2-8 - 94 Finite Element Analysis and Design 8 Use FEM to...

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94 Finite Element Analysis and Design 8. Use FEM to determine the axial force P in each portion, AB and BC , of the uniaxial bar. What are the support reactions? Assume: E = 100 GPa, area of cross sections of the two portions AB and BC are, respectively, 10 −4 m 2 and 2×10 −4 m 2 and F = 10,000 N. The force F is applied at the cross section at B . Solution: Element equations: (1) 11 1 2 1 2 uf EA u L f         , (2) 22 2 (3) 3 2 3 EA u L f     Assembly: 1 1 1 2 2 2 1 1 2 2 3 0 0 L R EA EA LL uR EA EA EA EA uF L L L L EA EA   Apply boundary conditions ( u 1 = u 3 = 0) by deleting rows and columns: 12 2 EA EA    By solving the above equation to yield:
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