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CALCULATION OF ELEMENTS ON THE BASIS

CALCULATION OF ELEMENTS ON THE BASIS
Elena Artamonova, professor, doctor of technical sciences, full professor

Saratov State Technical University, Russia

Championship participant: the National Research Analytics Championship - "Russia";

the Open European-Asian Research Analytics Championship;

УДК539.3

In this paper we study the deformation and durability cylindrical shell on the basis of the underlying. For a basisof model buildingwe takethe modelof elastic foundationVlasov-Leont'ev. To account for thedeformationof the rheologicalbaseused bythe integratedform of the lawof viscoelastic deformation.The resultingresolving equationsare presentedin incrementsaccording to the methodof successiveperturbationparametersV.V.Petrov.

Keywordsbasic problems, calculation, viscoelastic, deformation,durability,construction.

 

The social and economic changes in Russia have affected all aspects of society life including the construction industry. All participants in construction process became the quite real entities. The modern project is based on three managers: architect, designer and geotechnician. Еarlier understanding of this fact by a project manager will provide the more perfect geotechnical component of a design solution, the more reliable a projecting building, the safer technologies of its construction for surrounding buildings. The list of basic problems for modern city construction includes tight construction deadlines, aspiration to arrange an underground space under construction spot and yard space, increase of loads onto base.

Their successful solution can only be ensured by use of the modern geo-technologies adapted to the engineering-geological conditions of city, as well as by use of the latest tools for calculation the "building-foundation-base"system. The geotechnical norms TCN 50-302-96 directly require to consider the joint work of constructions' bearing structures with their base and correctly to model their joint work.

This paper presents a variant of techniques to solve this problem of the joint calculation for base and elements. Boundary conditions - the simple support. Equation of state in increments:

In tackling theusedmathematical modeling ofstaticviscoelasticstructural elements.You must havethe equilibrium equations, boundary conditions, andequation of staterelations for theequation of stateparameter changeson the parameters ofthe external process.

The approach is based on an extensive literature review of current damage concepts included in current mechanistic-based design procedures, soil permanent deformation laboratory data. Design outputs are compared in terms of reliability and thickness using these design procedures. It is shown that the provides higher reliability values compared to the probabilistic procedure. All the existing subgrades fail distress reliability such as rutting and top down cracking reliabilities. Currently uses a single load P value to deal with variability associated with subgrade strength design. Is used to generate full scale subgrades response and performance data for development and verification of subgrades design criteria.  The physical properties of subgrades structures significantly influence both the response of the subgrades to applied loads and the long-term performance.It is, therefore, of the utmost importance that full scale test subgrades be constructed with uniformity in material properties, layer thicknesses, and other considerations for which non-uniformity might result in nonrepresentative and nontypical behavior and failures. Current mechanistic-based design methods for the design of subgradesuse vertical strain criteria to consider foundationrutting.

A considerable number of measurements of the physical properties test basis  were made at all stages of construction and after construction was completed.  The measurements were made for three purposes: construction quality control, construction acceptance, and material characterization. The material characterization tests were performed to provide information for theoretical modeling and were not related to construction and contractual requirements. The material characterization tests were performed to provide information for theoretical modeling and were not related to construction and contractual requirements.Tests were conducted on the subgrade materials, base subbase, and surface layers. For a basisof  model buildingwe takethe modelof elastic foundation, Vlasov-  Leont'ev [2]  (Fig.1).                                                                  

           

Fig. 1 Modelof elastic foundation.

Here:  u(x,y,z)=0;  v(x,y,z)=0;

Increments of displacements of points:

The unknown functions  ΔUi, ΔWk; and - dimensionless  φi(z), ψk(z).                                                

The resolving equations:

Here [1]:

Elastic modulus - E,

D*, E*- Volterra integral operators.

The theory of hereditary creep includes all the theories based on rheological models. Condition of reliabilityε ≤ εdestructiv., (ε – deformation). To solve this problem apply the variational method of Bubnov-Galerkin, the calculation is performed onsmall intervalsof time.

L =length ofcasing5 m,the wall thicknessh = 0,4m,the shell radiusR =3m, Poisson's ratio ν = 0,35.Displacementgraphics element (curve 1), 2 - the base layer are shown in Fig. 2.

Fig. 2 Displacementcurves

Plots of thestresses and strains ofthe middle surface ofthe shellare shown in fig. 3.Taking into account nonlinearproperties (curve 1) significantlyaffect the results ofthe numerical calculation [3, p.4].

Fig. 3 Stresses and strains

 

 

 References:

  1. Petrov V.V. Construction of model of the non-uniform basis at a varied level of earth waters //Interuniversityscientific collection.- Saratov: SSTU, 2000.- P.6 -10.
  2. Petrov V.V. Dimensional model ofnonlineardeformableheterogeneousbase // Interuniversityscientific collection. - Saratov: SSTU, 2007.- P.6 -12.
  3. Artamonova E.N. On the design ofslabs onthe basis ofa non-uniform //  Moskau: INGN, 2012.- P.4.
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Your rating: None Average: 5.5 (4 votes)
Comments: 8

Elesin Mikhail

Urgency and complexity of the unconstrained setting, unfortunately not in the article draws conclusions on the work.

