AAE352_Summer_Lec28

# AAE352_Summer_Lec28 - Andrew J Ritchey [email protected]

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Andrew J. Ritchey [email protected] ARMS B144 765-494-5985 https://engineering.purdue.edu/AAE/Academics/Courses/aae352/2010/summer AAE 352 Summer 2010

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The ability of a flexible system to maintain a definite equilibrium form (or state) under a given loading condition AAE 352 Summer 2010
AAE 352 Summer 2010 Euler’s stability criterion A system is neutrally stable if – at a particular critical load – nearby or “proximate” equilibrium states also appear “Proximate” means “very near.” At neutral stability there is are two or possibly many different deflected shapes in addition to the one we have in mind We lose control of which state the system takes

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AAE 352 Summer 2010 Axial compressive loads placed on structural elements such as Columns Plates Shells Critical values of compression cause the structure to move sideways and develop bending loads lateral (side) deflections occur - they may be large Axial stiffness is reduced-it is easier to move the ends together Also torsion loads that create critical shear loads
AAE 352 Summer 2010

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AAE 352 Summer 2010   2 xx yy 1 E E E E E 0 E E     2 2 3 2 2 2 2 1 12 1 L Ebt L EI P cr wide plate with sides unsupported x y
AAE 352 Summer 2010   2 2 2 cr L 1 EI P a=L   2 2 3 2 a 1 12 Ebt bt P xx b   2 3 1 12 Et D

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AAE 352 Summer 2010 b y n sin a x m sin a ) y , x ( w 1 m 1 n mn  x y Edges can rotate 2 2 2 2 2 2 2 2 cr b n a m m D a t N xx x
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AAE352_Summer_Lec28 - Andrew J Ritchey [email protected]

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