FORCE DRIVEN VIBRATIONS OF NONLINEAR PLATES ON A VISCOELASTIC WINKLER FOUNDATION UNDER THE HARMONIC MOVING LOAD

In the present paper, the forced driven nonlinear vibrations of an elastic plate in a viscoelastic medium and resting on a viscoelastic Winkler-type foundation are studied. The damping features of the surrounding medium and foundation are described by the Kelvin-Voigt model and standard linear solid model with fractional derivatives, respectively. The dynamic response of the plate is described by the set of nonlinear differential equations with due account for the fact that the plate is being under the conditions of the internal resonance accompanied by the external resonance. The expressions for the stress function and nonlinear coefficients for different types of boundary conditions are presented.

ESTIMATION OF THE DEFECT HAZARD CLASS IN BUILDING STRUCTURES: A DECISION SUPPORT SYSTEM

Technical condition monitoring of building structures located on hazardous facilities is a necessary requirement for their sustainable functioning. In this regard, the problem of development intellectual monitoring systems that allow to detect and classify operating defects by the hazardous level becomes very urgent. The study presents an approach of building decision support system (DSS) for detecting defects in building structures and estimation of their hazard class. Proposed approach is based on multi-criteria assessment of consecutive measurements acquired by acoustic emission method. A distinctive characteristic of the proposed approach is the ability to take into account the evolution of defects by mapping each AE time-series to diagnostic features matrix and analysing these matrices in sliding windows with overlay. Each matrix is validated by two criteria that form the necessary and sufficient conditions of the existence the evolving defects in building structure. They include the criterion for changing the number of clusters and the criterion for changing the acoustic emission activity. Proposed method was verified on the experimental data acquired from the technical condition monitoring of the vertical oil tanks. The results obtained fromthe experiment confirm the proposal that this approach can be utilized for effectively solving the problem of conditionalmonitoring of building structures located on the hazardous facilities allowing to detect and classify defects by theirhazardous level.

NONLOCAL IN TIME MODEL OF MATERIAL DAMPING IN COMPOSITE STRUCTURAL ELEMENTS DYNAMIC ANALYSIS

In this paper the problem of numerical simulation of composite bending elements dynamic considering internal (material) damping. For this purpose the nonlocal in time damping model, called damping with memory, is proposed as an alternative to the classic local Kelvin-Voigt model. Damping with memory makes damping forces not only dependent on the instant value of the strain rate, but also on the previous history of the vibration process. Since finite element analysis is the most common method of structural analysis, the nonlocal damping model is integrated into FEA algorithm. The FEA dynamic equilibrium equation is solved using the explicit scheme. The damping matrix was developed using the stationary full energy requirement. One-dimensional nonlocal in time model was implemented in MATLAB software package. The results of three-dimensional numerical simulation of the composite beam vibration obtained in SIMULIA Abaqus were used for model calibration. The obtained results were compared to the results based on classic Kelvin-Voight damping model.

AIMED CONTROL OF THE FREQUENCY SPECTRUM OF EIGENVIBRATIONS OF ELASTIC PLATES WITH A FINITE NUMBER OF DEGREES OF MASS FREEDOM BY INTRODUCING ADDITIONAL GENERALIZED KINEMATIC DEVICES

As is known, targeted regulation of the frequency spectrum of natural vibrations of elastic systems with a finite number of degrees of mass freedom can be performed by introducing additional generalized constraints and generalized kinematic devices. Each targeted generalized constraint increases, and each generalized kinematic device reduces the value of only one selected natural frequency to a predetermined value, without changing the remaining natural frequencies and all forms of natural vibrations (natural modes). To date, for some elastic systems with a finite number of degrees of freedom of masses, in which the directions of mass movement are parallel and lie in the same plane, special methods have been already developed for creating additional constraints and generalized kinematic devices that change the frequency spectrum of natural vibrations in a targeted manner. In particular, a theory and an algorithm for the creation of targeted generalized constraints and generalized kinematic devices have been developed for rods. It was previously proved that the method of forming a matrix of additional stiffness coefficients, specifying targeted generalized constraint, in the problem of natural vibrations of rods can also be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which the directions of mass movement are parallel, but do not lie in the same plane. In particular, such systems include plates. The distinctive paper shows that the method of forming a matrix for taking into account the action of additional inertial forces, specifying targeted kinematic devices in the problem of natural vibrations of rods can also be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which the directions of mass movement are parallel, but do not lie in the same plane. However, the algorithms for the creation of targeted generalized kinematic devices developed for rods based on the properties of rope polygons cannot be used without significant changes in a similar problem for plates. The method of creation of computational schemes of kinematic devices that precisely change the frequency spectrum of natural vibrations of elastic plates with a finite number of degrees of mass freedom is a separate problem and will be considered in a subsequent paper.

CRITICAL REVIEW OF PHYSICAL MODELLING OF SNOW ACCUMULATION ON ROOFS WITH ARBITRARY GEOMETRY

A review of the most significant domestic and, due to numerical superiority, foreign works on physical modelling of snow transport and snow accumulation processes, in particular, for the purpose of determining snow loads on roofs with arbitrary geometry, is presented. The existing practice of development of recommendations on assignment of snow loads in Russian laboratories is considered and critically evaluated. Comparison of do-mesticworks with scientific articles in the advanced world scientific journals and foreign regulatory documents leads to unfavorable conclusions. Recommendations on assigning snow loads, issued by Russian laboratories on the basisof extremely outdated and poorly substantiated methodology, bear a serious risk for evaluating mechan-ical safety of modern structures, for which such recommendations are developed. Recommendations are offered to remedy this current dangerous practice. The article also gives some suggestions on forming a basis for field observations of snow loads on existing roofs.

