Sedov continuum mechanics 1. Books on continuum mechanics for students and schoolchildren. Continuum mechanics, dynamics of multiphase media

Continuum mechanics, dynamics of multiphase media

  • Aleshkevich V.A., Dedenko L.G., Karavaev V.A. Continuum mechanics. Lectures. M.: Physics Department of 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. Continuum mechanics course. M.: graduate School, 1972 (djvu)
  • Goldstein M.N. Mechanical properties of soils (2nd edition). M.: From the literature on construction, 1971 (djvu)
  • Goldshtein R.V., Entov V.M. Qualitative methods in continuum mechanics. M.: Nauka, 1989 (djvu)
  • Gorodtsov V.A. Sofia Kovalevskaya, Paul Painlevé and integrability nonlinear equations continuous media M.: Fizmatlit, 2003. (djvu)
  • Grishin A.M., Fomin V.M. Conjugate and nonstationary problems of mechanics of reacting media. Novosibirsk: Science, 1984 (djvu)
  • Gubaidullin D.A. Dynamics of two-phase vapor-gas-droplet 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 of thin film formation. SPb.: Science. 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 principles of aspiration. St. Petersburg: Khimizdat, 2005 (pdf)
  • Maze J. Theory and problems of continuum mechanics. M.: Mir, 1974 (djvu)
  • Nakoryakov V.E., Pokusaev B.G., Shreiber I.R. Wave dynamics of gas and vapor-liquid media. M.: Energoatomizdat. 1990 (djvu)
  • Neville A.M. Properties of concrete. M.: Publishing house. 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

The EqWorld website contains extensive information on solutions for various classes of ordinary differential equations, partial differential equations (equations of mathematical physics), integral equations, functional equations and other mathematical equations.

2004-2017 A. D. Polyanin

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

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

HYDROMECHANICS.
Hydrostatics.
Let's consider some sections of hydrostatics, i.e., the theory of equilibrium of liquids and gases relative to the chosen coordinate system.
The results and methods of hydrostatics have great importance for many practically important tasks. Hydrostatics deals with problems of the equilibrium of water in the oceans and air in the atmosphere; problems about the forces acting from liquid and gas on floating ships, submarines and balloons; problems about the stability of ships floating on the surface of water, and many other problems.

Application of integral relations to finite volumes of the material environment during steady motion.
In Chapters III and V, in relation to arbitrary finite volumes of the medium, the main integral relations of 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's now look at some important applications integral dynamic relations and the law of conservation of energy, written down in Chap. VII in the form of equations (4.8)-(4.11).


Free download e-book in a convenient format, watch and read:
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  • Mechanics in the USSR over 50 years, Volume 3, Mechanics of deformable solids, Sedov L.I., 1972
  • Mechanics in the USSR over 50 years, Volume 2, Mechanics of liquid and gas, Sedov L.I., 1970
  • Mechanics in the USSR over 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 textbooks and books:

M.: Nauka, 1970, 568 pp.
Hydromechanics.
Hydrostatics.
General theory of steady motions of ideal liquids and gases. Bernoulli integral.
The phenomenon of cavitation.
Bernoulli integral for adiabatic flows of a perfect gas.
The influence of compressibility on the shape of current tubes. Elementary theory of the Laval nozzle.
Application of integral relations to finite volumes of the material environment during steady motion.
Interaction of liquids and gases with streamlined bodies during steady motion.
Basic elements of the theory of jet propulsion.
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 on 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 basics of the theory of added masses.
Forces of influence of an ideal fluid on a body moving in an unlimited mass of fluid.
Gas motions with small disturbances.
Riemann.
Movement of a ball inside a viscous incompressible fluid. Movement of an incompressible viscous fluid in cylindrical pipes.
Turbulent fluid movements.
Laminar boundary layer equations.
Boundary layer when an incompressible fluid flows around a flat plate. Blasius' problem.
Some important effects of the motion of a viscous fluid in the boundary layer.
Determination of the velocity field from 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 on uniaxial tension of an elastic beam.
Deformations and stresses arising in a round pipe made of elastic material under the influence of internal and external pressures (Lame problem.
Saint-Venant's principle.
Beam bending problem.
Torsion of cylindrical rods.
Methods of strength of materials in problems of beam bending.
Variational methods in the theory of elasticity.
Elastic waves in an isotropic medium.
Plasticity theory.
Some effects that arise during the deformation of solids and cannot be described within the framework of an elastic body model.
Residual deformations. Loading surface.
Basic defining 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.


All books can be downloaded for free and without registration.

