Sedov Continuum Mechanics Volume 1. Continuum Mechanics, Multiphase Media Dynamics


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DI. Bardzokas, A.I. Zobnin. Mathematical modeling of physical processes in composite materials with a periodic structure. 2003 273 pp. djvu. 3.1 MB.
In this book on modern level mathematical methods for solving a wide class of problems in the theory of elasticity, thermal conductivity, thermo- and electroelasticity for composites with a regular structure are presented. For specialists in the field of continuum mechanics, composites, as well as graduate students and students of the Faculty of Mechanics and Mathematics and Physics, specializing in the field of materials science.

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F. Bell. Experimental foundations of the mechanics of deformable media. 1984 djvu.
Parting 1. Small deformations. 595 pages 8.3 Mb.
Part 2. Finite deformations. 430 pages 5.4 Mb.
The book is a translation of the first three sections of one of the volumes (VIa / 1) of the "Physical Encyclopedia", published by the Springer publishing house. The first part contains sections: introduction, non-linearity at small deformations and linear approximation. This monograph is unprecedented in terms of breadth of coverage and depth of analysis of the fundamental results of experimental solid mechanics. Experiments that were the source or turning point in the construction of the theory are discussed with particular care. Part II includes a section - finite deformations. The emergence of the latter is considered in various conditions, in various bodies and, in particular, taking into account the previous history of the stress state.
You can see the table of contents BELL. HTML
For specialists working both in the field of experimental mechanics and in the field of theory, and will also be useful for teachers, graduate students and students

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Berdichevsky V.L. Variational principles of continuum mechanics. 2083 year. 450 pages djvu. 4.4 MB.
The book systematically outlines the variational principles of fluid and gas mechanics and the mechanics of a solid deformable body. Direct qualitative methods of the calculus of variations are described (the theory of duality of variational problems, two-sided estimates, the study of functionals depending on a small parameter). Applications to the problem of averaging periodically and randomly microinhomogeneous media, to the construction of the theory of elastic shells and rods, and the theory of dispersed mixtures are considered.
For specialists in the field of continuum mechanics and applied mathematics.

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Vatulyan O.V. Inverse problems in the mechanics of a deformable solid body. 2007 224 pp. djvu. 1.3 MB.
Considered various classes inverse problems of mechanics of a deformable solid body - retrospective, boundary, coefficient, geometric, in which the coefficients of differential operators are determined from some additional experimental information about the solution, initial conditions, boundary conditions, geometry of internal defects (cavities, cracks). Statements of problems, fundamentals of general approaches in the theory of inverse and ill-posed problems, features of iterative schemes and regularization methods for solving specific inverse problems of the theory of elasticity, acoustics, viscoelasticity, electroelasticity, and thermal conductivity are outlined. Both schemes for constructing operator equations with compact operators and methods for proving uniqueness theorems are presented, and various ways constructing approximate solutions; numerical results based on regularization methods are presented.
For scientific and engineering workers in the field of mechanics of a deformable solid body, numerical methods, defectometry, geophysics, experimental mechanics, for senior students and graduate students specializing in the areas of "mechanics", "applied mathematics".

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G.E. Vekshtein. Physics of continuum media in problems. 2002 208 pp. PDF. 1.8 MB.
Readers are offered problems with solutions related to various sections of electrodynamics of continuous media, hydrodynamics, theory of elasticity and mechanics of liquid crystals. Along with typical learning tasks, a large number of problems constructed on the basis of striking and instructive phenomena and effects that have become "classics" in recent decades (Landau damping, nonlinear wave interaction, solitons, the Freedericksz transition, etc.). The manual is designed for students and teachers of physical specialties of universities.

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Gorshkov A.G., Starovoitov E.I., Yarovaya A.V. Mechanics of layered viscoelastic-plastic structural elements. 2005 year. 576 pp. djvu. 5.9 MB.
Statements and methods for solving problems of statics and dynamics of layered structural elements under complex force, thermal and radiation effects are systematically presented. The rheonomic and plastic properties of the layer materials are taken into account. A number of solutions for three-layer rods, plates and shells are given.
For researchers, engineers, graduate students and senior students of universities engaged in research in the field of solid mechanics.

