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Unformatted text preview: 2.094 Finite Element Analysis of Solids and Fluids Fall 08 Lecture 7- Isoparametric elements Prof. K.J. Bathe MIT OpenCourseWare Reading: Sec. 5.1-5.3 We want K = V B T CB dV , R B = V H T f B dV . Unique correspondence ( x,y ) ( r,s ) ( r,s ) are natural coordinate system or isoparametric coordinate system. 4 x = h i x i (7.1) i =1 4 y = h i y i (7.2) i =1 where 1 h 1 = (1 + r )(1 + s ) (7.3) 4 1 h 2 = 4 (1 r )(1 + s ) (7.4) ... 4 u ( r,s ) = h i u i (7.5) i =1 4 v ( r,s ) = h i v i (7.6) i =1 28 MIT 2.094 7. Isoparametric elements = Bu u T = u 1 u 2 v 4 (7.7) u x v = Bu (7.8) y u + v y x x y r r r x = (7.9) x y s s s y J x r = J 1 (7.10) y s J must be non-singular which ensures that there is unique correspondence between ( x,y...
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This note was uploaded on 12/29/2011 for the course ENGINEERIN 2.094 taught by Professor Prof.klaus-jürgenbathe during the Spring '11 term at MIT.
- Spring '11
- Finite Element Analysis