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prob_06_01_01

# prob_06_01_01 - Problem 6.1-1(a Complete calculations begun...

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Problem 6.1-1 (a) Complete calculations begun in Eq. 6.1-2, and obtain shape functions Ni. (b) Verify that the same results is provided by Lagrange interpolation Solution: (a) x 1 ξ ξ 2 ( ) a 1 a 2 a 3 = u 1 ξ ξ 2 ( ) a 1 a 2 a 3 = Eq. 6.1-1 x 1 x 2 x 3 A a 1 a 2 a 3 = A 1 1 1 1 0 1 1 0 1 := x 1 ξ ξ 2 ( ) A 1 x 1 x 2 x 3 = A 1 0 0.5 0.5 1 0 1 0 0.5 0.5 = N 1 N 2 N 3 ( ) 1 ξ ξ 2 ( ) A 1 = N 1 N 2 N 3 ( ) ξ 2 2 ξ 2 1 ξ 2 ξ 2 2 ξ 2 + = N 1 1 2 ξ 2 ξ ( ) = N 2 1 ξ 2 = N 3 1 2 ξ 2 ξ + ( ) = (b) Langrange Eq.3.2-7 with ξ in place of x N 1 ξ 2 ξ ( ) ξ 3 ξ ( ) ξ 2 ξ 1 ( ) ξ 3 ξ 1
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