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G Ya. Galin et al. CONTINUOUS MEDIA MECHANICS IN PROBLEMS. 1996 djvu.
1. Volume 1. Theory and problems. 396 pages 5.0 Mb. Volume 1 contains about 1000 problems and exercises in all major areas of continuum mechanics, including: general foundations of continuum mechanics and thermodynamics, fluid mechanics, gas dynamics, elasticity theory, plasticity theory, electrodynamics, basic modeling. Each section has a brief theoretical introduction - a summary of the necessary basic concepts and relationships.
2. Volume 2. Answers and solutions. 395 pages 4.7 Mb. Volume 2 contains answers, instructions and solutions to about 1000 problems and exercises given in Volume 1 in all major sections of continuum mechanics, including: general foundations of continuum mechanics and thermodynamics, fluid mechanics, gas dynamics, elasticity theory, plasticity theory, basic modeling.
For students, teachers and researchers in the field of mechanics and physics.

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Gorshkov A.G., Rabinsky L.N., Tarlakovsky D.V. Fundamentals of tensor analysis and continuum mechanics: Textbook. 2000. 214 pages 2.2 Mb.
The textbook consists of two parts: tensor calculus and continuum mechanics. In the first part, the algebra of tensors on linear spaces and spaces with a quadratic metric is considered. The basic concepts of invariants are given. Tensor analysis is constructed in arbitrary Euclidean point spaces with partial use of the theory of Riemannian spaces. In the second part, based on the apparatus of tensor analysis in arbitrary curvilinear coordinate systems, the main sections of continuum mechanics are outlined: the theory of deformations and stresses, thermodynamics, closed systems, and the formulation of the corresponding initial-boundary value problems. The substantiation of linearized models is given. Examples of classical models of continuous media are given.
For university students studying continuum mechanics and its sections, as well as graduate students of the relevant profile.

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O.V. Golubev. A course in continuum mechanics. Tutorial. 1972 368 pp. djvu. 6.0 Mb.
The course contains four parts. The first of them, common to all parts, outlines the basic concepts of kinematics and the basic equations of motion of an arbitrary continuous medium. The second part is devoted to the presentation of the elements of some sections of hydrodynamics: the equations of motion of an ideal and viscous fluid, aerodynamics, wave motions near the boundary layer. Special attention this section focuses on plane-parallel motions and two-dimensional motions along curved surfaces. The theory of filtration, which is the subject of the third part, is considered from the point of view of applying the methods of hydrodynamics to solving technical boundary value problems. The last, fourth, part is devoted to the equations of the theory of elasticity and their application to certain specific problems. The second and third parts, as well as partially the third part, are independent of each other and can be studied separately.
The book is intended for students of physics and mathematics faculties of pedagogical universities.

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Godunov S.K., Romensky E.I. Elements of continuum mechanics and conservation laws. 1998 280 pp. djvu. 2.8 MB.
This book is an extended and modern version monographs by S.K. Godunov "Elements of continuum mechanics", published in 1978 by the publishing house "Nauka" (Moscow) and awarded in 1993. Academician M.A. Lavrentiev of the Russian Academy of Sciences. This monograph was written on the material of a university course given in Novosibirsk state university, and contained based on the joint work of the author and E.I. Romensky exposition of the principles underlying the phenomenological derivation and qualitative study of the complete system of differential equations in continuum mechanics. This book contains revised chapters that were included in the monograph by S.K. Godunov "Elements of continuum mechanics", as well as new chapters based on recent research on the structure of conservation laws governing various processes in continuums (electrodynamics, superconductivity, superfluidity, etc.). p.), thermodynamic identities. Particular attention is paid to the connection of these identities and conservation laws with the criteria for the correct formulation of the corresponding mathematical problems.
For researchers, teachers, graduate students and students of physical and mathematical faculties of universities and higher educational institutions with in-depth physical and mathematical training.

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Eliseev VV Mechanics of a Deformable Solid Body. 2006 231 pp. PDF. 1.1 Mb.
The mechanics of a deformable solid body is one of the most developed and perfect areas of mathematical physics; it is an important part of the physical picture of the world. It is of great practical importance, without it it is impossible to seriously design structures - buildings, bridges, ships, etc. In this small book, the author tried to show both perfection and accessibility to the perception of modern mechanics of a deformable body.
He hopes that the book will also be a teaching aid - even for calculators.

