Calculate the sensitivity of the vertical displacement (left(v_{2} ight)) at node 2 in the threebar truss problem

Calculate the sensitivity of the vertical displacement \(\left(v_{2}\right)\) at node 2 in the threebar truss problem in example 10.4 with respect to \(b_{2}\). Compare the accuracy of calculated sensitivity with the finite difference sensitivity. Use \(1.0 \%\) perturbation size for the forward finite difference.

Data From Example 10.4:

For the threebar truss shown in figure 10.4, the goal is to find the crosssectional areas of bars so that the weight of the truss is minimal while the stresses in all members are less than the yield strength with the factor of safety \(=2.0\). Perform one iteration using fully stressed design. The current crosssectional areas are \(b_{1}=b_{2}=b_{3}=10 \mathrm{~mm}^{2}\). Use length \(L=1 \mathrm{~m}\), Young's modulus \(=80 \mathrm{GPa}\), and yield stress \(\sigma_{Y}=250 \mathrm{MPa}\).

Transcribed Image Text:

000 L3 2 X 1 (2) L Figure 10.4 Threebar truss for fully stressed design 1,000 N