Discrete Approximate Solution of Differential Inclusion with Normal Cone and Prox-Regular Set.

Our aim is to calculate the discrete approximate solution of di⁄erential inclusion with normal cone and prox-regular set, the question is how to calculate this solution? We use the discrete approximation property of a new variant of nonconvex sweeping processes involving normal cone and a nite element method. Knowing that The majority of mathematicians have proved only the existence and uniqueness of the solution for this type of inclusions, like: Mordukhovich, Thibault, Aubin, Messaoud, ...etc.

ON THE EFFECTIVENESS OF OBLIQUE CAISSON REINFORCED CONCRETE FLOORS

The distribution of forces in the beams of a straight and oblique monolithic reinforced concrete caisson fl oor of a square plan is compared. The forces in the beams are determined by well-known analytical methods and using fi nite element models of the SCAD PC. The calculations showed that the forces in the beams of the oblique caisson fl oor, determined analytically and using computer models, diff er signifi cantly, which indicates the complex operation of the spatial system, which is not taken into account by the analytical calculation method based on the theory of calculating plates supported by the contour. The obtained data indicate that a square caisson fl oor with beams installed at an angle of 450 to the reference contour has greater rigidity and lower values of bending moments compared to straight caissons. When the ratio of the sides of the overlap L2 > 1,5 . L1 to ensure the eff ect of supporting the contour, the location of the beams in relation to the outer contour should be at an angle of 45°.

FEATURES OF THE STRAIN-STRESS STATE OF BEAMS WITH A CORRUGATED WALL OF VARIABLE RIGIDITY

Corrugated steel beams represent a promising area of research in the fi eld of structural engineering today. The article studies the behavior of a metal beam with a corrugated wall of an I-profi le under bending conditions. Beam considered span of 12 m. A fi nite element model of the calculated structure was built in the LIRA-SAPR software package. The analysis of the stress-strain state of a corrugated beam of variable stiff ness, which has a fl at fragment in the central part of the wall, is carried out. The beam thus obtained has a number of advantages over beams with only a fl at or fully corrugated wall. The conclusions based on the results of the analysis of the calculation are presented.

MODELING OF STRESS-DEFORMED STATE OF BENDED REINFORCED CONCRETE ELEMENTS IN ZONES OF CLEAN AND TRANSVERSE BEND

The article deals with the analysis of the stress-strain state (SSS) of a bent reinforced concrete element in zones of pure and transverse bending. It is assumed that a bent element in the process of loading (after the formation of normal and oblique cracks) is divided into blocks, united by uncracked concrete and reinforcement that has adhesion to concrete. SSS was formed using the results of experimental studies of special prototypes in the PC “Lira-SAPR”. A fi nite element model of a prototype has been developed in the form of a reinforced concrete rectangular beam loaded with two identical concentrated forces in the span. By the method of successive approximations, the process of formation and formation of a system of cracks is realized, with which the beam is divided into blocks during loading. The results of calculating the fi nite element model and their comparison with experimental data are presented.

Finite element method in computer simulation for improved patient care in dentistry: A systematic review

Background. The fi nite element method is gaining acknowledgment in Russia and other developed countries in a range of areas, including medicine. In stomatology, the method is applicable in research and implication of novel treatment and relevant material design.Objective. The review highlights usage of the fi nite element method in computer simulation to improve quality of patient dental care.Methods. The review analyses the state-of-the-art in current scientific literature. Records were mined in the PubMed and e-Library databases at a depth of 10 years, with selective inclusion of earlier articles. The query keywords were: finite element method [метод конечных элементов], computer simulation [компьютерная симуляция], quality of life improvement [повышение качества жизни], oral diseases [заболевания полости рта], dental treatment [стоматологическое лечение].Results. The review systematically surveys 56 scientific papers in the focus area for current state-of-the-art in the finite element analysis-empowered simulation in dentistry. The method’s rising employment is conditioned by its flexibility, 3D-object modelling simplicity and the rapid acquisition of reliable high-quality output. Its undoubted paramount advantage in dentistry is an explicit software visualisation of reliable results through co-modelling of multiple oral parameters.Conclusion. The growing acquaintance, mastering and use of this technique among researchers around the globe will give impetus to novel diagnosis and treatment, as well as relevant management algorithms in particular patient categories to enable personalisation of even mass dental check-up. This will reduce the number of visits, peri- and posttreatment error and complication rates for the improved patient’s quality of life and social rehabilitation.