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Zarubin V.S., Kuvyrki, G.N. Mathematical models of thermomechanics. 2002 168 pages djvu. 2.0 Mb.
The main approaches to the construction of mathematical models of a continuum based on modern concepts of the thermodynamics of irreversible processes are outlined. The main attention is paid to the consideration of the generality of constructing models of a thermoelastic continuum, a linear fluid, thermoviscoelastic and thermoplastic media based on the concepts of velocity-type continuums, media with internal state parameters, and media with memory.
For scientists, engineers, graduate students and senior students of technical universities specializing in continuum mechanics and mathematical modeling.

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Zozulya V.V., Martynenko A.V., Lukin A.N. Continuum mechanics. 2003 600 pages djvu. 4.2 MB.
The proposed course on continuum mechanics (MCS) summarizes many years of teaching experience in teaching technical and natural science disciplines built on its basis (from classical theory of elasticity to CCM models in biology and medicine) at the Kharkiv National Automobile and Highway Technical University (HADI), at the Independent University state of Yucatan (Mexico) and in Kharkov national university them. V.N. Karazin. However, this book includes personal experience scientific research authors over the last quarter of a century. For students of the Mechanics and Mathematics departments of universities studying the MCC course; for students of technical specialties in the study of subjects based on knowledge of the MSS. For graduate students and teachers, the textbook can help with an in-depth study of the subject and with the lectures of the course "Continuum Mechanics".

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Ivlev D.D. Mechanics of plastic bodies. In 2 volumes. 2001-2002. djvu. .
Volume 1. 446 pages 2.6 Mb. The theory of ideal plasticity. The contents of the book are the author's articles devoted to the theory of ideal plasticity and its applications. The articles contain a presentation of the construction and study of the general relations of the theory of ideal plasticity based on a statically determinable system of hyperbolic type equations that adequately describe the shear nature of plastic deformation. Generalizations of the theory for the case of compressible and anisotropic media are presented, solutions are given for the indentation of rigid dies, the introduction of rigid bodies, the compression of a plastic layer by rough plates, etc.
Volume 2. 446 pages 3.3 Mb. General issues. Rigid-plastic and elastic-plastic state of bodies. hardening. deformation theories. Complex environments. The contents of the book are the author's articles on the theory of plasticity and its applications. The articles contain a study of the problems of an ideal elastic-plastic body, models of a hardening plastic body, as well as complex media. Deformation theories of plasticity are considered. Solutions to the problems of determining the ideal elastic-plastic and hardening state of bodies, etc. are given. The books are intended for scientists, graduate students, senior students specializing in the field of mechanics of deformable bodies and structures.

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Ishlinsky A.Yu., Ivlev D.D. Mathematical theory of plasticity. 2003 704 pages 3.0 Mb.
The monograph is devoted to one of the main sections of the mechanics of a deformable solid body - the mathematical theory of plasticity, where the authors own the results that are of fundamental importance for theory and applications. The construction of general relations of the theory of ideal plasticity, hardening material, as well as materials with complex rheological properties is outlined. The application of the theory to technological processes processing of materials by pressure, deformation and flow of plastic, viscoplastic bodies, etc.
It is intended for scientists, engineers, graduate students, senior students specializing in the field of mechanics of inelastic deformation of bodies and structures.

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A.G. Kalugin. Mechanics of anisotropic fluids. 2005 year. 64 pages pdf. 379 Kb.
Methods for constructing models of anisotropic fluids are outlined. A model of nematic liquid crystals is presented, the derivation of the equations of motion using variational and group methods of continuum mechanics is shown, and a number of exact solutions are given. The model of anisotropic simple liquids, the connection of the equations describing such a medium with the equations of magnetohydrodynamics and the model of nematic liquid crystals is shown. For students, graduate students and a wide range of specialists involved in the study of various models of continuous media,

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Korobeinikov S.M. Nonlinear deformation solids. year 2000. 262 pp. djvu. 2.3 MB.
The book provides a methodologically consistent formulation of geometrically and physically nonlinear problems in the mechanics of a deformable solid body, including problems of buckling and contact interactions tel. Equations are formulated with respect to velocities or increments of unknown quantities. Weak forms of the equations and variational formulations of the problems are given. The application of the finite element method to the solution of quasi-static and dynamic problems is considered. The following material models are used: isotropic linear elastic, incompressible nonlinear elastic Mooney - Rivlin, elastoplastic, thermoelastic plastic with allowance for creep deformations. Procedures for numerical solutions of nonlinear problems based on step-by-step integration of equilibrium (motion) equations are given. Peculiarities of procedures for numerical solution of problems of buckling and contact of bodies are considered.

