CVEN9802 - Energy Formulation 2.pdf

CVEN9802 - Energy Formulation 2.pdf - CVEN9802 Structural...

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1 CVEN 9802 Stability Page 1 CVEN9802 Structural Stability Energy Method – Numerical Formulation 2 University of New South Wales CVEN 9802 Stability Page 2 Outline Infinitesimal Strain Finite Strain – Green’s Strain First & Second Variation of Total Potential Beam Theory Stability of a Column Raleigh-Ritz Approximation Raleigh-Ritz General Formulation
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2 CVEN 9802 Stability Page 3 Figure Material Lines Before and After Deformation Before Deformation After Deformation ˆ s s u O P 2 1 2 3 , , x s s s 1 1 2 3 , , x s s s P Definition of 2D - Plane Strain CVEN 9802 Stability Page 4 Taylors Theorem – 1 variable 2 2 2 ( ) ( ) ... 2 x a df a d f a x a f x f a x a dx dx x a dx 2 , , ( ) ( ) ( ) ( ) ... 2 x a x xx dx f a dx f a f a dx f a Second Order
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