2-33 - 144 Finite Element Analysis and Design 33. Use FEM...

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144 Finite Element Analysis and Design 33. Use FEM to solve the plane truss shown below. Assume AE = 10 6 N, L = 1 m, = 20 10 -6 /C. The temperature of Element 1 is 100 o C below the reference temperature, while Elements 2 and 3 are in the reference temperature. Determine the nodal displacements, forces in each element and the support reactions. Show that the nodal equilibrium is satisfied at Node 4. Solution: Connectivity table Elm i-j l m AE/L AE  T 1 1-4 -45 .707 -.707 .707E6 -2000 2 2-4 0 1 0 1E6 0 3 3-4 45 .707 .707 .707E6 0 Element stiffness matrices and corresponding thermal load vectors: 1 2 (1) 4 4 1 1 1 1 1 1 1 1 [ ] .354E6 1 1 1 1 1 1 1 1 u v u v     k , (1) 1414 1414 {} 1414 1414 T l m AE T l m f 2 2 (2) 4 4 1 0 1 0 0 0 0 0 [ ] 1E6 1 0 1 0 0 0 0 0 u v u v k , (2) 0 0 0 0 T l
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2-33 - 144 Finite Element Analysis and Design 33. Use FEM...

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