## МИТ СПЕЦВЫПУСК_3-2011

## WIND RESONANCE OF CABLE WINDED FROM THE TWO WIRE

Maslennikov А. М.

Saint Petersburg state architectural-build university

e-mail: aleksmaslennikov@yandex.ru

It is offered to determine frequency a blast of winds by use the known data for cylinder and undertakes for this purpose a diameter of single wire. Then forces of friction between wires during the bend of the cable are taken into consideration.

Key words: wires, wind resonance, dissipation of energy.

## THICK SHELLS DYNAMIC DEFORMING’S THREE-DIMENSIONAL MODELS

Zhavoronok S. I.

Institute of Applied Mechanics of R.A.S.

An approximated three-dimensional shell’s theory is used to model thick and medium-thickness shells dynamics. A new formulation of motion’s equations as generalized Lagrange’s equations of second kind is proposed. An example of progressive wave’s modeling in the plane layer using three-dimensional shell’s theory is presented.

Key words: three-dimensional shell’s theory, wave’s modeling in the plane layer.

## TO CALCULATION OF THE IS INTENSE-DEFORMED CONDITION OF A SPHERICAL COVER AT LOCAL ACTION

Vidyushenkov S. А.,

Petersburg State Transport University

Zaharov М. V., Sokolov Е. V.,

Petersburg Machine Building State Institute

e-mail: baklava@mail.ru

In article the analytical decision in the closed kind, based on use of individual function is constructed. The received expressions allow to investigate the intense-deformed condition of a spherical cover under the influence of the uniform loading distributed on sector

Key words: spherical cover, the sector, the distributed loading, the intense-deformed condition, individual function.

## APPLICATION OF GRIFFITH ENERGY METHOD TO THE STRENGTH PROBLEM OF NON LINEAR ELASTIC MEDIUM WITH A NOTCH

Arutyunyan A. R., Arutyunyan R. A.

Sankt-Petersburg State University

e-mail: Robert.Arutyunyan@paloma.spbu.ru

On the basis of the power approach of Griffits of a statement criterion of strength for a non-linear – elastic medium with an excision. In a case of absolutely friable environment the received criterion coincides with criterion of Griffits. Generally criterion depends on weeping coefficient of lateral deformation. Thus the hyperbolic character of association of a critical length of fracture from magnitude of a critical stress is saved.

Key words: criterion of strength, non-linear – elastic, excision, stress, fracture.

## NONLINEAR VIBRATIONS OF DISCRETE DISSIPATIV SYSTEMS

Artemyeva l. M., Potapov A. N.

South Ural State University, Chelyabinsk

e-mail: artemyevalm@gmai.com

e-mail: potapov.alni@gmail.com

tel.: 8-351-265-47-85

Based on theory of time analysis mathematical models of nonlinear calculation of frame buildings under the action of pulsed loads developed. The energy dissipation is taken into account. Vibrations of 3-storey frame with columns of ideal elastoplastic material by the action of horizontal pulse load.

Key words: mathematical models, wireframe buildings, horizontal impulses.

## DIRECT METHOD FOR SOLUTION OF LINEAR ALGEBRAIC EQUATION SETS FOR FEA ANALYSIS ON MULTIPROCESSOR SHARED MEMORY COMPUTERS

Fialko S. Yu.

Tadeusz Kosciuszko Cracow University of Technology

e-mail: sfialko@poczta.onet.pl

The method of a solution of systems of the linear algebraic equations with air-break symmetrical matrix originating at application of a finite-element method (FEM) to tasks of a mechanics of a deformable solid and structural mechanics is offered. The method is oriented to multiprocessor table type computers with common storage.

Key words: finite-element method, systems of the linear algebraic equations, computers with multiprocessors.

## ATOMIC-FORCE MICROSCOPY FOR NANOMECHANICS

Mukhin D. S., Smirnov S. Yu., Sinitsyna O. V.,

Meshkov G. B., Filonov A. S., Bolshakova A. V., Yaminsky I. V.

