ABOUT THE COURSE:The course of Stability of Structures is designed for the graduate students, advance undergraduate students in Civil and Aerospace Engineering and for industry professional working for the stability design. The course introduces the basic and advanced concepts of stability analysis of structures and their implications in structural design. Both the topics of static and dynamic instability are discussed. Whereas the static stability principles are employed in routine design and formulating design stipulations; the dynamic stability largely influence the design of long-span cable stayed and cable suspension bridges by causing various aerodynamic instabilities such as flutter.INTENDED AUDIENCE: Senior undergraduate students in Civil, Aerospace and Mechanical engineering, graduate students in structural engineering, engineers working in industry for stability designPREREQUISITES: Solid Mechanics, Structural analysis, Engineering mathematics, Matrix/Finite element method in engineering, basic computer programming.INDUSTRY SUPPORT: Not sure about this aspect. But aerospace structural industry and structural steel design industry may show interest

Syllabus

Week 1: Concept of elastic stability; Energy approach. Linearized analysis and Post-critical behavior. Symmetric bifurcation with stable and unstable post-critical behavior, Asymmetric bifurcation with stable/unstable post critical behavior, Imperfection sensitivity, Koiter’s power law, Potential energy functional
Week 2:Mises truss, Snap through, Modal interactions in Augusti’s column, Bergan’s truss depicting coupled bifurcations and snap-through
Week 3:Beam-column; Deflection and Moment amplification, Lateral buckling of beam
Week 4:Torsional-flexural buckling of columns, Elastica, Elliptical integrals and post-critical behavior of column
Week 5:Matrix/Finite element method for stability analysis. Geometric stiffness matrix, Solved examples
Week 6:Review of plate bending, Equations for plate buckling; Solution for critical load under compressive and shear loading
Week 7:Post buckling analysis of plates, Von Karman-Foppl equation, Volmir’s solution, Reserve post-buckling strength
Week 8:Dynamic analysis of stability, Follower force, Flutter and divergence, Column under pulsating load, Parametric resonance
Week 9:Stability of Beck’s column, Aerodynamic flutter analysis of Tacoma bridge, Instability in shaft under compression
Week 10:Concept of Lyapunov stability, Solved example, Overview of shell buckling, Linearized analysis of cylindrical shell
Week 11:Linearized analysis of spherical shell panel, Nonlinear analysis and imperfection sensitivity
Week 12:Finite element analysis of shell buckling and imperfection sensitivity, Knock down factors, Stochastic buckling