An efficient approximation technique for frequency constraints in frame optimization

An efficient approximation technique is presented for dealing with frequency constraints in frame optimization. The method is based on a linear approximation of the eigenvalues with respect to the member section properties. Using this, an approximate optimization problem is solved treating the physical dimensions of the beams as design variables. When the eigenvalues are required, the section properties are first calculated. Then, using the approximation, the eigenvalues are estimated and returned to the optimizer. When the approximate optimum is found, a detailed analysis is performed and the process is repeated. Examples are presented to demonstrate the method. The method is simple, yet treats the physical dimensions of the structure as design variables, and allows for large move limits during the approximate optimization.