Moscow State University

Advanced Technologies Center

The аtomic-force microscopy is a powerful method for examination of a topography and local mechanical properties of a surface. For raise of self descriptiveness of АСМ-research: it is necessary alongside with topography to analyze force curves and force maps of a surface, the algorithms on operation with which one were implemented in the program « Femto Skan Online».

Key words: nanomechanics, аtomic-force microscopy, force curves and force maps of a surface.

## A GEOMETRICALLY NONLINEAR PLANE STRAIN ANALYSIS OF A PERFECTLY PLASTIC STRUCTURE

Shcherbakova A. O.

South-Ural State University

e-mail: allascherbakova@list.ru

For a solving of a task on deformation of a planar construction from material with ideal plasticity the design model with triangular isoparametric finite elements is generated. She allows to solve tasks about force (definition of stresses on given loads) and about a kinematic loading, when the deflections are set.

Key words: plane deformation, material with ideal plasticity, finite element.

ACCOUNTING CREEP AND STRENGTH CHARACTERISTICS DEGRADATION OF SOIL WHEN CALCULATING THE BEARING CAPACITY OF THIN-WALLED STRUCTURE AND SOIL

Kayumov R. A., Shakirzyanov F. R.

Kazan State University of Architecture and Engineering

e-mail: kayumov@rambler.ru

тел.: (843) 510-47-23

The procedure of an estimation of limiting condition of system a ground – thin-wall construction is offered in view of a degradation of a ground with current of time depending on intensity of the accumulated creeps and change of tight – strained state of system at a step-by-step extraction of a ground from foundation pit. The strength of a ground is valued by criterion of Drucker-Prager. The comparative analysis of an estimation of a breaking load by two expedients is conducted on the basis of the theory of elasto-plastic deformation and on the basis of the theory of a limiting equilibrium.

Key words: limiting condition, system a ground – construction, intensity of the accumulated creeps.

EXPERIMENTAL RESEARCH AND MACROSCOPICAL ENDOCHRONIC THE DESCRIPTION OF LONG CREEP AND DURABILITY OF LEAD

Temnov O. V., Fedorovsky G. D.

Sankt-Petersburg State University

e-mail: g.fed@pobox.spbu.ru

The test data of a lead are reduced at tension in a broad interval of loadings and time. On basis of the endochronic concept the new effective nonlinear indicial equations of a deformability and long-lived strength of a lead are built.

Key words: creep and durability of lead, long-lived strength, endochronic concept.

EXPLORATION OF THE INFLUENCE OF THE MATHEMATICAL MODEL ON THE ACCURACY OF THE CALCULATION FOR THE RADIAL TIRE

Odintsov O. A.

Bauman Moscow State Technical University

e-mail: odintsov@bmstu.ru

The confrontation of results of a solution of a task of contact of the automobile bus to the smooth unyielding basis in three different statements is resulted: with usage of certainly – element complexes Abaqus, Marc, and also author’s complex Cascad FEA. The confrontation is fulfilled for two models of buses: the automobile radial bus with a textile cord in a former, and freight of the bus with the brightly expressed anisotropy of properties structural multilayer shells. As a general performance used for comparison of results, the allocation of tensions of threads of stratums of a cord in meridional section of the bus under centre of a spot of contact is chosen.

Key words: a task of contact, a mathematical model, a radial tire.

ANALYSIS OF OSCILLATIONS OF CONSTRUCTIONS WITH COLLAPSE RELATIONS

Potapov A. N.

South-Ural State University

e-mail: potapov.alni@gmail.com

тел.: 8-(351)-265-47-85

The analysis of oscillations in discrete dissipative systems at collapse relations (connections) was realized. The analytical forms of parameters of the reaction were received. It is shown, what at the moment of collapse connections a number of reaction parameters have discontinuities.

Key words: a discrete dissipative system, vibrations, collapse relations.

ANALYSIS OF SPACE ROD SYSTEMS WITH THE LIMIT EQUILIBRIUM METHOD

Serpik I. N., Alekseytsev A. V.