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K.V. Krasnobaev. Lectures on the fundamentals of continuum. Uch. allowance. 2005 year. 108 pages djvu. 1.2 MB.
The proposed manual includes material that is generally integral part well-known course by L. I. Sedov “Continuum Mechanics” and aiming to introduce students to the circle of problems solved in continuum mechanics, to formulate, on the basis of physical laws, a system of equations describing the motion of a continuum. Considerable attention in the course is also paid to the study of classical models of continuous media and the formulation of initial and boundary conditions in the study various types movements.
For students of the Faculty of Mechanics and Mathematics of Moscow State University. M.V. Lomonosov, as well as for students of higher educational institutions studying in the specialties "Mechanics" and "Applied Mathematics".

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Fist. Fractal mechanics of materials. 2002 304 pp. djvu. 3.0 MB.
The methods of fractal theory, as a rule, are used in the most complex sections of theoretical physics - quantum field theory, statistical physics, the theory of phase transitions and critical phenomena.
The purpose of the monograph is to show that the ideas and methods of the theory of fractals can be effectively used in the traditional, classical section of mechanics - the mechanics of materials. The range of materials considered is quite wide: dispersed materials from metal powders to oxide ceramics, polymers, composite materials with various matrices and fillers, and printing materials. A statistical theory of the structure and elastic-strength properties of fractal disperse systems has been constructed. A fractal approach to the description of the processes of consolidation of dispersed systems has been developed. A self-consistent theory of the effective modulus of elasticity of disperse-reinforced composites with a stochastic structure has been developed in the full range of changes in the volume fraction of the filler. The theory has been generalized to composites with bimodal packing of fillers, as well as to composite materials with reinforcement along complex combined schemes. The application of the theory of fractals to study the microstructure and physical and mechanical properties of printing materials and technology of printing processes is considered.

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Levin V.A., Zingerman K.M. Plane problems of the theory of multiple superposition of large deformations. Solution methods. 2002 272 pp. djvu. 1.4 MB.
New plane problems on the successive formation of stress concentrators are considered in detail. various shapes in preloaded bodies. Methods for their solution, implemented in a specialized software complex"Overlay", based on analytical calculations on a computer.
The book is structured in such a way that a reader with minimal training in the field of deformable solid mechanics can read it without resorting to additional literature, and a specialist can read only those sections that are of interest to him, or simply use the results of solving specific problems.
For scientists, engineers, teachers, graduate students and students dealing with the problems of fracture mechanics, continuum mechanics, as well as specializing in the field of calculations of structural elements weakened by stress concentrators.

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Levin V.A., Morozov E.M., Matvienko Yu.G. Selected nonlinear problems of fracture mechanics. 2004 408 pages djvu. 5.7 MB.
A wide range of issues in fracture mechanics is covered, starting with micromechanisms of deformation and fracture of a crystal lattice, engineering approaches to the problems of fracture mechanics and ending with a mathematical analysis of the formation, coalescence and development of material defects. The physics and mechanics of microfracture are considered, including the formation and growth of microcracks. different types. The basic principles and methods of linear and nonlinear fracture mechanics are given along with the corresponding fracture criteria. Attention is paid to selected special problems of fracture mechanics, including the mechanisms of deformation and fracture of polymers. Mathematical methods for solving plane problems of the theory of elasticity under finite deformations under conditions of physical and geometric nonlinearity are presented in detail. Numerous examples of calculating the redistribution of stress and strain fields for different options stage-by-stage multistage loading of multiply connected areas. For scientists, engineers, teachers, graduate students and senior students dealing with the problems of continuum mechanics, fracture mechanics and calculations of structural elements weakened by cracks or other stress concentrators.

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Lotov K.V. Physics of continuous media. Inst. computer research 2002 144 pp. djvu. 800 Kb.
The book contains a concise presentation of the course of mechanics and physics of continuous media, read for students of the Faculty of Physics. It includes the fundamentals of continuum electrodynamics, hydrodynamics and elasticity theory.
For students and graduate students of physical specialties of universities, teachers.

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Maze J. Theory and problems of continuous media mechanics. 1974 318 pp. djvu. 4.6 MB.
The book sets out general principles continuum mechanics and describes the most commonly used mathematical models of continuums. The presentation is accompanied by carefully selected tasks. total number about five hundred; about two-thirds of them are given with solutions. This allows using the book as a kind of collection of problems in the course of continuum mechanics.
The book is written clearly and precisely. High methodological advantages make it possible to use it as a textbook for technical universities and universities in the course of continuum mechanics. It will be of interest to a wide range of applied mathematicians, mechanics and engineers working in the field of continuous mechanics.

