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# Due to more number of nodes it will not lose accuracy

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Unformatted text preview: e to more number of nodes, it will not lose accuracy at curved boundaries. Boundary Conditions: At line (y=b) : Material Properties: Material properties of steel are used: Young’s Modulus=E=210x109 GPa (Steel) Poisson’s Ratio=0.29 (Steel) Geometric Constraints: By using the symmetric conditions, we can draw only half of the geometry as show in figure above. So the Geometric Constraints are: At line (y=0): Symmetric Boundary Problem No 2 5 2 1 (1,1) t 9 6 3 4 7 Part (i) 8 s The shape functions have been derived as under: 1 1,1 1 4 1 1 4 1 1,1 1 4 1 1 4 1 1 11 11 1 1 1 1 1 1 11 1 1 1 1 1 1 4 1 1 11 1, 1 1 4 1 1, 1 1 4 1 1 4 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1, 2 1 2 1 1 2 1,0 1 2 1 11 1 1 1, 2 1 2 1 1 2 1 2 0,0 1 11 1 1 2 1 1 1 1 11 1 1 1 0 1 1 1 1 2 1 1 1 1 1 11 2 1 1 1 1 2 1,0 1 2 1 1 2 1 11 0 1 1 1 1 11 01 0 1 1 1 1 1 Part (ii) Weak form of heat equation is: At upper surface: q=q0. Therefore, the weak form becomes: 20 1 1 4 1 1 1 2 1 1 1 4 1 at t=1: Therefore, 1 1 2 1 : 1 1 2 1 1 1 2 1 1 1...
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