Krivuts Svetlana

Спасибо за статью. Специфика темы не дает возможности оставить расширенный комментарий.

Galina Pimenova

Работа имеет узкую специфику, посвящена оценке совместной работы "здание - фундамент - основание" и предлагает математический аппарат описания этой совместной работы сооружения и его основания с привлечением одной из геофизических методов оценки. Актуальность и сложность постановки задачи безусловны, учитывая, насколько в настоящее время продвинуты технологии возведения и архитектура. К сожалению, статья не воспринимается как исследование завершенное. Вряд ли можно признать достаточным выяснение зависимости "напряжения - деформации". Как трактовать эти данные? Они определяют какие-то новые возможности, позволяют расширить какие-либо границы?... Почему в статье, где приводится такой сложный математический аппарат, нет выводов? В остальном работа профессиональна, хотя представляться ей лучше в специализированных сборниках, где она сможет собрать больше заинтересованных читателей. Спасибо. Пименова

Elena Artamonova

Благодарю Галину Пименову за рецензию, замечания учту. Да, статья является кусочком многолетнего коллективного (нескольких даже кафедр) исследования по теории нелинейных неоднородных сооружений и методов их расчета для разработки методов расчета, конструирования и компьютерного моделирование уникальных строительных и транспортных сооружений в рамках Фундаментальных и прикладных исследований по приоритетным направлениям развития науки и техники. Представленные в работе графики изменений напряжений и деформаций срединной поверхности элемента показывают, что учет нелинейных свойств материала, меняющихся со временем (кривая 1) существенно влияет на результаты численного расчета; получено также, что стабилизация осадки происходит в течение двух лет. Предложенная методика позволит после вычисления функции перемещения поверхности вычислить значения всех компонентов напряжений в среде основания, а также перемещение w в любой точке. Также при варьировании параметров элемента возможно регулирование величин его перемещений, и, соответственно, перемещений основания, что позволит достигнуть оптимальных условий долговечности. Помимо профильных журналов целесобразно публиковаться во «всемирной паутине», например, на политематическом форуме данного интересного научного проекта. До новых встреч здесь же, наилучшие Новогодние пожелания!

Pavel Derevyankin

In paper this tends to produce smooth curves, which do not lend themselves to high resolution for interpretations? Another feature common to all potential field geophysical methods is that a particular distribution of potential at the ground surface does not generally have a unique interpretation. Although these limitations should be recognized, the non-uniqueness or ambiguity of the resistivity method is scarcely less than with the other geophysical methods. For these reasons, it is always advisable to use several complementary geophysical methods in an integrated exploration program rather than relying on a single exploration method.

Elena Artamonova

Thank you! The issues of deformation and durability cylindrical shell interacting with the underlying base considered with its viscoelasticity. As a starting base is used Vlasov- Leontiev model. For account the deformation of rheological base is used integral form of the deformation law. The obtained resolving equations are presented in increments according method of successive parameters' perturbations that letting go from the nonlinear problem to linearized regarding to load increments. Thus in the process of problem's solution used the mathematical modeling of the problem of static of viscoelastic structural elements with use the basic methods of deformable solid mechanics. As a starting base is used Vlasov- Leontiev model. For account the deformation of rheological base is used integral form of the deformation law. The obtained resolving equations are presented in increments according method of successive parameters' perturbations that letting go from the nonlinear problem to linearized regarding to load increments. Thus in the process of problem's solution used the mathematical modeling of the problem of static of viscoelastic structural elements with use the basic methods of deformable solid mechanics. To obtain the resolution system of equations describing the deformation process, it's necessary to have the equilibrium equations, boundary conditions, equations of state and relations for changes in parameters of the equation of state depending of the parameters of external process. We consider the cylindrical shell of circular shape interacting with the base. As the boundary conditions adopted swivel bearing. D*, E*- Volterra integral operators [3], for example E*=E₀(1- R*); R*∙ f(t) = ∫R(t-τ)∙ f(τ)dτ. Experimentally proved that the deformation of the base ground can be described by the Boltzmann-Volterra law of hereditary creep. The hereditary creep theory includes all the theories based on rheological models. By virtue of the said commonality of Boltzmann - Volterra hereditary creep theory it's possible to improve the accuracy of ground bases deformation studies by mathematical methods.Taking into account nonlinear properties significantly affects the results of the numerical calculation (Fig.2, curve 1); also obtained that the stabilization of draft occurs within two years.

Pavel Derevyankin

In paper this tends to produce smooth curves, which do not lend themselves to high resolution for interpretations?

