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.

Rods, plates and shells are the fundamental components of structural mechanics First and only monograph that treats rods exclusively Very detailed and comprehensive Contains solutions for many problems in various fields of engineering (endoscopes, spacecraft) Includes supplementary material: sn.pub/extras

Klappentext

The volume is devoted to the mechanics of rods, which is a branch of the mechanics of deformable bodies. The main goal of the book is to present systematically theoretical fundamentals of the 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 the mechanics of rods. Various types of external loads that a rod may be subject to are discussed. Advanced techniques that includes vector analyses, linear algebra, and distributions is used in the derivation of linear and nonlinear equilibrium equations. The use of these techniques helps us to make transformations and rearrangements 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 aerodynamic forces are presented.

Inhalt

1. Equilibrium Equations.- 1.1 Vector Equilibrium Equations.- 1.2 External Loads.- 1.3 Equilibrium Equations in the Attached and Cartesian Coordinate Systems.- 1.4 Equilibrium Equations for Small Displacements and Angles of Rotation.- 1.5 Problems.- 2. Integration of Equilibrium Equations.- 2.1 Integration of Linear Equilibrium Equations.- 2.2 Equilibrium Equations for Rods with Lateral Supports.- 2.3 Method of Step-by-Step Loading.- 3. Static Stability of Rods.- 3.1 Basic Concepts.- 3.2 Equilibrium Equations for a Rod After Loss of Stability.- 3.3 Plane Curvilinear Rods.- 3.4 Increments of Loads at Loss of Stability.- 3.5 Computer-Oriented Methods.- 3.6 Problems.- 4. Straight Rods.- 4.1 Rods of Straight Natural Configuration.- 4.2 Equilibrium Equations for Small Displacements and Angles of Rotation.- 4.3 Naturally Twisted Straight Rods.- 4.4 Straight Rods on Elastic Foundation.- 4.5 Application of Approximate Methods.- 4.6 Stability of Compressed-Twisted Rods.- 4.7 Stability of Straight Rods with Local Constraints.- 4.8 Problems.- 5. Curvilinear Rods.- 5.1 Plane Rods.- 5.2 Elementary Theory of Cylindrical Springs.- 5.3 General Theory of Cylindrical Springs.- 5.4 Flexible Rods in a Rigid Conduit.- 5.5 Stability of Plane Curvilinear Rods.- 5.6 Problems.- 6. Rods Interacting with Liquid or Air Flows.- 6.1 Introduction.- 6.2 Basic Concepts of Aerohydrodynamics.- 6.3 Experimental Results.- 6.4 Aerodynamic Forces Acting on Rods of Circular Cross Section.- 6.5 Stress-Strain State of a Rod Interacting with an Air Flow.- 6.6 Aerodynamic Forces Acting on Rods of Noncircular Cross Section.- 6.7 Increments of Aerodynamic Forces at Small Displacements of Axial Points.- 6.8 Rods Containing Internal Liquid Flows.- A. Appendices.- A.1 Elements of Vector Algebra.- A.1.1 Vector Bases; Coordinates of Vectors.- A.1.2 Scalar Product.- A.1.3 Vector Product.- A.1.4 Scalar Triple Product.- A.1.5 Vector Triple Product.- A.1.6 Transformation of Base Vectors.- A.2 Basics of Differential Geometry.- A.2.1 The Derivative of a Radius Vector.- A.2.2 Spatial Curves.- A.2.3 Derivatives of the Base Vectors.- A.2.4 Geometrical Meaning of the Components of the Vector æ.- A.2.6 Derivatives of a Vector in the Attached Coordinate System.- A.3 Increments of the Components of a Vector under Transformation of the Attached Coordinate System.- A.4 Distributions.- A.4.1 The ?-function.- A.4.2 The Nondimensional ?-function.- A.4.3 The Heaviside Function.- A.4.4 Applications of the ?-function.- A.4.5 Integrals Containing Derivatives of the ?-function.- A.5 Direction Cosines of the Unit Vector Tangent to a Rod Axis.- A.5.1 Plane Curve.- A.5.2 Spatial Curve.- A.6 Equations of the First and Higher Approximation.- B. Solution of the Problems.- B.1 To Chapter 1.- B.2 To Chapter 3.- B.3 To Chapter 4.- B.4 To Chapter 5.- References.