T 1 2 5 b 13 17 1 1 5 c 1 1 13

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Unformatted text preview: 0 1 3 0 Edge 1 1 2 1 3 # 1 2 2 5 4 3 3 4 Incidence Matrix Node 1 2 3 -1 1 0 -1 0 1 0 -1 Asquare = 0 0 -1 0 -1 0 0 4 0 0 1 1 1 Edge 1 2 3 4 5 T 0 -1 1 0 1 -1 1 -1 0 0 1 1 0 1 1 -1 1 Atriangle T Atriangle = 0 -1 -1 0 -1 0 -1 -1 1 0 0 -1 = 1 -1 0 1 1 -1 0 2 -1 -1 2 -1 = -1 -1 -1 2 # 5 Asquare T Asquare = -1 1 0 -1 0 1 0 0 -1 0 -1 0 -1 0 0 0 0 1 1 1 T -1 1 0 -1 0 1 0 0 -1 0 -1 0 -1 0 0 0 0 1 1 1 0 0 1 1 1 -1 1 0 -1 -1 0 0 -1 0 1 -1 1 0 0 -1 0 0 0 -1 = 0 1 -1 0 0 0 -1 0 0 0 1 1 1 -1 0 0 3 -1 -1 -1 -1 2 0 -1 = -1 0 2 -1 -1 -1 -1 3 # 3) Asquare u = 0 -1 1 0 -1 0 1 0 0 -1 0 -1 0 -1 0 0 0 0 1 1 1 0 u1 0 u2 u3 = 0 0 u4 0 one solution is the constant vector c c u= c c # w 0 -1 -1 0 0 -1 1 w2 0 1 0 0 -1 0 w3 = 0 0 1 -1 0 0 w4 0 0 0 1 1 1 w5 1 1 2 Asquare T w = 0 2 5 4 3 3 4 2 solutions are: 1 0 0 and W = 1 -1 0 1 1 0 -1 # 6 1 4 8) Element matrix for edge i connecting node j and k Ki = Ci -Ci -Ci Ci -C1 C1 -C4 C4 C1 row j row k K2 = C2 -C2 C5 -C5 0 0 0 0 0 -C3 C3 0 0 0 0 0 -C2 C2 K3 = 1 5 2 C3 -C3 3 -C3 C4 4 6 3 2 K1 = C1 -C1 C4 -C4 K4 = K5 = - C1 C1 0 0 0 C3 -C3 0...
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This note was uploaded on 05/02/2013 for the course MATH 101 taught by Professor Ns during the Fall '12 term at MIT.

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