Subbarayan one dimensional quadratic element 1 2 1 3

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Unformatted text preview: ape function to be one at its own node Chapter 26 Page 7 G. Subbarayan One-Dimensional Quadratic Element 1 2 (ξ + 1) 3 ξ (ξ − 1) N1 = Cξ (ξ − 1) N1 = 1 at ξ = −1 ⇒ C = 1 2 Similarly, N 2 = − (ξ + 1)(ξ − 1) N3 = ξ 2 (ξ + 1) Chapter 26 Page 8 G. Subbarayan Quadratic Triangular Elements The interpolation is: φ = a1 + a2 x + a3 y + a4 x + a5 xy + a6 y 2 2 this is of the form φ = C ( Lα − dα )( Lδ − dδ ) Therefore, N β = C ( Lα − dα )( Lδ − dδ ) Chapter 26 Page 9 G. Subbarayan Chapter 26 Page 10 G. Subbarayan N1 = C ( L1 − 0)( L1 − 1 ) 2 ⇒ C=2 Similarly, N 2 = C ( L1 − 0)( L2 − 0) = 4 L1 L2 Chapter 26 Page 11 G. Subbarayan Chapter 26 Page 12 G. Subbarayan Quadrilateral Elements Linear quadrilateral element Chapter 26 Page 13 G. Subbarayan N1 = 1 (1 − ξ )(1 − η ) 4 N 2 = 1 (1 + ξ )(1 − η ) 4 N 3 = 1 (1 + ξ )(1 + η ) 4 N 4 = 1 (1 − ξ )(1 + η ) 4 Chapter 26 Page 14 G. Subbarayan Lagrangian Element 9-noded element Chapter 26 Page 15 G. Subbarayan Chapter 26 Page 16 G. Subbarayan Eight-Node Quadratic Element Chapter 26 Page 17 G. Subbarayan Chapter 26 Page 18 G. Subbarayan...
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