7a-R-R Method-2010s

# 7a-R-R Method-2010s - MAE M168/CEE M135C Introduction to...

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© William Klug MAE M168/CEE M135C Introduction to Finite Element Methods Lecture 7a Approximation Techniques: Rayleigh-Ritz Method

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© William Klug Energy and the Weak Form ± Total Potential Energy: Minimizing energy implies weak form of BVP Π = 1 2 EA du dx 2 q x ( ) u x ( ) 0 L dx P 0 u (0) P L u ( L ) d d ε Π u + v = 0 = d d EA d dx ( u + v ) 2 q ( u + v ) 0 L dx = 0 P 0 d d [ u (0) + v (0)] = 0 P L d d [ u ( L ) + v ( L )] = 0 = EA du dx dv dx dx 0 L qvdx 0 L P 0 v (0) P L v ( L ) = 0
Rayleigh-Ritz Method • Approximate version of minimum potential energy principle. • Methodology: – Determine total potential energy – Substitute approximate displacement field – Determine coefficients c i by minimizing Π Π ( u ). ( ) ( ) 1

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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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7a-R-R Method-2010s - MAE M168/CEE M135C Introduction to...

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