DI. Bardzokas, A.I. Zobnin. Mathematical modeling of physical processes in composite materials of periodic structure. 2003 273 pp. djvu. 3.1 MB.
This book presents modern 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. For specialists in the field of continuum mechanics, composites, as well as graduate students and students of the faculties of mechanics, 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.
Part 1. Minor deformations. 595 pp. 8.3 MB.
Part 2. Finite deformations. 430 pp. 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, nonlinearity at small deformations and linear approximation. This monograph is unprecedented in its breadth of coverage and depth of analysis of the fundamental results of experimental mechanics of solid deformable bodies. Experiments that were the source or turning point in the construction of the theory are especially carefully discussed. Part II includes a section on finite deformations. The emergence of the latter is considered in different conditions, in different 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 450 pp. djvu. 4.4 MB.
The book systematically presents the variational principles of fluid and gas mechanics and the mechanics of solid deformable bodies. 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 deformable solids. 2007 224 pp. djvu. 1.3 MB.
Various classes of inverse problems of mechanics of a deformable solid are considered - retrospective, boundary, coefficient, geometric, in which, using some additional experimental information about the solution, the coefficients of differential operators, initial conditions, boundary conditions, and the geometry of internal defects (cavities, cracks) are determined. Statements of problems, the foundations 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; various ways constructing approximate solutions, numerical results based on regularization methods are presented.
For scientific and engineering workers in the field of mechanics of deformable solids, numerical methods, defectometry, geophysics, experimental mechanics, for senior and graduate students specializing in the areas of mechanics and applied mathematics.

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G.E. Vekshtein. Continuum physics in problems. 2002 208 pp. PDF. 1.8 MB.
Readers are presented with problems with solutions related to various sections of electrodynamics of continuous media, hydrodynamics, theory of elasticity and mechanics of liquid crystals. Along with standard educational problems, a large number of problems are presented that are based on the consideration of bright and instructive phenomena and effects that have become “classics” in recent decades (Landau damping, nonlinear interaction of waves, solitons, Fredericksz transition, etc.). The manual is intended for students and teachers of physical specialties at universities.

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Gorshkov A.G., Starovoytov E.I., Yarovaya A.V. Mechanics of layered viscoelastoplastic 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 influences are systematically presented. The rheonic and plastic properties of the layer materials are taken into account. A number of solutions are given for three-layer rods, plates and shells.
For researchers, engineers, graduate students and senior university students engaged in research in the field of mechanics of deformable solids.

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G Ya. Galin et al. MECHANICS OF CONTINUUM MEDIA IN PROBLEMS. 1996 djvu.
1. Volume 1. Theory and tasks. 396 pages 5.0 MB. Volume 1 contains about 1000 problems and exercises in all main sections of continuum mechanics, including: general fundamentals of continuum mechanics and thermodynamics, fluid mechanics, gas dynamics, theory of elasticity, theory of plasticity, electrodynamics, fundamentals of modeling. Each section contains a brief theoretical introduction - a summary of the necessary basic concepts and relationships.
2. Volume 2. Answers and solutions. 395 pp. 4.7 MB. Volume 2 contains answers, instructions and solutions to about 1000 problems and exercises given in Volume 1 on all main sections of continuum mechanics, including: general fundamentals of continuum mechanics and thermodynamics, fluid mechanics, gas dynamics, theory of elasticity, theory of plasticity, fundamentals of 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 pp. 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 quadratic metric. The basic concepts of invariants are given. Tensor analysis is constructed in arbitrary point Euclidean spaces with partial use of the theory of Riemann spaces. In the second part, based on the apparatus of tensor analysis in arbitrary curvilinear coordinate systems, the main sections of continuum mechanics are presented: the theory of deformations and stresses, thermodynamics, closed systems and the formulation of corresponding initial-boundary value problems. A rationale for linearized models is given. Examples of classical continuum models are given.
For university students studying continuum mechanics and its branches, as well as graduate students of the relevant profile.

