Ch_26

# Subbarayan one dimensional quadratic element 1 2 1 3

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This document was uploaded on 01/29/2014.

Ask a homework question - tutors are online