Haghighi 1 l1 x j yk x k yj yj yk x x

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Unformatted text preview: A 2 A 3 A L1 + L 2 + L 3 = + + = =1 A A AA y 1x 2 A1 L1 = , 2 A 1 = 1 X j Yj 2A 1 X k Yk Chapter 6 Page 7 K. Haghighi [ ( )( ) 1 L1 = X j Yk − X k Yj + Yj − Yk x + X k − X j y 2A Similarly L1 = Ni L2 = Nj L 3 = Nk Integral Equation: a! b! c! abc ∫A L1 L 2 L 3 dA = (a + b + c + 2) ! 2A Chapter 6 Page 8 K. Haghighi Examples: 1! 1! 0! 2A A ∫A NiN j dA = (1 + 1 + 0 + 2) ! 2A = 4! = 12 A 2! 0! 1! 2 2 ∫A Ni Nk dA = (2 + 0 + 1 + 2) ! 2A = 5x4x 3x 2x1 2A = 30 A 2A 1! 1! 1! ∫A Ni N j Nk dA = (1 + 1 + 1 + 2) ! 2A = 5x4x 3x 2x1 2A = 60 Chapter 6 Page 9 K. Haghighi Boundary Conditio...
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This document was uploaded on 01/29/2014.

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