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Author: V.A. Svetlitsky Publisher: Springer Science & Business Media ISBN: 3540455930 Category : Science Languages : en Pages : 396
Book Description
The volume is devoted to mechanics of rods, which is a branch of mechanics of deformable bodies. The main goal of the book is to present systematically theoretical fundamentals of mechanics of rods as well as numerical methods used for practical purposes. The monograph is concerned with the most general statements of the problems in mechanics of rods. Various types of external loads that a rod may be subject to are discussed. Advanced technique that includes vector is used in the derivation of linear analysis, linear algebra, and distributions and nonlinear equilibrium equations. The use of this technique helps us to make transformations and rearrangement of equations more transparent and compact. Theoretical basics of rods interacting with external and internal flows of fluid and the derivation of the formulas for the hydrodynamic and aerody namic forces are presented. The book consists of six chapters and appendices and may be convention ally divided into two parts. That is, Chapters 1 to 3 contain, in the main, theoretical material, whereas Chapters 4 to6 illustrate the application of the theoretical results to problems of practical interest. Problems for self-study are found in Chapters 1, 3, 4, and 5. The solutions to most of the problems are given in Appendix B. The monograph is addressed to scientists, institutional and industrial re searchers, lecturers, and graduate students.
Author: V.A. Svetlitsky Publisher: Springer Science & Business Media ISBN: 3540455930 Category : Science Languages : en Pages : 396
Book Description
The volume is devoted to mechanics of rods, which is a branch of mechanics of deformable bodies. The main goal of the book is to present systematically theoretical fundamentals of mechanics of rods as well as numerical methods used for practical purposes. The monograph is concerned with the most general statements of the problems in mechanics of rods. Various types of external loads that a rod may be subject to are discussed. Advanced technique that includes vector is used in the derivation of linear analysis, linear algebra, and distributions and nonlinear equilibrium equations. The use of this technique helps us to make transformations and rearrangement of equations more transparent and compact. Theoretical basics of rods interacting with external and internal flows of fluid and the derivation of the formulas for the hydrodynamic and aerody namic forces are presented. The book consists of six chapters and appendices and may be convention ally divided into two parts. That is, Chapters 1 to 3 contain, in the main, theoretical material, whereas Chapters 4 to6 illustrate the application of the theoretical results to problems of practical interest. Problems for self-study are found in Chapters 1, 3, 4, and 5. The solutions to most of the problems are given in Appendix B. The monograph is addressed to scientists, institutional and industrial re searchers, lecturers, and graduate students.
Author: Valery A. Svetlitsky Publisher: Springer Science & Business Media ISBN: 9783540242840 Category : Science Languages : en Pages : 472
Book Description
This is the first and only monograph on this subject, and provides a systematic presentation of theoretical fundamentals of the mechanics of rods as well as numerical methods used for practical purposes. Includes problems and solutions for self-study.
Author: Oliver M. O'Reilly Publisher: Springer ISBN: 331950598X Category : Mathematics Languages : en Pages : 434
Book Description
This book presents theories of deformable elastic strings and rods and their application to broad classes of problems. Readers will gain insights into the formulation and analysis of models for mechanical and biological systems. Emphasis is placed on how the balance laws interplay with constitutive relations to form a set of governing equations. For certain classes of problems, it is shown how a balance of material momentum can play a key role in forming the equations of motion. The first half of the book is devoted to the purely mechanical theory of a string and its applications. The second half of the book is devoted to rod theories, including Euler’s theory of the elastica, Kirchhoff ’s theory of an elastic rod, and a range of Cosserat rod theories. A variety of classic and recent applications of these rod theories are examined. Two supplemental chapters, the first on continuum mechanics of three-dimensional continua and the second on methods from variational calculus, are included to provide relevant background for students. This book is suited for graduate-level courses on the dynamics of nonlinearly elastic rods and strings.
Author: Valery A. Svetlitsky Publisher: Springer ISBN: 9783642063527 Category : Technology & Engineering Languages : en Pages : 0
Book Description
This is the first and only monograph on this subject, and provides a systematic presentation of theoretical fundamentals of the mechanics of rods as well as numerical methods used for practical purposes. Includes problems and solutions for self-study.
