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Ch_26 - ELEMENT SHAPE FUNCTIONS Quadratic elements Shape...

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Chapter 26 Page 1 G. Subbarayan ELEMENT SHAPE FUNCTIONS x Quadratic elements x Shape functions of one and two-dimensional elements
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Chapter 26 Page 2 G. Subbarayan Local Node Numbers x When number of nodes in element increases, need alternative notation for nodes I,j… no longer convenient x Element node numbers are called local node numbers
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Chapter 26 Page 3 G. Subbarayan
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Chapter 26 Page 4 G. Subbarayan Global Node Numbers x Local numbers and global numbers are related Global # e 2 3 6 5 2 4 5 8 7 3 1 2 5 4 1
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Chapter 26 Page 5 G. Subbarayan x The equation for variable in each element is: x Superscript = element # x Subscript = node # ( ) 1 (1) (1) (1) (1) 1 4 2 5 3 2 4 1 N N N N φ = Φ + Φ + Φ + Φ
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Chapter 26 Page 6 G. Subbarayan Evaluating Shape Functions x Earlier we started with: x To obtain: x Difficult to apply when number of nodes increases! 1 2 a a x φ = + i i j x X Xj x L L φ = Φ + Φ
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Chapter 26 Page 7 G. Subbarayan x Alternative procedure is to assume: x F β
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