Ch_6_part2

Ch_6_part2 - 2-D Elements Local Coordinate...

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Chapter 6 Page 1 K. Haghighi 2-D Elements Local Coordinate System: -independent of orientation? y y y y y y y y x t y s t s y x

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Chapter 6 Page 2 K. Haghighi -range Natural Coordinate System: A local system that permits the specification of a point within the element by a dimensionless number whose absolute magnitude never exceeds unity. s a to t b to t , s D L to s D 2 0 2 0 2 0 1 a 2 b 2 ?
Chapter 6 Page 3 K. Haghighi a 2 b 2 1 = ξ 1 = η 1 = ξ ξ 1 + = η η Rectangular Element 1 1 1 1 η ξ a r a b q b a r b q = η = ξ

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Chapter 6 Page 4 K. Haghighi ( )( ) ( )( ) ( )( ) ( )( ) η + ξ = η + ξ + = η ξ + = η ξ = 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 m k j i N N N N
Chapter 6 Page 5 K. Haghighi Triangular Element: Define 3 length ratios, such that: 3 2 1 L & L , L 1 0 1 1 = L h s L S = perpendicular distance from one side h = altitude of that side = Area coordinates 3 2 1 L & L , L

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Chapter 6 Page 6 K. Haghighi ( )( ) 1 1 1 2 2 2 2 2 L h s bh bs A A bh triangle of area A bs height base A = = = = = = =
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