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Ovsyannikov L.V. Introduction to continuum mechanics. Uch. manual in 2 parts. 1976-77 years. 75+69 pages djvu. in one archive 7.0.
The proposed textbook for the course "Introduction to Continuum Mechanics" was written based on lectures given by the author for a number of years at the Faculty of Mechanics and Mathematics of the Novosibirsk State University. It summarizes the mathematical apparatus used in mechanics and describes the principles for constructing basic models of continuous media. In methodological terms, this manual has a number of significant differences from the existing textbooks on this discipline and therefore can be useful not only for students of relevant specialties, but also for those who are already familiar with the material presented.

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Pobedrya, Georgievsky. Fundamentals of continuum mechanics. Lecture course. 2006 270 pp. djvu. Size 1.8 Mb.

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Yu.N. Radaev. Spatial problem of the mathematical theory of plasticity. 2004 142 pp. pdf. 1.9 MB.
The presented work is an attempt to present the current state of research on spatial problems of the mathematical theory of plasticity. The book contains a complete and systematic presentation of methods and results related to the study of three-dimensional equations of the mathematical theory of plasticity. In the presentation of the material, the emphasis is on new general methods that provide a solution applied tasks mathematical theory of plasticity.
A number of new results are included concerning the three-dimensional equations of the mathematical theory of plasticity with the Tresca plasticity condition and the flow law associated with it for the stress states corresponding to the edge of the yield surface. A remarkable invariant vector form of the equilibrium equations has been found, which makes it possible to study the geometry of the field of principal directions corresponding to the largest (lowest) principal stress.
A classification of solutions of three-dimensional static equations is given depending on the vorticity of the specified field of principal directions. Invariants are found that retain their values ​​along the lines of principal stresses. An analysis is given of three-dimensional equations of the mathematical theory of plasticity for increments of stresses and strains in orthogonal isostatic coordinates. New approaches are used to analyze the plane and axisymmetric problems. Self-similar solutions of the axisymmetric problem of the mathematical theory of plasticity are studied and new self-similar solutions generalizing the well-known Shield solutions are obtained.
It is intended for students of the Mechanics and Mathematics departments of universities specializing in Mechanics and Applied Mathematics, specializing in the field of mechanics of a deformable solid body, aiming to familiarize themselves with state of the art this science and the prospects for its development.

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V.V. Selivanov, researcher ed. Applied continuum mechanics. In 3 volumes. The textbook is based on the material of lectures given by the authors to students of the Moscow State Technical University. N.E.
Volume1. Fundamentals of continuum mechanics. The first volume of the complex of textbooks of the series contains the main elements of vector and tensor analysis, necessary and sufficient for studying short course"Fundamentals of continuum mechanics", stated with the help of the mathematical apparatus of tensor calculus. Concepts and corresponding physical quantities used to describe the motion and state of the material continuum. Equations and relations are derived that are valid for describing the behavior of any continuous media, regardless of their state of aggregation and physical and mechanical characteristics.
The main rheological models of continuous media are described and the corresponding physical relationships are given. General principles for setting problems in continuum mechanics and examples of setting a number of practical problems are given. The appendix contains examples of solving typical problems. 375 pp. djvu. 3.0 MB.
Volume 2. The second volume of the textbook presents modern ideas about the process of destruction of a deformable body under conditions of static, dynamic and shock wave loading.
The main phenomenological models of static, dynamic and shock wave destruction of a deformable body are systematized - from the physical representation of the process of deformation and destruction of the body to detailed description brittle and ductile fracture from the standpoint of micro- and macro-fracture.
The problems of body strength during deformation, as well as the formation and propagation of cracks in brittle and ductile materials, are considered. The fundamentals of scattered damage mechanics and linear fracture mechanics are given.
The processes of propagation of shock waves and rarefaction waves in solids, the mechanics and morphology of high-speed deformation and fracture of materials under shock-wave loading are described in detail. 420 pages djvu. 6.6 MB.
Volume 3. Numerical methods in problems of physics of fast processes. The third volume of the complex of textbooks of the Applied Continuum Mechanics series deals with the use of difference methods of computational mathematics in relation to problems in the physics of fast processes. The fundamental concepts of the theory of difference schemes are considered, the main difference schemes and methods for the numerical solution of one-dimensional problems are presented: grid methods, numerical method of characteristics, methods of the "particles in cells" family. Statements, numerical solution algorithms and results of solving a number of one-dimensional and two-dimensional non-stationary problems using Lagrangian, Euler-Lagrangian and Euler methods are presented. The problems of the technology of conducting a computational experiment are discussed and examples are given that demonstrate the possibilities of numerical simulation as a tool for studying fast processes.
The material of this textbook is intended for the initial acquaintance of students of higher technical educational institutions with the theory of difference schemes and the basics practical use numerical methods in solving problems of explosion physics and mechanics of high-speed impact of various deformable bodies and media. 520 pages djvu. 4.1 MB.

