AAE352_Summer_Lec11

# AAE352_Summer_Lec11 - AAE 352 Lecture 12 Matrix methods -...

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AAE 352 Fall 2009 12-1 AAE 352 – Lecture 12 Matrix methods - Part 6 Castigliano’s Theorems and strain energy

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Strain energy AAE 352 Fall 2009 12-2     11 22 i j i ij j W u P U u K u           Work = Force times distance=energy stored Force, P Distance, u
Castigliano’s Theorems AAE 352 Fall 2009 12-3 i i U P u i i U u P 1 1 2 2 ........ i i i ij j i U P K u K u K u u 2 ij ij U K uu 

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An example AAE 352 Fall 2009 12-4 1 2 3 E=29x10 6 psi A 1 =5 in 2 A 2 =3 in 2 A 3 =1 in 2 20 in. 20 in. 20 in. 1 2 3
Strain energy in each rod AAE 352 Fall 2009 12-5   2 1 1 2 1 1 2 U k u u  1 2 3   2 2 2 3 2 1 2 U k u u   2 3 3 4 3 1 2 U k u u       22 2 1 2 1 2 3 2 3 4 3 1 1 1 2 2 2 U k u u k u u k u u

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System stiffness element K 12 AAE 352 Fall 2009 12-6       22 2 1 2 1 2 3 2 3 4 3 1 1 1 2 2 2 U k u u k u u k u u 2 ij ij U K uu 
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## This note was uploaded on 01/18/2012 for the course AAE 352 taught by Professor Chen during the Fall '08 term at Purdue University-West Lafayette.

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AAE352_Summer_Lec11 - AAE 352 Lecture 12 Matrix methods -...

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