3-18 - 202 Finite Element Analysis and Design 18. The...

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202 Finite Element Analysis and Design 18. The stepped bar shown in the figure is subjected to a force at the center. Use FEM to determine the displacement field u ( x ), axial force distribution P ( x ), and reactions R L and R R . Assume: E = 100GPa, area of cross sections of the three portions shown are, respectively, 10 −4 m 2 , 2×10 −4 m 2 and 10 −4 m 2 , and F = 10,000 N. Solution: Define elements from left to right: Element 1: 0(left side)-0.3m Element 2: 0.3-0.5m(center position) Element 3: 0.5-0.7m Element 4: 0.7-1m(right side) (1) 8 1 1 1 10 3 EA k L , (2) 8 2 2 10 EA k L  , (3) 8 3 3 10 EA k L , (4) 8 4 4 1 10 3 EA k L Assembly: 1 2 8 4 3 4 5 11 0 0 0 33 0 14 1 0 0 0 0 1 2 1 0 10 10 41 0 0 0 1 0 0 0 0 L R R u u u F u u R         Applying boundary conditions: 2 84 3 4 4 10 0 3 10 1 2 1 10 40 01 3 u u u  
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This note was uploaded on 08/22/2011 for the course EML 4500 taught by Professor Staff during the Fall '08 term at University of Florida.

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3-18 - 202 Finite Element Analysis and Design 18. The...

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