Unlike Simulation, Mechanica employs a gradient-based solution technique for solving design problems. Accessing the optimization capability in Mechanica is similar to that of defining and solving an FEA, which is straightforward.
A static design study is created for the beam with boundary and load conditions shown in
Figure 3.50a.
Figure 3.50a also shows the finite element mesh (13 tetrahedron solid elements). The maximum bending stress fringe plot is shown in
Figure 3.50b, which shows maximum tensile and compressive stresses, respectively, at the top and bottom fibers of the beam close to the root end.
FEA results are also given in the status dialog box shown in
Figure 3.50c, in which maximum displacement and principal stress are 0.373 in. and 71.92 ksi, respectively.
An optimal solution is obtained in seven design iterations. At the optimum, the three design variables are length
ℓ = 5 in., width
w = 0.5 in., and height
h = 1.08 in. Constraint functions are stress
σmp = 64.99 ksi, and displacement
δx = 0.0766 in.; both are feasible. The total mass is 0.0007056 lbf s
2/in. (or 0.272 lbm), reduced from 0.002669 lbf s
2/in. (or 1.03 lbm) from the initial design. The optimization history graphs for objective and constraint functions are shown in
Figures 3.51a, b, and c, respectively.