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Sedov L.I. Chief Editor. Mechanics in 3 volumes. A.N.USSR. djv
Volume 1. GENERAL AND APPLIED MECHANICS. 1968 416 pages 4.7 Mb.
Theory of motion stability. Theory of vibrations. Dynamics of nonholonomic systems. Theory of optimal control systems. Mechanics of gyroscopic and navigation systems. Mechanics of space flight. Celestial.mechanics.Theory of mechanisms and machines.
Volume 2. MECHANICS OF LIQUID AND GAS. 1970 880 pages 11.9 Mb.
Theory of jets. Hydrodynamics of motion of bodies in water at high speeds. Some questions of hydrodynamics of surface waves. Aerodynamics of steady flow around bodies at subsonic speeds. Hydrodynamic theory of lattices. Theory of supersonic gas flows. Shock waves, strong explosions, physical processes in gas flows. Propagation of blast waves. Phenomena of unlimited cumulation. Theory of combustion and detonation. The mechanics of rarefied gas and plasma and magnetohydrodynamics. Mechanics of turbulence. Dynamics of viscous liquids and gases, theory of laminar and turbulent boundary layers. Hydrodynamic (numerical) "short-term weather forecast. Movement of liquids and gases in porous media. Quantum fluid properties. Hydraulics. Industrial aerodynamics.
Volume 3. MECHANICS OF A DEFORMABLE SOLID BODY. 1772. 480 pages 8.3 Mb. A theory of model building based on the use of the basic variational equation obtained with the help of the first and second laws of thermodynamics is developed, taking into account the thermodynamics of irreversible processes. Along the way, a general original theory of variations is developed. Methods are given for deriving closed systems of equations containing the Euler equations, equations of state, and conditions on surfaces of strong discontinuities. Developed general tricks reduction of three-dimensional problems to two-dimensional and one-dimensional (plates, shells, rods, etc.). A number of new models for matter and fields have been constructed.
For specialists in the field of continuum mechanics, graduate students and students of universities and technical colleges.

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Khristianovich S.A. Continuum mechanics. 1981 485 pp. djvu. 5.8 MB.
The book contains the works of academician S. A. Khristianovich on various issues continuum mechanics, closely related to critical issues modern technology. The publication is intended for a wide range of specialists in mechanics, engineers and physicists of various profiles.

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Ziegler. Mechanics of Solids and Fluids. Second edition. 2002 860 pages djvu. 6.7 MB.
The monograph was written by the famous Austrian scientist Franz Ziegler. This book provides a clear and consistent presentation of the fundamentals of solid and fluid mechanics.
Separately, modern approximate methods for solving static and dynamic problems of mechanics (the Rayleigh-Ritz-Galerkin method, the finite element method, etc.) are considered.
An important feature monograph is a detailed consideration of a large number of examples that have a clear technical focus, as well as the selection of a large number of interesting and diverse tasks in the main sections of the course, intended for independent solution.
The book is intended for students, graduate students and scientists specializing in various fields of natural science and technology. It can serve as a textbook and a collection of tasks on the mechanics of solids and fluids.

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Chernyak, Suetin. Continuum mechanics. Textbook allowance. 2006 350 pages djvu. Size 3.3 Mb.
The fundamental physical concepts of kinematics and dynamics of a continuum are outlined, its various models(solid, liquid and gas). Most of the textbook is devoted to the hydrodynamics of an ideal and viscous fluid. Elements of the theory of elasticity, gas dynamics and magnetohydrodynamics are included. It is shown how theoretical provisions are used to solve engineering tasks and to explain some natural phenomena. Questions for self-control and examples of problem solving given at the end of each chapter will help the reader to better understand the theory, acquire skills for independent solution of problems in continuum mechanics. Approved by the Ministry of Education and Science Russian Federation as a teaching aid for students of higher educational institutions studying in the direction of preparation of bachelors "Physics".

