5a-StrongForm-2010s

5a-StrongForm-2010s - William Klug MAE M168/CEE M135C...

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Unformatted text preview: William Klug MAE M168/CEE M135C Introduction to Finite Element Methods MAE 168 Lecture 5a Strong Forms of 1-D BVPs William Klug Strong and Weak Forms of BVPs ( ) displacement of material point originally located at x u x ( ) distributed body force (force per unit length) q x ( ), ( ), E x A x L x, u(x) Example in 1-D: Axial deformation of a linear elastic bar. William Klug Equilibrium Equation (1 st order ODE) From Taylor series expansion: ( ) ( ) ( ) dF x F x dx F x dx dx + = + ( ) internal axial force F x ( ) ( ) ( ) x F F x dx F x q x dx = + + = ( ) ( ) ( ) ( ) dF x F x dx F x q x dx dx + + = ( ) ( ) ( ) ( ) dF x q x or F x q x dx + = + = ( ) q x ( ) F x ( ) F x dx + x dx William Klug Some Definitions Normal Stress: ( ) ( ) ( ) F x x A x = ( ) ( ) ( ) ( ) lim ( ) dx l u x dx u x du x x u x l dx dx + = = = = ( ) ( ) ( ) x E x x = Strain: Hookes Law: William Klug Equilibrium Equation (2 nd order ODE)...
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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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5a-StrongForm-2010s - William Klug MAE M168/CEE M135C...

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