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O.V. Golubeva. Continuum mechanics course. Textbook. 1972 368 pp. djvu. 6.0 MB.
The course contains four parts. The first of them, common to all parts, sets out 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 elements of some sections of hydrodynamics: 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 the application of hydrodynamic methods to the solution of technical boundary value problems. The last, fourth part is devoted to the equations of the theory of elasticity and their application to some specific problems. The second and third parts, as well as part of the third part, are independent of each other and can be studied separately.
The book is intended for students of physics and mathematics faculties 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 expanded and modern version of the monograph by S.K. Godunov “Elements of continuum mechanics”, published in 1978 by the Nauka publishing house (Moscow) and awarded the prize named after them in 1993. Academician M.A. Lavrentieva Russian Academy Sci. 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's presentation of the principles underlying the phenomenological derivation and qualitative study of the complete system of differential equations of continuum mechanics. This book contains revised chapters that were included in S.K. Godunov’s monograph “Elements of Continuum Mechanics”, as well as new chapters based on recent research on the structure of conservation laws governing various processes in continuous media (electrodynamics, superconductivity, superfluidity and etc.), thermodynamic identities. Particular attention is paid to the connection between 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 physics and mathematics faculties of universities and higher education institutions educational institutions with in-depth physical and mathematical training.

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Eliseev V.V. Mechanics of deformable solids. 2006 231 pp. PDF. 1.1 MB.
Mechanics of a deformable solid is one of the most developed and advanced areas of mathematical physics; it is an important part of the physical picture of the world. It is of great practical importance; without it, serious design of structures is impossible - buildings, bridges, ships, etc. In this small book, the author sought to show both perfection and accessibility modern mechanics deformable body.
He hopes that the book will also be a teaching aid - even for computer scientists.

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Zarubin V.S., Kuvyrki, G.N. Mathematical models of thermomechanics. 2002 168 pp. djvu. 2.0 MB.
The main approaches to constructing mathematical models of a continuous medium based on modern concepts of the thermodynamics of irreversible processes are outlined. Main attention is paid to the consideration of the generality of constructing models of thermoelastic continuum, 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 the field of continuum mechanics and mathematical modeling.

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Zozulya V.V., Martynenko A.V., Lukin A.N. Continuum mechanics. 2003 600 pp. djvu. 4.2 MB.
The proposed course in continuum mechanics (MCM) summarizes many years of experience in teaching courses in technical and natural science disciplines built on its basis (from classical theory elasticity to MCC models in biology and medicine) in the Kharkov National Highway technical university(HADI), at the Independent University of the State of Yucatan (Mexico) and in Kharkov national university them. V.N. Karazin. At the same time, this book also includes personal experience scientific research authors over the past quarter century. For students of mechanical and mathematical faculties of universities studying the MSS course; for students technical specialties when studying subjects based on knowledge of MSS. The textbook can help graduate students and teachers with in-depth study subject and when delivering lectures in the course “Continuum Mechanics”.

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Ivlev D.D. Mechanics of plastic bodies. In 2 volumes. 2001-2002. djvu. .
Volume 1. 446 pp. 2.6 MB. The theory of ideal plasticity. The content of the book consists of articles by the author 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 definable system of hyperbolic type equations that adequately describe the shear nature of plastic deformation. Generalizations of the theory are presented for the case of compressible and anisotropic media, solutions are given for indentation of rigid dies, introduction of rigid bodies, compression of a plastic layer by rough plates, etc.
Volume 2. 446 pp. 3.3 MB. General issues. Rigid-plastic and elastoplastic state of bodies. Hardening. Deformation theories. Complex environments. The content of the book consists of articles by the author devoted to the theory of plasticity and its applications. The articles contain a study of problems of an ideal elastoplastic body, models of a hardening plastic body, as well as complex media. Deformation theories of plasticity are considered. Solutions to problems of determining the ideal elastoplastic and hardening state of bodies, etc. are given. The books are intended for researchers, graduate students, and 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 pp. 3.0 MB.
The monograph is devoted to one of the main sections of the mechanics of a deformable solid - the mathematical theory of plasticity, where the authors own results that are of fundamental importance for theory and applications. The construction of general relationships of the theory of ideal plasticity, a hardening material, as well as materials with complex rheological properties is outlined. An application of the theory to technological processes of processing materials by pressure, deformation and flow of plastic, viscoplastic bodies, etc. is given.
Intended for scientists, engineers, graduate students, and senior students specializing in the 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 liquids 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 is also considered, and the connection between 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 of 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, including problems on loss of stability and contact interactions of bodies. The equations are formulated with respect to rates or increments of unknown quantities. Weak forms of equations and variational formulations of problems are given. The application of the finite element method to solving quasi-static and dynamic problems is considered. The following material models are used: isotropic linear-elastic, incompressible nonlinear-elastic Mooney - Rivlin, elastoplastic, thermoelastoplastic taking into account creep deformations. Procedures for numerical solutions of nonlinear problems based on step-by-step integration of equilibrium (motion) equations are presented. The features of procedures for numerical solution of problems of loss of stability and contact of bodies are considered.

