Frame Optimization Including Frequency Constraints

The minimum weight optimum design of planar frame structures subject to frequency (or buckling) constraints, stress constraints, and member sizing constraints is covered by the finite element displacement method. Two design variables define the cross section of each planar frame element. The total number of design variables for a problem can be reduced by employing the design variable linking option. The mathematical programming problem is solved using a Sequence of Unconstrained Minimizations Technique (SUMT). In particular, the interior extended penalty function formulation is used in conjunction with the Davidon-Fletcher-Powell minimization algorithm. Potential difficulties in formulating the frequency (or buckling) constraints and gradients are reviewed. Results for small example problems are presented and evaluated. In addition, various recently developed structural synthesis approximation concepts which may be used to extend the approach to larger and more complex structural systems are mentioned.