Page 190 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

Design optimization • 177
• The changes in all design variables from the current design to the
best feasible design are less than their respective tolerances.
• The changes in all design variables between the last two designs are
less than their respective tolerances.

Sometimes the solution may terminate before convergence is reached.
This happens if one of the following conditions is true:

• The number of loops specified has been performed.
• The number of consecutive infeasible designs has reached the spec-
ified limit. The default number is 7.

5.2.2.2 First-order Method

Like the subproblem approximation method, the first-order method con-
verts the problem to an unconstrained one by adding penalty functions to
the objective function. However, unlike the subproblem approximation
method, the actual finite element representation is minimized and not an
approximation. The first-order method uses gradients of the dependent
variables with respect to the design variables. For each iteration, gradient
calculations (which may employ a steepest descent or conjugate direction
method) are performed in order to determine a search direction, and a
line search strategy is adopted to minimize the unconstrained problem.
Thus, each iteration is composed of a number of sub-iterations that include
search direction and gradient computations. That is why one optimization
iteration for the first-order method performs several analysis loops.
Convergence Checking: First-order iterations continue until either
convergence is achieved or termination occurs. The problem is said to be
converged if, when comparing the current iteration design set to the previ-
ous and best sets, one of the following conditions is satisfied:

• The change in objective function from the best design to the current
design is less than the objective function tolerance.
• The change in objective function from the previous design to the
current design is less than the objective function tolerance.

5.2.3 oPTiMizATion DeSign TooLS

In addition to the two optimization techniques, the ANSYS program offers
a set of strategic tools that can be used to enhance the efficiency of the
design process. For example, a number of random design iterations can be