FINITE ELEMENT ANALYSIS OF ROOT RESORPTION ASSOCIATED WITH TOOTH MOVEMENT: A SYSTEMATIC REVIEW”

Background: The purpose of this systematic review was to examine the available evidence of root resorption during orthodontic treatment with different force systems using nite element analysis. Methods: The following electronic databases were searched for literature till June 2021 : Pro-Quest Dissertation Abstracts and Thesis database, Cochrane Central Register of Controlled Trials (CENTRAL), PubMed, Google Scholar, Embase, US National Library of Medicine, and National Research Register. Root resorption studied under orthodontic forces, which simulated under various technique of nite element method (3D FEM) models were included in the study. The selected studies were assessed for the risk of bias using the Cochrane Collaboration risk of bias tool. The “trafc plot” and “weighted plot” risk of bias distribution were designed using the ROBVIS tool. The authors extracted and analyzed the data. Results: Fourteen studies fullled the inclusion criteria. The risks of biases were high for all studies.Data on quantity and direction of force applied, different type of root morphology and its various surface inuence on root resorption were extracted. The outcomes of the included studies were heterogeneous. Conclusion: Based on the current available literature, for reducing root resorption the excessive force may accelerate root resorption when it exceeds the typical human capillary blood pressure. Root resorption occurs more when extrusion/intrusion and tipping occur than when teeth actually move. A tooth with little or no orthodontic force load hardly shows any root resorption compared to one that has orthodontic force.

NUMERICAL SIMULATION OF SHELL AND TUBE HEAT EXCHANGER IN ANSYSFLUENT SOFTWARE

Numerical modeling of a water-to-water shell-and-tube heat exchanger using the capabilities of mathematical modeling by means of a fi nite element analysis package is considered. An algorithm for solving problems of heat and mass transfer in the ANSYSFluent software product is proposed. A distinctive feature of this algorithm is the simplicity and accuracy of the calculations. In the course of the study, the contours of the velocity and temperature distribution in the heat exchanger were obtained, and the data obtained using computer modeling were verifi ed with an analytical solution.

TESTING THE HYPOTHESIS OF THE COSINE DISTRIBUTION OF STRESSES IN THE SHAFT-HOLE CONTACT

One of the most common connection types in mechanical engineering and construction is the shaft-hole connection. The mechanical stresses caused by its loading are distributed in the contact zone of the loaded parts of the joint. In some cases, they can lead to destruction. Therefore, while designing, it is important to analyze the mechanical stresses in the contact zone. Traditionally, calculations assume that the contact stresses are distributed according to the cosine law. However, this is not entirely true, especially with diff erent shaft and hole diameters. The authors examined theoretical studies of the contact zone of the shaft and the hole (including the cases of diff erent diameters) and the stress distribution in the contact zone. Based on the studies, they performed numerical calculations in the APMWinMachine environment to determine the stresses in the volume of the shaft and the plate with a hole when loading the shaft-hole connection. The analyses were performed for the two-dimensional case by the fi nite element method in the APMStructure program. The results show that when the diameters in the connection are equal, the stress distribution is close to the cosine law. In this case, only one stress raiser occurs in the contact zone, which is located on the line of action of the loading force. However, if there is a slight discrepancy in the shaft and hole diameters, there are three stress raisers in which the connection may break – the central zone and two side zones. The angular distance between them can be determined based on the known theoretical formulas. The authors made an experiment with a plexiglass model, which qualitatively confi rmed the correctness of the analysis performed.

METHODS OF MODELING AND CALCULATION OF REINFORCED CONCRETE STRUCTURES OF OPERATED GTS, REINFORCED WITH PRESTRESSED BASALT COMPOSITE REINFORCEMENT

The development of a methodology for numerical modeling and calculation of reinforced concrete structures of operated hydraulic structures, reinforced with prestressed basalt composite reinforcement, including on the basis of experimental research data carried out in the branch of JSC“Institute Hydroproject”-“NIIES” is presented. Computational studies were carried out on the basis of spatial fi nite element models in the framework of the ANSYS software package. Developing the models, the results of experimental and theoretical studies of hydrotechnical reinforced concrete structures were used in which prestressed basalt composite reinforcement is placed both in the tensioned and compressed zones of the structures.

Estimation of square die backward extrusion forces of bar stock

Тhe results for estimation of the square die extrusion forces of cylindrical billets are presented. The study is performed on the basis of the fi nite element method. The results obtained during the simulation are analyzed statistically. Regression dependences for forces are obtained, with the help of which reverse extrusion studies are performed.