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K.V. Krasnobaev. Lectures on the fundamentals of continuum. Uch. allowance. 2005 year. 108 pp. djvu. 1.2 MB.
The proposed manual includes material that, in general, is integral part L. I. Sedov’s famous course “Continuum Mechanics” and aimed at introducing students to the range of problems solved in continuum mechanics, and formulating, on the basis of physical laws, a system of equations describing the motion of a continuous medium. Considerable attention in the course is also paid to the study of classical models of continuous media and the issues of setting initial and boundary conditions when studying 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.
Methods of fractal theory are usually used in the most complex sections theoretical physics- quantum field theory, statistical physics, theories 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 branch of mechanics - 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, printing materials. A statistical theory of the structure and elastic-strength properties of fractal disperse systems has been constructed. A fractal approach to describing the processes of consolidation of dispersed systems has been developed. A self-consistent theory of the effective modulus of elasticity of dispersed-reinforced composites with a stochastic structure has been developed in the full range of changes in the volume fraction of the filler. The theory is generalized to composites with bimodal packing of fillers, as well as to composite materials with reinforcement according to complex combined patterns. The application of the theory of fractals to study the microstructure and physical and mechanical properties of printing materials and printing process technology is considered.

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Levin V.A., Zingerman K.M. Plane problems in the theory of multiple superposition of large deformations. Solution methods. 2002 272 pp. djvu. 1.4 MB.
New plane problems on the sequential formation of stress concentrators are considered in detail various shapes in preloaded bodies. Methods for solving them are presented, implemented in a specialized software package “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 mechanics of deformable solids can read it without reference to additional literature, and a specialist can read only those sections that are interesting to him, or simply use the results of solving specific problems.
For scientists, engineers, teachers, graduate students and students dealing with problems of fracture mechanics, continuum mechanics, and also 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 pp. djvu. 5.7 MB.
Covers a wide range of topics in fracture mechanics, starting with micromechanisms of deformation and fracture crystal lattice, engineering approaches to problems of fracture mechanics and ending with mathematical analysis of the formation, merger 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 are given of calculating the redistribution of stress and strain fields at different options step-by-step multi-stage loading of multi-connected areas. For scientists, engineers, teachers, graduate students and senior students dealing with 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 summary of the course on mechanics and physics of continuous media, given to students of the Faculty of Physics. It includes the fundamentals of continuum electrodynamics, hydrodynamics and elasticity theory.
For undergraduate and graduate students of physics majors at universities and teachers.

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Maze J. Theory and problems of continuum mechanics. 1974 318 pp. djvu. 4.6 MB.
The book outlines the general principles of continuum mechanics and describes the most commonly used mathematical models of continuum. The presentation is accompanied by carefully selected tasks total number about five hundred; about two-thirds of them are provided with solutions. This allows you to use the book as a kind of collection of problems for a course in continuum mechanics.
The book is written clearly and clearly. High methodological advantages allow it to be used as a textbook for technical schools 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 solid mechanics.

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Ovsyannikov L.V. Introduction to continuum mechanics. Uch. manual in 2 parts. 1976-77. 75+69 pp. djvu. in one archive 7.0.
The proposed textbook for the course “Introduction to Continuum Mechanics” is written based on lectures given by the author over a number of years at the Faculty of Mechanics and Mathematics of NSU. It briefly presents the mathematical apparatus used in mechanics and describes the principles of constructing basic models of continuum In methodological terms, this manual has a number of significant differences from existing textbooks on this discipline and therefore can be useful not only to students of relevant specialties, but also to people 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 into 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. When presenting the material, the emphasis is on new general methods, which provide solutions to applied problems of the 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 associated flow law for stress states corresponding to an 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 greatest (smallest) principal stress.
A classification of solutions to three-dimensional static equations is given depending on the vorticity of the specified field of the main directions. Invariants have been found that retain their values ​​along the principal stress lines. An analysis of three-dimensional equations of the mathematical theory of plasticity for increments of stress and strain in orthogonal isostatic coordinates is given. Using new approaches, an analysis of a plane and axisymmetric problem was carried out. Self-similar solutions to the axisymmetric problem of the mathematical theory of plasticity have been studied and new self-similar solutions that generalize the known Schild solutions have been obtained.
Intended for students of mechanical and mathematical faculties of universities with specialties “Mechanics” and “Applied Mathematics”, specializing in the field of mechanics of deformable solids, aiming to familiarize themselves with current state this science and the prospects for its development.