Author: Teodor M. Atanackovic Publisher: World Scientific ISBN: 9810230540 Category : Technology & Engineering Languages : en Pages : 441
Book Description
This book treats stability problems of equilibrium states of elastic rods. Euler energy and dynamical methods of stability analysis are introduced and stability criteria for each method is developed. Stability analysis is accompanied by a number of classical conservative and non-conservative, two- and three-dimensional problems. Some problems are treated by all three methods. Many generalized versions of known problems are presented (heavy vertical rod, rotating rod, Greenhill's problem, Beck's column, Pflger's rod, strongest column, etc.). The generalizations consist in using either a generalized form of constitutive equations or a more general form of loading, or both. Special attention is paid to the influence of shear stresses and axis compressibility on the value of the critical load. Variational methods are applied to obtain estimates of the critical load and maximal deflection in the post-critical state, in a selected number of examples.
Author: Nikolai Nikolaevich Polyakhov Publisher: Springer Nature ISBN: 3030640612 Category : Technology & Engineering Languages : en Pages : 526
Book Description
Available for the first time in English, this two-volume course on theoretical and applied mechanics has been honed over decades by leading scientists and teachers, and is a primary teaching resource for engineering and maths students at St. Petersburg University. The course addresses classical branches of theoretical mechanics (Vol. 1), along with a wide range of advanced topics, special problems and applications (Vol. 2). This first volume of the textbook contains the parts “Kinematics” and “Dynamics”. The part “Kinematics” presents in detail the theory of curvilinear coordinates which is actively used in the part “Dynamics”, in particular, in the theory of constrained motion and variational principles in mechanics. For describing the motion of a system of particles, the notion of a Hertz representative point is used, and the notion of a tangent space is applied to investigate the motion of arbitrary mechanical systems. In the final chapters Hamilton-Jacobi theory is applied for the integration of equations of motion, and the elements of special relativity theory are presented. This textbook is aimed at students in mathematics and mechanics and at post-graduates and researchers in analytical mechanics.
Author: Yvonne Choquet-Bruhat Publisher: Gulf Professional Publishing ISBN: 9780444860170 Category : Mathematics Languages : en Pages : 666
Book Description
This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.
Author: Yury Vetyukov Publisher: Springer Science & Business Media ISBN: 3709117771 Category : Science Languages : en Pages : 280
Book Description
This book presents a hybrid approach to the mechanics of thin bodies. Classical theories of rods, plates and shells with constrained shear are based on asymptotic splitting of the equations and boundary conditions of three-dimensional elasticity. The asymptotic solutions become accurate as the thickness decreases, and the three-dimensional fields of stresses and displacements can be determined. The analysis includes practically important effects of electromechanical coupling and material inhomogeneity. The extension to the geometrically nonlinear range uses the direct approach based on the principle of virtual work. Vibrations and buckling of pre-stressed structures are studied with the help of linearized incremental formulations, and direct tensor calculus rounds out the list of analytical techniques used throughout the book. A novel theory of thin-walled rods of open profile is subsequently developed from the models of rods and shells, and traditionally applied equations are proven to be asymptotically exact. The influence of pre-stresses on the torsional stiffness is shown to be crucial for buckling analysis. Novel finite element schemes for classical rod and shell structures are presented with a comprehensive discussion regarding the theoretical basis, computational aspects and implementation details. Analytical conclusions and closed-form solutions of particular problems are validated against numerical results. The majority of the simulations were performed in the Wolfram Mathematica environment, and the compact source code is provided as a substantial and integral part of the book.
Author: Khanh C. Le Publisher: Springer Science & Business Media ISBN: 3642599117 Category : Technology & Engineering Languages : en Pages : 415
Book Description
Intended for engineers who deal with vibrations of rods and shells in their everyday practice but who also wish to understand the subject from the mathematical point-of-view, the results contained here concerning high-frequency vibrations may be new to many. The book serves equally well as an advanced textbook, while remaining of interest to mathematicians who seek applications of the variational and asymptotic methods in elasticity and piezoelectricity. Only a minimum knowledge in advanced calculus and continuum mechanics is assumed on the part of the reader.
Author: V.A. Svetlitsky
Author: V.A. Svetlitsky
Author: Valery A. Svetlitsky
Author: Oliver M. O'Reilly
Author: Valery A. Svetlitsky
Author: Teodor M. Atanackovic
Author: Nikolai Nikolaevich Polyakhov
Author: Clifford Truesdell
Author: Yvonne Choquet-Bruhat
Author: Yury Vetyukov
Author: Khanh C. Le