AAE352_Summer_Lec09

AAE352_Summer_Lec09 - Transformation Matrices Andrew J....

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June 24, 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 Transformation Matrices 9-1
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Write MATLAB programs to help you solve the problems AAE 352 Summer 2010 https://engineering.purdue.edu/AAE/Academics/Courses/web_pages https://engineering.purdue.edu/AAE/Academics/Courses/aae352/ June 24, 2010 9-2
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AAE 352 Summer 2010 d 11 d 12 L 1 F F 12 d 21 d 22 L 2 F 21 F 22 P 1 P 2 P 3 u 1 u 2 u 3 ij k   ij K We need to trade in element(local) forces & displacements for global forces & displacements June 24, 2010 9-3
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AAE 352 Summer 2010 d 11 d 12 L 1 F F 12 d 21 d 22 L 2 F 21 F 22 P 1 P 2 P 3 u 1 u 2 u 3 3 2 1 12 0 1 0 0 0 1 u u u d 3 2 1 22 21 1 0 0 0 1 0 u u u 1 2 3 1 11 1 12 1 10 01 00 F F F F F       1 2 3 2 21 2 22 2 F F F F F element node number F Step 1 – local displacements to global displacements Step 2 – local forces to global forces June 24, 2010 9-4
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AAE 352 Summer 2010 P 1 P 2 P 3 u 1 u 2 u 3 3 2 1 12 11 0 1 0 0 0 1 u u u d 3 2 1 22 21 1 0 0 0 1 0 u u u 1 2 3 1 11 1 12 1 1 0 0 0 1 0 T F F F F F       1 2 3 2 21 2 22 2 0 1 0 0 0 1 T F F F F F element node number F These are the “transpose” of each other June 24, 2010 9-5
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AAE 352 Summer 2010 P 1 P 2 P 3 u 1 u 2 u 3 3 2 1 12 11 0 1 0 0 0 1 u u u d 1 2 3 1 11 1 12 1 1 0 0 0 1 0 T F F F F F       1 2 3 1 1 11 1 1 1 2 12 1 1 1 3 10 1 0 0 1 0 0 01 0 1 0 0 1 0 00 T F u F k k Fu F k k u F  June 24, 2010 9-6
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AAE 352 Summer 2010 P 1 P 2 P 3 u 1 u 2 u 3 1 2 3 1 1 11 1 2 1 3 1 0 0 1 0 0 0 1 0 0 1 0 T F u kk Fu u F       1 2 3 1 1 1 2 1 3 10 0 01 0 00 F u u F 1 2 3 1 1 1 1 1 1 1 2 1 3 0 0 0 0 0 F k k u F k k u u F  June 24, 2010 9-7
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AAE 352 Summer 2010 P 1 P 2 P 3 u 1 u 2 u 3 3 2 1 12 11 0 1 0 0 0 1 u u u d 1 2 3 1 1 1 2 1 3 1 0 0 1 0 0 0 1 0 0 1 0 T F u kk Fu u F       element Transformation global displacements matrix displacements 
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AAE352_Summer_Lec09 - Transformation Matrices Andrew J....

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