DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

EXAMINATION OF THE STRESS-STRAIN STATE OF HETEROGENEOUS BODIES THROUGH THE EMPLOYMENT OF THE METHOD OF BOUNDARY EQUATIONS

Вестник МГСУ 7/2012
  • Khodzhiboev Abduaziz Abdusattorovich - Tajik Technical University named after academic M.S. Osimi Candidate of Technical Sciences, Associated Professor, Chair, Department of Structural Mechanics and Seismic Resistance of Structures, +7 (992) 918-89-35-14, Tajik Technical University named after academic M.S. Osimi, 10 Akademikov Radzhabovyh St., Dushanbe, 734042, Republic of Tajikistan; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .

Страницы 96 - 100

The subject matter of the article represents a solution to the problem of the stress-strain state of a heterogeneous structure resting on the elastic half-plane. The condition of continuity of deformations and stresses alongside the line of contact between the sections of the structure and between the structure and the half-plane is observed; the system of boundary equations is derived on the basis of the above. Coefficients associated with unknown values of the structure are identified with the help of Kelvin's fundamental solutions, while the coefficients associated with the half-plane are identified on the basis of the Mindlin's solutions. The mathematical model and the analytical algorithm developed by the author are implemented within the framework of the examination of the stress-strained state of an earth dam.
Analysis of application of the algorithm has proven that concentrated shearing stresses emerge in the area of the upper wall alongside the line of contact between the structure and the half-plane, while mechanical properties of sections of the structure and the half-plane influence the distribution of vertical relocations of the half-plane contour line.

DOI: 10.22227/1997-0935.2012.7.96 - 100

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STRESS-STRAIN STATE OF AN ELASTIC HALF-PLANE AT A LINEAR SHIFT OF A PART OF ITS BOUNDARY

Вестник МГСУ 2/2017 Том 12
  • Bogomolov Aleksandr Nikolaevich - Institute of Architecture and Civil Engineering of Volgograd State Technical University (IACE VSTU) Head of Department of Hydraulic and Earthwork Structures, Deputy Director for Science, Institute of Architecture and Civil Engineering of Volgograd State Technical University (IACE VSTU), 1 Akademicheskaya str., Volgograd, 400074, Russian Federation.
  • Ushakov Andrey Nikolaevich - 1 Akademicheskaya str., Volgograd, 400074, Russian Federation Professor, Department of Mathematics and Information Technology, 1 Akademicheskaya str., Volgograd, 400074, Russian Federation, 1 Akademicheskaya str., Volgograd, 400074, Russian Federation.

Страницы 184-192

Loads cause vertical shifts of foundations of all structures, and the safe operation of buildings depends on the value thereof. The article presents a solution of the problem of stress distribution in a homogeneous and isotropic soil mass under vertical linear shift of a part of its boundary obtained by the complex potentials method. Expressions for stress components and strain components of the second basic boundary plane problem of the theory of elasticity for half-plane at the linear shift (the law of linear shift) of a part of its boundary are determined in a closed form. Patterns of isolines of stress and strain components are built; they illustrate that numerical values of all like-named components located at corresponding points on opposite sides of the symmetry axis are equal in value but opposite in sign. The formula of subsidence that occurs at the shift of the half-plane boundary part was derived. The value of subsidence is directly proportional to the boundary part shift value and inversely proportional to the lateral soil pressure coefficient value. Conclusions: expressions for stress and strain components of the second basic boundary plane problem of the theory of elasticity for half-plane are obtained in a closed form. Values of the stress and strain components are symmetric relative to the origin and opposite in sign; the formula of subsidence for half-plane boundary vertical shift is obtained on the basis of the expression for the vertical strain component.

DOI: 10.22227/1997-0935.2017.2.184-192

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