Pile-foundation system shock loading in an axisymmetric approach

Vestnik MGSU 8/2015
  • Vasenkova Ekaterina Viktorovna - Moscow State University of Civil Engineering (National Research University) (MGSU) Senior Lecturer, Department of Higher Mathematics, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zuev Vladimir Vasil’evich - Moscow State Institute of Radio Engineering, Electronics and Automation (MIREA Doctor of Physical and Mathematical Sciences, Professor, chair, Department of Applied Mathematics and Informatics, Moscow State Institute of Radio Engineering, Electronics and Automation (MIREA, 20 Stromynka str., Moscow, 107996, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 101-108

The basic problem of structural mechanics, namely the problem of pile shock loading sunk in a foundation, has been examined in an axisymmetric approach within defining relations for irreversible deformations offered earlier in the space of deformations. As a model of the theory of plasticity, the Mises model generalized by the authors has been accepted, the use of which solves a nonstationary system of nine two-dimensional equations with various entry and boundary conditions. Enlightened attitudes use approximate engineering approaches which allow estimating the behavior of a pile-foundation system. A solution is constructed mainly with the use of the theory of linear-elastic continuum. However they do not enable to consider various peculiarities of deformation behavior of soils and pile materials and to give an appropriate detailed picture of a system mode of deformation. Mechanical peculiarities of the behavior of foundation and pile materials discovered recently demand more enlightened attitudes to analyze a mode of deformation in a pile-foundation system considering both plasticity and fracture. The offered approach enables to give a complete picture of a mode of deformation in a pile-foundation system at any time and a picture of occurrence and development of plasticity and fracture zones.

DOI: 10.22227/1997-0935.2015.8.101-108

References
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Essential FEM statements applied to structural mechanics problems. Part 1

Vestnik MGSU 11/2014
  • Ignat’ev Aleksandr Vladimirovich - Volgograd State University of Architecture and Civil Engineering (VSUACE) Candidate of Technical Sciences, Associate Professor, Department of Structural Mechanics, Volgograd State University of Architecture and Civil Engineering (VSUACE), 1 Akademicheskaya str., Volgograd, 400074, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 37-57

In the article, the author shares his classification of FEM statements that may serve as a guide in respect of the huge number of works that are published and being published with a view to the FEM efficiency improvement. The author provides a summarized history of the finite element method, and classifies its configurations and versions. The author also provides FEM statements applicable to the deflection method. Derivation of the rigidity matrix designated for shaft-based finite elements is demonstrated in the article. The author employs one-dimensional framing as an example aimed to demonstrate the convergence of the FEM method in terms of deflections, if the finite element grid is refined. However it is also noteworthy that in the event of a fine grid, the finite element designed for plates does not coincide with the finite element of a thin plate designed as the initial physical model. However, the system of equations, provided by the author, takes account of the influence produced by the load onto the finite element and generates the exact solution irrespective of any finite values of the length that are equal to the physical model of a finite element.

DOI: 10.22227/1997-0935.2014.11.37-57

References
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  52. Bathe K.-Yu. Metody konechnykh elementov [Finite Elements Methods]. Transl. Into Russian. Moscow, FIZMATLIT Publ., 2010, 1024 p.
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Main formulations of the finite element method for the problems of structural mechanics. Part 2

Vestnik MGSU 12/2014
  • Ignat’ev Aleksandr Vladimirovich - Volgograd State University of Architecture and Civil Engineering (VSUACE) Candidate of Technical Sciences, Associate Professor, Department of Structural Mechanics, Volgograd State University of Architecture and Civil Engineering (VSUACE), 1 Akademicheskaya str., Volgograd, 400074, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 40-59

The author offers a classification of Finite Element formulations, which allows orienting in a great number of the published and continuing to be published works on the problem of raising the efficiency of this widespread numerical method. The second part of the article offers examination of straight formulations of FEM in the form of displacement approach, area method and classical mixed-mode method. The question of solution convergence according to FEM in the form of classical mixed-mode method is considered on the example of single-input single-output system of a beam in case of finite element grid refinement. The author draws a conclusion, that extinction of algebraic equations system of FEM in case of passage to the limit is not a peculiar feature of this method in general, but manifests itself only in some particular cases. At the same time the obtained results prove that FEM in mixed-mode form provides obtaining more stable results in case of finite element grid refinement in comparison with FEM in the form of displacement approach. It is quite obvious that the same qualities will appear also in two-dimensional systems.

