Effective scaling procedures for approximate structural optimization

Improved approximations of displacements and stresses, achieved by the following types of scaling, are presented: (a) scaling of the initial stiffness matrix; (b) a new type of scaling of displacements; and (c) mixed scaling of stiffness and displacements, where the two types of scaling are combined. The geometric interpretation of the various scaling types is illustrated and methods for selecting the scaling multipliers based on geometrical considerations, mathematical criteria and the reduced basis approach, are demonstrated and compared. It is shown that high-quality approximations can be achieved for very large changes in cross-section and geometrical variables with a small computational effort. The results presented indicate that scaling procedures have high potential in future applications where effective reanalysis is essential.