Stability of Structures: Modern Problems and Unconventional Solutions
July 16, 2001 — July 20, 2001
Coordinator:
- Isaac Elishakoff (Florida Atlantic University, Boca Raton, Florida, USA)
Stability of structures is ever-changing and ever-invigorated field. This course is dedicated not just to the modern state-of-the-art, but to fundamental problems, concepts and numerical side along to qualitative understanding. It includes modern exact solution methods, inverse problems, optimization, dynamic instability, and numerical methods. Emphasis will be placed on deep understanding of the mechanics side, rather than encyclopedic or cook-book type approaches. Controversial topics and their resolutions, known paradoxes and the today’s view upon them will be the most strong characteristic of this course.
The course presents recent achievements and knowledge on bifurcation theory, sensitivity analysis of stability characteristics, general aspects of non-conservative stability problems, study of pre- and post-critical behavior, analysis of singularities of boundaries of the stability domains, stability analysis of multi-parameter linear periodic systems, and optimization of structures under stability constraints. Both systems with finite degrees of freedom and continuous models will be considered. It is intended to combine within this course mathematical foundation and interesting classical and modern mechanical problems.
A number of mechanical problems illustrating how bifurcations and singularities change behavior of systems and lead to new physical phenomena are discussed. Among these problems we consider systems of rotating bodies, tubes conveying fluid, elastic columns under action of periodic forces and follower forces (e.g. rocket thrust), optimization problems for conservative and non-conservative systems etc. The methods to be presented in the course are constructive and easy to implement in computer programs. Recent exciting experiments on dynamic stability of non-conservative systems will be shown on VIDEO.
The course is addressed to graduate and Ph.D. students, researchers and engineers working in aerospace, naval, civil and mechanical engineering areas. No special background is needed, except basic knowledge in mathematics and mechanics.