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Вопросы динамики сыпучей среды

139764

Г.А.Гениев

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The scientific report contains research on the theory of motion of a granular medium. Equations for the dynamics of a granular medium are given for the case of a plane problem, and a general technique for their solution is presented. Several specific problems are considered: the problem of soil bulging under load, the problem of a retaining wall; a general solution of the problem of the flow of bulk material in a silo along the so-called second form of outflow is given. The question of Or-causes of increased horizontal pressures on the walls of the silo during the outflow of bulk is analyzed. The book is intended for researchers and graduate students. INTRODUCTION The study of the stress state of a granular body is one of the oldest problems in continuum mechanics. The foundations of the theory of the limiting equilibrium of a granular medium, proposed in the middle of the 18th century by Coulomb, laid the foundation for systematic research in the field of theory and practice of granular solids. Without dwelling on the history of the issue, we note the direction in the theory of granular medium that appeared at the beginning of the 20th century, characterized by the use of equilibrium equations and the equation of limit equilibrium, which is valid for each point of a granular body. This direction received the most complete analytical completion in the works of V. V. Sokolovsky, who gave a complete theory of the statics of a granular medium. The attempt made in this work to obtain a theory of the motion of a granular medium (dynamics of a granular medium) was caused by the urgent need for a theoretical generalization of the laws governing the movement of granular medium, in particular, when they flow out of containers1. The paper presents the material reported in an abbreviated form at the 'Conference on the study of strength, plasticity and creep of building materials [1, 12] (TsNIPS, Moscow, 1954), as well as at a meeting on the theory of elasticity, the theory of plasticity and theoretical 1 Large experimental studies related to the study of the laws of flow of bulk from vertical containers were carried out by S. G. Takhtamyshev, M. S. Bernshtein, V. S. Kim. Articles by A. Yu. Ishlinsky [3] and Shield [4] are devoted to the issue of the theory of motion of a granular medium, the content of which is considered below. 3 TABLE OF CONTENTS Page Introduction .................. 3 § 1. Basic physical premises and derivation of equations state of a moving granular medium....... 4 § 2. Research and solution of the basic system of differential equations of the dynamics of a granular medium ... 17 § 3. Derivation of the fifth equation of the system for the second (macro- structural) solution ......... 30 § 4. Investigation of the basic system of differential equations of the dynamics of a granular medium for a macrostructural version of the solution .............................. 39 § 5. Generalization of solutions to the case of a compressible granular Wednesdays ........................ 49 § 6. Volros for setting boundary conditions ...... 58 § 7. The law of mechanical similarity for a moving granular medium.................'59 § 8. The problem of unilateral bulging of soil under load ................., bG § 9. The problem of a retaining wall............. 75 § 10. The problem of the movement of bulk in a vertical container according to the second form of expiration ........... 79 § 11. The problem of the unsteady motion of a compressible granular medium in a container according to the second form of outflow with a variable angle of internal friction ....... 92 Literature..................120

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Publisher Академия науки и архитектуры СССР
Publication date 1958
Number of Pages 120
Bookbinding Softcover

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