency identification (RFID) technology integrated in the fibreglass laminates of aircraft structures to detect internal defects based on deformation behaviour of passive RFID tag antenna. The experiments proved the potential of using RFID technology in fibreglass composite laminates when using tensile tests applied on specimens with different structural properties. Therefore, the implementation of passive RFID tags into fibreglass composite structures presents the possibilities of detecting internal cracks and structural health monitoring. The result and conclusion of the basic research is determination of the application conditions for our proposed technology in practice. Moreover, the basic research provides recommendations for the applied research in terms of the use in real composite airframe structures.

Nonassociative black ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks

We construct nonassociative quasi-stationary solutions describing deformations of Schwarzschild black holes, BHs, to ellipsoid configurations, which can be black ellipsoids, BEs, and/or BHs with ellipsoidal accretion disks. Such solutions are defined by generic off-diagonal symmetric metrics and nonsymmetric components of metrics (which are zero on base four dimensional, 4-d, Lorentz manifold spacetimes but nontrivial in respective 8-d total (co) tangent bundles). Distorted nonassociative BH and BE solutions are found for effective real sources with terms proportional to $$\hbar \kappa $$ ħ κ (for respective Planck and string constants). These sources and related effective nontrivial cosmological constants are determined by nonlinear symmetries and deformations of the Ricci tensor by nonholonomic star products encoding R-flux contributions from string theory. To generate various classes of (non) associative /commutative distorted solutions we generalize and apply the anholonomic frame and connection deformation method for constructing exact and parametric solutions in modified gravity and/or general relativity theories. We study properties of locally anisotropic relativistic, optically thick, could and thin accretion disks around nonassociative distorted BHs, or BEs, when the effects due to the rotation are negligible. Such configurations describe angular anisotropic deformations of axially symmetric astrophysical models when the nonassociative distortions are related to the outer parts of the accretion disks.

Spatial and Time Warping for Gauge Adjustment of Rainfall Estimates

Many satellite-based estimates use gauge information for bias correction. In general, bias-correction methods are focused on the intensity error and do not explicitly correct possible position or timing errors. However, position and timing errors in rainfall estimates can also lead to errors in the rainfall occurrence or the intensity. This is especially true for localized rainfall events such as the convective rainstorms occurring during the rainy season in sub-Saharan Africa. We investigated the use of warping to correct such errors. The goal was to gauge-adjust satellite-based estimates with respect to the position and the timing of the rain event, instead of its intensity. Warping is a field-deformation method that transforms an image into another one. We compared two methods, spatial warping focusing on the position errors and time warping for the timing errors. They were evaluated on two case studies: a synthetic rainfall event represented by an ellipse and a rain event in southern Ghana during the monsoon season. In both cases, the two warping methods reduced significantly the respective targeted (position or timing) errors. In the southern Ghana case, the average position error was decreased by about 45 km by the spatial warping and the average timing error was decreased from more than 1 h to 0.2 h by the time warping. Both warping methods also improved the continuous statistics on the intensity: the correlation went from 0.18 to at least 0.62 after warping in the southern Ghana case. The spatial warping seems more interesting because of its positive impact on both position and timing errors.

Damage Identification Method Using Additional Virtual Mass Based on Damage Sparsity

Damage identification methods based on structural modal parameters are influenced by the structure form, number of measuring sensors and noise, resulting in insufficient modal data and low damage identification accuracy. The additional virtual mass method introduced in this study is based on the virtual deformation method for deriving the frequency-domain response equation of the virtual structure and identify its mode to expand the modal information of the original structure. Based on the initial condition assumption that the structural damage was sparse, the damage identification method based on sparsity with l1 and l2 norm of the damage-factor variation and the orthogonal matching pursuit (OMP) method based on the l0 norm were introduced. According to the characteristics of the additional virtual mass method, an improved OMP method (IOMP) was developed to improve the localization of optimal solution determined using the OMP method and the damage substructure selection process, analyze the damage in the entire structure globally, and improve damage identification accuracy. The accuracy and robustness of each damage identification method for multi-damage scenario were analyzed and verified through simulation and experiment.

Roll-over stability as a problem of high-rise buildings’ designing

Roll-over stability of tall buildings under wind loads is considered. The nonlinear nature of the problem is taken into account, including geometric, physical, and structural non-linearity. The problem is solved on the base of a system of linearized incremental equations of structural mechanics that describes the behavior of a system tall building - foundation soil. Several methods are examined for solving nonlinear problems of roll-over stability, specifically: 1) deformation method of systems equilibrium states tracing; 2) method of linearization of nonlinear equations and systems equilibrium states tracing; 3) method of linearization of nonlinear physical relations of a systems with constructive, static, geometric nonlinearity; 4) method of linearization of nonlinear physical relations of a system with constructive nonlinearity based on nonlinear incremental structural mechanics; 5) method of the deformation process tracing for a physically nonlinear soil base, given the increase of discharge zones and constructive nonlinearity. Each of these methods is used to solve a model task. These tasks take into account roll-over stability of high structures under action of wind loads. In general, the problem of roll-over stability of a high object can be represented as repeatedly nonlinear one with various types of non-linearity. In this regard, in the practice of high-rise buildings designing, it is necessary to develop scientifically and methodically substantiated methods of assessing roll-over stability, considering non-linear factors. Taking these factors into account will make it possible to assess the roll-over stability of a high-rise object more accurate.

CALCULATION OF FUNDAMENTAL STRUCTURES BY THE METHOD OF DEFORMATIONS

The unceasing process of urbanization all over the world and the constantly growingcost of land plots allotted for development makes investors, scientists and engineers look for and findways to reduce the unit cost of construction of useful areas of buildings and structures for variouspurposes.The most effective way to reduce the unit cost of construction of useful areas of buildings andstructures is to increase their number of storeys and depths of underground parts. But with an increasein the height of buildings, the loads on their foundations also increase, stimulating scientists andengineers to search for more advanced methods and methods for solving problems related todetermining the rational parameters of the foundations of buildings and structures, improving thequality and reliability of the calculation methods used.The results obtained using modern methods of calculating foundations in some cases lead to anoverestimation of the costs of building materials, in some – to a decrease in comparison with the realstrength and deformation indicators of the foundations of construction objects.This book describes a deformation method that allows you to improve the calculations of thestress-strain state of pile and some other types of foundations by expressing the deformations offoundation structures by the dependence of the foundation settlement on the rigidity of the«foundation-foundation» system and the coefficient of foundation rigidity, which varies along thelength or depth of the foundations, which will significantly improve the performance of buildings andstructures.Based on the hypothesis of direct proportionality (Winkler), we use the ability of such a modelof the basis to take any variable stiffness along the length of the structure that transmits the load tothe ground. Representing a system of unconnected springs of different stiffness, such a base is able tomimic the resolution of the currently used different models within the base of the foundations. However, outside the sole, Winkler cannot consider the resolution of the real soil in terms ofinteraction with adjacent foundations. Thus, we are going to take into account only the «internal»resolution of different models of the basis. It is not difficult to obtain this information using analyticaland numerical methods for determining the stress-strain state of the soil base.