CRITICAL REVIEW OF MODERN NUMERICAL MODELLING OF SNOW ACCUMULATION ON ROOFS WITH ARBITRARY GEOMETRY

The calculation of snow loads on roofs of buildings and structures with arbitrary geometry is a complex problem, solving which requires simulating snow accumulation with acceptable engineering accuracy. Experiments in wind tunnels, although widely used in recent years, do not allow to reproduce the real full-scale effects of all snow transport subprocesses, since it is impossible to satisfy all the similarity conditions. This situation, coupled with the continuous improvement of mathematical models, numerical methods, computer technologies and related software, makes the development and future implementation of numerical modelling in real construction practice and regulatory documents inevitable. This paper reviews currently existing mathematical models and numerical methods used to calculate the forms of snow deposits. And, although the lack of significant progress in the field of modelling snow accumulation still remains one of the major problems in CFD, use of existing models, supported by field observations and experimental data, allows to reproduce reasonably accurate snow distributions. The importance of the “symbiosis” between classical experimental methods and modern numerical models is specifically emphasized in the paper, as well as the fact that only the joint use of approaches can comprehensively describe modelling of snow accumulation and snow transport and provide better solutions to a wider range of problems.

NUMERICAL STUDY OF THE PUNCHING SHEAR MECHANISM FOR THIN AND THICK REINFORCED CONCRETE SLABS

The assessment of the punching shear capacity for reinforced concrete slabs, carried out according to the regulatorydocuments of a number of countries, leads to significantly various results. At the same time, the results of thecalculated forecast may have great differences from the experimental data. A great influence on the accuracy of the resultsof the calculated forecast is exerted by the thickness of the examined slabs, as well as the value of longitudinal reinforcement.These parameters determine the features of the mechanisms of destruction of slabs in case of the punching shearmechanism, as indicated by individual interpretations of the results of experimental studies. In order to determine thefeatures of the punching shear mechanism of reinforced concrete slabs of various thicknesses, numerical studies of theprocess of cracking and destruction of slabs of different thicknesses have been performed. Differences in the mechanismof formation and development of cracks in thin and thick slabs are revealed. The paper shows that the behavior of thinand thick slabs has qualitative distinctions at the initial stages of formation and development of the cracks leading todestruction. The authors have also shown the difference between stress-strain state of thick and thin slabs before destruction.In conclusion, it was established that the influence of longitudinal reinforcement on the strength during punching inthick slabs is much less than in thin ones.When evaluating the punching shear capacity of reinforced concrete slabs, the regulatory documents of different countries give significantly different results. In this case, the calculation results may differ significantly from the experimental data. The deterioration of the thickness of the calculated slabs, as well as the value of the longitudinal reinforcement has a great influence on the accuracy of the calculation results. These parameters determine the features of the destruction mechanisms of slabs under punching. This fact is indicated by some interpretations of the results of experimental studies. In order to establish the peculiarities of the punching shear mechanism of reinforced concrete slabs of different thicknesses, a numerical investigation of the cracking and destruction of slabs of different thicknesses have been performed. Differences in the mechanism of formation and development of cracks in thin and thick slabs have been revealed. The paper shows that the behavior of thin and thick slabs has qualitative differences at the initial stages of the cracks formation and development that leads to destruction. The difference between stress-strain state of thick and thin slabs before breaking have been shown. It was found that the effect of longitudinal reinforcement on the punching shear strength in thick slabs is much less than in thin ones.

NONLINEAR STRUCTURAL ANALYSIS BASED ON THE MODIFIED SEQUENTIAL LOAD METHOD

The article discusses ways to improve the accuracy of solving problems of nonlinear structural mechanics. It is shown that the combination of the method of sequential loading and the Newton-Kantorovich method can improve the accuracy of the solution and reduce the complexity of obtaining results. The solution of the given linear equations can be obtained by numerical and approximate methods known in the literature.

NUMERICAL SOLUTION OF THE PROBLEM FOR POISSON’S EQUATION WITH THE USE OF DAUBECHIES WAVELET DISCRETE-CONTINUAL FINITE ELEMENT METHOD

Numerical solution of the problem for Poisson’s equation with the use of Daubechies wavelet discrete continual finite element method (specific version of wavelet-based discrete-continual finite element method) is under consideration in the distinctive paper. The operational initial continual and discrete-continual formulations of the problem are given, several aspects of finite element approximation are considered. Some information about the numerical implementation and an example of analysis are presented.

STRESS-DEFORMED STATE OF THE FOUNDATION OF HYDRAULIC STRUCTURES AT CONTROLLED COMPENSATION DISCHARGE

Nnumerical simulation of the process of injection of mortar into the thickness of the sandy base during the work on lifting and leveling the structure by the method of compensatory injection is carried out. An author's program has been developed that implements the finite element method (FEM) in a spatial formulation, taking into account the elastic-plastic nature of soil deformation, in which a special element in the form of a spheroid has been developed to describe the expanding area at the location of the injector, which changes its volume during the injection of mortar. During the verification of the program, the results of mathematical modeling were compared with the data of a physical experiment conducted by PhD Luca Masini from the University of La Sapienza (Rome, Italy). Numerical modeling of the stress-strain state of the base of the structure during repair work is considered by the example of lifting the foundation plate of the Zagorskaya PSPP-2. A number of tasks are being solved related to minimizing the number of injection columns, their location, the pitch of the cuffs, the selection of portions of the injected solution, taking into account the requirements for uniform lifting of the foundation plate in order to avoid additional cracking.