DOI: 10.22227/1997-0935.2014.12.40-59

References
  1. Gorodetskiy A.S., Zavoritskiy V.I., Lantukh-Lyashñhenko A.I., Rasskazov A.O. Metod konechnykh elementov v proektirovanii transportnykh sooruzheniy [Finite Element Method in Transport Constructions Design]. Moscow, Transport Publ., 1981, 143 p. (In Russian)
  2. Postnov V.A., Kharkhurim I.Ya. Metod konechnykh elementov v raschetakh sudovykh konstruktsiy [Finite Element Method in Ship Structures Calculation]. Leningrad, Sudostroenie Publ., 1974, 344 p. (In Russian)
  3. Sekulovich M. Metod konechnykh elementov [Finite Element Method]. Translated from Serbian Yu.N. Zueva, editor V.Sh. Barbakadze. Moscow, Stroyizdat Publ., 1993, 664 p. (In Russian)
  4. Ignat’ev A.V. Osnovnye formulirovki metoda konechnykh elementov v zadachakh stroitel’noy mekhaniki. Chast’ 1 [Essential FEM Statements Applied to Structural Mechanics Problems. Part 1]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2014, no. 11, pp. 37—57. (In Russian)
  5. Bogner F., Fox R., Schmit L. A Cylindrical Shell Discrete Element. AIAA. 1967, vol. 5, no. 4, pp. 745—750. DOI: http://dx.doi.org/10.2514/3.4056.
  6. Allman D.J. Treugol’nye konechnye elementy dlya rascheta izgibaemykh plastin pri postoyannykh i lineyno raspredelennykh izgibayushchikh momentakh [Trigonal Finite Elements for Bending Plates Calculation in Case of Permanent and Linearly Distributed Bending Moments]. Raschet uprugikh konstruktsiy s ispol’zovaniem EVM [Calculation of Elastic Structures Using Computer]. Translated from English, editor A.P. Filin. Leningrad, Sudostroenie Publ., 1974, pp. 80—101. (In Russian)
  7. Klochkov Yu.V. Razvitie teorii lineynogo i nelineynogo deformirovaniya obolochek na osnove MKE s uchetom smeshcheniya kak zhestkogo tselogo i izmeneniya tolshchiny [Development of the Theory of Linear and Non-linear Deformation of Shells Basing on FEM with Account for the Displacement as Stiff Entire and Change of the Width]. Dissertation of the Doctor of Technical Sciences. Volgograd, Volgogradskaya GSKhA Publ., 2001, 326 p. (In Russian)
  8. Bathe K.-J., Wilson E.L. Numerical Methods in Finite Element Analysis, New Jersey, Prentice-Hall, 1976, 528 p.
  9. Bathe K. Metody konechnykh elementov [Finite Elements Methods]. Transl. from English by V.P. Shidlovskiy. Moscow, FIZMATLIT Publ., 2010, 1024 p. (In Russian)
  10. Tsybenko A.S. Primenenie treugol’nykh trekhuzlovykh nesoglasovannykh elementov dlya resheniya osesimmetrichnykh zadach teorii uprugosti [Application of Trigonal Nonconforming Elements for Solving Axisymmetric Tasks of Elasticity Theory]. Problemy plastichnosti [Elasticity Problems]. 1986, no. 3, pp. 79—83.
  11. Semenov V.A., Semenov P.Yu. Hybrid Finite Elements for Analysis of Shell Structures. Proc. International Congress ICSS—98, 22—26 June 1998, Moscow, Russia. Moscow, 1998, vol. 1, pp. 244—251.
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The history and development prospects of one of the methods for solving multidimensional problems of structural mechanics

Vestnik MGSU 12/2015
  • Stankevich Anatoliy Nikolaevich - Kyiv National University of Construction and Architecture (KNUCA) Candidate of Technical Sciences, Associate Professor, chair, Department of Strength of Materials, Kyiv National University of Construction and Architecture (KNUCA), 31 Vozdukhoflotskiy prospekt, Kiev, 03680, Ukraine; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 76-91

The equations describing stress-strain state of the majority of the calculation models in linear statement are considered in frames of the theory of elasticity (statics and dynamics) and thermoelasticity. These equations are defined in three-dimentional space or with account for symmetry in teo-dimentional space and are belong to complicated tasks of mathematical physics. The famous mathematicians and nechanics had already offered solutions for the simplest cases of such tasks. But it is impossible to solve the majority of tasks, especially the dynamic ones, using analythical solutions. In this work the authors deal with the modern methods for solving multidimensional problems of structural mechanics. The attention is paid to the methods of dimension reduction of the initial equations. The development and improvement of the method of lines is considered in detail, the shortcomings of the existing approaches are enumerated and the possible development direction of the method to the new task classes is offered.

DOI: 10.22227/1997-0935.2015.12.76-91

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SCIENTIFIC APPROACHES TO CALCULATION AND DESIGN OF LARGE-SPAN STRUCTURES

Vestnik MGSU 2/2017 Volume 12
  • Sysoeva Elena Vladimirovna - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Technical Sciences, Associate Professor, Department of Buildings and Constructions Design, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 131-141

The article presents the four stages of creation and development of the theory of plate and shell which led to the development of a mechanism of calculation of spatial structures of large span buildings and constructions on an advanced level. Each of the stages of the unique buildings calculation method development includes a description of the main achievements in the sphere of structural mechanics, the theory of elasticity and resistance of materials which became the basis for the modern theory of calculation of plates and shells. In the first stage the fundamentals of solid mechanics were developed; this is presented in works of such outstanding scientists as G. Galilei, J.-L. Lagrange, R. Hooke, L. Euler, Kirchhoff, A. Law etc. Development of the theory of plate and shell would be impossible without these works. But absence of such construction material as reinforced concrete did not enable engineers and architects to create a thin roof. Thickness of coverings was intuitively overstated to ensure durability of buildings. The second stage is interesting by formulation of the general theory of calculation of plate and shell and by transition from the working state analysis of structures to the limit state analysis. Beginning of use of reinforced concrete resulted in decrease of a roof thickness to the diameter of its base, compared to buildings made of stone and brick. The third stage is characterized by development of computational systems for calculation of strength, stability and oscillations of core and thin-walled spatial structures based on the finite element method (FEM). During this period a design of buildings and constructions with spans over 200 m with the use of metal was begun. Currently, or during the fourth stage, structures with the use of metal and synthetic materials for spans up to 300 meters are designed. Calculations of long-span buildings and structures are performed using FEM and taking into account different types of nonlinearity. Each stage selected from the history of construction is exemplified by completed projects, hereat characteristics of roofs indicating the applied construction material are given. Transition from natural stone to concrete, metal and synthetic materials in construction of large-span buildings is illustrated in the table. At the end of each stage the scientists’ and designers’ main achievements in the sphere of science, construction and engineering education are shown.

DOI: 10.22227/1997-0935.2017.2.131-141

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