Bryansk State Technological Academy of Engineering

e-mail: iserpik@online.debryansk.ru

e-mail: dep@iserpik.pptus.ru

e-mail: aalexw@mail.ru

тел.: 8(4832) 74-67-44

The computing scheme for an estimation of a reserve of bearing capacity of dimensioned beams systems is recommend on the basis of the static theorem of a method of a limiting equilibrium. The solution of an extreme task is fulfilled on discrete sets of parameters by developmental simulation.

Key words: beams systems, method of a limiting equilibrium, developmental simulation.

THE DEVELOPMENT OF DURABILITY CHECK IN SINGULARS POINTS KORPERS

Sadikov P. V., Kharlab V. D.

St.-Petersburg State University of Architecture and Civil Engineering

e-mail: vdx33@mail.ru

The updating of a method of check of strength in singular points offered the second co-author is considered. The approach also is grounded on a gradient theory of strength, but tenders diverse transition to a singular point. In particular, the problem solving about a bending of plates under lateral loads under an operation of single forces is resulted.

Key words: singular points, a gradient theory of, strength, a bending of plates.

NUMERICAL SIMULATION OF PECTUS EXCAVATUM SURGICAL TREATMENT

Gavrushin S. S., Gribov D. A.

Moscow State Technical University n.a. N. E. Bauman

Kuzmichev V. A.,

M. Vladimirsky Moscow Regional Research Clinical

Institute

e-mail: gss@spacenet.ru

e-mail: gss@rk9.bmstu.ru

The examination is dedicated to mining of a mathematical model of a breast cage of the man permitting to conduct simulation of process of surgical treatment for correction of funnel-shaped deformation. Usage of modern programmatic complexes for making three-dimensional certainly – element models of breast cages and process of simulation of a procedure Nassa is considered. The adequacy of models is valued. The criteria of an estimation of the received results are established.

Key words: numerical modeling, breast cage of the man, surgical treatment for correction, simulation of a procedure Nassa.

SPALL STRENGTH OF MATERIALS UNDERGOING INTENSIVE SHORT-TERM LOADS

Utkin A. A.,

Institute of Problems of Mechanical Engineering

Smirnov I. V.,

St.-Petersburg State University

e-mail: a.utkin51@gmail.com

Through the structural – time approach is studied spall strength in a broad band of speeds of loading. The effects detected at holding of experiments on spall in nanosecond band of a loading surveyed. The opportunity of their description is rotined through the structural – time approach

Key words: short-term loads, spall strength, structural – time approach.

A NUMERICAL-ANALITIC ANALYSIS OF CONSTRUCTIONS WITH CRACKS

Matrosov A. V.

St.-Petersburg State University

e-mail: avmatrosov@mail.ru

The algorithm of numerical – analytical calculation of elastic systems working in conditions of a plane problem of a theory of elastic strength, founded on decomposition of system on rectangular areas and construction for each of them of a common solution is submitted(shown) on the basis of a method of original functions with their consequent «glueing "together" on lines of contact with usage of conditions of interaction of areas among themselves for construction of system of simple equations of definition of unknowns of coefficients in solutions. The fracture in a construction is modeled by absence of interaction of two adjacent ribs of the next rectangular areas generatrix shore of uncovering fracture. The results of calculation of a beam with vertical fracture located in its lower part are reduced.

Key words: a plane problem of a theory of elastic, a method of original functions, beam with vertical fracture.

THE MASTS DRIVE IN THE ASPECT OF SUBMARINE EVOLUTION

Bogdanov A. S.

St. Petersburg Marine Design Bureau «Malachit»

e-mail: malach@mail.rcom.ru

tel.: (812) 378-65-81

Article dedicate the system analysis results of drive hosting and lowering mast development in the aspect of the indigenous submarine evolution

Key words: drive, electric drive, hydraulic drive, nonpenetrating masts, submarine.

ABOUT THE THEORIES OF DYNAMIC DURABILITY.

THE ENDOCHRONIC CONCEPTION

Fedorovsky G. D.

