3a-SpringsEnergy-2011s

3a-SpringsEnergy-2011s - MAE M168/CEE M135C Introduction to...

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Unformatted text preview: MAE M168/CEE M135C Introduction to Finite Element Methods Lecture 3a Spring models: energy formulation Summary & Review k (1) k (2) D 1 D 2 Q 1 Q o Q 2 D o P Al Steel 1. Discretize Body 2. Local element behavior ( ) e ( ) ( ) ( ) ( ) ( ) 1 1 1 1 e e i i e e e j j d f k d f - = - i j k ( ) e i f ( ) e j f ( ) e i d ( ) e j d 3. Assemble global equilibrium equations (code numbers) (1) (1) (1) (1) (1) k- = - k k k k 1 1 (2) (2) (2) (2) (2) k- = - k k k k 1 2 1 2 Element Code 1 0 1 2 1 2 k (1) + k (2)- k (2)- k (2) k (2) D 1 D 2 = Q 1 Q 2 Alternative to Direct Stiffness Method: Energy Approach Important theorem for elastic structures: Example: k The equilibrium shape of a structure is also a shape that minimizes the structures total potential energy....
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This note was uploaded on 08/09/2011 for the course MAE 168 taught by Professor Klug during the Spring '11 term at UCLA.

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3a-SpringsEnergy-2011s - MAE M168/CEE M135C Introduction to...

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