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V.V. Selivanov, scientific. ed. Applied continuum mechanics. In 3 volumes. The textbook is based on the material of lectures given by the authors to students of MSTU. N.E.
Volume 1. Fundamentals of continuum mechanics. The first volume of the series of textbooks contains the basic elements of vector and tensor analysis, necessary and sufficient for studying short course"Fundamentals of continuum mechanics", presented using the mathematical apparatus of tensor calculus. The concepts and corresponding physical quantities, used to describe the movement and state of the material continuum. Equations and relationships 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 posing problems in continuum mechanics and examples of posing a number of practical problems are given. The appendix provides examples of solutions typical tasks. 375 pp. djvu. 3.0 MB.
Volume 2. The second volume of the textbook outlines 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-fractures.
The problems of body strength during deformation, as well as issues of the formation and propagation of cracks in brittle and ductile materials are considered. The basics of diffuse 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 destruction of materials under shock wave loading are described in detail. 420 pp. djvu. 6.6 MB.
Volume 3. Numerical methods in problems of physics of fast-flowing processes. The third volume of the set of textbooks in the series “Applied Continuum Mechanics” outlines the issues of using 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, algorithms for numerical solution and results of solving a number of one-dimensional and two-dimensional non-stationary problems using Lagrangian, Eulerian-Lagrangian and Eulerian methods are presented. The problems of technology for conducting computational experiments are discussed and examples are given that demonstrate the capabilities of numerical modeling as a tool for studying fast processes.
The material in this textbook is intended for initial familiarization of students of higher technical educational institutions with the theory of difference schemes and the basics of the practical use of numerical methods in solving problems of explosion physics and mechanics of high-speed collisions of various deformable bodies and media. 520 pp. 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 pp. 4.7 MB.
Theory of motion stability. Oscillation theory. Dynamics of nonholonomic systems. Theory of optimal control systems. Mechanics of gyroscopic and navigation systems. Mechanics space flight. Celestial.mechanics.Theory of mechanisms and machines.
Volume 2. MECHANICS OF LIQUID AND GAS. 1970 880 pp. 11.9 MB.
Jet theory. Hydrodynamics of the movement of bodies in water at high speeds. Some questions of hydrodynamics 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. Mechanics of rarefied gas and plasma and magnetic hydrodynamics. 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. Properties of quantum fluid. Hydraulics. Industrial aerodynamics.
Volume 3. MECHANICS OF DEFORMABLE SOLID BODY. 1772 480 pp. 8.3 MB. A theory for constructing models has been developed, based on the use of a basic variational equation obtained using the first and second laws of thermodynamics, taking into account the thermodynamics of irreversible processes. Along the way, a general original theory of variations was developed. Methods are given for deriving closed systems of equations containing the Euler equations, equations of state and conditions on the surfaces of strong discontinuities. General techniques have been developed for reducing three-dimensional problems to two-dimensional and one-dimensional ones (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 colleges.

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

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Ziegler. Mechanics of solids and liquids. Second edition. 2002 860 pp. 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.
Modern approximate methods for solving static and dynamic problems of mechanics (Rayleigh-Ritz-Galerkin method, finite element method, etc.) are separately considered.
An important feature of the monograph is a detailed consideration large number examples with a clear technical focus, as well as a selection of a large number of interesting and varied tasks in the main sections of the course, intended for independent decision.
The book is intended for undergraduates, graduate students and researchers specializing in various fields of natural science and technology. Can serve as a textbook and collection of problems on solid and fluid mechanics.

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Chernyak, Suetin. Continuum mechanics. Educational allowance. 2006 350 pp. djvu. Size 3.3 MB.
Fundamental physical concepts kinematics and dynamics of a continuous medium, its various models are considered ( solid, liquid and gas). Most of teaching aid devoted to the hydrodynamics of ideal and viscous fluids. Elements of the theory of elasticity, gas dynamics and magnetic hydrodynamics are included. Shows how theoretical principles are used to solve engineering problems and to explain certain natural phenomena. Questions for self-control and examples of problem solving given at the end of each chapter will help the reader better understand the theory and acquire the skills to independently solve 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 field of bachelor's training "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 tasks. 396 pp. Volume 1 contains about 1000 problems and exercises in all main sections of continuum mechanics, including: general fundamentals of continuum mechanics and thermodynamics, fluid mechanics, gas dynamics, theory of elasticity, theory of plasticity, electrodynamics, fundamentals of modeling. Each section contains 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 fundamentals of continuum mechanics and thermodynamics, fluid mechanics, gas dynamics, elasticity theory, theory plasticity, basics of modeling.

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