Screen LibraryStability theory of elastic rods /
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- a...
Saved in:
| Main Authors: | |
|---|---|
| Corporate Authors: | |
| Published: |
World Scientific Pub. Co.,
|
| Publisher Address: | Singapore : |
| Publication Dates: | 1997. |
| Literature type: | eBook |
| Language: | English |
| Series: |
Series on stability, vibration and control of systems. Series A ;
v. 1 |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/3402#t=toc |
| Summary: |
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, Pfluger'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. |
| Carrier Form: | 1 online resource (xiii,425pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 405-422) and index. |
| ISBN: | 9789812819673 |
| CLC: | O343.9 |
| Contents: | ch. 1. Introduction. 1.1. Rod, rod axis and cross-section. 1.2. Rod models for stability analysis. 1.3. Methods of stability analysis -- ch. 2. Basic equations. 2.1. Basic equations for a plane deformation of an elastic rod. 2.2. Linearized equations of the plane elastic rods. 2.3. The influence of shear stresses on the plane deformation. 2.4. Basic equations for spatially deformed rods with inextensible axis. 2.5. Euler angles. 2.6. Summary of equations for a spatially deformed rod with inextensible axis. 2.7. Kirchhoff's analogy. 2.8. Concentrated forces and couples acting on spatially deformed rod. 2.9. Spatially deformed rod with extensibility and shear. 2.10. Solutions of differential equations for some finitely deformed rods and columns. 2.11. An inverse problem: the shape of a piston ring. 2.12. Negativism -- ch. 3. The adjacent equilibrium method for stability analysis. 3.1. The adjacent equilibrium method (Euler method) and its relation to bifurcation theory. 3.2. Rod with a constant cross-section loaded at end points. 3.3. The influence of compressibility and shear on the stability bounds for the rod with the constant cross-section. 3.4. Column loaded by two forces. 3.5. Column with a step change in the cross-section. 3.6. Column with a variable cross-section loaded by a concentrated force. 3.7. Rod on an elastic foundation. 3.8. Heavy vertical column. 3.9. Heavy column with a variable cross-section. 3.10. Buckling by extension. 3.11. Rod with overhang. 3.12. Pfluger's rod. 3.13. Heavy rod on a horizontal plane. 3.14. The strongest centrally compressed rod. 3.15. Heavy rotating column. 3.16. Circular ring loaded by uniform pressure. 3.17. Rod loaded by a force and a couple. 3.18. Lateral buckling of a rod. 3.19. Lateral buckling of a cantilever. 3.20. Heavy cantilever -- ch. 4. The energy method for stability analysis. 4.1. The energy method and its relation to Euler method. 4.2. Column with a constant cross-section loaded at end point. 4.3. Heavy compressible column with end force. 4.4. Rod with a constant cross-section loaded at end points. 4.5. Heavy column with a shear compressibility and end force. 4.6. Heavy rotating column with imperfections. 4.7. Vertically positioned heavy rotating column. 4.8. Use of canonical transformations. 4.9. Various variational principles and a priori estimates. 4.10. Rayleigh-Ritz and Galerkin methods for stability problems -- ch. 5. The dynamic method of stability analysis. 5.1. Equations for planar and spatial motion of a rod. 5.2. Liapunov definitions of stability. 5.3. Stability theorems. 5.4. Eigenmodal analysis. 5.5. Simply supported, centrally compressed rod and heavy column. 5.6. Leipholz's column. 5.7. Beck's column. 5.8. Uniformly accelerated rod under follower force. 5.9. Fluid conveying tube. 5.10. Simply supported and Pfluger's rod with shear and compressibility. |