EN0175-03

EN0175-03 - EN0175 09 / 12 / 06 Intro to FEM (continued)...

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EN0175 09 / 12 / 06 Intro to FEM (continued) Examples of using FEM to solve a problem and comparison with exact solution: We consider a problem already discussed in the previous class: g ρ x Solution by exact method: () x L x E g u = 2 x L g 2 2 = σ 0 L x u 2 L 2 gL 2 gL L 2 L 0 x Now we will solve the same problem by FEM: In FEM, the displacement is discretized as and the governing equation is reduced to algebraic equation: = = n k k k x w u x u 1 ) ( ) ( F KU = or j n k k jk F u K = = 1 where , (see notes of () () = L k j jk x x w x w E K 0 ' ' d x x w g x x w f F L j L j j d d 0 0 = = 1
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EN0175 09 / 12 / 06 previous lecture). FEM nodes: j 1 j w 0 L 1 j 1 + j x () [] = + + + otherwise , 0 , , , , 1 1 1 1 1 1 j j j j j j j j j j j x x x x x x x x x x x x x x x w Case study 1: In the simplest possible case, we choose only one node, i.e. 1 = n . In this case, we have one node and 2 elements. 2 / L ( ) ( ) x w u x u 1 1 = < < < < = L x L L x L L x L x x w 2 , 2 2 0 , 2 1 < < < < = otherwise , 0 2 , 2 2 0 ,
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This note was uploaded on 01/10/2010 for the course EN 0175 taught by Professor Huajiangao during the Spring '06 term at Brown.

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EN0175-03 - EN0175 09 / 12 / 06 Intro to FEM (continued)...

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