St.-Petersburg State University

e-mail: g.fed@pobox.spbu.ru

Are analysed and are generalized on datum(basis) endochronic of the concept (natural time) basic engineering theories of nonlinear creep: the theory of crystal ageing (of time hardening), theory of current and theory of a strain hardening with functions of creepage Baly and Norton. In space of this time the modified equations of creepage have a canonical quasilinear aspect. They enable of more complete and unified description of nonlinear processes.

Key words: endochronic of the concept, theories of nonlinear creep.

INVESTIGATION OF THE TRANSPORT CONSTRUCTIONS ELEMENTS’ DEFORMATION COOPERATING WITH THE GROUND OF THE DIFFICULT PHYSICAL NATURE

Balafendieva I. S., Berezhnoi D. V., Sekaeva L. R.

Kazan (Volga region) federal university, Russia

e-mail: dmitri.berezhnoi@ksu.ru

The purpose of operation is the simulation of process of interaction of a ground with underground elements of transport structures. The procedure and results of calculation of deformable constructions partially located in a ground is submitted(shown) in view of their share deformation.

Key words: ground, underground of transport structures, share deformation.

NONLINEAR ANALYSIS OF FERROELECTROELASTICS UNDER COMPLEX ELECTROMECHANICAL LOADING WITH RHEOLOGICAL MODELS

Le-Zakharov S. A., Melnikov B. E., Semenov A. S.

St.-Petersburg State Polytechnical University

e-mail: lezah@mail.ru; strength@mtr.hop.stu.neva.ru;

e-mail: semenov.artem@googlemail.com

For the description of nonlinear scleronomous conduct segnetoelectric and ferroelastics at a combined electromechanical loading the rheological (structural) model permitting to describe an electrical and mechanical hysteresis, curves in the form the butterfly, saturation and depolarization is offered. The comparison of the forecasts of model with experimental data is carried out. The results of a finite – element solution of a series of test nonlinear boundary value problems segnetoelectricelasticsare received.

Key words: nonlinear conduct segnetoelectric, a combined loading, finite – element solution.

ANALYSIS OF THE KINETICS OF FATIGUE, CREEP AND THERMAL FATIGUE CRACK GROWTH OF GAS TURBINE BLADES IN GTE

Nazarenko A. A., Semenov S. G., Semenov A. S.

St.-Petersburg State Polytechnical University

Getsov L. B.,

e-mail: ssgrus@gmail.com;

e-mail: semenov.artem@googlemail.com

With the help of tendered procedures, the growth kinetics of fractures of a different nature in blade of gaseous turbines installations are determined. The changes of aircraft attitude of front of fracture are investigate in during operation of blade of turbines.

Key words: gaseous turbine installations, a blades, kinetics of the growth of front of fractures.

MODELING OF FRACTURE PROCESSES IN PIEZOELECTRIC CERAMICS UNDER COMBINED ELECTROMECHANICAL LOADING

Uystraykh K. B., Semenov A. S., Melnikov B. E.

St.-Petersburg State Polytechnical University

e-mail: kostya111@gmail.com

e-mail: strength@mtr.hop.stu.neva.ru

e-mail: semenov.artem@googlemail.com

тел.: +7-(812)-552-63-03

The results of a numerical modeling of processes of breaking down piezoceramic are shown is model at different orientation of an original polarization with usage of three-dimensional physical nonlinear phenomenological model of a ferroelastic. The confrontation with results of experiments is conducted.

Key words: processes of breaking down piezoceramic, a numerical modeling, three-dimensional physical nonlinear phenomenological model.

FINITE ELEMENT ANALYSIS OF INELASTIC DEFORMATION OF ICEBREAKER TORSION SHAFT UNDER NONPROPORTIONAL VARIABLE LOADING BASED ON ELASTOPLASTIC PROCESS THEORY

Shamkin A. A., Semenov A. S., Melnikov B. E.

