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unit16 - MIT 16.20 Fall 2002 Unit 16 Bifurcation Buckling...

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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

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MIT - 16.20 Fall, 2002 V. Stability and Buckling Paul A. Lagace © 2001 Unit 16 - 2
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

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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
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

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MIT - 16.20 Fall, 2002 Snap-Though Buckling Figure 16.3 Representation of column with curvature (shallow arch) with load applied perpendicular to column Figure 16.4 Basic load-deflection behavior of shallow arch with transverse load arch “snaps through” to F when load reaches C Thus, there are nonlinear load-deflection curves in this behavior Paul A. Lagace © 2001 Unit 16 - 6
MIT - 16.20 Fall, 2002 For “deeper” arches, antisymetric behavior is possible Figure 16.5 Representation of antisymetric buckling of deeper arch under transverse load (flops over) before snapping through Figure 16.6 Load-deflection behavior of deeper arch under transverse load ABCDEF - symmetric snap- through ABF - antisymmetric behavior A D E Paul A. Lagace © 2001 Unit 16 - 7

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MIT - 16.20 Fall, 2002 Will deal mainly with… Bifurcation Buckling First consider the “perfect” case: uniform column under end load.
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