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M.E. Eglit editor. Continuum mechanics in problems. In 2 volumes. 1996 djvu. in one archive 9.7 Mb.
Volume 1. Theory and problems. 396 pages. Volume 1 contains about 1000 problems and exercises in all major sections of continuum mechanics, including: general foundations of continuum mechanics and thermodynamics, fluid mechanics, gas dynamics, elasticity theory, plasticity theory, electrodynamics, basic modeling. Each section has a brief theoretical introduction - a summary of the necessary basic concepts and relationships.
Volume 2. 395 pages. Volume 2 contains answers, instructions and solutions to about 1000 problems and exercises given in Volume 1 in all main sections of continuum mechanics, including: general foundations of continuum mechanics and thermodynamics, fluid mechanics, gas dynamics, elasticity theory, theory plasticity, basics of modeling.
For students, teachers and researchers in the field of mechanics and physics.

Continuum Mechanics, Volume 2, Sedov L.I., 2004.

In the two-volume textbook by Academician L. I. Sedov, mechanics, thermodynamics, electrodynamics and the corresponding mathematical methods are presented as a whole in relation to solid, liquid and gaseous bodies and the theory of the electromagnetic field. Mathematical methods and, in particular, tensor calculus are given in an improved and simple interpretation.

HYDROMECHANICS.
Hydrostatics.
Let us consider some sections of hydrostatics, i.e., the theory of equilibrium of liquids and gases with respect to a chosen coordinate system.
The results and methods of hydrostatics have great importance for many practical tasks. In hydrostatics, problems are considered about the equilibrium of water in the oceans and air in the atmosphere; problems on the forces acting from the side of liquid and gas on floating ships, submarines and balloons; problems of the stability of ships floating on the surface of the water, and many other problems.

Application of integral relations to the finite volumes of the material environment in steady motion.
AT chapters III and V in relation to arbitrary finite volumes of the medium, the main integral relations of a mechanical and thermodynamic nature are formulated. For continuous motions they are equivalent to the corresponding fundamental differential equations; in ch. VII integral relations were used to obtain conditions on the surfaces of strong discontinuities.
Let us now consider some important applications of the integral dynamic relations and the law of conservation of energy, written in Chap. VII in the form of equations (4.8)-(4.11).


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  • Mechanics in the USSR for 50 years, Volume 3, Mechanics of a Deformable Solid Body, Sedov L.I., 1972
  • Mechanics in the USSR for 50 years, Volume 2, Fluid and gas mechanics, Sedov L.I., 1970
  • Mechanics in the USSR for 50 years, Volume 1, General and Applied Mechanics, Sedov L.I., 1968
  • Fundamentals of macroscopic theories of gravity and electromagnetism, Sedov L.I., Tsypkin A.G., 1989

The following tutorials and books:

M.: Nauka, 1970, 568 pages.
Hydromechanics.
Hydrostatics.
General theory of steady motions of ideal fluids and gases. Bernoulli integral.
The phenomenon of cavitation.
Bernoulli integral for adiabatic flows of a perfect gas.
Influence of compressibility on the shape of stream tubes. Elementary theory of the Laval nozzle.
Application of integral relations to the finite volumes of the material environment in steady motion.
Interaction of liquids and gases with streamlined bodies in steady motion.
Basic elements of the theory of jet thrust.
Cauchy - Lagrange.
Potential motions of an incompressible fluid. Properties of harmonic functions.
The problem of the motion of a sphere in an infinite volume of an ideal incompressible fluid.
Kinematic problem of the motion of a rigid body in an unlimited volume of an ideal incompressible fluid.
Energy, momentum, angular momentum of a liquid when a rigid body moves in it and the foundations of the theory of added masses.
Forces of action of an ideal fluid on a body moving in an infinite mass of fluid.
Gas motions with small perturbations.
Riemann.
Movement of a ball inside a viscous incompressible fluid Movement of an incompressible viscous fluid in cylindrical pipes.
Turbulent fluid motions.
Laminar Boundary Layer Equations.
Boundary layer in an incompressible fluid flow around a flat plate. Blasius problem.
Some important effects of the motion of a viscous fluid in a boundary layer.
Determination of the field of velocities by given vortices and sources.
Important examples of vortex fields.
Dynamic theory of cylindrical vortices.
Motion of a system of continuously distributed vortices in an ideal fluid.
Theory of elasticity.
Introductory remarks.
Elastic body model.
Problems of uniaxial tension of an elastic bar.
Deformations and stresses arising in round pipe from an elastic material under the action of internal and external pressures (the Lame problem.
Principle of Saint-Venant.
Beam bending problem.
Torsion of cylindrical rods.
Methods of resistance of materials in problems of beam bending.
Variational methods in the theory of elasticity.
Elastic waves in an isotropic medium.
Theory of plasticity.
Some effects that arise during the deformation of solid bodies and are not described within the framework of the elastic body model.
Residual deformations. Load surface.
Basic constitutive relations in the theory of plastic bodies.
Examples of models of plastic bodies.
The problem of torsion of a cylindrical rod made of an elastic-plastic material without hardening.
Introduction to the theory of plane problems of the theory of elasticity and the theory of cracks.
Plane Problems of the Theory of Elasticity.
Stress concentration.
Theory of cracks.
Literature.
Subject index.

