AAE352_Summer_Lec10 - An Example Andrew J. Ritchey...

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June 25, 2010 AAE 352 Summer 2010 Andrew J. Ritchey aritchey@purdue.edu ARMS B144 765-494-5985 https://engineering.purdue.edu/AAE/Academics/Courses/aae352/2010/summer An Example 10-1
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AAE 352 Summer 2010 2 u 3 u 4 1 u 1 u 2 3 u 5 u 6 4 u 7 u 8 1 u 1 u 2 2 u 3 u 4 3 u 5 u 6 4 u 7 u 8 Step 1: number the nodes and create the displacements There is more than one way to do this Some ways are better than others June 25, 2010 10-2
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AAE 352 Summer 2010 2 u 3 u 4 1 u 1 u 2 3 u 5 u 6 4 u 7 u 8 1 u 1 u 2 2 u 3 u 4 3 u 5 u 6 4 u 7 u 8 1 2 3 4 5 6 7 8 u u u u u u u u     1 2 3 4 5 6 7 8 u u u u u u u u June 25, 2010 10-3
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AAE 352 Summer 2010 2 u 3 u 4 1 u 1 u 2 3 u 5 u 6 4 u 7 u 8 Step 2: Disassemble the structure into component elements 1 2 3 4 5 6 7 8 u u u u u u u u     u 1 u 2 u 3 u 8 u 7 u 4 u 6 u 5 4 1 3 2 1-2 1-3 1-4 d 11 12 q =-135 o June 25, 2010 10-4
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AAE 352 Summer 2010     22 ( , ) cos sin cos cos sin cos sin cos sin sin cos sin cos sin cos cos sin cos sin cos sin sin cos sin xy ij k k k k k k k k Fu k k k k k k k k q     u 2i-1 u 2i u 2j-1 u 2j q i j June 25, 2010 10-5
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AAE 352 Summer 2010 u 1 u 2 u 3 u 8 u 7 u 4 u 6 u 5 4 1 3 2 1-2 1-3 1-4 d 11 21 q =-135 o (1 3) (1 2) (1 4) 1 1 1 1 P F F F June 25, 2010 10-6
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AAE 352 Summer 2010 u 1 u 2 u 3 u 8 u 7 u 4 u 6 u 5 4 1 3 2 1-2 1-3 1-4 d 11 21 q =-135 o u 1 u 2 u 5 u 6 1 2 3 4 u u u u     u 5 u 6 u 1 u 2 =-135 o June 25, 2010 10-7
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AAE 352 Summer 2010 (1 3) (1 2) (1 4) 1 1 1 1 P F F F 1 2 (1 3) 2 2 1 1 3 1 3 1 3 1 3 1 3 1 3 5 6 cos sin cos cos sin cos u u EA F u L u q       1 2 (1 4) 2 2 1 1 4 1 4 1 4 1 4 1 4 1 4 7 8 cos sin cos cos sin cos u u EA F u L u 1 2 (1 2) 2 2 1 1 2 1 2 1 2 1 2 1 2 1 2 3 4 cos sin cos cos sin cos u u EA F u L u June 25, 2010 10-8
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AAE 352 Summer 2010 u 1 u 2 u 5 u 6 1 2 3 4 u u u u     u 5 u 6 u 1 u 2 q =-135 o 6 5 2 1 ) 3 1 ( 6 ) 3 1 ( 5 ) 3 1 ( 2 ) 3 1 ( 1 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 u u u u L EA F F F F June 25, 2010 10-9
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AAE 352 Summer 2010 Step 2: Disassemble the structure into component elements u 1 u 2 u 3 u 8 u 7 u 4 u 6 u 5 4 1 3 2 1-2 1-3 1-4 u 7 u 8 u 1 u 2 1 2 7 8 u u u u     u 7 u 8 u 1 u 2 90 o q June 25, 2010 10-10
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AAE 352 Summer 2010 1
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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_Lec10 - An Example Andrew J. Ritchey...

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