St.-Petersburg State Polytechnical University

e-mail: strength@mtr.hop.stu.neva.ru

e-mail: semenov.artem@googlemail.com

On the basis of experimental data the parameters for functionals of the theory of elastoplastic processes are determined at deformation of a material on rectilinear search patterns with a rupture. The comparison of the forecasts of tight – strained state of a material under the theory of a plastic flow, deformation theory, theory of elastoplastic processes and effects(results) of experimental examinations is effected for the given aspect of search patterns. On the basis of model of elastoplastic processes the certainly – element analysis of tight – strained state of a shafting is fulfilled at his(its) simultaneous twist and tension.

Key words: composite tight – strained state of a shafting, theory of elastoplastic processes, elastic-plastic strains, search pattern of deformation with a rupture, software package CES, FE a programmatic complex PANTOCRATOR.

FINITE ELEMENT MODELING OF INELASTIC DEFORMATION AND DESTRUCTION OF REINFORCED CONCRETE STRUCTURES

Benin A. V.,

Petersburg State Transport Universit

Semenov A. S., Semenov S. G., Fedorov I. V.,

St.-Petersburg State Polytechnical University

e-mail: semenov.artem@googlemail.com;

e-mail: ssgrus@gmail.com; fedorov.ilya.v@gmail.com

The conventional approaches of certainly – element problem solving of structural mechanics do not allow correctly to describe bond of armature with concrete. In the given operation at deriving the glow iris, relevant to experiment, of bond with the account ниспадающей of a branch the different methods, bound with introduction of lack of adhesion on a surface of jointing, account of accumulation of damages and usage of inelastic models of deformation of concrete are applied. The opportunities of the surveyed approaches are analysed on an example of problem solving about extraction of a reinforcing bar from the concrete block and bending of a reinforced collar beam.

Key words: finite – element solution, inelastic models of deformation of concrete, extraction of a reinforcing bar from the concrete block.

MODELING OF POLYCRYSTALLINE PIEZOCERAMICS ON THE BASE OF FINITE-ELEMENT HOMOGENIZATION TECHNIQUE

Balke H., Dresden University of Technology

Semenov A. S., Melnikov B. E.

St.-Petersburg State Polytechnical University

e-mail: strength@mtr.hop.stu.neva.ru

The opportunity of forecasting of nonlinear conduct of a polycrystallic piezoelectric ceramics is investigated at composite electromechanical effect on the basis of application of a method of finite – element homogenization for representative volume of the polycrystal consisting of multidomain monocrystals, oriented by a casual fashion. The comparison of results of calculations with results of known experiments for different grades of a piezoelectric ceramics and conditions of a loading is carried out.

Key words: nonlinear conduct, polycrystallic piezoelectric ceramics, a method of finite – element homogenization, multidomain monocrystals oriented by a casual fashion.

ABOUT SIMULATION OF BREAKING DOWN MINERAL PITCH OF CONCRETE COVER BY TENONS ANTI OF SLIP

Bratov V. A., Peters Y. V.

IPMash RAS, St.-Petersburg

St.-Petersburg State University

e-mail: Vladimir@bratov.com;

e-mail: yp@yp1004.spb.edu

It is ground of the Russian and foreign publications, and also experimental examination on a dynamic percussion loading bituminous concrete, conducted in the Nizhniy Novgorod State University, are defined elastic and strength (static and dynamic) property in use bituminous concrete for now. The effect of possible change of properties of such materials on static and dynamic strength of a property bituminous concrete is estimated. The analytical models (task spall are built, a contact task of a Hertz), ground which one the qualitative estimations(rates) of effect of change of properties bituminous concrete on his(its) dynamic strength are conducted in case of loadss, reference for impact by an automobile tenon anti of slip on bituminous concrete to a cloth. Is rotined, that at an abatement of the elastic module bituminous concrete, the critical speed of effect leading to initiation breaking downs in bituminous concrete, increases. Thus, the opportunity of an abatement of velocity of erosive breaking down bituminous concrete of a cloth by change of an elastic moment bituminous concrete, used is rotined at structure of high-speed bands (strips) of highways.

Key words: automobile tenon, breaking down mineral pitch of concrete, simulation, anti of slip, task spall are built, a contact task of a Hertz.