Continuum mechanics, dynamics of multiphase media

  • Aleshkevich V.A., Dedenko L.G., Karavaev V.A. Continuum mechanics. Lectures. Moscow: Faculty of Physics, Moscow State University, 1998 (djvu)
  • Berdichevsky V.L. Variational principles of continuum mechanics. M.: Nauka, 1983 (djvu)
  • Vorovich I.I., Lebedev L.P. functional analysis and its applications in continuum mechanics. M.: University book, 2000 (djvu)
  • Vorozhtsov E.V. Difference methods for solving problems in continuum mechanics (textbook). Novosibirsk: NSTU, 1998 (pdf)
  • Golubeva O.V. A course in continuum mechanics. M.: graduate School 1972 (djvu)
  • Goldstein M.N. Mechanical properties of soils (2nd edition). M .: From the literature on construction, 1971 (djvu)
  • Goldstein R.V., Yentov V.M. Qualitative Methods in continuum mechanics. M.: Nauka, 1989 (djvu)
  • Gorodtsov V.A. Sofia Kovalevskaya, Paul Painlevé and integrability of nonlinear equations of continuums. M.: Fizmatlit, 2003. (djvu)
  • Grishin A.M., Fomin V.M. Conjugate and non-stationary problems of the mechanics of reacting media. Novosibirsk: Science, 1984 (djvu)
  • Gubaidullin D.A. Dynamics of two-phase vapor-gas-drop media. Kazan: Publishing House of the Kazan Mathematical Society, 1998 (djvu)
  • Sommerfeld A. Mechanics of deformable media. M.: IL, 1954 (djvu)
  • Kolesnichenko A.V., Marov M.Ya. Turbulence of multicomponent media. M.: Nauka, 1999 (djvu)
  • Kukushkin S.A., Slezov V.V. Dispersed systems on the surface of solids (evolutionary approach): mechanisms for the formation of thin films. SPb.: Nauka. 1996 (djvu)
  • Kutateladze S.S., Nakoryakov V.E. Heat and mass transfer and waves in gas-liquid systems. Novosibirsk: Science, 1984 (djvu)
  • Logachev I.N., Logachev K.I. Aerodynamic fundamentals of aspiration. St. Petersburg: Himizdat, 2005 (pdf)
  • Maze J. Theory and problems of continuous media mechanics. M.: Mir, 1974 (djvu)
  • Nakoryakov V.E., Pokusaev B.G., Shreiber I.R. Wave dynamics of gas and vapor-liquid media. Moscow: Energoatomizdat. 1990
  • Neville A.M. properties of concrete. M.: Ed. lit. on construction, 1972 (djvu)
  • Nigmatulin R.I. Dynamics of multiphase media, part 1. M.: Nauka, 1987 (djvu)
  • Nigmatulin R.I. Dynamics of multiphase media, part 2. M.: Nauka, 1987 (djvu)
  • Prager V. Introduction to continuum mechanics. M.: IL, 1963 (djvu)
  • Sedov L.I. Continuum mechanics, volume 1. M.: Nauka, 1970 (djvu)
  • Sedov L.I. Continuum mechanics, volume 2. M.: Nauka, 1970

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