MT-1620 al.2002 Unit 16 Bifurcation Buckling Readings Rivello 14.1.14.2.144 Paul A Lagace, Ph. D Professor of aeronautics Astronautics and Engineering Systems Paul A Lagace @2001
MIT - 16.20 Fall, 2002 Unit 16 Bifurcation Buckling Readings: Rivello 14.1, 14.2, 14.4 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering Systems Paul A. Lagace © 2001
MT-1620 al.2002 V. Stability and Buckling Paul A Lagace @2001 Unit 16-2
MIT - 16.20 Fall, 2002 V. Stability and Buckling Paul A. Lagace © 2001 Unit 16 - 2
MT-1620 al.2002 Now consider the case of compressive loads and the instability they can cause. Consider only static instabilities (static loading as opposed to dynamic loading [ e.g., flutter) From Unified, defined instability via a system becomes unstable when a negative stiffness overcomes the natural stiffness of the structure (Physically, the more you push, it gives more and builds on Itselt Review some of the mathematical concepts. Limit initial discussions to columns Generally, there are two types of buckling/instability Bifurcation buckling Snap-through buckling Paul A Lagace @2001 Unit 16-3
MIT - 16.20 Fall, 2002 Now consider the case of compressive loads and the instability they can cause. Consider only static instabilities (static loading as opposed to dynamic loading [e.g., flutter]) From Unified, defined instability via: “A system becomes unstable when a negative stiffness overcomes the natural stiffness of the structure.” (Physically, the more you push, it gives more and builds on itself) Review some of the mathematical concepts. Limit initial discussions to columns. Generally, there are two types of buckling/instability • Bifurcation buckling • Snap-through buckling Paul A. Lagace © 2001 Unit 16 - 3
MT-1620 Fall 2002 Bifurcation Buckling There are two(or more)equilibrium solutions(thus the solution path bifurcates) from Unified Figure 16.1 Representation of initially straight column under compressive load X Paul A Lagace @2001 Unit 16-4
MIT - 16.20 Fall, 2002 Bifurcation Buckling There are two (or more) equilibrium solutions (thus the solution path “bifurcates”) from Unified… Figure 16.1 Representation of initially straight column under compressive load Paul A. Lagace © 2001 Unit 16 - 4
MT-1620 al.2002 Figure 16.2 Basic load-deflection behavior of initially straight column under compressive load Actual behavior Note: Bifurcation is a mathematical concept. The manifestations in an actual system are altered due to physical realities/imperfections sometimes these differences can be very important (first continue with ideal case Perfect ABC-Equilibrium position, but unstable behavior BD-Equilibrium position There are also other equilibrium positions Imperfections cause the actual behavior to only follow this as asymptotes(will see later) Paul A Lagace @2001 Unit 16-5
MIT - 16.20 Fall, 2002 Figure 16.2 Basic load-deflection behavior of initially straight column under compressive load Actual behavior Note: Bifurcation is a mathematical concept. The manifestations in an actual system are altered due to physical realities/imperfections. Sometimes these differences can be very important. (first continue with ideal case…) Perfect ABC - Equilibrium position, but unstable behavior BD - Equilibrium position There are also other equilibrium positions Imperfections cause the actual behavior to only follow this as asymptotes (will see later) Paul A. Lagace © 2001 Unit 16 - 5