Kissamedin Guljan Mustahkyzy

Статья заслуживает внимания специалистов в области инженерии.
Comments: 8

Elesin Mikhail

Urgency and complexity of the unconstrained setting, unfortunately not in the article draws conclusions on the work.

Krivuts Svetlana

Спасибо за статью. Специфика темы не дает возможности оставить расширенный комментарий.

Galina Pimenova

Работа имеет узкую специфику, посвящена оценке совместной работы "здание - фундамент - основание" и предлагает математический аппарат описания этой совместной работы сооружения и его основания с привлечением одной из геофизических методов оценки. Актуальность и сложность постановки задачи безусловны, учитывая, насколько в настоящее время продвинуты технологии возведения и архитектура. К сожалению, статья не воспринимается как исследование завершенное. Вряд ли можно признать достаточным выяснение зависимости "напряжения - деформации". Как трактовать эти данные? Они определяют какие-то новые возможности, позволяют расширить какие-либо границы?... Почему в статье, где приводится такой сложный математический аппарат, нет выводов? В остальном работа профессиональна, хотя представляться ей лучше в специализированных сборниках, где она сможет собрать больше заинтересованных читателей. Спасибо. Пименова

Elena Artamonova

Благодарю Галину Пименову за рецензию, замечания учту. Да, статья является кусочком многолетнего коллективного (нескольких даже кафедр) исследования по теории нелинейных неоднородных сооружений и методов их расчета для разработки методов расчета, конструирования и компьютерного моделирование уникальных строительных и транспортных сооружений в рамках Фундаментальных и прикладных исследований по приоритетным направлениям развития науки и техники. Представленные в работе графики изменений напряжений и деформаций срединной поверхности элемента показывают, что учет нелинейных свойств материала, меняющихся со временем (кривая 1) существенно влияет на результаты численного расчета; получено также, что стабилизация осадки происходит в течение двух лет. Предложенная методика позволит после вычисления функции перемещения поверхности вычислить значения всех компонентов напряжений в среде основания, а также перемещение w в любой точке. Также при варьировании параметров элемента возможно регулирование величин его перемещений, и, соответственно, перемещений основания, что позволит достигнуть оптимальных условий долговечности. Помимо профильных журналов целесобразно публиковаться во «всемирной паутине», например, на политематическом форуме данного интересного научного проекта. До новых встреч здесь же, наилучшие Новогодние пожелания!

Pavel Derevyankin

In paper this tends to produce smooth curves, which do not lend themselves to high resolution for interpretations? Another feature common to all potential field geophysical methods is that a particular distribution of potential at the ground surface does not generally have a unique interpretation. Although these limitations should be recognized, the non-uniqueness or ambiguity of the resistivity method is scarcely less than with the other geophysical methods. For these reasons, it is always advisable to use several complementary geophysical methods in an integrated exploration program rather than relying on a single exploration method.

Elena Artamonova

Thank you! The issues of deformation and durability cylindrical shell interacting with the underlying base considered with its viscoelasticity. As a starting base is used Vlasov- Leontiev model. For account the deformation of rheological base is used integral form of the deformation law. The obtained resolving equations are presented in increments according method of successive parameters' perturbations that letting go from the nonlinear problem to linearized regarding to load increments. Thus in the process of problem's solution used the mathematical modeling of the problem of static of viscoelastic structural elements with use the basic methods of deformable solid mechanics. As a starting base is used Vlasov- Leontiev model. For account the deformation of rheological base is used integral form of the deformation law. The obtained resolving equations are presented in increments according method of successive parameters' perturbations that letting go from the nonlinear problem to linearized regarding to load increments. Thus in the process of problem's solution used the mathematical modeling of the problem of static of viscoelastic structural elements with use the basic methods of deformable solid mechanics. To obtain the resolution system of equations describing the deformation process, it's necessary to have the equilibrium equations, boundary conditions, equations of state and relations for changes in parameters of the equation of state depending of the parameters of external process. We consider the cylindrical shell of circular shape interacting with the base. As the boundary conditions adopted swivel bearing. D*, E*- Volterra integral operators [3], for example E*=E₀(1- R*); R*∙ f(t) = ∫R(t-τ)∙ f(τ)dτ. Experimentally proved that the deformation of the base ground can be described by the Boltzmann-Volterra law of hereditary creep. The hereditary creep theory includes all the theories based on rheological models. By virtue of the said commonality of Boltzmann - Volterra hereditary creep theory it's possible to improve the accuracy of ground bases deformation studies by mathematical methods.Taking into account nonlinear properties significantly affects the results of the numerical calculation (Fig.2, curve 1); also obtained that the stabilization of draft occurs within two years.

Pavel Derevyankin

In paper this tends to produce smooth curves, which do not lend themselves to high resolution for interpretations?

Kissamedin Guljan Mustahkyzy

Статья заслуживает внимания специалистов в области инженерии.
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